?? «an ':‘h‘&L(r~alsq a t -,. hunch M “‘5 Huh» zai‘ 14w 9' ' "fi‘iififi‘i n1 5‘} 8 N {CL‘g'nf If" V ,nm “-J4JTS‘ y); “nu..." .1 dr‘A- ‘ . v. .,‘. .A u. w... mumv .. ‘. 4.1 .n.‘. .x III/ll ”WW suns us ill![Ill/Illl/IIH/I/fl/l/Ill! l/I//////I//I/HII///I/ll 3 1293 01055 0766 This is to certify that the dissertation entitled The Development and Use of an Immobilized Enzyme Reactor for Studying the Effect of Amino Acid Deprivation on Leukemic Blood presented by Steven R. Reiken has been accepted towards fulfillment of the requirements for Ph .D . ’degree in fihemicalflgineering gig-Me ”buwmtb# Major professor Date_1/30/92 #_ 0-12771 MSU i: an Affirmatiw Action/Equal Opportunity Institution LIBRARY Michigan State University ~a~~ can. PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. l'|-=DATE DUE DATE DUE DATE DUE l Ll |l__J MSU is An Affirmative Action/Equal Opportunity Institution cmmut THE DEVELOPMENI.AND USE OF'AN’IHHDBILIZED ENZXHE.REACTOR FOR STUDYING THE EFFECT OPNAHINO.ACID DEERIVKIION ON'LEDKEHIC BLOOD By Steven.R~ Reiken. A.DISSERILIION Submitted to Michigan State university in partial fulfillment of the requirements fer the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1992 '1' (tr k & U) A .7 ,. -f. , 0 ABSTRACT THE DEVELOPMENT AND USE OF AN IMMOBILIZED ENZYME REACTOR FOR STUDYING THE EFFECT OF AMINO ACID DEPRIVATION ON LEUKEMIC BLOOD BY Steven R. Reiken The use of an immobilized enzyme reactor for studying the in vitro effect of lysine deprivation on leukemic blood is investigated. L-lysine a-oxidase and catalase are co-immobilized in the porous region of a polyamide hollow fiber, which is then encased in a protective glass shell. This single fiber reactor (SFR) is used for the enzymatic removal of lysine from blood. Operating parameters such as flow rate and the amount of the two enzymes immobilized in the reactor are optimized to maximize the conversion of lysine. In addition, pulsatile flow is used to enhance SFR performance by decreasing diffusion limitations. Models are developed that accurately predict conversion of lysine in the single fiber reactor under both normal and pulsatile flow operation. The SFR is an important tool for developmental work because it is easy to use and requires small amounts of blood and biochemicals for testing; however, data obtained from the SFR are valid for use in a clinical-size hollow fiber cartridge. By varying the treatment time, the amount of lysine removed from the blood can be precisely controlled. This allows for studying the effect of different levels of lysine removal on the cell population of leukemic blood. A computer simulation is developed that predicts the effect of the enzymatic reactor treatment on the number of white cells Steven Reiken and the number of abnormal, proliferating lymphocytes present in the leukemic blood. When approximately 80% of the lysine has been removed from the blood by the enzymatic reactor, a 25 % decrease in the total number of white cells in the blood is observed 24 hours after treatment. Similar results are shown for the proliferative capacity of the lymphocytes. These results along with preliminary data from in vitro experiments involving human leukemic blood demonstrate the potential of L-lysine a-oxidase and the enzymatic reactor in treating leukemia. In addition, the enzymatic reactor has several advantages over the clinically used method of enzyme injection. These advantages include preventing immunological responces from the patient by preventing direct contact between the enzyme and the blood and minimizing negative side-effects from the therapy by controlling the amount of amino acid removed. To the memory of my cousin, Adam Karsch. Someday we will find a cure. iv ACKNOWLEDGEMENTS I wish to extent special thanks to my thesis advisor, Dr. Daina Briedis, for her guidance and friendship throughout my graduate study. I also would like to thank the other members of my committee for their time and assistance: Dr. John B. Kaneene, Dr. Donald K. Anderson, Dr. R. Mark Worden, and Dr. Dennis J. Miller. Further thanks needs to be extended to Dr. H. Kusakabe and the Yamasa Shoyu company for donating the enzyme L-lysine a-oxidase and Romicon, Inc. for donating the hollow fibers used in this investigation. Without the help of these companies, this study could not have been undertaken. I also need to acknowledge those who have provided special assistance to specific portions of this investigation. First, Dr. Brunning-Fann and Cathy Knapp for their assistance in drawing blood from sheep. Other people that need to be acknowledged include Sue Soriano and St. Lawrence Hospital for their help with flow cytometry analysis of blood, Carolyn Haines and the Clinical Pathology Laboratory of the Large Animal Clinic at MSU for conducting other blood analyses, Dr R.D. Schultz of the University of Wisconsin for sending leukemic sheep blood, and Dr. Roshni Kulkarni and the staff of the pediatric department of Sparrow Hospital for their assistance in the human blood experiments. Finally, I would like to thank the many friends I have made over the last few years who have made my stay at MSU so woderful, especially Julie Caywood, Fred Michel, Greg Kudlac, Craig Chmielewski, Bob "the Bob Factor" Carpenter, Steve Summerfelt, Gerald Bockstanz, Andy Grethlein, Brent Larson, and the members of the Chemical Engineering softball team. LIST OF TABLES TABLE OF CONTENTS LIST OF FIGURES ................................................. Chapter 1. INTRODUCTION ....................................... 2. BACKGROUND ......................................... Leukemia ........................................ Amino Acids and Leukemia Therapy ................ Methods of Enzyme Immobilization ................ Hollow Fiber Reactor Models .......... Extracorporeal Blood Treatment .................. Enzyme Selection ................................ Animal Models of Human Leukemia ...... ANALYTICAL TECHNIQUES ................... Lowry Protein Determination .......... Lysine Determination ................. Hydrogen Peroxide Determination ...... Catalase Activity Determination ...... L-lysine a-oxidase Activity Determination Source of BLV-Infected Blood ......... Cell Counts .......................... RBC and Platelet Counts .............. WBC Counts ........................... Serum Creatine Kinase Activity ....... Serum Potassium Concentration ........ Flow Cytometry ....................... Methods of Data Analysis ............. Factorial Design ..................... Analysis of Biocompatibility Data .... ENZYME IMMOBILIZATION AND RETENTION ON FIBERS Materials and Methods ................ Single Fiber Reactors ................ Enzyme Immobilization ................ Protein and Activity Determination ... Results Enzyme Immobilization and Localization vi Enzyme Stability ..................... ........... ........... ........... ........... ........... 1o 14 21 23 27 29 29 32 38 39 41 41 42 42 43 44 45 46 48 48 50 52 52 52 54 56 58 60 60 Chapter Page 5. REACTOR OPERATION AND OPTIMIZATION ................. 63 Introduction .................................... 63 Factorial Design ................................ 65 Operating Parameters ............................ 67 Effect of Flow Rate ............................. 67 The Effect of L-lysine a-oxidase ................ 69 The Effect of Catalase .......................... 69 Optimum Operating Conditions .................... 71 Pulsatile Flow .................................. 73 6. REACTOR MODELLING AND SCALE-UP ..................... 78 Evaluation of the Effectiveness Factor .......... 78 Reactor Model ................................... 8O Permeability and Diffusivity Determination ...... 81 Permeability/Diffusivity Experiments ............ 83 Fiber Fouling ................................... 87 Fouling Experiments ............................. 88 Evaluation of the Intrinsic Kinetic Parameters .. 89 SFR Model With Pulsatile Flow ................... 95 Determining PIn and Pa ........................... 97 Scale-Up ........................................ 103 Hollow Fiber Cartridge Operation ................ 106 7. BIOCOMPATIBILITY OF THE SINGLE FIBER REACTOR ....... 112 Introduction .................................... 112 Biocompatibility Experiments .................... 113 Results ......................................... 118 8. THE EFFECT OF LYSINE DEPRIVATION 0N LEUKEMIC BLOOD . 120 Introduction .................................... 120 Mathematical Model .............................. 120 Experimental Procedure .......................... 122 Determining a' and b' ........................... 123 Determining kl and k2 ........................... 128 Computer Simulation ............................. 131 Accuracy of the Computer Simulation ............. 133 Significance of Results ......................... 137 The Effect of L-lysine a-oxidase on Human Leukemic Blood .......................... 140 9. CONCLUSIONS AND RECOMMENDATIONS ................. 142 Summary of Results ............................. 142 Recommendations ................................. 145 Future Work: Reactor Development ............... 145 Future Work: Amino Acid Deprivation Studies .... 147 vii Chapter Page APPENDIX ....................................................... 150 Runge-Kutta-Gill Method ......................... 150 Program I ....................................... 158 Program II ...................................... 165 Program III ..................................... 166 Program IV ...................................... 172 LIST OF REFERENCES ............................................. 175 viii NHUN ...: LIST OF TABLES Michaelis Constant of Selected Antitumor Enzymes .......... Concentrations Used to Construct the Lysine Standard Curve Concentrations Used to Construct the H202 Standard Curve .. Design Matrix for SFR Experiments ......................... Yate's Algorithm for the SFR Experiments .................. Results of Pulsatile Flow Experiments (Four Hour Run) ..... Results of the PAlO Fiber Permeability Study for D-lysine . L-lysine a-oxidase Kinetic Parameters ..................... Results of Initial Hematological Study .................... Minimum Experiments Needed for Statistical Accuracy in Hematology Study ..................................... Results of Complete Hematological Study ................... Results From Plotting Equation (8.3) ...................... Mathematical Model and Model Parameters The In Vitro Effect of Lysine Deprivation on Human Leukemic Blood ix Page 24 33 39 66 66 76 87 93 116 117 118 124 131 141 LIST OF FIGURES FIGURE 2.1 Electron micrograph of a single hollow fiber .............. 2.2 Schematic of a hollow fiber cartridge showing the two modes of operation used in systems design (from Waterland et al., 1975) ................................... 2.3 Schematic of cross sectional views of a hollow fiber. The figure shows the cylindrical geometry of the 'hollow fiber (figure not drawn to scale) ................... 3.1 Standard curve for the Lowry Method for determining protein concentration ...................................... 3.2 Standard curve for determining lysine concentration using saccharopine dehydrogenase method .................... 3.3 Standard curve for ammonia electrode ...................... 3.4 Standard curve for determining hydrogen peroxide concentration .............................................. 4.1 Single fiber reactor (SFR) - Shell material is borosilicate glass, 21.5 cm overall length, 0.8 cm O.D.. ‘ Fittings illustrated on left were applied to both ends of the reactor: L - male and female Luer lock fittings; C - Tygon tube; HF - hollow ultrafiltration fiber. The hollow fiber was retained by a plug of epoxy potting resin (Dow Chemical) between the Luer lock fittings and the hollow fiber 4.2 Schematic representation of the system used to sanitize the SFR 4.3 Schematic of the SFR showing backflush and ultrafiltration modes of operation ......................... 4.4 Change in relative enzyme activity during storage .......... 5.1 Single Fiber Reacto; System (SFR) - Res - reservoir flask; P - pump; f1,f2 - flowmeters; p1 - lumen-side inlet port; p2 - shell-side inlet port; p3 - lumen outlet port; p4 - shell-side outlet port; t1 - 15 psig pressure transducer; t2 - 5 psi differential pressure transducer; X - tubing clamps for stopping flow ............ 5.2 Plot of % conversion of lysine vs. flow rate ............... Page 12 13 15 31 .35 37 4O 53 '55 57 61 64 68 Plot of % conversion of lysine vs. the amount of L-lysine a-oxidase immobilized ............................. 70 Plot of % conversion of lysine vs. the catalase to oxidase loading ratio ...................................... 72 Single Fiber Reactor System with pulsatile flow. P - gear or perristaltic pump; p1 - lumen-side inlet port; p2 - shell-side inlet port; p3 - lumen outlet port; p4 — shell-side outlet port; X - tubing clamps for stopping flow. The two inlet pumps are set at different flow rates and the timer is used to switch from one pump to the other .................................. 74 Dual closed loopdialysis system for studying membrane permeability ............................................... 84 Plot of Equation (6.7) for determining permeability ........ 86 Plot of Equation (6.7) for determining the extent of fiber fouling .............................................. 90 Data from a 36 hour SFR performance study .................. .92 Plot of effectiveness factor vs. modulus for the SFR over the lysine concentration range being studied .......... 94 Plot of lysine concentration vs. time for an optimum loaded SFR operating under pulsatile flow .................. 99 Plot of lysine concentration vs. time for an optimum loaded SFR operating under normal flow conditions; predicted concentrations and experimental results are both shown ................................................. 101 Plot of lysine concentration vs. time for a SFR (50% optimum enzyme loading) operating under pulsatile flow conditions; predicted concentrations and experimental results are both shown ..................................... 102 Plot of design time vs. % conversion of lysine for the single fiber reactor ....................................... 105 Plot of lysine concentration vs. time in a hollow fiber cartridge: predicted concentrations and experimental results are both shown ..................................... 108 The effect of uneven enzyme distribution on the accuracy of the model assuming an apparent 12% loss in enzyme activity ................................................... llO Decrease in white cells over an eight hour period (Clys - 0.6 mM) .................................................... 125 xi Plot of -ln[Nt/Nto] vs. time (blood lysine concentrations - 0.2, 0.6, and 1.0 mM) .................................... 126 Plot of -1n[Nt/Nt0] vs. time (blood lysine concentrations - 0.4 and 0.8 mM) .......................................... 127 Plot of l/K' vs. lysine concentration ...................... 129 The effect of reactor treatment on total white cell count in leukemic blood; both experimental and computer simulation results are presented ........................... 134 The effect of reactor treatment on the number of proliferating cells in leukemic blood; both experimental and computer simulation results are presented .............. 135 The effect of lysine deprivation on total white cell count. Exposure time is 24 hours .......................... 138 The effect of lysine deprivation on lymphocyte proliferative capacity. Exposure time is 24 hours ......... 139 A comparison between the calculated and experimental lysine concuntrations that were used to evaluate the intrinsic kinetic parameters ............................. 153 A comparison between the calculated and experimental lysine concuntrations for pulsatile flow operation. These concentrations were used to determine the parameters Pm and Pa ....................................... 156 xii CHAPTER 1 INTRODUCTION The primary objective of the research conducted for this dissertation was to develop an immobilized enzyme reactor both as a clinical tool in leukemia therapy and as a laboratory method (or research tool) for studying the effect of amino acid deprivation on leukemic blood. A secondary objective was to model the effect of reactor treatment on the leukemic cells. In order to be effective against leukemia, a treatment must exert a differential cytotoxic effect upon the leukemic cell. One way in which leukemic cells differ from normal, healthy blood cells is that leukemic cells metabolize certain amino acids more quikly. Depleting these amino acids from the bloodstream of leukemic patients should therefore have a preferential effect on the leukemic cells. This depletion can be performed enzymatically; the enzyme L-asparaginase is currently being used in the clinical treatment of leukemia. In this treatment, L- asparaginase is injected directly into the bloodstream of leukemic . patients and is used in conjunction with other chemotherapeutic agents. Although the combination therapy utilizing asparaginase has been successful in treating leukemia, there are several problems associated with enzyme injection. These problems include nonrecovery of expensive enzymes, the eliciting from the patient of negative immunological responses to the enzyme, and toxicological problems (due to the removal of all of the amino acid from the bloodstream) associated with enzyme injection. It was for these reasons that a reactor consisting of an antileukemic enzyme immobilized within the void space of the porous region of ultrafiltration hollow fibers was investigated for dialyzer- type treatment of leukemic blood. In addition to being viewed as a potentially superior alternative to enzyme injection, the enzymatic reactor has the additional advantage of being able to precisely control the level of amino acid removal from the blood. This provides an opportunity for the fundamental study of the effect of amino acid deprivation on leukemic blood. The specific enzyme/substrate system studied in this work was L-lysine a-oxidase and L-lysine. The description of the work conducted in this dissertation is divided as follows. Chapter 2 discusses the motivation for the research. A literature review on several aspects of leukemia relevant to this project is presented. This includes a rationale for the project, and backgrounds for hollow fiber reactors and the enzyme L- lysine a-oxidase. Potential animal models for the study of human leukemia are also discussed. Chapter 3 describes the analytical techniques that were necessary to evaluate the performance of the reactor. Methods for the determination of the total protein content, lysine concentration, hydrogen peroxide concentration, and enzyme activity in a given sample are discussed in this section. Also presented are techniques for measuring hematological properties such as cell counts, cell viability, plasma potassium concentration, plasma creatine phosphokinase activity, and cell proliferative capacity (using flow cytometry). The first major accomplishment of this research was to design and construct single fiber reactors (SFRs). SFRs consist of a single hollow fiber encased in a protective glass shell (see Chapter 4). The SFR is an ideal tool for developmental work because it is easy to use and requires only small amounts of blood and biochemicals for testing. In Chapter 4, the choice of fiber material and method of enzyme immobilization are addressed. The ability of the enzymatic reactor to remove lysine from blood is investigated in Chapter 5. As will be discussed in this chapter, reactor performance was improved by the co-immobilization of catalase in the reactor. This enzyme generates oxygen (which may be the limiting reactant in the L-lysine a-oxidase reaction) from the cytotoxic chemical hydrogen peroxide. Other important information presented in Chapter 5 include the evaluation of the operating conditions that maximize the conversion of lysine in the reactor and the use of pulsatile flow as a means of enhancing reactor performance. A method for determining fiber permeability is presented in Chapter 6. This method was used to determine the effective diffusivity of lysine within the reactor and also to investigate the possibility of fouling of the polyamide fibers by blood components. No evidence of fouling was observed in these experiments. Also in this chapter, reactor modelling and scale-up are discussed. An important concern involving enzymatic blood treatment is the possibility of undesirable adverse interactions with the patient's blood. Because of the nature of the polyamide hollow fiber and because the membrane prevents direct contact between the blood and the enzyme, adverse effects should be minimized. Chapter 7 discusses the evaluation of the biocompatibility of the SFR. The results from the experiments described in this chapter indicate that there was no noticeable effect of circulating blood through the lumen of the SFR on the hematological properties of the blood. With the biocompatibility of the SFR established, the next goal of this research was to study the effect of lysine deprivation on leukemic blood. Blood from leukemic sheep was used in the experiments of Chapter 8 to accomplish this goal. Data obtained on blood cell counts were used to determine the parameters of a model that describes the effects of lysine deprivation on the population of both the total white cells in the blood and the fraction of the lymphocytes that are actively proliferating. This blood model was combined with the reactor model for lysine conversion in the SFR (Chapter 6) to develop a computer simulation that predicts the in 21319 effects of the enzymatic reactor treatment on the leukemic cell population. The computer simulation gives less than a 4% error between the simulation and experimental results for the effect of treatment on total white cell count and less than a 7.5% error for the effect on the proliferating fraction of the leukemic lymphocytes. As discussed above, a main objective of this dissertation was to develop an immobilized enzyme reactor for clinical use in cancer therapies. The results of the experiments described in the chapters following indicate a good potential for achieving this goal; however, further experiments are needed. The performance of the clinical-size hollow fiber cartridge using whole blood instead of buffer as the substrate solution must be evaluated. It is also hoped that future work may be conducted in conjunction with with the Department of Animal Science of the College of Veterinary Medicine at Michigan State University to allow 13 vivo testing of the hollow fiber cartridge in animal models. CHAPTER 2 BACKGROUND Leukemia Leukemia is a disease of unknown cause characterized by rapid and abnormal proliferation of leukocytes in the blood forming organs (bone marrow, spleen, lymph nodes) and the presence of immature leukocytes in the peripheral circulation. During normal blood cell production, the cells differentiate into specific types. In leukemia, the differentiation into specific cells is blocked. This disturbance of normal differentiation is a malignant process that, left unattended, will ultimately cause the death of the person afflicted. Leukemia results from the progressive expansion of a population of cells derived from a few, perhaps a single, progenitor cell which has malignantly transformed [Henderson and Lister, 1990]. Most clinicians place the site of this transformation within the bone marrow, although the thymus, spleen, and lymph nodes have also been implicated. The nature of the transformation is similarly open for debate. Viruses are convincingly identified as leukemogenic in many mammalian species, including primates, but have been implicated in only one relatively rare form of human leukemia (adult T-cell leukemia). Exposure to ionizing radiation and to a growing number of chemicals and the inheritance or acquisition of a number of diseases are associated with an increased risk of developing leukemia. In most cases, these conditions cause injury to the DNA. Increased proliferation, suppression of immunocompetence, and/or a deficiency in DNA repair can be identified in many cases [Graf, 1988]. In other disorders, changes to the DNA can be less readily attributed to either hereditary or genetic injury and occur with a frequency that could be explained by random gene mutation coupled to physiological signals for cell proliferation [Greaves, 1988]. In virtually no instance can a single all-pervasive leukemogenic event be identified. Because of this, it is postulated that multiple factors must occur in precise sequence in order for clinical leukemia to evolve. For many years, the leukemias have been separated into two main categories, acute and chonic. This was to reflect both a short-term disease, which was rapidly fatal in the majority of patients in its acute form and a long-term illness in its chronic form. An additional subdivision within each category, myeloid and lymphoid, allows for morphologic subtyping. Myeloid refers to cells produced in the bone marrow whereas lymphoid cells are produced in the lymph nodes. Until 1947, there was no specific treatment for acute leukemia (AL). At that time, the median survival for both children and adults was about two to four months, and a cure was essentially unknown [Bierman et al., 1947; Tivey, 1954]. During the next 40 years, research has produced curative regimens for acute lymphocytic leukemia (ALL) plus rationale for the chemotherapy of all cancers. Unfortunately, the treatment of chronic leukemias (CLs) has not improved significantly so that the life expectancy of patients with AL in many cases exceeds that of patients with CL. The terms acute and chronic are maintained only for nosologic reasons. To be effective against leukemia, a drug must exert some differential cytotoxic effect upon the malignant cell. Qualitative biochemical differences between leukemic cells and normal cells which would permit the design of drugs having specific cytotoxicity for leukemic cells are not known. Consequently, present chemotherapy must rely on small quantitative differences between the sensitivity of leukemic cells and of normal cells that are the target of the drug's toxicity. Amino Acids and.Leukemia Therapy Exogenous amino acids have been shown to be primary nutritional requirements for certain types of leukemic cells. This requirement is the result of either a failure of the cell to synthesize the amino acid in an amount needed for the maintenance of normal metabolism [Horowitz, 1968; Regan et al., 1969] or an increased demand for certain amino acids necessary for protein synthesis. Since various studies have shown that specific amino acids are required for the optimal growth of malignant versus normal cells [Iyer, 1959; Dimitrov et al., 1971; Kusakabe et al., 1980], it is believed that the depletion of selected amino acids can abrogate leukemic cell growth by preferentially affecting the leukemic cells.~ These amino acids include asparagine, methionine, serine, glycine, leucine, phenylalanine, threonine, arginine, and lysine [Dimitrov et al., 1971; Kreis, 1979; Kusakabe et al., 1980]. In particular, lysine and serine have been shown to be consumed to the greatest extent [Kusakabe et al., 1980]. Dietary restriction of amino acids has proven to be unsuccessful largely due to the overall detrimental effects on patient health [Sugimura et al., 1959]. Recently, several enzymes that degrade essential amino acids have been shown to depress tumor growth. Phenylalanine ammonia-lyase from Rhodotorula glutinis inhibits both growth of murine (mouse) and human leukemic cells in xitrg [Abell, Stith, and Hodgins, l972] and growth of L5178Y mouse leukemia in 2123 [Abell, Hodgins, and Stith, 1973]. Kreis and Hession [1973] reported that methionine y-lyase from Clostridium sporogenes causes inhibition of the growth of P815 and L1210 cells in 21519. Threonine deaminase from sheep liver, which catalyzes the irreversible a,fi-elimination of L- threonine, was shown to inhibit mouse leukemia cells [Greenfield and Wellner, 1977.]. Kusakabe et a1. [1980] found that L-lysine a-oxidase, an enzyme that catalyzes the oxidative deamination of L-lysine, demonstrates growth-inhibitory activity against L5178Y mouse leukemic cells. Enzyme therapy is principally based on the higher sensitivity of cancer cells to the deprivation of essential nutrients than that of normal cells. Of the antitumor enzymes studied, only L-asparaginase has been accepted clinically for the treatment of acute lymphatic leukemia (ALL). L-asparaginase is an enzyme that splits asparagine into aspartic acid and ammonia. It was introduced into clinical practice because of the reports that tumor cells had a greater requirement for preformed asparagine-than normal cells [Henderson and Lister, 1990]. After administration of L-asparaginase, plasma levels of asparagine fall rapidly to undetectable levels [Neuman and McCoy, 1956]. This .inhibits protein synthesis in those cells that are unable to form their own asparagine. The drug is inactive when given orally and must be given parenterally by intravenous (IV) injection. Clinically, asparaginase is combined with vincristine (an alkaloid) and prednisone (a steroid) in remission induction therapy of ALL. Vincristine acts by preventing formation of the mitotic spindle which produces mitotic arrest [Broome, 1961] while prednisone inhibits the incorporation of thymidine into DNA in lymphoid tissue and can affect RNA transcription, RNA polymerase activity, and translation from messenger RNA. Transport of glucose and amino acids is also inhibited [Creasey, 1975]. A typical treatment regimen consists of prednisone in daily oral dosages of 40 to 80 mg/m2 of total body surface area, a single IV dosage of 2.0 mg/mz/week of vincristine, and biweekly daily IV infusions of asparaginase at a dosage of 10-600 mg/m2 [Rosen and Milholland, 1975]. The regimen is conducted for approximately one month. Ortega, Nesbit, and Donaldson [1977] achieved an overall remission induction rate of 93% in children with ALL utilizing the combination of asparaginase, vincristine, and prednisone. A five year survival rate of 60% has also been achieved. Although the use of asparaginase has been successful, there are several problems associated with the use of the enzyme in treating leukemia. Large amounts of enzyme are required to maintain adequate therapeutic levels in the blood, since the average half-life of intravenously injected L-asparaginase is only between 5.5 and seven hours [Wahn et al., 1983]. Moreover, because they are foreign proteins, injected enzymes often elicit unwanted immunologic responses and invoke antibody production with repeated administration. This might not only lead to negative side-effects (allergic responses with fever, nausea, and skin rash), but can also make the therapeutic effects of the enzyme transient due to cellular resistance and allergic reactions quickly nullifying its acceptance by leukemic cells and patients [Holland and Oknuma, 1981]. In addition, L-asparaginase therapy has a spectrum of severe toxicity resulting from a) its ability to cause the cessation of protein biosynthesis in tissues dependent on exogenous asparagine and b) the uncontrolled, unmanaged total depletion of asparagine from the blood of patients which is a typical result of enzyme injection treatments [Cremer et al., 1988; Meschi et al., 1981; Cairo, 1982; Hanefeld and Riehm, 1980.]. 10 The disadvantages of present methods of enzymatic cancer therapy suggest the use of immobilized enzyme treatments. Since the enzyme is immobilized, it maintains its catalytic activity for longer periods, it is protected from attack by the patient's immune system, and the enzymes are reusable, the last point potentially offering lower treatment costs to the patient. Methods of Enzyme Immdbilization Enzymes immobilized within artificial cells have been studied by several researchers [Chang, Shu, and Grunwald, 1982; Shu and Chang, 1980; Grunwald and Chang, 1981]. These cells consist of spherical ultrathin membranes of cellular dimensions enveloping an aqueous interior of enzyme solution or suspension; these cells are injected into the patient's blood stream [Chang, 1976]. The semipermeable membranes theoretically prevent enzyme leakage or enzyme contact with external impermeant macromolecules. However, permeant substrates can equilibrate rapidly across the ultrathin membrane to be acted upon by the enveloped enzymes. One problem in using artificial cells therapeutically is that, after injection, they are difficult to remove from the circulation. The immunological reactions which are associated with the use of foreign proteins/enzymes in 3129 are enhanced in many artificial cell systems [Edman, Nylen, and Sjooholm, 1988]. In addition, sinceproducts of enzymatic reactions within the artificial cells may diffuse into the blood, if any of these products are potentially toxic, harmful side- effects may result. To facilitate the use of enzymes for the reduction of amino acids in blood in a clinically acceptable manner, reactors can be developed with the enzyme immobilized in the matrix of the outer layer of n: S‘. ll asymmetric hollow ultrafiltration (UF) fibers. A bundle of these fibers is then encased in a protective outer shell. These fibers (Figure 2.1) consist of a thin semipermeable inner membrane approximately 0.5 microns thick and an outer supporting macroporous spongy layer (approximately 1.0 mm thick). In such reactors, which are similar in construction to hollow fiber cartridges used in hemodialysis, the enzyme is immobilized in the outer wall of the hollow fiber and is separated by the porous membrane from the blood that is circulated through the lumen of the fibers. The pores of the hollow fiber membrane are of such dimension that small molecules can readily cross from the blood to the spongy layer; however, proteins and immunologically active cells are excluded. Thus, small molecular substrates, such as amino acids, can be exposed to high concentrations of enzyme and in turn be rapidly degraded, without the enzyme entering the blood, being metabolized, or eliciting immunological reactions. Waterland, Robertson, and Michaela [1975] demonstrated that enzymes could be immobilized in the spongy layer by static loading. In this technique, the shell-side of the cartridge is filled with enzyme solution, and the enzyme diffuses into the spongy layer of the fibers. By repeatedly filling and draining the shell-side with stock enzyme solution, the concentration of enzyme in the spongy layer eventually approaches that of the stock solution. Breslau and Kilcullen [1978] used backflush loading to entrap enzymes within hollow fibers. To backflush load enzyme, pressure is applied to the shell-side, and enzyme stock solution is forced from the shell-side to the lumen-side of the fibers as depicted in Figure 2.2a. This method achieves significantly higher enzyme concentrations than static loading. After loading, shell-side solutions are drained from 12 Region 3 (Spongy Layer) egion l (Lumen) Region 2 (Ultrathin Membrane) .‘Jv. . ._ _._. .... . 3.... .....- s- -- ,‘V‘fl’n‘t‘xeibfl.-no a-le'zrh - '4‘” ‘ . ‘- ' *b‘c-s’??~'é-~"*«?‘e”“ N . »-.c..~4 3:95.“. = ~ . ~' -- 3%? ' 3 "-‘7 "33%;: ~ ‘. a ' - *2 “'1'. 5.x“? a: Aeifi {ew- m, - vmfiéfé n hflhfiqflm" s.’ i .1 $3}. ,- g ., . 5.;- -2;.._-, D " i '5' .;.v::. . _ 3.2 75’s: ' ., - .' 2T£.w£~.;..o .31); «'5 ”fig?” {1'qu r ., , J‘ u e“ l ,0 3!. ”t b 9‘ . ,- 'i' lhf "flur- :I. . $.00 '52:: J “Ed I I, S e e“ ifié .21.? 0 kéqfi' I“ v 9;? . ' ..I- . . .fi‘ 0 $33,. \‘.)a 3"! \"v go Oh") i 31. t J! K? I i: v \ 3!!) l .1} ‘h ’- - " a'rr 1" . . y. 3"" '5' .0 QE’IJUA Figure 2.1: Electron micrograph of a single hollow fiber. 13 IMMK 00" PROCESS 00f WI! " a. Backflushing b. Recycling Figure 2.2: Schematic of a hollow fiber cartridge showing the two modes of opration used in systems design (from Waterland et al., 1975). 14 the hollow fiber reactor (HFR). Normal operation of the reactor involves pumping substrate solution through the lumen at low pressure in the recycle mode (Figure 2.2b). During operation, the shell-side ports are closed, and the shell-side contains no liquid. Substrate is transported from the lumen via diffusion through the membrane and into the spongy layer where it reacts with the enzyme. Products of the reaction then diffuse back across the membrane and exit the reactor in the lumen-side outlet stream. Advantages of physical immobilization of enzymes in hollow fiber reactors include [Chambers, Cohen, and Baricos, 1976; Powell, 1988]: 1) quick and easy reactor preparation without chemically altering the enzyme, 2) relatively small effects on the kinetic properties of the enzyme, 3) prevention of microbial access to the enzyme, 4) selectivity of products and substrates through the selectivity of the membrane, 5) large surface area to volume ratio, 6) no enzyme leakage, 7) reuse of the enzyme, and 8) continuous operation at low pressures. Hollow Fiber Reactor Models As shown in Figure 2.3, a hollow fiber is physically divided into three regions; the lumen (region 1), the ultrathin membrane (region 2), and the spongy layer (region 3). Several models have been developed to predict conversions in hollow fiber reactors [Kleinstreuer and Poweigha, 1984]. The most complete models consider the mass transfer in the three .15 membrane Figure 2.3: Schematic of cross sectional views of a hollow fiber. The figure shows the cylindrical geometry and the dimensions of the hollow fiber (figure not drawn to scale). 16 regions, axial flow and radial diffusion in the lumen, radial diffusion across the UF membrane, and radial diffusion and subsequent reaction in the spongy layer. Other mass transport mechanisms including axial diffusion and bulk flow across the membrane due to transmembrane pressure gradients are assumed negligible. Several investigators have presented models to predict conversions in HFRs using steady state assumptions [Waterland, Michaels, and Robertson, 1974; Lewis and Middleman, 1974; Kim and Cooney, 1976; Webster and Shuler, 1981]. Using the system conceptualization depicted in Figure 2.3, it is seen that the mass transfer equation within the lumen can be represented by simple diffusion/convection assuming laminar Newtonian flow and negligible axial diffusion: Region 1 (lumen): ”1 .3. [r “I ] - Uz_dfl_ (2.1) r dr dr dz where the subscripts refer to the particular region of the fiber, D is the substrate diffusivity, S is the substrate concentration, r is the radial dimension, a is the distance from the center of the lumen to the inner surface of the membrane, and z is the axial dimension. Uz(r) is assumed to follow a Poiseuille type radial velocity profile in which U0 is the center line velocity. Within the membrane of the hollow fiber, it is assumed that the substrate concentration may be described by a simple diffusion equation: 17 Region 2 (membrane): D2 d [ r as, ] - o (2.2) r dr dr Finally, it is assumed that a simple diffusion/reaction equation governs the substrate concentration within the spongy matrix: Region 3 (spongy matrix): D, d [ r as, ] _ v s, (2.3) r dr dr K.m where the first-order limit of Michaelis-Menten kinetics (low substrate concentration relative to Km) has been assumed in which Km and Vmax are the Michaelis constant and the maximum attainable reaction rate, respectively. For hollow fiber reactors, the following initial conditions are usually used: 51 ' So at t - 0 S2 - 0 for all z (2.4) 83-0 - and the boundary conditions are: at r - 0 d5! - o (2.5) dr l8 D2 dS2 D1 d5, (see Figure 2.3) (2.6) St " '1 32 D2 dS2 _ Ds ds3 at r - b dr dr (2.7) (see Figure 2.3) 83 " '7 $2 at r - d ‘13: (see Figure 2.3) dr 0 (2.8) The symbol 1 represents the membrane partition coefficient. Solutions to this problem are discussed in a number of sources. Waterland et a1. [1975] discuss this problem for hollow fiber reactors and present solutions for a variety of conditions. They include nonlinear kinetics in their analysis. Even in the case of linear kinetics, numerical methods must be used to obtain a solution because Equations (2.1) - (2.3) are coupled. The results of their solution are presented in terms of the Thiele modulus: 2 V a _ ___HEDL______ ¢ K D (2.9) m 3 Z - -;-—;- (2.10) where l9 2____. (2.11) is the Peclet number, D1 is free-solution substrate diffusivity, a is the inner radius of the fiber, U0 is the maximum flow velocity, 2 is the axial coordinate, Vmax is maximum enzyme reaction rate, Km is the Michaelis constant, and D3 is the spongy layer substrate diffusivity. Several assumptions that were used in calculating the predictions from Waterland's model are worth noting. The enzyme in the spongy layer was regarded as being evenly distributed. Also, since the solvent in the spongy layer is the same as that in the lumen, and, given the macroporous nature of the spongy layer, the free solution diffusivity of substrate was assumed for this region. Lacking data to describe diffusion across the ultrafiltration layer, Waterland et a1. assumed a tenfold higher mass transfer resistance for the membrane than for the free solution. While the solution to the model presented by Waterland accurately predicts conversion in the hollow fiber reactor, its calculations are quite cumbersome [Kim and Dooney, 1976]. The model may also be unnecessarily rigorous in its consideration of the UP membrane since varying the assumed ratio Dl/D2 between 5 and 20 yielded negligible changes in predicted conversions [Waterland, Michaels, and Robertson, 1974]. Other models have been presented which are modifications of the Waterland model. One such model is presented by Lewis and Middleman [1974]. In their analysis they assume slow kinetics (in the sense of a low Thiele modulus) and negligible mass transfer resistance due to the ultrafiltration membrane. These assumptions permit incorporating 20 Equations (2.1) and (2.2) and the condition of radial flux continuity into the expression: Uo a dS1 dr a 4 dz D, (2.12) Equations (2.3) and (2.12) are then amenable to analytical solution. Using data for static loaded urease in a HFR, the model was tested at Thiele moduli of 10.1 and 4.4 x 10-2. Experimental conversions conformed with the model's predictions particularly well at the lower Thiele modulus value, and a small but consistent error was observed at the higher value. Another approach treats a hollow fiber reactor as a continuous stirred tank reactor (CSTR) rather than a plug flow reactor [Webster and Shuler, 1978; Webster, Shuler, and Rooney, 1979; Webster and Shuler, 1981; Davis and Watson, 1985]. A common method of operation is to use a recycle loop to generate a high recirculation rate which yields nearly constant concentrations in the lumen. Such operation eliminates the consideration of axial and radial concentration gradients in the lumen. ~The governing equations for the lumen, membrane, and spongy layer are the same as Equations (2.1), (2.2), and (2.3) where dSl/dr - 0. As above, analytical solution requires simplification to first or zeroeth order kinetics. The above models use a number of simplifying assumptions to develop the descriptive equations and analytical solutions. These models assume that the diffusivity of substrate in the spongy region of the fiber is equal to the free solution diffusivity, and that the substrate diffusivity across the membrane is some multiple of the free solution 21 diffusivity. In addition, simplified enzyme kinetics are also assumed. Finally, attempting to use such models with data obtained from the experiments conducted in this dissertation may be complicated due to the method of enzyme immobilization. These models assume evenly distributed catalytic activity in the spongy layer. Backflush loading may, however, yield an enzyme profile in which the enzyme is concentrated around the inner membrane of the spongy region [Chambers, Cohen, and Baricos, 1976]. The existence of such a profile greatly increases the rate of reaction possible in the region surrounding the lumen and reduces the mean diffusion path required for substrate reaction. Because of these limitations, it was important to develop a model that accurately predicts the conversion of substrate in the reactor system being studied. In addition to modelling the reactor system, it was also necessary to determine the biocompatibility of the hollow fiber reactors. No negative hematological effects were expected to be caused by the circulation of blood through the lumen of these fibers. As mentioned above, immobilized enzyme hollow fiber reactors are similar in construction to hollow fiber cartridges used in hemodialysis, although the materials of construction are typically different. In addition, other investigators have used reactors identical to the ones used in this research for other blood treatments [Edman, Nylen, and Sjoholm, 1988; Ambrus et al., 1988]; no detrimental hematological effects were observed due to imposed shear fields or contact with membrane materials. Extracorporeal Blood Treatment Ambrus et a1. [1988] have reported the use of enzyme reactors in the treatment of phenylketonuria. In this condition, phenylalanine 22 accumulates in the blood and tissues because of an inborn deficiency of phenylalanine hydroxylase. Mental retardation caused by excess phenylalanine has been prevented by early institution of a low- phenylalanine diet. However, for the child of school age with phenylketonuria, a low-phenylalanine diet becomes increasingly difficult to maintain. In addition, a shift to a diet of conventional food in these children can result in deterioration of intelligence and school performance, as well as personality changes. Ambrus and her colleagues developed reactors with immobilized L-phenylalanine ammonia-lyase, an enzyme that metabolizes phenylalanine to trans-cinnamic acid and ammonia without the need for a coenzyme. These investigators treated a patient with phenylketonuria using a phenylalanine ammonia-lyase reactor in an extracorporeal circulation system. A phenylalanine level of 1.82 mmol/L (for the 6 years before treatment) decreased to 1.24 mmol/L after 5.5 hours of treatment, without the enzyme entering the circulation. Total phenylalanine depletion from blood and tissue stores was estimated at 1,800 mg. The hemodialysis-like procedure proved to be without side- effects and specific for phenylalanine. From this preliminary research, it may be concluded that the extracorporeal use of enzyme reactors represents a new, safe, and effective therapeutic technique for lowering blood substrate levels. The use of extracorporeal devices has also been investigated as a technique for the treatment of leukemia. The application of the extracorporeal irradiation of blood as a method for destroying leukemic leukocytes in humans has been investigated clinically [Epstein et al., 1965; Schiffer et al., 1966]. In addition, Edman et a1. [1988] recently reported the reduction of L-asparagine concentration in the blood of sheep to undetectable levels by the use of enzymatic reactor treatment. 23 They immobilized L-asparaginase-loaded microparticles within the pores of hollow fibers; this immobilization was necessary to avoid the immunological reactions associated with this enzyme's introduction into the body. Although in 2119 experiments in sheep showed that the L- asparagine concentration in the blood was reduced to zero by the L- asparaginase reactor, the initial asparagine concentration in the blood was partly restored in 24 hours. This rebound phenomenon was enhanced when the treatment was repeated. Later treatments had little effect on the plasma L-asparagine level which the authors attributed to the resynthesis of the amino acid in the liver by induction of L-asparagine synthetase. In a clinical trial with one human patient, the rebound phenomenon was observed in 10 days. Because essential amino acids (such as lysine) are not synthesized in the human body, greater control of the plasma concentration of these substrates can therefore be expected with an appropriate immobilized enzyme reactor. Enzyme Selection As mentioned above, several enzymes have demonstrated positive effects in inhibiting growth of leukemic cells. This growth-inhibiting effect is related to the enzyme's ability to catalyze the irreversible degradation of an essential amino acid in plasma. ’The rate at which an enzyme can perform this task depends on its kinetic parameters. Enzyme kinetics are commonly described by the Michaelis-Menten, model. In this model, the Michaelis constant (Km) is a measure of the strength of the enzyme/substrate complex (a low Km indicates strong binding). The Michaelis constants for several enzymes are listed in Table 2.1 [Kusakabe et al., 1980]: 24 Table 2.1 Michaelis Constant of Selected Antitumor Enzymes Michaelis constant nz e K (mM) Phenylalanine ammonia-lyase 0.25 Methionine 1-lyase 78-90 Tyrosine phenol lyase 0.28 Threonine deaminase 8.0 L-Lysine a-oxidase 0.04 L-asparaginase 0.02 L-lysine a-oxidase was chosen as the enzyme for this investigation for several reasons. First, Table 2.1 shows that, of the antitumor enzymes that have been investigated, only L-asparaginase has a lower Michaelis constant (Km). A low K.m indicates a strong enzyme/substrate affinity and is therefore desirable. In addition, the enzyme substrate, L-lysine, is one of the more concentrated and highly metabolized amino acids in the plasma of leukemic patients [Faguet, 1986]. Finally, the rebound phenomena associated with L-asparaginase should not be encountered because L-lysine is an essential amino acid and is not synthesized in mammals. This will give more precise control of the plasma lysine level during treatment. It was for these reasons that L- lysine a-oxidase was chosen as the enzyme for this investigation. Kodama et a1. [1980] were the first to isolate and identify the antitumor activity of L-lysine a-oxidase. These authors reported the identification of the mold strain Trichoderma viride Y244-2 and the conditions necessary for the maximum production of the enzyme. The maximum enzyme production of the mold grown on wheat bran was observed after 10 and 14 days of incubation with and without NaNOB, respectively. 25 The addition of NaNO3 to the medium stimulated the production of the enzyme. The fungal enzyme was designated as L-lysine a-oxidase. It has a molecular weight of 112,000 and was found to catalyze the a-oxidative deamination of L-lysine as follows: L-lysine + 02 + H20 ------- > a-keto-e-aminocaproate + NH3 + H 0 (2.13) 2 2 + i t _ H20 1 A-piperidine-Z-carboxy1ate The effect of L-lysine a-oxidase on the growth of L5178Y mouse leukemic cells was determined in experiments conducted by Kusakabe et a1. [1980] in which these cells were grown in RPMI 1640 medium containing 10% calf serum [Machida et al., 1979] in the absence or presence of the enzyme. L-lysine a-oxidase completely inhibited the growth of L5178Y mouse leukemic cells in 21519 when measured by trypan blue exclusion [Kusakabe et al., 1980]; more than 99% of the cells lost viability when incubated with a L-lysine a-oxidase concentration of 10 milliunits (mu) per m1. A unit is defined as the amount of enzyme required to oxidize one pmol of lysine per minute at pH 7.4 and 30°. Furthermore, l mu/ml was sufficient to produce 50% inhibition of cell growth. After the addition of enzyme to the medium, the investigators monitored the lysine concentration present. At the dose that caused complete cell growth inhibition, no lysine was detected. In addition, lysine concentration decreased by about 40% when the enzyme caused 50% inhibition of growth. The authors also showed that the growth of L5178Y cells was depressed about 70% by preincubation of the medium with lysine 26 a-oxidase, and that growth was fully restored by the addition of lysine. These findings show that the growth-inhibitory effect of the enzyme on the cells is at least in part based on a decrease in lysine concentration in the culture medium. Kusakabe and his colleagues also examined whether the enzymatic reaction products from lysine oxidation participated in the cell growth inhibition. L5178Y cells were incubated with 0.5 mM Aipiperidine-Z- carboxylate and ammonia in the RPMI 1640 medium for 72 hr. Cell proliferation was not inhibited by either compound. The other reaction product, H202, inhibited the growth of these cells in culture at a concentration higher than 0.033 mM, and no growth was exhibited at 0.2 mM. This was to be expected; Freese et al. [1967] reported that hydrogen peroxide is a cytotoxic chemical that cleaves the sugar- phosphate backbone of DNA sufficiently to cause the inactivation of cell proliferation. It was thus determined that the in 31:19 cytotoxic effect of L-lysine a-oxidase on L5178Y cells is ascribable to a combination of the deprivation of L-lysine from the medium and the action of the reaction product H202 on the cells. If lysine is . completely oxidized in human blood, the concentration of H202 will reach 0.22 mM, which is high enough to have a detrimental effect on cells. This potential problem has been addressed in this dissertation work. Kusakabe et a1. [1980] also conducted in 2139 studies on the effect that the oxidase enzyme had on mice bearing L1210 leukemia. L1210 cells were inoculated intraperitoneally into mice on day 0. The administration of a dose of 70 units/kg-day of L-lysine a-oxidase intraperitoneally on days 1 to 5 resulted in an increase in life-span by 34 to 48% over the control animals. The effect of the enzyme on the lysine level in the plasma of the mice was also determined. A single 27 intravenous injection of 30 units/kg reduced the lysine concentration in the plasma from 0.33 mM to an undetectable level after 1 hr; this depressed lysine level persisted for 12 hr followed by a gradual increase. The lysine level was almost fully recovered in 24 hr after the injection. These results suggest that there is a correlation between the theraputic effectiveness of the enzyme and the decrease in the concentration of lysine in the plasma of the mice. Animal Medals of Human Leukemia As described earlier, leukemia is a disease manifested by the abnormal and uncontrolled proliferation of leukocytes in the blood- forming organs and the presence of immature leukocytes in peripheral circulation [Hardisty and Weatherall, 1974]. Leukemic cells progress through the normal phases of cell division (G1~S~G2*M) [Alberts et al., 1983]. In the G, phase, protein and RNA are actively synthesized, but DNA is not. Following the GI phase, the chromosomes are replicated (DNA and protein synthesis) in the S phase. The significance of the G2 phase is not fully understood at present. After the completion of the 62 phase, cell division starts (M phase). Sometimes cells enter a resting state designated as the Go phase. In leukemic cells, the S phase is considerably prolonged [Greenberg, 1979], making leukemic lymphocytes particularly sensitive to drugs which inhibit protein and DNA synthesis. The development of lymphoproliferative disease in humans and a variety of animal species has been attributed to infection by retroviruses [Alberts et al., 1983]. Bovine leukemia virus (BLV) is an exogenous retrovirus which causes naturally occurring lymphoproliferative diseases of cattle [Miller et al., 1969]. BLV is biochemically and biologically similar to human T-cell leukemia virus 28 (HTLV I), an oncogenic retrovirus of humans implicated in the etiology of adult T cell leukemia [Gross, 1983]. Both viruses cause rapidly fatal leukemia and lymphoma. Because of these similarities between BLV and HTLVs, interest has arisen concerning the role of BLV as a model virus for studying human leukemia and lymphomas caused by retroviruses. Dr. John Kaneene (Professor, Large Animal Clinical Sciences and consultant to this dissertation work) has developed an animal model for studying HTLV infection by using BLV infection in sheep. There are several advantages for using sheep as an animal model for studying leukemias. BLV has been easily transmitted to sheep and, as with BLV infection in cattle, both leukemia and lymphoma have been produced [Dimmock et al., 1986; Suneya et al., 1984; Paulsen, 1976]. The lag phase between infection and development of leukemia in sheep is short (14 months). The same type of cell is infected in BLV-infected sheep and HTLV-infected humans [Sugimura et al., 1959; Popovic, Sarin, and Robert-Guroff, 1983; Solbach, 1984], and the viruses have many other common characteristics. The usefulness of sheep is enhanced by their availability, low purchase price, and low maintenance costs relative to other species infected by retroviruses. We have had available to us a self-propagating flock of sheep chronically infected with BLV. In addition, blood from leukemic sheep (also infected with BLV) has been sent to us by Dr R.D. Schultz (Professor, Department of Pathology, University of Wisconsin, Madison). Blood samples from BLV-infected sheep have been used in the evaluation of the enzymatic reactor. Before the reactor could be evaluated, however, certain analytical techniques and methods of data analysis had to be chosen. These techniques are described in the next chapter. CHAPTER 3 ANALYTICAL TECHNIQUES The following chapters will discuss the immobilization of the enzymes within the hollow fibers, the reactor performance and optimization, reactor modeling, the biocompatibility of the reactor, and the effect of lysine deprivation on leukemic blood. Several analytical techniques and methods of data analysis are common to the experiments described in these chapters. The following paragraphs describe these techniques including methods for determining enzyme activity, protein, lysine, and hydrogen peroxide concentrations as well as hematological properties such as cell counts, cell viability, plasma potassium concentration, plasma creatine phosphokinase activity, and cell proliferative capacity. Lowry'Protein Determination As will be discussed in Chapter 4, it was often necessary to determine the protein concentration in a given sample. The Lowry reaction can be used to perform this analysis [Lowry et al., 1951]. The first step in this procedure involves the formation of a copper/protein complex in alkaline solution. This complex then reduces a phosphomolybdic—phosphotungstate to yield an intense blue color. The absorbance of this blue solution can be determined spectroscopically and is directly proportional to the total protein concentration in the sample. The procedure for the Lowry analysis is as follows: 29 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 30 Reagent A is prepared by dissolving 100 g Na2003 in 1 liter (final volume) of 0.5N NaOH. Reagent B is prepared by dissolving l g CuSO4oSH20 in 100 m1 (final volume) of distilled water. Reagent C is prepared by dissolving 2 g potassium tartrate in 100 ml (final volume) distilled water. The reagents prepared in steps 1 to 3 may be stored indefinitely. A 0.3 mg/ml protein standard solution is prepared by making the appropriate dilution to a 10 g/dl solution of bovine albumin obtained from Sigma (catalog No. 690-10). The UV/Vis spectrophotometer (Perkin Elmer Lambda 3A) is then turned on to warm up. Test tubes are numbered and placed in a test tube rack. One of each of the following volumes of the protein standard solution is then carefully pipetted into each tube: 0, 0.1, 0.2, 0.4, 0.6, 0.8, and 1.0 ml. The total volume of each tube is brought up to 1.0 ml by the appropriate addition of distilled water. 15 ml of reagent A, 0.75 ml reagent B, and 0.75 ml reagent C are mixed thoroughly in a 125 m1 Erlenmeyer flask. 1.0 ml of the solution made in step 8 is added to each tube. The tubes are vortexed to assure proper mixing. The tubes are incubated for 15 minutes at room temperature. While the tubes are incubating, 5.0 ml of 2N Folin-phenol reagent is diluted to 50 ml with distilled water in a 125 ml Erlenmeyer flask and mixed thoroughly. At the conclusion of the incubation period (step 10), 3.0 ml of the solution prepared in step 11 is forcibly pipetted into each tube. The resulting solution is vortexed immediately. The addition to and mixing of each test tube is completed before proceeding to the next. The absorbance of each sample is determined at a wavelength of 540 nm. The data are plotted as shown in Figure 3.1 to obtain a standard curve. Samples of unkown protein concentration are assayed using procedures identical to those used for the standard curves. The major precaution to be observed when performing the Lowry assay concerns the addition of Folin's reagent. This reagent is stable only 31 ass ... sass .8 «mangoes 5383850 5395 wmmmmfiefiow . .8.“ 352: mused 2: .8.“ 953 enaucaum "Hem «Swen occoetowfi. fie so to. no . 0.0 .VoP No? 0.1. . _ . _ . _ . $K-O A S (Jelfl/OW) uogmiueouog [115;de 00v .. 32 at acidic pH; however, the reduction described above occurs only at pH 10.0. Therefore, when Folin's reagent is added to the alkaline copper/protein solution, mixing must occur immediately so that the reduction can occur before the phosphomolybdic-phosphotungstate Folin's reagent breaks down. Another concern is the sensitivity of the method to foreign ions. Precautions must be taken to keep the samples ion- free. This assay procedure is very accurate for protein concentrations between 30 and 300 pg/ml. For samples with higher concentrations, a dilution step is first required. Samples that are low in protein concentration are ”spiked” with protein by adding 0.1 ml of the protein standard prepared in step 4 above to 0.9 ml of the sample before assaying. In addition, it is important to note that this technique only gives the total amount of protein in a sample. For samples where individual enzyme concentrations are needed, a separation step must be performed before using the Lowry method. Lysine Determination Lysine concentrations were usually determined by the method described by Nakatani, Fujioka, and Higashino [1972]. This method uses saccharopine dehydrogenase which catalyzes the following reversible reaction: lysine + a-ketoglutarate + NADH + H+ = saccharopine + NAD+ + H O (3.1) 2 No structural analogs of L-lysine and a-ketoglutarate are known to serve as substrates for saccharopine dehydrogenase. In addition, the equilibrium of the reaction is greatly in favor of saccharopine 33 formation [Nakatani and Fujioka, 1970]. By taking advantage of these two facts, it is possible to determine the concentration of lysine in a given sample by simply following the disappearance of NADH caused by reaction (3.1). Incubation of a small amount of lysine with saccharopine dehydrogenase in the presence of excess a-ketoglutarate and NADH results in a decrease in NADH absorbance at 340 nm that is proportional to the amount of lysine present. The lysine (Catalog No. L5626), a-ketogluterata (Catalog No. K410-2), NADH (Catalog No. N8129), and saccharopine dehydrogenase (Catalog No. 83633) were all obtained from Sigma. In order to obtain a standard curve for lysine, lysine solutions at the concentrations listed in Table 3.1 were prepared by making the appropriate dilutions with buffer to a 10.0 mM lysine stock solution: Table 3 . 1 Concentrations Used to Construct the Lysine Standard Curve :1 O O QNQUIJ-‘WMH 00000000 0 0‘ One ml of each solution is measured into a test tube. The total volume of each test tube is then brought up to 3.0 ml by the addition of 1.0 m1 of 0.1 M phosphate buffer (pH 7.0), 0.9 ml of a 0.5 mg/ml NADH solution 34 prepared by diluting the solid into 0.1 M phosphate buffer (pH 7.0), and 0.1 ml of a 0.1 M a-katoglutarate solution. To initiate reaction, 1.0 ml of saccharopine dehydrogenase stock solution is added to each test tube. The stock solution consists of 100 units (:1 mg) of enzyme dissolved in 50 ml of 0.05 M potassium phosphate buffer (pH 6.8). Five mg of bovine serum albumin (obtained from Sigma) is added to the stock solution to increase enzyme stability during storage [Ogawa and Fujioka, 1978]. After 30 minutes, the absorbance of each solution is measured using 0.1 M phosphate buffer (pH 7.0) as the blank. The change in absorbance of a solution is taken as the difference of absorbance between that solution and the sample with no lysine present (test tube 1). As mentioned earlier, the amount of lysine that is present in a solution is proportional to the amount of NADH that is consumed by reaction (3.1) which, in turn, is proportional to the change in absorbance. Therefore a curve of lysine concentration versus change in absorbance at 340 nm can be constructed (Figure 3.2). This technique is accurate for lysine concentrations up to 0.2 mM. For samples with higher concentrations, it is usually sufficient to include a dilution step prior to analysis. For the determination of lysine in blood, two ml of the blood is centrifuged at 3,500 rpm for 20 minutes in a Sorvall RCZ-B centrifuge to remove the red blood cells. After centrifugation, the top, clear portion, which is the plasma, is aspirated and an equal volume of 1.0 M perchloric acid is added. The precipitate is washed twice with 0.5 M perchloric acid, each time using 40% of the volume of the original sample. The combined supernatant solution is neutralized with 6.0 M KOH. The potassium perchlorate formed is removed by centrifugation, and the supernatant solution is analyzed for lysine concentration using the 35 .693 u erg: .8 Essence €52: awesomoeuhcmu ommmouaaoomm wen: comumuemmomoo Snub wEEEbtu e8 953 Encarta ”ad enema. 8:096qu E mmcogo no ....o no «.0 no .03 _ p _ . _ . No.0 ”.0 (mm) uogonueou‘og eugsk] 36 technique described earlier. Due to the number of centrifugation steps involved, this technique is time consuming when determining the lysine concentration of blood samples. In order to reduce the time for analysis, an alternative method for determining plasma lysine concentration was investigated. This method utilizes L-lysine a-oxidase and an ammonia electrode (Orion, Model 95-12). As mentioned in Chapter 2, one of the byproducts of the oxidase reaction is ammonia. The blood sample is incubated with 10 units of L-lysine a-oxidase and 50 units of catalase for 30 minutes at 30°C. This is sufficient to convert all of the lysine. The blood sample is centrifuged at 3,500 rpm for 20 minutes to remove the red blood cells. After centrifugation, the ammonia concentration of the plasma can be measured directly in the following manner: 1) 100 ml of ammonia standard solutions are prepared using ammonium chloride and distilled water. These solutions are measured into 150 ml beakers. The standards have ammonia concentrations of 5.0, 1.0, 0.5, 0.1, and 0.05 mM. 2) To adjust solution pH to the operating range of the electrode, two m1 of the ionic strength adjuster (ISA) is added to each 100 ml of standard. The ISA is a 5 M NaOH/0.05 M Disodium EDTA/10% methanol solution with a color indicator. Blue color persists when solution pH is correct. 3) The electrode is rinsed with distilled water, dried, and placed into one of the standard solution beakers. When a stable millivolt readout is obtained from the Brinkmann 632 pH-meter, the millivolt value and the corresponding standard concentration is recorded. 4) The procedure is repeated for the remaining standards. Between measurements, the electrode tip is immersed in a 1.0 mM standard with ISA added. 5) A calibration curve is prepared by plotting logarithm of ammonia concentration versus the millivolt values (see Figure 3.3 for an example). 6) The plasma sample is measured into an appropriate beaker, and ISA is added until the blue color persists. The minimum sample size is 2.5 ml in a 30 ml beaker. 37 . . .23.: u mesa: .3 assuage 38820 «3955 .8.“ 02.3 caawnfim and 23mm 3.8:: oh... mm! m _. .7... an»... mm__.l an F... . NI! l . ,_ I [uoppnueouoo oguowwv] 501 38 7) The electrode is rinsed with distilled water, dried, and placed into the beaker. When a stable millivolt readout is obtained, the value is recorded. 8) Using the calibration curve prepared in step 5, the ammonia concentration of the plasma sample is determined. As seen by the stoichiometry of the L-lysine a-oxidase reaction, the amount of lysine that is present in solution is proportional to the amount of ammonia that is generated by reaction (2.13). Therefore, the plasma ammonia concentration that is measured is equal to the lysine concentration of the original blood sample. The major advantage of this technique is that it is quicker and easier to use than the sacchoropine dehydrogenase method discussed earlier. In addition, the ammonia electrode has a concentration range of 10-7 M to 1.0 M, and therefore is more accurate and more sensitive to small changes in blood lysine concentration. Hydrogen Peroxide Determination Hydrogen peroxide concentration can be determined directly by using its absorbance at 240 nm. The first step in this procedure is to _ prepare H202 solutions at the concentrations listed in the first column of Table 3.2 by diluting a 30% (v/v) hydrogen peroxide stock solution with an appropriate amount of 0.1 M potassium phosphate buffer, pH 7.0. One ml of each of the solutions listed in Table 3.2 is measured into a test tube and diluted to a total volume of 3 ml with phosphate buffer. This results in having ten test tubes with hydrogen peroxide concentrations (Table 3.2, second column) ranging from 0.5 to 30.1 mM. 39 Table 3 . 2 Concentrations Used to Construct the 3202 Standard Curve Solutions lest tubes 1.5 mM 0.50 mM 3.8 mM 1.27 mM 5.9 mM 1.97 mM 13.5 mM 4.50 mM 17.8 mM 6.90 mM 24.0 mM 8.00 mM 27.3 mM 9.10 mM 44.7 mM 14.90 mM 60.2 mM 20.07 mM 90.3 mM 30.10 mM The absorbance at 240 nm of the solutions in each of the test tubes is measured and recorded. A solution containing a 2:1 ratio (volume basis) of catalase to buffer served as a blank. These data are used to create a standard curve of H202 concentration versus absorbance (Figure 3.4). Catalase Activity Determination For the experiments described in Chapter 5, it was necessary to determine whether enzyme activity was affected by the type of hollow fiber material used. The activity of catalase is defined as the amount of substrate converted per mg of enzyme per minute, and is determined by the method of Chance and Herbert [1950]. This technique uses the direct measurement of the decrease of light absorbance at a wavelength of 240 nm caused by the decomposition of hydrogen peroxide by catalase. In order to determine the activity of catalase in a given sample, 1.0 ml of the sample is incubated with a 30 mM hydrogen peroxide solution. The absorbance of H202 at 240 nm is recorded with time using the UV/Vis spectrophotometer in the local mode. From this information and a 40 A535 u batman: mo «nomommooov 5333850 02839 sowed»: mnmfifiaouoc «8.025 upmwcflm "Wm madman 8:09.83 on. . .mx. . .mu. _ .wflo. _ ..xo. . .060 H... .... .8. (ww) uogwiueouoo apgxwed uebonKH 41 standard curve of hydrogen peroxide versus absorbance prepared in the manner described above, the amount of H202 converted per minute can be determined. The Lowry method is then used to determine the catalase concentration of the sample which, in turn, is used for the calculation of catalase activity. Irlysine a-oxidase Activity Determination The method used for the determination of lysine a-oxidase activity is similar to the one described for catalase. Two m1 of a 2.0 mM solution of lysine is pipetted into a test tube which is then placed in a water bath (Lab Line,Inc., Model 3540) at 37°C. One ml of the sample being tested is added to the test tube. After one minute, 0.2 ml of 25% trichloroacetic acid (TCA) solution is added to stop the reaction. The amount of lysine remaining in the solution is determined by the saccharopine dehydrogenase method discussed above. From this, the amount of lysine converted is calculated and used with the L-lysine a- oxidase concentration obtained from the Lowry analysis to determine activity. Source of BEN-Infected Blood A self-propagating flock of sheep chronically infected with bovine leukemia virus has been the source of blood for most of the experiments conducted for this thesis. Cathy Knapp, a student in Veterinary Medicine, has assisted in the collection of blood samples. The wool around a small area of the sheep's neck is clipped using an A5 Oster animal clipper. This is done to allow easier acces to the vein from which blood will be drawn. Alcohol is used to sterilize the clipped -area. The needle of one end of the blood collection set is inserted 42 into a vein. Once blood begins to flow, the other end is inserted in a plasma collection bottle which contains anticoagulant (Acid-Citrate- Dextrose). Approximately 200 ml is collected per experiment; up to one liter of blood may be withdrawn without endangering the animal. Blood is used as soon as possible after withdrawal and preparation. The effect of lysine deprivation on leukemic blood will be discussed in Chapter 8. Since none of our sheep had developed leukemia at the time these experiments were conducted, it was necessary to have leukemic blood from BLV-infected sheep sent to us from Dr. R.D Schultz, Professor of Veterinary Science at the University of Wisconsin. Cell Counts Blood analyses were performed by the Veterninary Clinic's pathology lab. Cell counts were determined using the Technichon H1 blood analyzer (Metpath, Inc., Des Plaines, IL). The Technicon H1 is a discrete mode bench top hematology analyzer designed to perform a complete blood count. This instrument is a three module system that functions as a single integrated unit. Red blood cells are sized and counted using a helium neon laser to determine high and low angle light scatter. A separate module called the peroxidase channel is used to determine the white blood cell (WBC) count. RBC and Platelet Counts A 2.0 pl aliquot of EDTA-buffered whole blood is diluted 1:625. The RBCs are lightly fixed by the RBC diluent which preserves their spherical shape. The RBC/platelet fluid is pumped into the appropriate module and the helium-neon laser (tuned to 632.8 nm) is used for -counting and sizing. Counting is done with a single light scatter 43 detector and darkfield optics. Controls are used to calibrate the counts . WBC Counts There are two types of white cells; granulocytes (those posessing granules in their cytoplasm) and agranulocytes (those lacking granules). Granulocytes include neutrophils (cells that stain with neutral dyes), basophils (cell that stain with basic dyes), and eosinophils (cells that stain with the acid dye eosin). Agranulocytes include lymphocytes and monocytes. The peroxidase channel is used to determine the total leukocyte count and a portion of the leukocyte differential count by identifying five types of white blood cells based on size and peroxidase activity of the cell. Peroxidase is contained in predictably varying amounts in three of the cell types (neutrophils, monocytes, and eosinophils) and is absent in two (lymphocytes and basophils). The peroxidase method involves a two step reaction. A 12.0 pl aliquot of EDTA-buffered blood is diluted 21-fold by reagent 1 (detergent, formaldehyde) and heated from 40°C to 72°C in twelve seconds. The RBCs are lysed, and the hypertonic solution dehydrates the WBCs which are then fixed by the formaldehyde. Next, hydrogen peroxide and 4-chlor-l-napthol are added and heated for thirteen seconds. The peroxidase activity in the cells converts these substrates to an intensely stained precipitate that is examined by forward light scatter and absorbance. The staining intensity coupled with sizing by photo-optical forward light scattering allows for clear separation of the cell populations. Basophils are not specifically identified in this channel and are included in the 44 lymphocytes. Results from the basophil channel are used with the peroxidase channel to compute the differential count. The basophil channel shares the flow cell with the RBC/platelet system. A 12.0 pl aliquot of EDTA- buffered blood is reacted with acid and surfactant. The RBCs are lysed and the cytoplasm of all white cells, except basophils, is stripped off. Basophils are resistant to this treatment. The laser is used to determine both high and low angle scatter of the cells. This enables discrimination of basophils. Serum Creatine Kinase Activity In order to get an understanding of the effects of immobilized enzyme treatment on important blood enzyme systems, creatine kinase was chosen as the test enzyme. It was therefore necessary to determine the activity of creatine kinase (CK) in the serum of treated blood samples. This analysis was done by the Veterinary Clinic's pathology laboratory. Abbott Spectrum CK-NAC reagent (obtained from the diagnostics division of Abbott Laboratories, List No. 1337) is used with the Abbott Spectrum high performance diagnostic system (Abbott Laboratories) for the quantification of total creatine kinase in serum. Creatine kinase in the sample being analyzed catalyzes the transfer of a high energy phosphate group from creatine phophate to ADP. The ATP produced is subsequently used to phosphorylate glucose to produce glucose-6- phosphate (G-6-P) in the presence of hexokinase (MK). The G-6-P is then oxidized by glucose-6-phosphate dehydrogenase (G-6-PDH) with the concomitant reduction of NAD+ to NADH. The CK-NAC reagent is prepared by adding the volume of distilled water stated on the label of the reagent cartridge. This reagent 45 contains all the substrates and enzymes (except creatine kinase) necessary for the following reactions: CK creatine phosphate + ADP ----- + creatine + ATP (3.2) HK Glucose + ATP ----- 4 G-6-P + ADP (3.3) G-6-P + NAD+ + H20 _§:§:EP§,¢ 6-phosphagluconate + NADH + H+ (3.4) The rate of formation of NADH is monitored at 340 nm and is proportional to the creatine kinase activity in the sample. Sera with known concentrations of creatine kinase are used for calibration and the technique is accurate between six and 2,000 IU/L. The minimum sample volume is 30 p1. Serum Potassium Concentration The lysis of blood cells causes an increase in the serum potassium concentration due to the high concentration of potassium within the cells. Measuring serum potassium concentration can therefore give a measure of the degree of cell lysis caused by the enzymatic reactor treatment. An Abbott Spectrum High Performance Diagnostic system was used to determine serum potassium concentration. This analysis was also performed by the pathology laboratory of the Veterninary Clinic. Potassium ions interact with the ion-specific membrane of the potassium electrode. This interaction results in the generation of an electric potential across the membrane which is measured potentiometrically. The magnitude of the potential is proportional to the concentration of -potassium ion in the sample. Potassium standards (obtained from Abbott 8C 01 46 Laboratories) are used to calibrate the electrode. The electrode is accurate between potassium concentration of 1.0 and 20.0 mmol/L. Serum or heparinized plasma are suitable for analysis. Flow Cytometry As mentioned in Chapter 2, leukemic cells progress through the normal phases of cell division (G1*S*G2*M). Cells in the different stages of the cell cycle have different, but predictable amounts of DNA. Because of this, the DNA labelling technique of flow cytometry can be used to determine the exact number of cells in each phase of the cell cycle (Go/GI, S, and Gg/M). and the proliferative capacity of the lymphocytes (defined as the percentage of cells in the S plus Gz/M phases) can be calculated. Flow cytometry was used to determine the proliferative capacity of treated and control lymphocytes. This technique was performed in the pathology laboratory of St. Lawrence Hospital (Lansing, Michigan). The analysis is based on the following principles: flourochromes are available that stoichiometrically bind to DNA, and, as discussed earlier, cells in different stages of the cell cycle have different, but predictable amounts of DNA. Normal cells are euploid and have a known amount of DNA, whereas malignant cells are frequently aneuploid (have an abnormal number of chromosomes). The first step in utilizing flow cytometry is to separate the white cells from the whole blood. This is done by a sedimentation technique in which anticoagulated blood is layered onto a solution of Ficoll and sodium diatrizoate (obtained from Sigma). Three ml of the Ficoll solution is added to a 15 ml conical centrifuge tube and is brought to room temperature. Three m1 of whole blood is layered onto the solution 47 which is then centrifuged at 400 x g for thirty minutes at room temperature. During this centrifugation, erythrocytes and granulocytes are aggregated by Ficoll and rapidly sediment, whereas the lymphocytes remain at the opaque interface. After centrifugation, the upper layer is aspirated with a Pasteur pipet and discarded. The opaque interface is then transfered to a clean conical centrifuge tube. Ten ml of RPMI 1640 medium (obtained from Sigma) is added. The solution is gently mixed and is then centrifuged at 250 x g for ten minutes. The resulting supernatant is aspirated and discarded. The cell pellet is resuspended with 5.0 m1 of RPMI 1640 medium, mixed by gentle aspiration, and centrifuged at 250 x g for ten minutes. Finally, the RPMI 1640 washing steps are repeated. Erythrocyte contamination is negligible and most extraneous platelets are removed by the low speed centrifugation during the washing steps. After the lymphocytes are isolated, they are stained with propidium iodide (P1). With this procedure, the cell cytoplasm is removed through the action of trypsin and the detergent Nonidet-P40 (both obtained from Sigma). Spermine (Sigma) is added to stabIlize this reaction. RNase is added to remove any RNA to ensure that the PI binds only to DNA. Trypsin inhibitor is included in the RNase solution to inactivate any further digestion by trypsin. The resulting bare nuclei are stained with a saturated solution of PI (approximately 400 mg/dL) which stoichIometrically binds to double stranded DNA. The final phase of the procedure is the analysis of the PI stained nuclei on the flow cytometer. The labelled cells are pumped under slight pressure into the Becton-Dickenson FAG-SCAN flow cytometer. The cells enter a detection .zone where they are illuminated by a precisely focussed laser beam. 48 This technique measures physical and chemical charateristics of the cells as they pass single file in a fluid stream through the focussed laser beam. The energy of the laser excites the propidium iodide stain attached to the cells. The fluorescence intensity of the stain is a direct measure of the amount of nuclear DNA. The data are acquired and analyzed by a computer program developed by St. Lawrence. Flourescence intensity and light scatter signals can be evaluated simultaneously. Information on relative cell size, relative granularity, and flourescence intensity can be recorded for a large number of cells in a short time. From this analysis, the number of cells in each phase of the cell cycle (Go/GI, S, and Gz/M) can be determined. Methods of Data Analysis In Chapter 6, the statistical technique of factorial design was used to determine which reactor operating parameters have the greatest effect on reactor performance. For the experiments of Chapter 7, it was necessary to determine the required number of experiments to obtain statistically significant data. This was necessary because the available statistical parameters on the hematological analysis methods discussed above are highly variable. The methods of data analysis used in these chapters are discussed below. Factorial Design Factorial design is a statistical technique that can be used to evaluate the effect that a given variable has on the observed response of a process [Box, Hunter , and Hunter, 1978]. To perform a general factorial design, a fixed number of levels for each of a number of vvariables is selected and experiments are conducted with all possible 49 combinations. If there are 1, levels for the first variable, 12 levels for the second, ..., and IR levels for the kth, the complete arrangement of 11 x 12 x ... x lk experimental runs is called an 11 x 12 x ... x lk factorial design. For example a 2 x 3 x 5 factorial design requires 2 x 3 x S - 30 runs, and a 2 x 2 x 2 - 23 factorial design requires eight runs. In this dissertation, designs in which each variable occurs at only two levels were used. For each variable, a "-" level and a "+” level were designated. The effect of a variable in a factorial design is defined as the change in the observed response caused by moving from the "-" to the "+" level of that variable. All variables under investigation are of equal interest as is the possibility that these variables interact. If two variables interact then the individual effects cannot be simply added to give the total effect that the variables have on the observed response of the system. There are several methods for the analysis of a factorial design. One such method uses Yates's algorithm [Box, Hunter, and Hunter, 1978] as a quick technique for determining the effects of the variables. This algorithm is applied to the observations of the experiments of the factorial design after they have been arranged in standard order. A 2k factorial design is in standard order when the first column of the design matrix consists of successive minus and plus signs, the second column of successive minus and plus signs, the third column of four minus signs followed by four plus signs, and so forth. In general, the k'l minus signs followed by 2]"-1 plus signs. An kth column consists of 2 example of a factorial design in standard order is shown in Table 5.1. After the design matrix has been arranged in standard order, the results of the experiments are recorded in the observed response column 50 of the algorithm. The Yates calculations consider the responses in successive pairs. The first entries in the first calculated column are obtained by adding the pairs together. The second set of entries are obtained by subtracting the top number from the bottom number of each pair. In the same manner that the first column is obtained from the response column, the second column is derived from the first, and so on. For a 2k factorial design, k columns will be generated by adding and subtracting the appropriate pairs of numbers. To obtain the effects, the entries of the kth column are divided by the proper divisors. The first divisor will be 2k, and the remaining divisors will be 2k-1. The first estimate is the grand average of all the observations. The remaining effects are identified by locating the plus signs in the design matrix. Effects that differ greatly from zero are said to be significant. A more detailed description of factorial design is given in Chapter 10 of Box, Hunter, and Hunter [1978]. Analysis of Biocompatibility Data An initial study of 20 experiments was used to estimate the variance and the mean values of blood cell counts for both the control and the treated samples. The number of observations to obtain statistically significant data was then be computed from the following equation [Steele and Torrie, 1980]: tho + t1]2 52 62 where N is the minimum number of experiments for a two-sided Ialternative, to is the t value associated with Type I error (a - .05), 51 t, is the t value associated with Type 11 error (5 -.20), s is the standard deviation of all the samples, and 6 is the difference between the mean of the controls and the mean of the dialysis samples obtained from the initial study. The data was analyzed by analysis of variance (ANOVA). The analytical techniques and methods of data analysis described in this chapter were used extensively in the work that will be presented in the sections that follow. A thorough understanding of these methods was necessary as the first step in the development and testing of an immobilized enzyme hollow fiber reactor. CHAPTER 4 ENZYME IMMOBILIZATION AND RETENTION 0N FIBERS Materials and.Hethods Extensive details on the construction of single fiber reactors, the method of enzyme immobilization, and choice of fiber type used in this research have been described elsewhere [Reiken, 1988]. The procedures and results of these experiments will be summarized in this chapter. A11 UF fibers were donated by Romicon, Inc.. Folin phenol reagent for the Lowry protein assay was manufactured by Fisher Scientific. The reagents and analytical equipment used for the determination of catalase and oxidase activity were described in the Chapter 3. Enzyme solutions were prepared in 0.1 M potassium phosphate buffer (pH 7.0). Single Fiber Reactors The SFR consists of a single hollow fiber encased in a glass shell giving a typical shell-and-tube configuration (Figure 4.1). Construction is described elsewhere [Reiken, 1988]. Shell material is borosilicate glass, 21.5 cm long, 0.8 cm o.d., and the shells were constructed by the Chemistry Glass Shop at Michigan State University. The SFR is assembled by pushing 3 cm sleeves of Tygon tubing (3/16 in. i.d.) over the ends of the glass reactor shell. The ultrafiltration fiber is then fed through the shell. Male and female Luer fittings are then slid onto both ends of the fiber, and the female fittings are pushed into the Tygon sleeves. A sealant that consisted of a mixture of an epoxy resin and curing agent (Dow Chemical Co., Inc.) is applied to the inside of the female Luer fitting, and the male/female connections are made. Three days are allowed for the epoxy to cure. 52 53 Figure 4.1: Single fiber reactor (SFR) - Shell material is borosilicate glass, 21.5 cm overall length, 0.8 cm O.D.. Fittings illustrated on left were applied to both ends of the reactor: L = male and female Luer lock fittings; C = Tygon tube; HF = hollow ultrafiltration fiber. The hollow fiber was retained by a plug of epoxy potting resin (Dow Chemical) between the Luer lock fittings and the hollow fiber. 54 Before enzyme immobilization, the SFR was cleaned and sanitized according to manufacturer's instructions. The SFR was installed in the SFR sanitizing system (Figure 4.2). Cleaning consisted of four cycles: A Tergazyme (a protease obtained from Alconox, Inc.) cycle to remove protein buildup within the fiber, an acid cycle (pH 2-3, 0.045 M H3P04, 0.10 M KH2P04)' a base cycle (1% NaOH), and a sanitizing cycle (200 ppm NaOCl). The protocol for each cycle was to simultaneously pump the appropriate liquid through the tube and shell-sides of the reactor. The cleaning solutions were pumped countercurrently for approximately 45 minutes. After each cycle, all loops of the system were flushed with approximately two system volumes of distilled water. Between the cleaning process and the enzyme loading, the SFRs were checked for leakage by pressurizing the tube-side to 15 psig with air from a syringe and checking for escaping air bubbles. Enzyme Immbbilization An important consideration in the design of hollow fiber reactors (HFRs) is the technique used to immobilize the enzymes into the hollow fiber. Backflush loading was chosen as the most efficient method for achieving high enzyme concentrations in HFRs. Compared to static loading, it is a more rapid method and allows for higher immobilized enzyme concentrations [Breslau and Kilcullen, 1978]. Since the enzymes are entrapped in the pores of the fiber and are not chemically cross- linked or bound to the support, the recovery of enzyme and reuse of fibers is possible. Before enzyme immobilization, the SFR system was flushed with buffer. To backflush load enzyme, a syringe containing approximately 15 55 ll u A A SFR '/- \ % / ”(RE tube-side shell-side reservoir reservoir /_-:1 El Figure 4. 2. Schematic representation of the system used to sanitize the SFR. 56 m1 of the enzyme is mounted on a syringe pump (Sage Instruments, Model 341A) and attached to one of the shell-side ports of the SFR. The pump is turned on with the SFR held in a vertical position to help eliminate the formation of air bubbles and is allowed to run until the shell-side of the reactor is filled with enzyme solution. After clamping the SFR in a horizontal position, the remaining shell-side port and one of the tube-side ports are closed, creating the backflush loop (Figure 4.3a). Backflush effluent from the remaining tube-side outlet is collected in sample tubes. After enzyme loading, the reactor is drained, and the tube-side is rinsed with buffer. Approximately 20 ml of buffer is then forced through the fiber in an ultrafiltration mode (Figure 4.3b). The ultrafiltrate is collected in four 4.0 ml fractions. The backflush effluent and ultrafiltrate fractions are analyzed for both protein content and enzyme activity. Protein and.Activity Determination The amounts (mass) of catalase and L-lysine a-oxidase in samples were determined by the Lowry method described in Chapter 3. This technique was found to be accurate for the enzymes being studied by preparing solutions of the enzymes and comparing the known values of the concentrations (pg/ml) to the measured ones. For samples that contained both catalase and L-lysine a-oxidase, gel chromatography was first performed to separate the enzymes before the amount of each was determined [Reiken, 1988]. Activity assays were performed in all experiments to determine whether backflush loading and ultrafiltration had any negative effects on the enzyme reactivity. The activity of catalase in samples was . determined by the rate of reaction at a hydrogen peroxide concentration 57 backflush solution in effluent out a. backflush mode ultrafiltrate out I’ll/’III’I’II’IIIIIIIIIII’ll/III,I’ll/IIIIII’IIIII’ll/I’ll. 'IIIIII’ll/I’ll[III[III/III,IIIIIIIIIII’III. ultrafiltration solution. in b. ultrafiltration mode Figure 4.3: Schematic of the SFR showing backflush and ultrafiltration modes of operation. 58 of 30 mM as described in Chapter 3. These reaction rates were determined relative to the catalase stock solution. L-lysine a-oxidase activity in samples was measured by the method described in Chapter 3 and was compared to the activity of the stock solution. Enzyme activity was measured in units of pmols of substrate reacted per minute per mg of enzyme. The total activity in an experimental solution was found by multiplying the measured activity by the mass of enzyme in the sample. Results Material and activity balances around the fibers are used to determine the loss of enzyme due to loading on the fibers. The amount lost, L, is calculated according to the following equation [Powell, 1988]: L - COVo - (CBVB + CFVF) (4.1) where Co is the concentration of enzyme in the stock solution; V0 is the volume of the enzyme stock solution; CB is the concentration or activity of enzyme in the backflush loading effluent; VB is the volume of the backflush effluent; CF is the concentration or activity of protein in the ultrafiltrate; and VF is the volume of the ultrafiltrate. Comparing loss of activity with loss of enzyme protein permitted assessment of enzyme inactivation on the fibers. Experiments of this type indicated that the fibers best suited for the co-immobilization of catalase and L-lysine a-oxidase were PA10 fibers [Reiken, 1988]. These fibers are made from polyamide and have a _ molecular weight cutoff of 10,000. Polysulfone (PM30) and polyamide 59 (PA10 and PA30) ultrafiltration (UF) fibers were compared for retention of protein, retention of enzyme activity, and the ability to recover enzyme. The polysulfone fibers caused an inactivation of catalase and were difficult to recover enzyme from. Results for the PA30 fibers indicated that the effective pore size of the fiber is too large for the enzymes, and only a minimal amount of the protein was retained. PA10 fibers were then tested for their ability to retain the enzymes. Ten m1 of a solution containing 50.0 units of both enzymes was backflush loaded into the fiber, and the effluent was collected. After loading, buffer was pumped through the fiber in the ultrafiltration mode resulting in four 4.0 ml fractions. In order to determine the total amount of protein in the ultrafiltrate these fractions were combined, and both this solution and the backflush effluent were passed through a gel chromatography column. Because the separation resulted in diluting the samples beyond the concentration range that could be determined accurately by the Lowry method, the samples were first spiked with 30 pg/ml of the appropriate enzyme. This "spiking" method was determined to be accurate by testing it on known concentrations of both enzymes. It was found that 86.3% of the catalase and 82.8% of the oxidase were retained by the PA10 fiber. These experiments were repeated using catalase to L-lysine a-oxidase ratios of 1:2 and 2:1. Approximately the same percentage of the enzymes was retained for all cases regardless of the loading ratio. Because of the time-consuming nature of gel chromatography, these numbers were generally assumed for the remainder of the experiments conducted, but were checked periodically. 60 Enzyme Stability In order for a hollow fiber reactor cartridge to have practical applications in medical treatments, extended storage of the cartridge with the loaded enzyme must be possible [Reiken and Briedis, 1990]. The retention of lysine a-oxidase activity upon immobilization in the fiber was evaluated. Two storage procedures were tested; 1) storage in reactor with 0.2 mM lysine solution in the lumen, and 2) storage without the lysine solution. The reactors were operated under optimum conditions after storage, and the conversion of lysine after two hours of operation was determined. After each experiment, the reactor was stored in a refrigerator for five days before its next use. From Figure 4.4, it is seen that after 30 days, the enzyme retained 82% of its original activity on the fiber that was stored with lysine and 67% of its original activity without lysine. Enzyme Immobilization.and Localization Localization of enzyme affects the parameters in modelling of immobilized reactor operation. Therefore, the effects of two different lysine solution flow regimes on the distribution of enzyme in the fiber wall were evaluated. In order to accomplish this, L-lysine a-oxidase was labelled with flourescein isothiocyanate dye (Sigma, catalog No. F- 7250) according to the technique described by Reiken and Briedis [1990]. The labelling of the enzyme enabled its visualization in the immobilized state under ultraviolet light. Under the first flow regime (9 ml/min flow), no discernable movement of enzyme in either the axial or radial direction of the SFR was detected after four hours of operation. However, at a flow rate of 18 ml/min, leakage of enzyme » radially out of the fiber was observed due to the increased pressure 61 unused my 6920?. A989 0.8.; “>53 2835 $332 3 ewnmao "vé 0.83m on O_N O... 0 052A. :65? oWEBw xix ” new». 5? codes» «In H. v\ n (uonmos was .to x) mev ewfizua 62 gradient associated with the higher flow rate. The flow rate of substrate within the fiber was therefore limited due to the eventual radial flux of enzyme in the fiber wall. This set flow limits for the experiments described in the following chapter. For the reasons discussed above, it was determined that backflush loading would be used to immobilize the enzyme in the SFR and that PA10 fibers would be used for all remaining experiments due to this fiber's compatibility with and ability to retain the enzymes being studied. With the selection of the appropriate immobilization technique and fiber type, the performance of an immobilized enzyme reactor could be investigated. CHAPTER 5 REACTOR OPERATION AND OPTIMIZATION Introduction The objective of the experiments described in this chapter was to determine the optimum conditions needed in the reactor system to maximize the amount of lysine converted. PA10 single fiber reactors described in Chapter 4 were used. Manufacturer's specifications list fiber dimensions at 1.118 mm inner diameter, 2.007 mm outer diameter, and an inner membrane thickness between 0.1 and 1.0 pm. Two different sets of experiments were used to evaluate the effects of the important operating parameters on conversion in the SFR. A buffered lysine solution served as the source of substrate in the first group of experiments [Reiken, 1988] while whole blood was used in the second. Before and after each use, the SFR was cleaned and sanitized according to the procedure described in Chapter 4. After cleaning, the SFR was installed in a laboratory reactor system (Figure 5.1). The fluid-conducting elements of the system consisted of Tygon tubing (3/16 inch i.d.) with a polyethylene T and quick-disconnect connectors at the junctions. All tubing was wrapped with foam insulation. Valves at the junctions were adjusted to determine the liquid circulation pattern. Both the reservoir and the reactor were held at 37°C in a shaker water bath (Lab Line,Inc., Model 3540). During reactor experiments, the shell-side of the system was closed. The reservoir contained 120 ml of whole sheep blood (lysine concentration z 1.0 mM). With the recycle loop opened, the substrate solution was pumped from the reservoir through the fiber lumen. To collect samples, the recycle loop was closed and the sample port was 63 64 ‘4 4+ \\.__\_\_\\_\\_____\\\\\\\\\\\\\\\‘ Recycle Reservoir Figure 5.1: Single Fiber Reactor System (SFR) - Res = reservoir flask; P = pump; f1,f2 = flowmeters; p1 = lumen- side inlet port; p2 = shell-side inlet port; p3 = lumen outlet port; p4 = shell-side outlet port; t1 = 15 psig pressure transducer; t2 = 5 psi differential pressure transducer; X = tubing clamps for stepping flow. 65 opened. After an experimental run was completed, the exact flow rate was determined by timing the collection of liquid in a graduated cylinder. The samples were then assayed for lysine content by the spectrophotometric technique described in Chapter 3. Factorial Design The SFR reactor operation was studied using a 23 factorial design. This design used the conversion of lysine after four hours as the observed response. The design matrix is represented in Table 5.1. Three operating parameters were evaluated for their effects on conversion: flow rate, the number of units of oxidase immobilized, and the catalase/oxidase loading ratio. Yates's algorithm (Chapter 3) was applied to the results of the experiments after they had been arranged in standard order. These calculations for the reactor system data are shown in Table 5.2. Column y shows the percent of lysine converted for each experiment, and the remainder of the matrix columns were obtained in the manner described in Chapter 3. The estimate column represents the estimate of the effect of . the variables on the conversion of lysine. Effects that are estimated to be less than one are considered to be statistically insignificant. The first estimate is the grand average of all the observations. The remaining effects are identified by locating the plus signs in the design matrix. Thus, in the third row a plus sign occurs only in the oxidase column, so that the effect in that row is the L-lysine a-oxidase effect. In the seventh row, plus signs occur in both the oxidase and catalase columns, so that the effect in that row is the interaction between these variables. From the algorithm, it is seen that each of the variables being 66 Table 5.1 Design Matrix for SFR Experiments Experiment # A. C Variable - + 1 - - - A.flow rate (ml/min) 3.0 9.0 2 + - - B oxidase (units 15 30 3 - + - C catalase/oxidase 0 2/1 4 + + - 5 - - + 6 + - + 7 - + + 8 + + + Table 5 . 2 Yate's Algorithm for the SFR Experiments Expt. % Conversion Esti- # y’ (l) (2) (3) Divisor, mater, IIJD. 1 11.3 32.1 72.3 188.2 8 23.53 ave 2 20.8 40.2 115.9 41.6 4 10.40 A 3 19.7 43.4 20.3 37.2 4 9 30 B 4 30.5 72.5 21.3 2.6 4 0 65 AB 5 21.7 9.5 8.1 43.6 4 10.90 C 6 31.7 10.8 29.1 1.0 4 0.25 AC 7 30.6 10.0 1.3 21.0 4 5.25 BC 8 41.9 11.3 1.3 0.0 4 0.00 ABC 67 studied has a significant effect on the observed response of the reactor system. It is also seen that the only significant variable interaction is between the amount of catalase and oxidase immobilized into the spongy region of the hollow fiber. In order to determine the optimum operating conditions, a more detailed investigation on the effect of the variables on lysine conversion was conducted. Operating Parameters The optimum operating conditions of flow rate, amount of L-lysine a-oxidase immobilized, and the catalase/oxidase loading ratio was previously reported for the reactor system in which a buffered lysine solution was recycled through the SFR [Reiken and Briedis 1990]. To summarize the results found from these experiments, the optimum flow rate, lysine a-oxidase loading, and catalase to oxidase loading ratio were found to be 9.0 ml/min, 3.97 units/cmz, and 2.5:1, respectively. The purpose of the following experiments was to determine whether these optimum parameters were valid for the system in which whole sheep blood was substituted for the buffered lysine solution. Effect of Flow'Rate In order to determine the effect of flow rate on the conversion of lysine, all other variables were held constant. Forty units of L-lysine a-oxidase and 100 units of catalase were co-immobilized in a SFR. The flow rate was adjusted by changing the setting on the pump and was measured by timing the collection of liquid in a graduated cylinder both before and after an experimental run. Lysine concentration was measured after four hours of total recycle operation. Results from these experiments are shown in Figure 5.2. For the 68 Sweeper“ .m> cums: mo sausages as we «2m "mum enema agabso flow so: 2 2 re a . N. m m l 0' '4' 40 UOlSJOAUOO % 1 eulsfl 69 single fiber reactor, a flow rate change from 3 to 9 ml/min gave an increase from 32% to 45% in lysine conversion. The conversion leveled off at 45% despite further increases in flow. The Effect of L-lysine a-oxidase For the experiments described in this section, the flow rate was kept constant at 12 ml/min, and no catalase was present. The amount of L-lysine a-oxidase that was immobilized on the fiber was varied from 15 to 60 units. The results of this investigation are shown in Figure 5.3. It is seen that the amount of lysine converted reached an optimum level when 30 units of L-lysine a-oxidase was immobilized. Additional enzyme had no effect on the conversion of lysine. This corresponds to an 2 optimum loading of 3.97 units/cm of fiber surface area. The Effect of Catalase Initial studies of SFR performance were conducted by Paula McMahon [1986]. In these studies, large discrepencies were observed in the amount of lysine conversion expected and that obtained in the SFR. This was suspected to be due to the deficiency of oxygen within the hollow fiber walls which may occur as the reaction proceeds. The reaction therefore may become oxygen limited. In addition to eliminating the cytotoxic effect of hydrogen peroxide in blood, it was thought that the addition of catalase could also affect the amount of lysine converted by removing one of the products (H202) and providing oxygen for further consumption. The results from the factorial design also indicated that catalase had a more significant effect on lysine conversion when blood (lysine concentration - 1.0 mM) was substituted for the buffered lysine solution (lysine concentration - 0.2 mM) as the source of substrate. 7O ..eosmmaofifim 083x08 mammbémo «macaw 23 .3 053 do montage es .3 «2m 5m enema vouzzoEE. omoflxoio «3.216214% «:5 ON. mm mm was mm mN . mp . _. . _ . _ . _ . _ t _ . . ON lo uogwenuoo % ..'l OUISK NW 71 This is explained by the fact that there is probably an increased limitation of oxygen within the hollow fiber at higher reaction rates (due to the higher concentration of lysine) during the experiments with. blood in which no catalase was immobilized in the fiber, For the experiments conducted in this section, the optimal lysine a-oxidase loading of 3.97 units/cm2 and a flow rate of 12 ml/min were used. The ratio of catalase to oxidase was adjusted by altering the relative concentration of the enzymes in the stock solution that was backflush loaded on the SFR. This ratio was varied from 0 to 4:1 (unit basis). Results of this study are shown in Figure 5.4. An increase in catalase caused an increase in the efficiency of the reactor until the optimum ratio of 2.5:1 was reached. It appears that too much catalase can cause an inhibitory effect that lowers the conversion of lysine. This could be due to "crowding" which reduces the accessibility of the substrate to L-lysine a-oxidase. Optimum.0perating Conditions The experiments described in this section were used to determine the optimum operating conditions for the single fiber reactor using blood as the source of substrate. Results were similar to those found when a buffered lysine solution was the source of substrate; the optimum flow rate, lysine a-oxidase loading, and catalase to oxidase loading ratio were found to be 9.0 ml/min, 3.97 units/cmz, and 2.5:1, respectively. The optimum operating conditions were used as a basis for reactor scale-up to be described in the next chapter. 72 .83.. 95:3. omaExo 3 3588 2: .3 05mm— .Lo homepages as do 85 ”twee—swarm 053. 9.5003 0825\82300 . .v. m N «V o 10 ,to UOlSJeAUOO % ‘1 ewe/i 73 Pulsatile Flow In normal hollow fiber operation the amount of lysine that can be converted is limited by its rate of diffusion through the spongy layer of the hollow fiber to the enzyme. Lewis and Middleman [1974] reported that diffusion was apparently the dominant mechanism for substrate transport in hollow fiber systems. This is also verified by the modeling results presented in Chapter 6. The reactor productivity could be increased in proportion to the increase in the amount of enzyme per unit area of membrane in the reactor if diffusion limitations could be eliminated. This objective could be accomplished by forcing the substrate to flow convectively into the fiber wall. Several investigators have shown that pulsatile flow, or ultrafiltration swing, in a membrane-enzyme reactor may improve the performance of the reactor as compared to the steady flow operation [Kim and Chang 1983; Park, Kim, and Chang 1985]. The pulsatile flow process essentially involves the same basic reactor system shown in Figure 5.1, but two pumps are used to pump feed through the SFR at different flow rates, and a third pump is added as a withdrawal pump (see Figure 5.5). The withdrawal pump guarantees the maintenance of the average flow rate throughout the reactor system. During the high flow rate half-cycle of the pulsatile flow, the flow of substrate solution into the fiber is greater than the flow of substrate out of the fiber. The difference in flow rates results in ultrafiltration and an increase in the transmembrane pressure drop across the fiber wall. Both the ultrafiltration and the incease in pressure drop result in a increase in substrate transport into the immobilized enzyme region. In addition, the high flow rate half-cycle causes a localized increase in the pressure in the spongy region of the fiber. Mass-transfer is in the ‘74 “ inlet pumps : P ‘ 4' Recycle @— ' outlet pump Reservoir Figure 5.5: Single fiber reactor system with pulsatile flow. P = gear or perristaltic pump; p1 = lumen- side inlet port; p2 = shell-side inlet port; p3 = lumen outlet port; p4 = shell-side outlet .port; X '=tubing clamps for stopping flow. The two inlet pumps are set at different flow rates, and the timer is used to switch from one pump to the other. - 75 opposite direction during the second half-cycle at the lower flow rate which causes the flow out of the fiber to be larger than the flow into the fiber. This results in the substrate solution being drawn out of the spongy layer and into the fiber lumen. In addition, the low flow rate half-cycle causes an instantaneous decrease in the pressure in the lumen which, along with the localized increased pressure in the spongy region caused by the high flow rate half-cycle, allows product to be transported back into the feed stream. The ultrafiltration swing can cause an increase in the conversion of substrate by minimizing diffusion limitations in a hollow fiber reactor system. The schematic representation of the experimental apparatus used to determine the effect of pulsatile flow in the lysine a-oxidase/catalase SFR system is shown in Figure 5.5. The optimum values of seventy-five units of catalase and 30 units of oxidase were immobilized in the hollow fiber. Sheep whole blood was delivered to the tube-side in two modes. When the reactor was operated without the ultrafiltration swing, only one of the inlet pumps was used to feed the substrate into the reactor. A three-way valve was rotated such that the outlet pump was bypassed, and the reactor effluent was recycled back to the reservoir. For pulsatile operation, the three-way valve was turned towards the outlet pump, and the outlet flow rate was set at 12 ml/min, the mean value of the pulsatile inlet flow rate. A timer (Fisher Scientific, Model CD-4) was used to switch between one inlet pump (set at a flow rate greater than 12 ml/min) and the other (set at a flow rate less than 12 ml/min) periodically (every minute) to produce a pulsed inlet flow. The concentration of lysine in the reservoir was determined every thirty minutes. The total conversion of lysine after four hours was compared for reactors operating with and without pulsatile flow. 76 The results of the pulsatile flow experiments are shown in Table 5.3 below: Table 5.3 Results of Pulsatile Flow Experiments (Four Hour Run) case 1 case 2 case 3 case 4 case 5 Flow rate Pump 1(ml/min) 12.0 13.5 15.0 16.5 18.0 Flow rate Pump 2(ml/min) 0.0 10.5 9.0 7.5 6.0 Pressure in lumen High flow (psig) 1.25 1.40 1.56 1.71 1.87 Pressure in lumen Low flow (psig) ~--- 1.09 0.94 0.78 0.62 % conversion of lysine 45.2 52.9 58.6 48.4 32.1 When the two inlet pumps were set at 15 and 9 ml/min, pulsatile flow resulted in a large increase in conversion over normal flow conditions. This indicates that pulsing the inlet flow to the reactor had a significant effect in decreasing the diffusion limitations in the reactor. However, pulsatile flow at a larger amplitude swing, 18 to 6 ml/min, resulted in decreased conversion. This was due to the leakage of enzyme from the hollow fiber caused by the transmembrane pressure drop associated with the pulsed flow. Therefore, the amplitude of the pulse was limited due to the eventual radial flux of enzyme in the fiber wall as observed in the labelled enzyme experiments discussed in the previous chapter. 77 The purpose of the experiments described in this chapter was to evaluate the performance of the SFR and to determine the operating parameters of the reactor that would maximize the conversion of lysine. With these experiments completed, the next major goal of this research was to develop a model that accurately predicts the conversion of lysine in the SFR, and to determine whether the data from the SFR experiments could be scaled up to a clinical-sized hollow fiber cartridge. CHAPTER 6 REACTOR MODELLING AND SCALE-UP Previously reported mathematical models for predicting substrate conversion in hollow fiber reactors have been limited in accuracy because of their use of free-solution kinetic parameters in described rates of reaction. This chapter describes a method for determining the permeability of lysine within the SFR. Permeability was used as a measure of the extent of fiber fouling by whole blood. Also presented is a technique for evaluating the intrinsic kinetics of enzymes immobilized in hollow fiber reactor systems using a mathematical model for diffusion and reaction in porous media and an optimization procedure to fit intrinsic kinetic parameters to experimental data. Evaluation of the Effectiveness Factor One of the more important concerns in the development of a hollow fiber reactor system is the effect that the immobilization has on the intrinsic kinetics of the enzymes. This ultimately influences overall reactor design and performance. In most heterogeneous catalytic systems, conversion is viewed as a competition between the rate of reaction and the rate of transport. This has been modelled for a variety of enzymatic reaction schemes by Moo-Young and Kobayashi [1972]. Their model is expressed in terms of an effectiveness factor (E) and a generalized modulus (m). The effectiveness factor and modulus used by these authors are defined below: E-_exaeflman£allx_2hssrxed_ream2n_r_ue ideal free-solution reaction rate (6'1) 78 79 k S _ L r(S) [ OJ. Ds r(a) d0 1' (6.2) [T m where S is the bulk concentration of substrate in the lumen, L is the characteristic length and is defined as the ratio of catalyst volume (Vc) to lumen surface area (AL) [Froment and Bischoff, 1979], r(a) is the intrinsic reaction rate, which should represent the immobilized enzyme kinetics, and Ds is the in situ substrate effective diffusivity. The modulus is usually viewed as a ratio of substrate reaction rate to substrate diffusion rate. Moo-Young and Kobayashi have developed a simplified equation for the effectiveness factor in a hollow fiber membrane which avoids the rigorous integration and solution of a more complex set of equations. Since L-lysine a-oxidase obeys a Michaelis-Menten kinetic relationship with no inhibition (from catalase or any of the reaction products), the resulting equations for the effectiveness factor are as follows. When 61 (defined as the ratio of the Michaelis-Menten constant of the enzyme to the bulk substrate concentration, Km/S) is close to zero, the effectiveness factor may be evaluated by the following equation: m S l) 1) . (6.3) VIA 1 (o E ' E0 ' [ l/m ] (m When 51 becomes infinity, the effectiveness factor is given by: E - E, - tanh ” (6.4) m In the intermediate range of 61, the effectiveness factor can be approximated by the following equation: 80 E _ Ea + 3151 (6.5) 1 + 31 In this derivation, the enzyme is assumed to be evenly distributed within the reactor with negligible changes in substrate and product diffusivities. The equations resulting from the Moo-Young and Kobayashi analysis show the effectiveness factor for the reactor to be dependent on the intrinsic kinetic parameters of the immobilized enzyme. Reactor Model Since the SFR is operated at total recycle, it can be modelled as a batch reactor. For L-lysine a-oxidase coimmobilized with catalase, the rate of the reaction in the hollow fiber recycle reactor is represented by [Reiken, Knob, and Briedis, 1990]: [e] V S v . 41L- - E. 149" (6.6) Rate of reaction - res dt S + Km In this equation, Vres is the volume of the reservoir (ml), 8 is the substrate concentration (pmols/ml), and [e] is the amount of enzyme immobilized (mg). E is the effectiveness factor which is determined using the Moo-Young and Kobayashi model for the case with no inhibition. Km is the immobilized intrinsic Michaelis constant (pmol/ml), and vmax is the maximum reaction rate (pmols of substrate reacted per mg of enzyme per minute). It is seen that the kinetic parameters affect the rate of reaction in the SFR directly (through the right hand side of Equation (6.6)) as well as indirectly through the kinetic and transport parameters in the effectiveness factor. 81 In deriving these equations, the mass transfer resistance in the membrane has been neglected. The hollow fiber reactor results presented by Waterland et al. [1975] and discussed in Chapter 2 showed that this is a good simplifying assumption. Typically, most investigators have calculated effectiveness factors and moduli based on free-solution enzyme kinetics. Strictly speaking, the effectiveness factor should be based on the maximum possible reaction rate in situ, i.e., the intrinsic kinetics of the enzyme in the immobilized state. The above equations may be used in data analysis in order to obtain these intrinsic parameters. Since the effectiveness factor depends on the effective diffusivity of the substrate within the hollow fiber reactor (through the generalized modulus), the first step in our approach was to determine the diffusivity of lysine independently. Permeability and Diffusivity Determination For mass transfer from the lumen of the hollow fiber to the shell- side of the SFR, the overall permeability resistance, R0, can be broken down into component resistances in series: Ro- RLT+ Rm + RSR + RLS (6.7) or in terms of mass transfer coefficients, K: + 4 _ _L + _L + _1_ 1 (6.8) Ko KLT Km KSR KLs where Km is the membrane permeability and the subscripts LT, SR, and LS represent the tube-side liquid film, the spongy region of the fiber, and 82 the shell-side liquid film, respectively [Smith et al., 1968]. In the experiments described below, flow rates were chosen so as to minimize liquid film mass transfer resistances. Therefore, the resistance to mass transfer is due mainly to the membrane and spongy region of the hollow fiber. In most permeability studies involving hollow fiber membranes, the overall permeability has been determined by following the concentration changes between the tube-(lumen) and shell-side of the hollow fiber in a dialysis mode of operation [Colton et a1. 1971; Farrell and Babb 1973; Kim and Chang 1983]. Substrate solution is pumped through the tube- side, the substrate diffuses across the fiber wall, and is collected in a "blank” solution flowing countercurrently on the shell-side. Material balances between the tube-side and the shell-side are used to calculate the overall membrane permeability (K0) for the transported species (see Equation (6.9) below). The effective diffusion coefficient may be calculated from the overall membrane permeability as follows. Using the wet membrane thickness as the diffusion path length (0.0445 cm), the effective diffusivities are calculated as Deff - K0 * wet membrane thickness [Colton et al. 1971]. D-lysine was used as the diffusing species so that the effect of the presence of immobilized enzyme on substrate diffusivity could be evaluated without interference from the enzymatic reaction. The diffusivity of L-lysine was assumed equal to that of D- lysine. The overall membrane permeability for D-lysine for a hollow fiber membrane was calculated with the unsteady-state material balance equation used by Park, Kim, and Chang [1985]: 83 (st - s§) K A - ln (s _ s ) - ——°——-V v (vt + vs) t (6.9) to SO I: S where Vt and Vs are the volumes of solute solution in the tube- and shell-side, respectively; St and SS are the concentrations of solute in the tube- and shell-side; S o and Sso are the initial concentrations of t solute in the tube- and shell—side; A is the mass transfer area of the 2 hollow fiber membrane (7.75 cm ); and t is the time of sample. Since these are all known or measured quantities, the term {-ln [(St - SS)/ ((8 -Sso))]} may be plotted versus time. The slope of the plot is to equal to KOA(Vt+Vs)/(Vtvs) as shown by Equation (6.9). The overall membrane permeabilities and diffusivities of the transported species may then be calculated directly. Permeability/Diffusivity Experiments A SFR was constructed and used in experiments designed to evaluate the permeability of substrate and product through the hollow fiber wall. The SFR used in this study was assumed to be representative of the characteristics of other PA10 fibers, although the characteristics of ' individual PA10 fibers may vary slightly. The SFR was used in a dialysis mode in which the test species was circulated through the tube-side, and a "blank" solution was circulated through the shell-side to collect the diffusing species. The dialysis configuration used was similar to the one described by Farrell and Babb [1973] which uses a counter-current flow pattern through the reactor (see Figure 6.1). Pulse dampeners were placed upstream of the reactor to reduce the effects of pulsatile flow. The D-lysine permeability experiments were conducted both in the absence and presence of 84 inlet EaretéxsuurfI )gauge tlet ressur u e ‘ sh -si e on (nib eosidec)a ga g A A v W A A v v V e rotometer ” rese air reservoir ‘ inlet pressure gauge 6 (tub e-side) Tube-side Loap ' Shell-side 'Laop Figure 6.1: Dual closed loop dialysis system for - studying membrane permeability. 85 immobilized L-lysine a-oxidase and catalase. In the experiments involving immobilized enzyme, the optimum amount of enzyme was immobilized. One PA10 SFR was used throughout each series of experiments. In these experiments, the SFR was maintained at a temperature of 37°C in a water bath. The shell- and tube-side solutions were pumped through bypass lines in each independent flow circuit until equilibria in temperature and in flow rate were reached (approximately 10 mins). Once overall equilibrium was achieved, the solutions were allowed to pass through the SFR. The hydrostatic pressure difference between each side of the reactor was monitored and minimized by creating back pressure on the low pressure side. This was done to prevent any pressure driven enzyme leakage and to avoid any convective flows due to transmembrane pressure gradients. Samples were collected over an eight- hour period and analyzed for D-lysine concentration. Experiments were repeated at several flow rates. The shell-side flow rates ranged from 3.6 to 18.2 ml/min while the tube-side flow rates were fixed at values between 6.0 and 12.6 ml/min. As mentioned above, flow rates were chosen so as to minimize liquid film mass transfer resistances. Figure 6.2 shows a plot of Equation (6.9). The results from these experiments are shown in Table 6.1. The diffusivity of amino acids in free-solution has been reported to be on the order of 10-6cm2/sec [Annette 1936; Polson 1937; Cohn and Edsall 1943] which corresponds to the value found from the experiments with no enzyme immobilized within the fiber wall. It should be noted that the diffusivity of lysine decreased by an order of magnitude in the presence of immobilized enzyme (under optimum loading conditions). 86 35538 at 9.3 management .85 ”as 6.5me 52388.33 9335.6 3.5. can 0an .oow seamen essence o: oExuca 63:30.85“ 5“: X .4 .901 x {[(Oss - ”ism Ss - 13)] av} 87 Table 6.1 Results of the PA10 Fiber Permeability Study for D-lysine D-Lysine WWW Overall Membrane 3 Permeability (cm/min) x 10 2.45 0.237 Effective Diffusivity 2 e Deff (cm /sec) x 10 1.82 0.176 The effect of immobilized enzyme on lysine diffusivity within the SFR was further investigated by evaluating the permeability of D-lysine in a SFR in which 30% of the optimum L-lysine a-oxidase and the optimum amount of catalase were immobilized. Under these conditions, the diffusivity of lysine was found to be 8.91 x 10-. cmz/sec. These results are important because the use of free-solution diffusivities in hollow fiber reactor modelling will lead to errors in calculated values of moduli and effectiveness factors. Fiber Fouling In order for the enzymatic reactor to have clinical applications, it must be compatible with blood for extended periods of time. If blood should cause severe fouling of the polyamide fibers, reactor performance would be affected. One effect of fouling would be to increase the resistance to flow through the SFR, which would cause an observable increase in the pressure drop across the SFR. 88 Experiments in which blood was recirculated through the SFR at 9 ml/min were performed, and the pressure drop was measured. In addition, several fibers were dissected and inspected under a microscope for evidence of fouling. No increase in pressure drop or physical evidence of fouling was observed. Because there was no evidence of substantial fouling, it was decided that fouling would be studied more closely by following the permeability of lysine from the lumen to the shell-side of the SFR. Fouling of polyamide fibers by dairy products has previously been studied by Knob [1988], and the experimental protocol is well established. Knob's research found polyamide fibers to be resistant to fouling by dairy products which are considered to be severely fouling substances. It was therefore expected that there would be minimal fouling problems associated with blood. The objective of this portion of the work was to test this hypothesis and to determine whether the reactor performance was hindered by fouling with blood proteins and formed elements. The possibility of fouling with blood was studied in the context of its effect on membrane permeability. In these studies, fouling was defined as the decrease in the mass transfer of lysine across the fiber, and would be characterized by a decrease in the slope of the plot of Equation (6.9). Fouling Experiments Permeability was determined by the method discussed above. The apparatus used is shown in Figure 6.1. Blood was circulated through the lumen of the single fiber reactor, and a solution of buffer was circulated through the shell-side of the reactor to collect the 89 diffusing lysine. These experiments were conducted with no enzyme immobilized in the SFR. Data for lumen-side and shell-side lysine concentrations were collected over an eight hour period. Experiments were repeated several times with the same fiber. The results are shown as a plot of Equation (6.9) (see Figure 6.3). Figure 6.3 shows no decrease in the slope of the plot which indicates no change in fiber permeability. This is a good indicator that no fouling is occuring. In addition, no change in the permeability was observed when a fiber was reused. Finally, after a fiber had been used in several experiments, it was opened and examined under a microscope. No evidence of fouling was observed. These results demonstrate that reactor performance is not affected by its extended use in the treatment of blood. Evaluation of the Intrisic Kinetic Parameters During reactor experiments to determine intrinsic enzyme kinetics, the liquid-free shell-side of the system was closed. The reservoir contained a 5.0 mM lysine solution. With the recycle loop opened, the solution was pumped from the reservoir through the fiber lumen at the optimum rate of 9 ml/min. To collect samples, the recycle loop was closed and the sample port was opened. This mode of operation represents a total recycle reactor which may be modelled as a batch reactor (Equation (6.6)). Data were collected and analyzed over a 36-hour period. An extended time period experiment was necessary so that a broad range of substrate concentration was covered and an accurate determination of the intrinsic kinetics could be made. Samples were taken at regular time intervals and were promptly analyzed for lysine concentration by the 90 com . .358 .8 am no 385 05 wnmnmfiuflau .8.“ 9.8 cassava“ mo «2m £6 95me $33.3 2:: 09‘ . can com .oas . . o I O N I O l”) ow ' 9m: x {[(Oss - (”Sm ss - ‘s)]u1-} 91 saccharopine dehydrogenase method discussed in Chapter 3. The data from the extended reactor operation experiments were plotted as lysine concentration versus time (Figure 6.4). An optimization program (Program I of the Appendix) was written to use the experimentally measured lysine concentrations to fit the intrinsic immobilized kinetics in the model using the Moo-Young and Kobayashi equations for the effectiveness factor and Equation (6.6). This program uses an initial guess for the immobilized kinetic parameters and evaluates the calculated concentration of lysine at various times from Equation (6.6) using the Runge-Kutta-Gill method [Fogler 1986] for solving this differential equation. In this method, the initial concentration of lysine is used along with a specified time period (thirty seconds) to calculate a new value of the concentration. This corresponds to the concentration of lysine at the end of the specified time period. This new value of the concentration is then used to calculate the subsequent value after a second time period, and so forth. Calculations continue until the desired time of treatment has been achieved. These calculated lysine concentrations are then compared to those obtained experimentally. The program minimizes the sum of the square of the residuals between the observed and calculated lysine concentrations by adjusting the values of the kinetic parameters. Results of the optimization are shown in Table 6.2. Free-solution kinetics are also reported for comparison. Results similar to those listed in Table 6.2 were obtained using different levels of enzyme loading and operating conditions. In addition, the results were verified using blood as the substrate solution. 92 . Scam 8588.“an ”am So: mm a 89a Sam #6 ounwmm A2306 mEc. O._Nn Odom 9% F 0d . 0.0 J:- A (mix) uopfoJiueouog 'augsfl'l 93 Table 6.2 L-lysine a-oxidase Kinetic Parameters MW e - ut t * Vmax - 7.44 units /mg. Vmax - 45.6 units/mg. K - 0.688 mM K - 0.06 mM m m *One unit will consume 1 pmol of 02 per minute with L-lysine as substrate at pH 7.4 and 30°C. For L-lysine a-oxidase, the intrinsic immobilized enzyme kinetics obtained from the optimization method show a decrease in both enzyme activity and affinity of the enzyme for the substrate relative to the free-solution kinetics. In general, a larger Km value indicates decreased affinity [Stryer 1981]; this may be explained by the restricted conformation or decreased accessibility of the substrate to the enzyme within the fiber matrix. This change in kinetics may also be due to the compaction of protein caused by physical forces of immobilization. The kinetic parameters can be used to determine the mode of reactor operation (diffusion-limited, reaction-limited, mixed) . Equation (6.2) can be used to show that for the reactor system being studied and for the lysine concentration range of interest, the moduli are high (greater than three). This means that Equations (6.3) - (6.5) reduce to the effectiveness factor being approximately equal to the inverse of the modulus (Figure 6.5). In the experiments conducted for this research, the effectiveness factor is always less than 0.26 indicating that the SFR operates in a diffusion-limited mode. This can explain why the pulsatile flow experiments described in Chapter 5 were so effective in 94 633% mass owns.” 8383.038 «593 05 SS Nam. 23 you 3:62: ..m» 38am mmosmzuooam «0 ”BE” 66 0.83m mas—co: .1010!) 3 sews/$09,113 95 increasing the conversion in the reactor. In addition to giving important insights into the mode of reactor operation, the kinetic parameters may also be used to model the reactor system. Under normal flow conditions, the model for predicting conversion in the SFR is expressed in Equation (6.6). Since pulsatile flow was often used to increase conversion in the SFR, it was also necessary to develop a model for the SFR under pulsatile flow operation. This model is described in the next section. SFR.Hbdel With Pulsatile Flow The use of pulsatile flow was the best method of achieving high conversions of lysine in the SFR in a relatively short period of time. It was therefore necessary to develop a model that describes conversion of lysine under pulsatile flow operation. Because of the nature of pulsatile flow, the reactor is modelled as a two compartment reactor separated by the ultrafiltration membrane. Substrate is transported to compartment 2, the spongy region of the fiber containing enzyme, and the reaction products back to compartment 1, the lumen of the fiber, by diffusion and convection. The transport equation may be written according to Kedem and Katchalsky [1965]: Ju-Pm AS +vas (6.10) where Pm is the permeability of the membrane (cm/min) and Ju and Jv refer to solute flux and solvent velocity, respectively. The concentration difference between the two compartments is represented by the term AS. Since lysine is a small molecule, it can readily pass 96 through the membrane so that the membrane sieving coefficient, x, is assumed to be 1. Mass balances for the solute in compartments 1 and 2 are d(v,s,) - A J (6.11) (it u .3533531 - A Ju - Vmsx.82 (6.12) dt Km + 32 where S is the concentration of lysine, A is the mass transfer area of the SFR, Vma and Km are the immobilized kinetic parameters (determined x earlier), and the subscripts refer to the respective compartment of the reactor. With these parameters defined, Equation (6.10) can be rewritten as Ju a Pm (s1 - 52) + x JV f(t) (6.13) f(t) _ 1 S1 during high flow rate cycle (6.14) S2 during low flow rate cycle In all of the pulsatile flow experiments conducted for this dissertation, a square-wave pulse was used. The period of a pulse (T) is defined as the time required to complete one cycle consisting of a high flow rate half cycle and a low flow rate half cycle. A square-wave pulse is one in which the reactor is operated for T/2 minutes at the high flow rate, then T/2 minutes at the low flow rate, then T/2 minutes at the high flow rate, and so forth. When a square-wave pulse is used, the solvent velocity varies with time as 97 Jv - g(t) Pa (6.15) where P8 is the convection velocity (cm/min) and _ 1 during high flow rate cycle 8(t) 1 - 1 during low flow rate cycle (6'16) Combining Equations (6.11) and (6.12) with Equations (6.13) - (6.16) gives the following: M - A P (s. - 82) - A Pa g f(t) (6.17) dt m .3921). - A P (S. - 82) + A P am m) + Vmsx 3* (6.18) dt m 8 Km + 32 This model assumes that there is no concentration gradient in the spongy region of the fiber (compartment 2). For the reactor system being studied, the high rate of reaction in this region ensures the validity of this assumption. Determining PlandPa As mentioned above, Pm is the permeability of the membrane. The shell-side liquid film resistance to mass transfer that is part of the overall mass transfer coefficient (K0 in Equation (6.9)) is therefore not included in Pm' In addition, the flow rate of blood through the lumen of the fiber is such that the resistance to mass transfer in this region is negligible. For these reasons, both Pm and Pa must be determined experimentally. 98 The optimum amount of enzyme was immobilized in a SFR which was then installed in the laboratory reactor system (see Figure 5.5). Pulsatile flow was generated by setting the high flow rate, low flow rate, and withdrawal pumps at 15.0, 9.0, and 12.0 ml/min, respectively. Sheep whole blood was pumped through the SFR, and the period of the pulse was four minutes. Lysine concentration was determined every 32 minutes for 248 minutes. Results of this experiment are shown in Figure 6.6. A computer program was written (Program III of the Appendix) that enables the user to take an initial guess of the values for Pm and Pa' The program then uses a Runge-Kutta solution of Equations (6.17) and (6.18) to calculate lysine concentrations in the reservoir at various times. Pm and Pa are adjusted to minimize the sum of the square of the residual between the calculated lysine concentrations and the experimental concentrations obtained above. The values of Pm and Pa that best fit the data are 3.29 x 10'2 cm/min and 4.606 x 10.2 cm/min, respectively. It is important to note that these results indicate that the mass transfer resistance in the hollow fiber membrane is an order of magnitude less than the overall resistance. This is due primarily to the much shorter mass transfer path length associated with the membrane. As mentioned above, the flow rate in the lumen of the fiber is such that the mass transfer resistance in this region can be neglected. Combining this fact with the value of the membrane permeability reported here enables the determination of the mass transfer resistance in the spongy region of the fiber from Equation (6.8). From this calculation, the diffusivity of lysine in the shell-side liquid was determined to be 1.96 -e 2 Ax 10 cm /sec. This is of the same magnitude of the reported value of 99 upon 2:839 sounswamfimmo Mam 333 535:? . _ ca .8.“ 6:5 .8. countenance 65.65 mo .85 66 8&3 wmflasEvoEfi com owe. a (ww) uogwweouoo eugsx'] 100 the free solution diffusivity of amino acids [Annetts 1936; Polson 1937; Cohn and Edsall 1943]. In order to verify the values of Pm and Pa described above, two separate experiments were conducted. In the first experiment, Equations (6.17) and (6.18) were used to predict conversions in a SFR under normal flow conditions (P8 is zero). Optimum conditions of enzyme loading and flow rate were used in this experiment. The second experiment consisted of installing a SFR with 50% of the optimum enzyme immobilized and operating the SFR under pulsatile flow. Flow rates and the period of the pulse were the same as above. A computer program (subroutine Pulse of Program III of the Appendix) was used to determine concentration profiles for the two experiments using the values of Pm and Pa found above. Figures 6.7 and 6.8 show both the experimental and predicted concentrations of lysine versus time. The model accurately predicts the conversion of lysine in the SFR under pulsatile flow operation. These results help verify the accuracy of the values of Pm and Pa reported above. The work described above has demonstrated that the kinetic and permeability data obtained from experimentation accurately describe the charateristics of the SFR. This is evident in the accuracy of the models for predicting conversion in the SFR under both normal and pulsatile flow operation. However, in order for the SFR to be a useful experimental tool, the kinetic and permeability data must be valid for a larger, clinical-scale hollow fiber reactor. This is described in the next section. 101 . 853m 53 98 33mm: BEE—€033 can 38933850 @3835 «mmoumvnoo Boa Emacs noun: Morgana ”Em nouns 85530 as .8.“ «83 .M.» nomuanunoonoo «£9: .3 «3m 86 «Burn $335888? SN 9.: on o EcuEtmaxo x _ovoE E8» boys—Coca ..I.. m6 (ww) uogonueouoo eugsk] .8587. £3 98 338.“ 3585 88 use 3.0533880 3866.5 £35656 Boa ofiaflnn sous: massage Sandovofimuno Engage $omv «Em a .8.“ «Em .9» 5329838 05E mo «2m .m 6 Emma mmfiaéEvoEc. com one . a EcoEtoaxo x 6.0 _ovoE Eon... .3333 ..|.. 102 (ww) uogonueouoj eugsk; 103 Scale-up As with the SFR, the hollow fiber cartridge system is also modelled as a batch reactor in which the feed stream is recycled through the cartridge until a desired conversion is achieved. The rate of lysine conversion in the reactor is modelled as follows [Reiken and Briedis, 1990]: O Rate of lysine _ v es dS _ _ E [ v ax s ] (6.19) conversion n [e] A dt S + Km where Vre is the amount of liquid in the reservoir (ml), n is the total 3 number of fibers in the cartridge, and the intrinsic immobilized kinetics in the right hand parentheses are multiplied by the effectiveness factor, B, to describe the global kinetics of the reactor. In this expression, V'max has units of pmols of lysine reacted per minute per pmol of enzyme. The enzyme concentration loaded per unit surface area of hollow fiber is represented by the term [e] (pmols of enzyme/cmz), and S is the bulk lumen concentration of substrate (pmols/m1). Surface area per fiber, A (cmz), in contact with the substrate solution is used as the basis for scale-up. The dimensionless quantities S - S/So and Kh.- Km/So (S0 is the initial concentration of lysine in the reservoir) are introduced into Equation (6.19) which is then rearranged and integrated to give the following: 8 d8 n [e] A t I j V S - -———————- I dt (6.20) 1 max 80 0 - E [ S + K. ] res 104 The right hand side of the equation, defined as the "design time", is a grouping of design variables and constants. Depending on what in the process is fixed and/or known, the remaining variables in the design time may be calculated directly from the integrated results using the SFR immobilized intrinsic kinetics and the equations for the effectiveness factor described earlier. To obtain the "design curve", Equation (6.20) is integrated from S - l (S - So at time zero) to the desired final concentration, e.g. S - 0.5 for 50% conversion or S - 0.25 for 75% conversion. Because of the dependence of E on the substrate concentration, the integration must be done numerically (Program II of Appendix). The design curve is generated by plotting the right hand side of Equation (6.20) versus the percent conversion of lysine (shown in Figure 6.9). Earlier in this chapter, the values of Vma and Km for L-lysine a- x oxidase were determined to be 7.44 pmoles/mg-min and 0.688 mM, respectively. The proper units for vmax were obtained by using the molecular weight of L-lysine a-oxidase (112,000) to convert mg of enzyme into pmols of enzyme (Vmax - 833.28 pmoles/pmol of enzyme-min). These values for the kinetic parameters were used to generate the design curve. From this integration, it is found that the design time needed to achieve 50% conversion is 0.0127 minutes, or [(n [e] A t)/ (Vres 80)] - 0.0127 minutes. This means, for example, that if a cartridge which contains 62 fibers with [e] - 2.125 x 10" pmols/cm2 and A - 12.59 cm2 per fiber is used, 2,000 ml of whole sheep blood (initial lysine concentration 2 1.0 mM) would be processed to 50% conversion in 154 minutes, or 1,000 ml of plasma in 77 minutes, and so on. For certain reactor applications, the same design curve technique £988.“ .3 an 035m 05 .5 can: do sausage... as .m> can summon we SE a.» charm 0593 .6 8382.00 N 105 pm pm 0% cm a n n n n — -. 000° . G 9 mo: -86 w u w . 9 \I/ m. ..Noo m 1.! 9 . S ( l . .. nod 106 may be used to determine the optimum number of cartridges needed to perfom a certain conversion. For example, assume that it is known that the lysine conversion necessary for optimum leukemia therapy is 80%. It is also desired to remove the lysine within three hours in order to ensure patient comfort. By constructing a design curve for the cartridge similar to the curve in Figure 6.9, but also including a factor for the surface area per cartridge, the calculation of the number of cartridges needed to perfom this conversion is straightforward. Hollow Fiber Cartridge Operation Backflush loading was used to immobilize the enzyme within the hollow fiber cartridge. The solution for the loading was prepared by mixing 5.1 m1 of lysine a-oxidase stock solution, 3.1 m1 of catalase stock solution, and 200 m1 of 0.1 M potassium phosphate buffer (pH 7.0) in a 250 m1 Erlenmeyer flask. This solution was pumped through the cartridge in the backflush mode described in Chapter 4. The effluent was collected in 10 m1 fractions. The Lowry method (Chapter 3) was then used to determine the protein concentration of the backflush solution and all the effluent fractions. Results from this assay indicated that 85.4% of the protein loaded was retained by the cartridge. This represents the optimum catalase/oxidase loading ratio and 30% of the optimum amount of lysine a-oxidase loaded per cm2 of the total fiber surface area in contact with substrate. Thirty percent of the optimum was used because of the limited supply of fairly expensive enzyme. The effective diffusivity of lysine within the reactor under these conditions was found earlier to be -e 2 8.91 x 10 cm /sec. 107 The cartridge was placed in a water bath that was kept at a constant 37°C by a submersion heater (Haake E3). Two liters of a 1.0 mM lysine solution was also placed in the water bath and kept well mixed by a magnetic stirrer. The lysine solution was pumped through the lumen of the cartridge in recycle mode at a flow rate of 9 ml per minute per fiber in the cartridge. Samples were taken at numerous times and measured for their lysine content using the saccharopine dehydrogenase method described in Chapter 3. Experimental results from the hollow fiber reactor operation are shown as a plot of percent conversion of substrate versus time in Figure 6.10. Also shown is the predicted conversion using SFR data and Equation (6.20). Approximately 175 minutes of operation is required to convert 50% of the lysine whereas the predicted time for 50% conversion is 154 minutes. It is seen that the actual conversion time is longer than predicted, probably due to the fact that the model assumes that the operating parameters of each of the fibers in the cartridge are identical. This would be the case if all fibers were identical and if the enzyme was loaded into the individual fibers which were then assembled into a cartridge. As described earlier, however, the enzyme solution was backflush loaded into a commercially available cartridge with the fibers already in place. Even distribution of enzyme among all fibers of the cartridge and identical fiber properties are therefore unlikely. The optimum enzyme loaded per fiber has previously been shown to be 7.09 x 10-‘pmol/cm2 [Reiken and Briedis, 1990]. Enzyme in excess of this optimum causes no additional increase in the conversion of lysine. Fibers that contain more than the optimum amount of enzyme yield an ' apparent overall loss in enzyme activity. This has been verified in 108 .888 53 0.8 «:88 55855898 3.3 30595838 8858.5 835.538 .555 .5235 a E 355 .3 333.5838 35% mo BE ..3 w «ERR $33555 .oEfi on: _o_voE. E9... “830593 I _3coE_._oaxo q (ww) uogonueouoo eugsk] 109 experiments in which the intrinsic kinetic parameters for enzyme immobilized in the hollow fiber cartridge were evaluated. Compared to the SFR, a 12% decrease in vmax and no change in Km were observed in the hollow fiber cartridge [Reiken, 1988]. Because it is dependent on the intrinsic kinetics of the enzyme, the effectiveness factor is also affected by this apparent loss of enzyme activity. Figure 6.11 shows that the accuracy of the model is greatly improved if the effects of the apparent loss of enzyme activity caused by the uneven distribution of enzyme in the cartridge is accounted for. The open circled curve represents the predicted conversion for which a 12% decrease in overall enzyme activity and the corresponding change in the effectiveness factor have been taken into account. Despite these small changes in effectiveness factor from the small scale to the larger, the SFR remains a valuable tool for designing towards optimal hollow fiber cartridge performance. The results of this study demonstrate that conversion data obtained from a SFR are directly scaleable to a bench-scale dialyzer. Fiber surface area was used as the basis for scale-up, and the conversions predicted for a hollow fiber cartridge using SFR data in the recycle (batch) model were within experimental error. This work has demonstrated that the SFR is a useful tool for enzyme reactor development, affording the ability to perform cost- and time- effective experiments without sacrificing any information on the important variables for scale-up. With these results as a strong basis, the SFR was chosen as the primary reactor to evaluate the effect of lysine deprivation on leukemic blood. It was first necessary, however, to determine the biocompatability of the SFR with blood. Before - clinical acceptance of the immobilized enzyme hollow fiber reactor would . _ .5358 3330 E as $3” . 38s has. as 35588 How 03 25 mo A8308 25 no 855525me 2.838 5335.5 mo 5.8.50 05H. ”36 0.83m @3253 08:. 110 new owe a .ouoE E95. noun—noun ll .nm 0 n . ESE. .8338 E8... 8383 one . 4 n 3588538 4 ...vd rm. 4 a. tulle q a .3 a . O . m 10.0 O . a a .. w. :56. m 4 . W" a ...wd ..u x) . .w .3 (Wx 111 be possible, it was necessary to demonstrate that circulating blood through the hollow fiber causes no negative effects on the hematological properties of the blood. These experiments are described in the next chapter. CHAPTER 7 BIOCOMPATIBILITY OF THE SINGLE FIBER REACTOR INTRODUCTION An important, primary consideration of enzymatic blood treatment is the possibility of undesirable adverse interactions with the patient's blood. These include interactions between the blood cells and the hollow fiber membrane, cell lysis, disruption of serum enzyme systems, and leakage of the enzyme and reaction products into the patient's blood. Because of the particular nature of the polyamide hollow fiber membranes and because the membranes prevent direct contact between the patient's blood and the enzyme, these adverse effects should be minimized. In addition, these enzyme reactors differ substantially from standard renal dialyzers ("artificial kidneys") in which certain compounds are removed from blood by filtration through a dialysis membrane. The immobilized enzymatic reactor should not remove small molecules (vitamins, minerals, electrolytes, enzyme co-factors) from the blood to a significant degree. Only the enzyme substrate (lysine) is removed from the blood by its reaction in the immobilized enzyme region. It was the purpose of the experiments described in this chapter to determine the compatability of the single fiber reactor with whole blood. The effect of circulating blood through the lumen of the fiber on the hematological properties of the blood such as blood cell counts, cell lysis, and creatine phosphokinase activity (as an indicator of enzyme imbalances) were investigated. 112 113 Biocompatibility Experiments The blood of both healthy and BLV-infected sheep was used in these experiments. Blood was collected from animals by the method discussed in Chapter 3. After collection, the blood was divided into two samples. One sample served as the control while the other sample was circulated through the SFR. Both samples were maintained at 37°C. In order to isolate the mechanical and hydrostatic effects on blood due to its circulation through the small diameter hollow fibers, no enzyme was immobilized in the SFR in these experiments. Our initial experiments indicated a high degree of cell lysis caused by circulating blood through the hollow fiber reactor system. Hemolysis can be caused by stesses which disrupt the integrity of the cell membrane. These stresses can arise from either the hydrodynamic interaction between the cell and the solid surface of the hollow fiber or from the shear stresses associated with blood flow through the reactor. As mentioned in Chapter 2, hollow fiber reactors have been used for the treatment of blood by other investigators; therefore, the fiber/blood cell interaction is an unlikely source of the cell lysis. The shear rate in the reactor system can also be shown to be too low to cause cell lysis. If the flow within the SFR is assumed to obey Poiseuille's law, then the volumetric flow rate (Q) is described as follows: C Q-J'a'BL—fiz' (7.1) where R is the inner radius of the hollow fiber (- 0.0559 cm), AP is the 2 axial pressure drop down the fiber (dynes/cm ), L is the length of the 114 fiber (21.5 cm), and p is the viscosity of the blood which is 3.0 centipoise [Cooney, 1976]. In Poiseuille flow, the shear stress varies linearly with radial distance from a zero value at the fiber's center to a maximum value at the wall. The wall shear stress (1w) for this situation is given by M (7.2) Equations (7.1) and (7.2) can be used to determine the shear rate at a given blood flow rate. For example, Equation (7.1) can be used to determine that the pressure drop across the reactor at a flow rate of 15.0 ml/min (the maximum blood flow rate used in this investigation) is 42,048 dynes/cmz. This pressure drop is then used to determine that the maximum shear stress under these conditions is 55 dynes/cmz. This stress is far below the 2,000 dynes/cm2 necessary to cause hemolysis [Middleman, 1972]. After consulting with Dr. Penner (Professor, College of Human Medicine, Michigan State University), it was determined that the peristaltic pump used in the reactor system (Cole Farmer, Catalog Number 7553-10) could be the source of the lysis. A Sarns 3M (Ann Arbor, MI) 7800 centrifugal pump system was used to replace the peristaltic pump. This pump system was specifically designed for use with blood. Sarns 3M donated this pump for use in this project. The experimental reactor system used was the same as the one described in Chapter 5 (shown in Figure 5.1) with the exception of this change in pumps. The main difference in operating a centrifugal pump is the necessity of priming the pump before operation. This is accomplished in 'the following manner. First, the pump inlet is clamped while the 115 reservoir is filled. Next, the inlet line is slowly unclamped and a syringe is attached to the outlet line. Thesyringe is used to slowly draw blood into the pump, which causes air to exit upward through the outflow tubing. After the pump is completely primed, the outlet line is clamped. The primed pump is now used in priming the rest of the circuit. Before each experiment, the reactor system was sterilized to prevent bacterial contamination of the blood. A solution of 80% ethanol was circulated through both the shell and tube-sides of the system for approximately two hours. The centrifugal pump was primed with the ethanol solution and then used to circulate the ethanol through the tube-side of the reactor. A gear pump was used to pump the ethanol through the shell-side of the system. After the reactor system had been sterilized with ethanol, sterile water was circulated through the entire system for one hour to remove any excess ethanol and prepare the SFR for operation. Blood was circulated through the lumen of the SFR for a total of four hours. After the experiment was completed, samples of both the control and the treated blood were collected in ten ml Vacutainers (Beckton Dickinson, Rutherford, NJ). These Vacutainers were then transported to the pathology laboratory of the MSU Veterinary Clinic where they were analyzed for hematological properties including red blood cell (RBC) counts, white blood cell (WBC) count, differential white cell count, platelet count, serum potassium, and serum creatine phosphokinase (CPR) activity as an indicator of enzyme imbalances. The methods used for these analyses were discussed in Chapter 3. The statistical parameters on the analytical techniques used to ‘measure the hematological properties of blood are highly variable. It 116 was therefore necessary to conduct an initial study of 20 experiments which was used to estimate the variance (3’) and the mean values of the hematological properties for both the control and the treated samples. The results of this study are shown in Table 7.1 below: Table 7 . 1 Results of Initial Hematological Study Hematological Mean Value Mean Value Standard Property Control Treated Deviation (s) White Cell Count 4.08 4.29 0.30 (x 103/#1) Red cell Count 8.26 8.20 0.08 (x 103/m1) Platelet Count 281.9 284.0 2.87 (x 103/#1) Serum Potassium 2.80 2.90 0.14 (mEquivalents/L) Serum CPK 59.0 55.6 6.10 (IU/L) ' These results were used to calculate the number of observations required to make statistically significant statements about the effect of circulating blood through the SFR on the hematological properties of blood. Equation (3.1) is rewritten here for convenience: 2 [to + t1]2 s2 (7.3) 52 117 For a given hematological property, the variables on the right hand side of the equation are all known from the initial study. This study consists of n (20) observations and has (n - 1) degrees of freedom. From this information, the values of to and t1 are found from standard statistical tables [Steele and Torrie, 1980] to be 1.725 and 0.861, respectively. The value of s for a given property is found directly in Table 7.1. Finally, the value of 6 can be calculated by taking the difference between the mean of the control and the mean of the treated sample for the property of interest. The calculated values for N (the minimum number of experiments for a two-sided alternative) are shown below: Table 7 . 2 Minimum Experiments Needed for Statistical Accuracy in Hematology Study Hematological . Number of Experiments Needed Property (Calculated From Equation (7.3)) White Cell Count 27.3 Red Cell Count 23.7 Platelet Count 25.0 Serum Potassium ' 26.2 Serum CPK 25.7 From these results, it is seen that the most experiments were required to accurately determine the effect of the treatment on the total white cell count of the samples. Eight additional experiments were conducted ‘50 that data from a total of 28 experiments were collected. 118 RESULTS Results from the complete biocompatibility study (all 28 experiments) are shown below: Table 7 . 3 Results of Complete Hematology Study Hematological Mean Value Mean Value Standard Property Control Treated Deviation (s) White Cell Count 4.05 4.25 0.29 (x 103/#1) Red cell Count 8.16 8.23 0.09 (x 10‘/ml) Platelet Count 283.9 282.0 2.78 (x 103/#1) Serum Potassium 2.82 2.93 0.16 (mEquivalents/L) Serum CPK 58.7 54.4 6.25 (IU/L) The values for the means and for the standard deviation presented in Table 7.3 were used in Equation (7.3) as before. It was found that no additional experiments were required for the biocompatibility study. Although the means of the various hematological properties for the treated samples were slightly different than that of the controls, the differences are within the accuracy of the analytical techniques used. In addition, there was no pattern observed for any of the properties during the course of this study. Sometimes the control sample would have a higher value for a particular property and other times the 119 opposite would be true. For example, when compared to the control samples in the initial study, the treated samples had a higher platelet and lower red blood cell count. In the complete study, however, it was the control samples that had the higher platelet and lower red blood cell count. These results indicate that circulating blood through a SFR caused no noticeable effect on the hematological properties of the blood. Pulsatile flow also had no significant effect on blood properties. The experiments described in this chapter were used to establish the biocompatibility of the SFR with sheep blood. The ability of the SFR to remove lysine from blood has been demonstrated in Chapters 5 and 6. The next chapter discusses the use of the SFR to control the levels of lysine removal so that the effect of lysine deprivation on leukemic blood can be evaluated. CHAPTER 8 THE EFFECT OF LYSINE DEPRIVATION ON LEUKEMIC BLOOD Introduction Present methods of chemotherapy in leukemia treatment rely on small quantitative differences between the sensitivities of normal cells and leukemic cells that are the target of the drug's toxicity. One way in which leukemic cells differ from normal cells is that leukemic cells have a much higher metabolism of lysine. It was the purpose of the experiments discussed in this chapter to determine the effect of lysine deprivation on leukemic blood cells. Blood from leukemic sheep was treated in gitrg with the immobilized enzyme reactor. The reactor treatment is able to vary and control levels of lysine removal by choice of the amount of enzyme immobilized, the volume of blood treated, the blood flow rate, and the treatment time. For the experiments described in this chapter, lysine removal was primarily controlled by the time of treatment. This enabled us to study the effect of different levels of lysine deprivation on the leukemic blood. Data obtained in this manner were used to develop a mathematical model to describe the effects of lysine deprivation on leukemic blood. Mathematical Mbdel A major objective of this work was to develop a mathematical model that describes the relationship between lysine concentration and leukemic cell population balances. The model was used to generate a computer simulation of the in 21519 effects of reactor treatment on leukemic lymphocyte survival rates. Experimental data obtained as described from lysine depletion experiments were used to calculate 120 121 model parameters as described below. The effect of the concentration of lysine in the blood (C ) on lys cell proliferation kinetics is evaluated using a kinetic model of population balances on both the populations of total white cells, Nt’ and the proliferative fraction, Np’ of the leukemic lymphocytes. The time rate of change of cell numbers is a measure of cell survival rate after enzymatic reactor treatment. Change in the total white count is due to a combination of cell death and an increase in cell number resulting from mitosis. It was believed that the increase in the number of cells due to mitosis would be negligible. First, the time period in which these experiments could be conducted was only long enough to allow cells that were initially in the 8, G2 or M phases of the cell cycle to have sufficient time to complete the mitotic cycle; these cells represent only a small fraction of the total. Analysis time was limited due to the schedule of the Veterinary Clinic's pathology laboratory and the expense of the analyses. In addition, not all cell divisions result in viable cells. For the above reasons and the fact that modelling mitosis was beyond the scope of this project, it was felt that it would be best to start with a simple model that describes the change in white count as a function of cell death only. The death function is expected to be of the form suggested by Scott et a1. [1984], and the relationship describing total white cell count was modelled as follows: dN , t lys where a' and b' are constants. 122 A cell population balance was also derived for the proliferative fraction of the leukemic lymphocytes. This fraction is of interest because it is generally much higher in adult leukemic blood than it is in normal, healthy blood. Using a population balance on this fraction, the time change in proliferative lymphocytes is due to cell death caused by lysine deprivation, cell birth, and cells entering and leaving the nonproliferative stages of the cell cycle. If cell birth (mitosis) is neglected, these relationships may be described by the following mathematical expression: dN ——P— - D - klN + k2N (8.2) p up dt where Np is the number of lymphocytes in the proliferative fraction, D is the death function described in Equation (8.1), k1 is the rate constant associated with the transfer of cells out of the proliferative fraction, and k2 is the rate for the transfer of cells from the nonproliferative fraction (an) to the proliferative fraction. It was the purpose of the experiments described in the next section to determine these model parameters. Experimental Procedure The experiments described below were used to evaluate SFR performance using the blood of BLV-infected sheep. Since none of the MSU sheep had developed leukemia at the time of these experiments, it was necessary to have leukemic blood from BLV-infected sheep sent to us from Dr. R.D Schultz's laboratory at the University of Wisconsin. The leukemic blood was collectedin vials which were then packed in ice. Blood was received approximately 20 hours after it had been drawn from 123 the sheep. Although the blood was completely viable, it was important to determine whether significant changes in blood lysine concentration had occured during shipping. The lysine concentration of the shipped blood varied from 0.8 mM to 1.1 mM and no significant decrease in lysine concentration was observed within a 24 hour period. It was therefore assumed that there was no significant detrimental effect on the blood caused by the shipping process. After receiving the blood, the treatment procedure used was similar to the one used for the biocompatibility experiments discussed in Chapter 7. The blood was divided into two samples. One sample was continuously recirculated through the immobilized enzyme reactor for about four hours; blood aliquots were taken from the treated blood at regular intervals for analysis. The amount of lysine removed from the blood was controlled by varying the time of treatment. The other sample served as a control and was maintained at the same temperature over the same time period as the treated blood. Both the treated and control samples were analyzed for total white cell counts and lymphocyte proliferative capacity. White cell counts were measured every two hours over an eight hour period. Lymphocyte proliferative capacity was determined immediately after the treatment and twice more within the next 24 hours. Analyses of these data were used to establish correlations between lysine concentration and cell proliferation (or cell mortality) kinetics and to evaluate model parameters. Determining a' and.b' For a given concentration of lysine, the term [a'/(b' + C )] in lys Equation (8.1) is constant. This equation was rearranged and integrated over time to give the following result: 124 1n (Nt/Nto) - - K' t (8.3) where ._ __a'__ x [... .1 1 yS In Equation (8.3), Nt is the total number of white cells at time t and Nto is the number of white cells at the beginning of an experiment (t-O). Blood was treated as described above to give five different values of lysine concentration to test the effect of Clys on the total white cell count in the blood. After treatment, the blood was analyzed for white cell count over an eight hour period. A typical result is shown in Figure 8.1. These experiments were repeated several times for the five different values of Clys' For a given lysine concentration, a plot of -ln (Nt/Nt0) vs. time was prepared (see Figures 8.2 and 8.3). The correlation of linearity for these data were greater than 0.99. From Equation (8.3), it is seen that the slope of theSe plots is equal to K'. Results from these experiments are shown in Table 8.1 below: Table 8.1 Results From Plotting Equation (8.3) e o atio K',}$,lO3 1 0 mM 5.50 i 0.06 0 8 mM 6.61 i 0.08 0 6 mM 8.31 i 0.12 0 4 mM 11.06 i 0.09 0 2 mM 16.54 i 0.05 125 .85 es .... £9 85% .58: Emma. 33 .88 38 33>» 5 88.580 Adm 953m @305 we: 9.01:: Warez) 81mm 126 .023 :4 33 66 .N6 n 3335838 3?: 835 355 .m> ”37:556. 5.. mo 52m “flw 8.5me $505 25:. ES 0.. ..u .38 use». 0 A26 25.0.0 n 6:00 3.90 4 2E Nd .... .300 2594 x 127 A23 wd 03 v.0. n 3835838 25.: 838 3: 3 ~ansz 5. .s as as BEE $.5on eEfi 2E 0.0 u .38 can». a 2.5.30 I ”38 3%». x 128 Identical values for K' were found when Equation (8.1) was applied to only the lymphocytes instead of the entire white cell population. The lymphocytes are of particular interest because bovine leukemia virus causes a leukemia that affects this type of white cell. These results were used to determine the constants a' and b' in Equation (8.1). Equation (8.4) was inverted to give the following expression: l/K' - (l/a') C + a'/b' (8.5) lys The data in Table 8.1 were used to construct a plot of l/K' vs. Clys (Figure 8.4). Using the slope (l/a') and the intercept (a'/b') of this plot, values of a' and b' were determined directly: a' - 0.0066 i 0.0008 pmol/ml-hr b' - 0.199 t 0.006 pmol/ml The correlation of linearity for Figure 8.4 was 0.993. These values of a' and b' were used to determine the remaining model parameters. Determining‘k1 and]:2 To determine R1 and R2, the rate constants for cell transfer between the proliferative and nonproliferative fraction of the lymphocytes, blood was treated with the enzymatic reactor using different treatment times which gave different values of C The lys' death function for the proliferating lymphocytes was assumed to be equal to the death function for the entire white cell population found earlier 129 o... .oouabnmoooo 0&9: .m> .VS me SE 6.» Scary“ 925v 203228200 0593 wd ad #6 _ n . p _. . . _ ..-. — 130 (a' and b' are equal to the values found above). Equation (8.2) is divided by the number of nonproliferative lymhocytes and integrated over time to give the following: N N - A + B-A *EXP -C t (8.6) p/ up < > [ 1 where k2 A K' + k1 , (8.7) n B - -—n-P-— (8.8) np t - O, and C - K' + k1 (8.9) Due to our limited access to the flow cytometer at St. Lawrence Hospital, it was possible to measure the proliferative capacity and, hence, the number of proliferating lymphocytes over only a few time intervals in a given period. Because the control and treated samples came from the same source, it was assumed that all the blood samples initially had the same concentration of white cells and the same proliferative capacity. In order to evaluate the remaining model parameters, it was decided that the best approach was to measure the number of proliferative lymphocytes before treatment to determine the value of B and twice more within a 24 hour period after treatment. Data obtained in this manner were used to fit an expression of the form of Equation (8.6) to obtain 131 the remaining constants, A and C. With these constants and assumming K' to be equal to the values found in Table 8.1, the parameters k1 and k2 were determined. It was found that both k1 and R2 are independent of lysine concentration. Table 8.2 summarizes the mathematical model and the model parameters found from these experiments: Table 8 . 2 Mathematical Model and Model Parameters Model Total white cells: 3&— _ D _ _ -—5'—-— N dt b'+ (:1 t ys Proliferating Cells: dN . ——P—-- —L-— N-k,N+1<2N dt p np Parameters a' - 0.0066 i 0.008 pmol/ml-min b' - 0.199 i 0.006 mM 1 -3 - -5 _1 k1 - 3.29 i 0.21 x 10 hr k2 - 8.98 i 0.15 x 10 hr The above models describe the time rates of change of both the total number of white cells and the number of proliferating lymphocytes in the leukemic blood. These models were next used to develop a computer simulation that predicts the effect of the enzymatic reactor treatment on the leukemic cell population. Computer Simulation The computer simulation couples the description of reactor performance, i.e. the time course of lysine removal from the blood, with 132 the kinetics of white cell proliferation under conditions of lysine deprivation. In order to achieve high conversions of lysine, pulsatile flow was used. The reactor model for lysine removal from blood using pulsatile flow was discussed in Chapter 6. The reactor equations that describe the change in lysine concentration with respect to time are rewritten here for convenience _E£Z§§l) ' - A P (31 - $2) - A P g(t) f(t) (8.11) dt m a 11233.). - A P (s. - 52) + A P am f(t) + Vm 52 (8.12) dt m 3 Km + s, where the parameters in the above equations were defined in Chapter 6. This expression describes changes in lysine concentration, 81, in the blood volume being treated, V , during reactor operation. The effects of the reactor are linked to the cell population kinetics through the death function and Clys(clys - 81). A computer program was written (Program IV in the Appendix) that enables the user to input the value of Clys before treatment, the treatment time, and the cell exposure time (defined as the period between the time at the end of the treatment and the time at the beginning of the blood analyses). The user is also able to input the concentration of white cells in the blood and the proliferative capacity of the lymphocytes before treatment. Because Equations (8.11) and (8.12) are solved using a Runge-Kutta scheme, new concentrations of lysine in the blood are calculated every time period (20 seconds). These new values for Clys are then used in Equations (8.3), (8.4), and (8.6) to determine new values for the total number of white cells and the number of proliferating cells. This continues until the desired 133 treatment time has been reached. At this point, the value of C is lys equal to the blood lysine concentration after treatment. The calculated value of the blood lysine concentration is then used in Equation (8.4) to determine K'. With K' known, the total number of white cells can be determined using a balance on the cells similar to Equation (8.3). The number of proliferating lymphocytes in the blood after the specified exposure time can be determined directly using Equations (8.7) through (8.10). Accuracy of the Computer Simulation Experiments were conducted in order to determine the accuracy of the computer simulation. Blood was circulated through the SFR containing immobilized enzyme using pulsatile flow. Before treatment, the blood was analyzed for lysine concentration using the methods discussed in Chapter 3. Samples were taken and the treatment time was recorded. The blood samples were analyzed both before treatment and again 24 hours after the completion of the treatment. The 24 hour period was to allow sufficient exposure of the blood cells to reduced lysine levels in the blood. Analysis of the treated blood samples included both total white cell counts and lymphocyte proliferative capacity. Results from these experiments as well as theoretical results from the computer simulation are shown in Figures 8.5 and 8.6. Figure 8.5 shows that the computer simulation accurately predicts the effect of reactor treatment on the total white cell count in the leukemic blood with less than 4% error. This suggests that the assumptions made about the effect of mitosis on total white cell count are valid for the time of the experiment. In addition, the model parameters involved in the death function (a' and b') accurately 134 68.583 2..“ 33mm: soaflafim 3:27:08 use 3325.398 Eon Eco:— 38333 E :58 :8 SEE 33 no “5888.5 Summon mo “8am 23. “mm vacuum 33:2:5 mEfi on com 2: - BEoEtoaxo . x coma—3E3 .33an0 E9: II $.01 X {ti/8119:) 9mm 135 63583 98 3:63 nous—35m. .8395". can 3582858 53 “was: 383?2 E 230 $338233 .3 32:5: 2: so E358: .Suomon .«o “3&0 23. 6.m charm Ammgcwfv 08:. com com car a .3cuEtoaxo x sausage toga—Eco Eat i... 000— loovp I 4‘ Jemwom Jed snag Bulimewwd 136 describe cell death under periods of lysine deprivation. In Figure 8.6, it is seen that the computer simulation is also accurate in predicting the effect of the treatment on the number of proliferating cells in the blood. The largest errors in the simulation occur at long treatment times. These errors can be attributed to the limitations in determining the model parameters due to the difficulty in collecting data. Difficulties were caused by our limited access to and expense of using the flow cytometer and the fact that none of the MSU sheep developed leukemia. The result of this was the necessity of assuming that the death function is the same for the proliferating cells and the nonproliferating cells. Since this assumption was used to evaluate the remaining model parameters (k1 and k2), the accuracy of the computer simulation is very dependent on the accuracy of this assumption. Despite these problems, errors in the computer simulation are consistently less than 7.5%. The work described above has established the accuracy of the computer simulation in predicting in Vitro effects of lysine deprivation on leukemic blood. An important goal of future work will be to verify the model parameters in vivg. The rationale for developing a mathematical model for in_xixg computer simulations is that the modelling will allow for physiologically realistic interpretation of experimental results and eventually may serve as an a priori tool for simulating and choosing leukemia treatment protocols. A model also will quantify the effects of amino acid deprivation on leukemic cell proliferation kinetics to further our understanding of the development of leukemia. 137 Significance of Results Figure 8.7 shows the effect of lysine deprivation on the total number of white cells in the leukemic blood. It is seen that as the amount of lysine removed from the blood increases, the total number of white cells in the blood decreases until approximately 70% of the lysine has been removed. At this point, the lysine deprivation effect levels off. Figure 8.8 shows similar results for the proliferative capacity of the lymphocytes. The inflection point present in these curves is due mainly to the dependence of K' on the concentration of lysine (see Table 8.1). These results are important for two reasons. First, the reduction of both the total white cell count and the proliferative capacity of the lymphocytes represents the first step in the induction of remission of leukemia. Remission is defined to occur when the white cell counts and proliferative fraction are within specified ranges for normal sheep. Although the cell counts and proliferative capacity of the treated blood are still above the norm (the normal white cell count in sheep is approximately 4,000 white cells/pl with less than 1% in the proliferative stages of the cell cycle), these results represent the effect of lysine deprivation after only one treatment with the cells being exposed to the reactor for less than five hours and to a decreased level of lysine in the blood for only a 24 hr period. A normal treatment regimen would keep lysine at some acceptably low level for approximately one month. Therefore, the 25% decrease in total white cell count and the decrease in proliferative capacity represent an important step towards the induction of remission. In addition, these experiments indicate that the effects of lysine ‘ deprivation level off before all the lysine has been removed from the 138 .953 3 mm 0:5 enamomxm .358 :3 333 :38 no mousing 2:93 we Huntsman. 8.x 033m ZOF.._ N amnoaom/S'nao ELLIHM 139 4.0 % 3.0 %" 2.0 %— 10%“ remission °‘°%— 0.0% 25% 60% 80% 95% % LYSINE DEPRIVATION Figure 8.8: The effect of lysine deprivation on lymphocyte proliferative capacity. Exposure time is 24 hours. 140 blood. This is important clinically because exogenous amino acids are important for the metabolism of normal cells and tissues. Use of the SFR demonstrates that the depletion of lysine can be controlled in such a manner as to have a significant effect in inducing remission of this disease, but still leave some exogenous amino acid in the bloodstream for the function of healthy cells and organs. What the minimum levels for maintenance of healthy cells and organs is not presently known. The Effect of L-lysine a-oxidase on.Human.Leukemic Blood As mentioned in Chapter 2, leukemia is characterized by both an abnormal number of leukocytes and the presence of immature leukocytes, or blasts, in the circulation. The first step in the treatment of leukemia is to try to induce remission which is defined as the abatement of the symptoms of the disease, i.e. a decrease in the total amount of white blood cells and blast cells down to the levels found in normal blood. It was the purpose of the following experiments to demonstrate the potential of L-lysine a-oxidase in inducing remission of human leukemia. These experiments were done in cooperation with Sparrow Hospital (Lansing, MI). Blood from two separate human patients was used in this investigation. "Patient A" was diagnosed with adult accute lymphoblastic leukemia and had a total white cell count of 115,700 cells/p1, 73% of which were blast cells, while "Patient B" was diagnosed with the childhood form of this disease and had a total white cell count of 7,100 cell/pl with 55% blasts). Healthy adults have approximately 7,000-8,000 white cells/pl, none of which are the abnormal blast cells. Approximately 12 ml of blood was drawn from each of the leukemic patients. After the blood was drawn, it was analyzed for lysine 141 concentration and then separated into three samples. One sample served as the control. The other two samples were treated with different levels of L-lysine a-oxidase removing all of the lysine from one of the samples and approximately 45% of the lysine from the other. Four hours after the enzyme treatment, these three samples were analyzed for lysine concentration, total white cell count, and percentage of blast cells. Results from these experiments are shown below in Table 8.3: Table 8.3 The In yitxg Effect of Lysine Deprivation on Human Leukemic Blood PATIENT A PATIENT B White Cells % Blasts White Cells % Blasts per pl per pl Control 115,700 73.0% 7,100 55.0% 45% lysine removal 111,200 72.2% 6,900 54.0% 100% lysine removal 97,600 69.8% 6,400 51.6% The L-lysine a-oxidase had a positive effect on the leukemic blood. Removing all of the lysine from the blood of Patient A caused a 16% decrease in the total white cells and a significant decrease in the percentage of blast cells after only four hours. In addition, it is seen that over 90% of the white cells that ”died" as a result of the enzyme treatment were the abnormal blast cells, indicating that the abnormal cells were preferentially affected by the lysine deprivation. Similar results were obtained with the blood from Patient B, and from these results, a qualitative relationship between lysine deprivation and remission-like responses in human leukemic blood has been established. CHAPTER 9 Conclusions and Recommendations The overall objective of the research conducted for this dissertation was to develop an immobilized enzyme reactor for removing amino acids from blood. An enzyme immobilization technique involving enzyme entrapment in hollow fiber membranes was investigated. The specific problem studied was the removal of lysine from the blood of leukemia patients by its conversion with the enzyme L-lysine a-oxidase. This reactor not only has potential applications in the clinical treatment of leukemia, but also can be used to obtain important information on the effect of amino acid deprivation on leukemic cell proliferation kinetics. This dissertation has discussed the work conducted during the development of the immobilized enzyme reactor. These studies included determining the best method for immobilizing enzyme within hollow fibers and the most suitable fiber type for the immobilization, finding the operating parameters of a single fiber reactor that maximized conversion, developing models for the reactor system, evaluating the biocompatibility of the reactor, and determining the effect of lysine deprivation on leukemic blood. The important results are summarized below. Summary of'Results As mentioned in the introduction, this thesis presents initial data for the application of an immobilized enzyme hollow fiber reactor in cancer therapies. The important results include the following: 142 1) 2) 3) 4) 5) 6) 143 Backflush loading was chosen as the best method for immobilizing enzyme in the SFR. When compared to static loading, backflushing achieves higher enzyme concentrations within the spongy region of the fiber. Polyamide fibers were found to be compatible with both L- Lysine a-oxidase and catalase. Fibers with a molecular weight cutoff of 10,000 retained 85% of the total enzyme that was backflush loaded. L-lysine a-oxidase immobilized in a polyamide SFR retained over 80% of its original activity after 30 days of refrigerated storage. No leakage of enzyme from the fiber wall was noted. The important variables that influence the performance of the reactor in removing lysine from blood were flow rate and the amount of both enzymes that were immobilized within the spongy layer of the hollow fiber reactor. Further studies showed that the optimum SFR operating conditions were a flow rate of 9 ml/min, 3.97 units of L-lysine a—oxidase immobilized per cm2 of the fiber's surface area, and a catalase to oxidase loading ratio of 2.5:1. These results are consistent with those found for a system in which buffered lysine (instead of blood) was recirculated through the SFR. Under optimum conditions, 45.2% of the lysine in whole sheep blood was converted in four hours of reactor operation. The lysine concentration of whole sheep blood is approximately 1.0 mM. For the concentration range of lysine studied in this dissertation, the reaction within the single fiber reactor approaches a diffusion controlled regime (effectiveness factor is below 0.3). 144 7) Pulsatile flow reduced diffusion limitations and improved conversion in the SFR from 45.2% to 58.6%. 8) The intrinsic immobilized Michaelis constant (Km) and maximum attainable reaction rate (V ) for L-lysine a- max oxidase were determined to be 0.688 mM and 7.44 units/mg, respectively. 9) A model was developed to predict conversion in the SFR under pulsatile flow conditions. This model was accurate (less than 4.0% error) in predicting conversion in a SFR operating with pulsatile flow using two different enzyme loading conditions. 10) Circulating blood through the SFR had no significant adverse effect on the hematological properties of the blood under both normal and pulsatile flow operation. In addition, the blood had little effect on fiber fouling indicating that reactors could be reused with no decrease in performance. 11) The ability to precisely control the level of amino acid removal with the immobilized enzymatic reactor has been demonstrated. This control is obtained by varying the length of time blood is circulated through the fibers. 12) Models were developed that describe the effect of lysine deprivation on the population balances of both the total white cells and the proliferative fraction of the leukemic lymphocytes. 13) The population balances were combined with the model describing lysine conversion in the SFR. The resulting computer simulation was accurate in predicting the in gitrg effects of the enzymatic reactor treatment on both the total white cells with less than 4% error and the proliferating lymphocytes with less than a 7.5% error. 145 14) A 25% decrease in the total number of white cells and a significant decrease in the number of proliferating lymphocytes was achieved when approximately 70% of the lysine was removed from the blood. This demonstrates the potential of the enzymatic reactor for the induction of remission in leukemia patients. Recommendations The main objective of this dissertation was to develop an immobilized enzyme reactor for clinical use in cancer therapies. The results summarized above indicate a good potential for achieving this goal. Before the enzymatic reactor treatment discussed in this dissertation could have practical applications, however, several factors require further investigation. In the paragraphs that follow, suggestions for additional work are made that will help to increase our understanding of reactor performance and leukemic cell kinetics under periods of amino acid deprivation. Future Work: Reactor Development The combination of reactions catalyzed by the enzymes in the spongy region of the fiber results in 1/2 of a mole of oxygen being produced per mole of lysine consumed. Since the L-lysine a-oxidase reaction requires these substrates in equal amounts, there is still a possibility that the reaction in the spongy region is oxygen-limited. In order to evaluate this possibility, a SFR should be operated with oxygen or air flowing through the shell of the reactor. An increase in reactor performance under these operating conditions would suggest that the rate of reaction within the SFR is dependent on the concentration of oxygen. 146 As mentioned in Chapter 4, PA10 hollow fibers were chosen for this research because of their compatibility with and high retention of the enzymes being studied. However, the polyamide fibers were only compared with polysulfone fibers which weren't suitable for this project because of an incompatibility with catalase. Additional fiber types should be investigated to determine whether polyamide fibers are indeed the best fiber for immobilizing the enzymes of interest. The search for the best fiber type is especially important when additional enzymes are studied (see below). In addition, the company that has been supplying the polyamide fibers (Romicon, inc.) no longer manufactures polyamide fibers. Pulsatile flow was used in this research to minimize diffusion limitations and increase lysine conversion in the SFR. Although many experiments were conducted to determine the conditions of SFR operation that maximized conversion, one important parameter that wasn't studied was the period of the pulse during pulsatile flow operation. The pulse period used in this research was chosen for its convenience. Additional experiments need to be conducted to determine whether varying the period . of the pulse has any effect on the amount of lysine removed from the blood by the SFR treatment. If this operating parameter is found to have a significant effect on reactor performance, research should be conducted to determine the period of the pulse that maximizes lysine conversion in the reactor system. Overall, more experiments with the clinical-sized hollow fiber cartridge are needed. These experiments require large amounts of enzyme and were therefore limited by the availability and cost of L-lysine c- oxidase. In particular, experiments need to be conducted to determine whether the model parameters found for the SFR operating under pulsatile 147 flow conditions can be scaled-up to the large-scale hollow fiber cartridge. This can be tested in a way analogous to the method used to determine that the kinetic parameters from SFR Operation were valid for the cartridge. As discussed in Chapter 6, the kinetic parameters were verified by accurately predicting conversion in the cartridge using the batch reactor model for the SFR and multiplying the rate of conversion by the number of fibers in the cartridge. To verify the scaleability of the pulsatile flow model, pulsatile flow must be used to convert lysine in a hollow fiber cartridge. The data from this type of experiment will be compared to the predicted conversion of lysine from the SFR pulsatile flow model (accounting for the number fibers in the cartridge). As was the case with the batch reactor model, the accuracy of the pulsatile flow model will be limited by the assumption of evenly distributed enzyme in the cartridge. Another factor that should be investigated is the use of an alternative method of sterilizing the hollow fiber reactor. Sterilization was accomplished by circulating 80% ethanol through both the tube and shell-sides of the SFR. The ethanol treatment shortened the lifespan of a particular fiber. Ethylene oxide or a suitable antibiotic should be tested as a possible replacement for the ethanol treatment. The use of ethylene oxide or an antibiotic should be milder than the ethanol treatment. This change should increase the longevity of the fibers. Future Work: .Amino Acid Deprivation Studies A major goal of future work should be to collect more data on the effect of amino acid deprivation on leukemic blood. Future work should '148 concentrate on developing enzymatic reactors with antileukemic enzymes other than L-lysine a-oxidase. There are several antileukemic enzymes available which may or may not be more effective in treating leukemia in an enzymatic reactor. In addition, a combination of enzymes may be the most effective type of enzymatic reactor treatment. It is hoped that the effect of reducing the concentration of several essential amino acids in patient blood at once will give the multienzyme system the advantage of not having to remove any specific amino acid to a significant degree. This can be important in maintaining an adequate supply of exogenous amino acid in the bloodstream for the normal function of healthy cells, tissues, and organs. Another important group of experiments that need to be conducted is the in xixg evaluation of the enzymatic reactor treatment. This would be accomplished by treating a leukemic sheep extracorporeally with the hollow fiber cartridge. The model parameters describing the effect of lysine deprivation on leukemic blood in 21219 must be valid in 2129. This would be demonstrated by the ability of the in yitgg parameters to accurately predict the in 3129 effects of amino acid deprivation. In addition, examination of the sheep's bone marrow would give important information on the effect of amino acid deprivation on cell birth. In order to be an effective treatment, the decreased levels of amino acid in the blood caused by the enzymatic reactor must have a positive effect in decreasing leukemic cell production in the marrow. In 2129 experiments would also demonstrate the long-term effects of lysine deprivation on leukemic blood and show whether the enzymatic reactor treatment can cause remission and/or an increase in the life expectancy of a leukemic animal. Finally, the in vivo data can also be .used to develop a computer simulation describing the effect of enzymatic 149 reactor treatment on the leukemic animal. This simulation would incorporate the bone marrow data and would help establish treatment protocols that maximize both leukemic cell death and normal cell survival. The research conducted so far has given important insights into the potential use of an immobilized enzyme reactor in cancer therapies. It is hoped that future work may be conducted to allow for improvement of reactor performance, evaluation of the potential of a multienzyme reactor treatment, and in vivg testing of the hollow fiber device. APPENDICES APPENDIX Runge-Kutta-Gill Method The Runge-Kutta-Gill method is one of the most widely used techniques for solving first-order differential equations [Fogler, 1986]. For the equation dY dx - mm!) the solution takes the form Y1+1 - Y1 + -%3— [k1 + (2 - J’2")k, + (2 + f2")1<, + k‘] (A.l) where k, - f(X1,Yi) k2 - f [x1+—%K—, Y1+k,-A§-] k, - f [ x1 + -§X-, Yi + (1/1‘2' - l/2)AX k, + (1 - l//_2_)AX k2 ] k, - f[Xi+AX,Yi-7A-22§- k,+(1+1//‘2")AX1<,] As discussed below, this numerical method was an important technique for solving several first order differential equations presented in this dissertation. Programs I, la, and lb Program I was used to determine the intrinsic immobilized kinetic (parameters of L-lysine a-oxidase. As described in Chapter 6, two liters 150 151 of a 5.0 mM lysine solution was pumped through the lumen of these reactors, and the concentration of lysine in the reservoir was determined at given intervals. The results of this study were shown in Figure 6.4. The concentration of lysine in the reservoir can also be determined mathematically by solving the equation for the reaction rate (Equation (6.6)) numerically using the Runge-Kutta-Gill method discussed above. Recalling Equation (6.6) e] V S _ ...Qfi__ , ,I max Rate of reaction vres dt E S + Km (A.2) where Vres is the volume of the reservoir, [e] is the amount of enzyme immobilized, and S is the substrate concentration. E is the effectiveness factor which is determined using the Moo-Young and Kobayashi [1972] model for the case with no inhibition. Km is the immobilized intrinsic Michaelis constant, and,Vmax is the maximum reaction rate (pmols of substrate reacted per mg of enzyme immobilized per minute). Comparing this equation with Equation (A.l) gives 43.. - —3§. . M and (V /v ) S f(X,Y) - E- __§max_:rs§_i___ (A.4) m The computer program was then established to use the experimentally obtained lysine concentrations to fit the intrinsic immobilized kinetic 152 parameters (Vma and Km) to the Runge-Kutta solution of the above model x (using At - AX - 0.5 minutes). The main program sets the initial values for these parameters and calls both the Pattern and Calc subroutines. Pattern minimizes a cost function by adjusting the values of the parameters being fitted. Calc uses Equations (A.l-A.4) to determine a calculated lysine concentration (S) and then defines the cost function to be the sum of the square of the residuals between the calculated and experimental concentrations. Once the intrinsic kinetic parameters were determined, these parameters can be used in the Gale subroutine of Program I to generate data for both the effectiveness factor vs modulus plot (Figure 6.5) and Figure Al. Figure Al shows the comparison between the calculated (using Program Ia) and experimental lysine concentrations. It is seen that the greatest disparities occur at the higher lysine concentrations. Even at these concentrations, the largest difference in the calculated reaction rate was less than 4%. This indicates that the model and, therefore, the fit parameters, were very accurate in describing the reactor system under investigation. Programs 11 and 11a Program II was used to generate data for the design time vs. percent conversion of lysine plot (Figure 6.8). Recalling Equation (6.20) 5 ds n [e]-A t I V S . - -—-—-—-——' I dt (A.5) so me; 0 - E [ S + Km J res 153 338883 333:: 32:35 3: 33:86 3.68: 0.83 33: 833.3538 05.92 3582098. 36 #8333338 35 5333 53.8288 d ”3. 953m 9.305 95% ONO. Ova 06 _. onw 0.0 _ . _ . _ o. EEmoi m5»: .6quan l.. BEoEtodxo x o m. l_. m... U 3 m 0 a . U n... In M... .0 u U \I/ I? w W ( 154 where the parameters are all defined in Chapter 6. The concentration range over which the left-hand side of this equation is evaluated is chosen to be small enough such that the effectiveness factor (E) is constant. Under these conditions, the left-hand side of the equation can be solved analytically. the resulting equation is Design Time - -——El§——— [ so - s + Km ln(so/s) ] (A.6) max Program II uses this equation to calculate the design time at various conversions of lysine. These values of the design time are then used in Equation (A.S) to generate data for predicting lysine concentrations at various times for the hollow fiber cartridge operation (Figure 6.8) discussed in Chapter 6 (Program IIa). Progran.III As discussed in Chapter 6, the use of pulsatile flow was the best method of achieving high conversions of lysine in the SFR in a relatively short period of time. Because pulsatile flow causes an added convective flow from the lumen to the spongy, reactive region of the fiber, the reactor is modelled as a two compartment reactor separated by the ultrafiltration membrane as follows: d(V151) d - A Pm (s1 - 52) - A Pa g(t) f(t) (A.7) t 39.2531 - A Pm (s1 - s.) + A Pa g(t) f(t) + Bag 52 (MD dc K + $2 ' m 155 (see Chapter 6 for definition of the parameters). These equations can be rearranged in the form of Equation (A.l) and solved simultaneously using a Runge-Kutta scheme. Experimental data was obtained in the manner described in Chapter 6. The optimum amount of enzyme was immobilized in-a SFR which was then installed in the laboratory reactor system. Sheep whole blood was pumped through the SFR, and the period of the pulse was four minutes. Lysine concentration was determined every 32 minutes for a total of 248 minutes. Results of this experiment are shown in Figure 6.6. Program III was written to evaluate the parameters Pm and Pa in Equations (A.7) and (A.8) by fitting the experimental data to the model (using At - AX - 20 seconds). The main program sets the initial values for these parameters and calls both the Pattern and Pulse subroutines. As discussed earlier, Pattern minimizes a cost function by adjusting the values of the parameters being fitted. Calc uses Equations (A.l), (A.7) and (A.8).to determine a calculated lysine concentration (SI) in the reservoir and then defines the cost function to be the sum of the square of the residuals between the calculated and experimental concentrations. Once Pm and P8 are determined, the Pulse subroutine can be used to detemine the calculated concentrations of lysine used to evalute these parameters. Figure A2 shows the comparison between the calculated and experimental lysine concentrations. These concentrations are in good agreement with each other indicating that the fit parameters were very accurate in describing the reactor system under pulsatile flow operation. In addition, the Pulse subroutine was also used to generate the calculated lysine concentrations shown in Figures 6.7 and 6.8. 156 km was Em E30823 afi «32:33 3 can: 93% 883.5538 «35. .3393 no Ea gunman e8 3335338 0593 3325.8 98 can 33333 «5 :353 sommsmmfioo .fl "N4 2de AmmbagEva: oou om. _ . . 0:23.53» 33%»: oouozuoa ll .3coEtoqxo x o no . (mu m. U .2 e O O U 0 a U \l... 15.0 m nun a 0 U \I/ . w -mg. mm. a 157 P 0 ram V Program IV also uses the subroutine Pulse to calculate lysine concentrations during pulsatile flow operation. Because a Runge-Kutta scheme is used, new concentrations of lysine are determined every time period (20 seconds). These calculated concentrations of lysine are then used in Equations (8.3) and (8.4 - 8.8) to calculate the total number of white cells and the number of proliferating cells in the blood, respectively. The program is set up to evaluate the effect of decreasing lysine concentration in the blood both during treatment and after a specified exposure period. COHPUTERPROGRAHS COMPUTER PROGRAMS PROGRAM I C THIS FILE IS THE MAIN PROGRAM WHICH INITIATES C THE SEARCH ROUTINE BY CALLING PATTERN. IT ALSO C CONTAINS THE INITIAL GUESES OF THE OF THE KINETIC C PARAMETERS AND OTHER FORMATTING INSTRUCTIONS FOR C PATTERN. C C DIMENSION P(1000), STEP(1000) C C SET INITIAL CONDITIONS AND SEARCH PARAMETERS C P(1) - 6.0 P(2) - 0.6 STEP(1) - 0.1 STEP(2) - 0.01 IO - 2 NP - 3 NRD - 3 C C CALL PATTERN C CALL PATTERN (NP,P,STEP,NRD,IO,COST) STOP END C C THIS FILE IS A PAIR OF SUBROUTINES WRITTEN TO BE C COMPATIBLE WITH THE PATTERN OPTIMIZATION C SUBROUTINE. THEY SIMULATE A PROCESS AND COMPARE C THE SIMULATION OUTPUT WITH THE EXPERIMENTAL OUTPUT C (READ IN THROUGH A DATA FILE). THESE SUBROUTINES C THEN CALL CALC WHICH CALCULATES AN ERROR OR A COST C ASSOCIATED WITH THE SIMULATION. PATTERN USES THE C SUBROUTINES ITERATIVELY IN ORDER TO FIND THE C OPTIMUM SET OF TRANSFER FUNCTION (THE KINETIC C PARAMETERS) TO FIT THE DATA. C C SUBROUTINE PROC(P,COST) DIMENSION P(1000),STEP(IOOO) C C INITIALIZE ARRAY C COST - 0.0 C C PERFORM SIMULATION AND CALCULATE ERROR C CALL CALC(P,COST) RETURN ‘ END 158 159 [396353 1 (cont.) SUBROUTINE BOUNDS (P.IOUT) DIMENSION P(IOOO),STEP(iOOO) IOUTIO IF (P(I).LT.0.) IOUTII IF (P(2).LT.0.) IOUTCI IF (P(3).LT.O;) IOUTII RETURN ' END SUBROUTINE PATERN(NP. P. STEP. NRD. IO, COST) DIMENSION P(1000), STEP(IOOO). 81(100). 82(100). XT(100). 8(100) C-¢--- 1 RETURN ~CALL 9300(p.c1) STARTING POINT L31 ICKIZ ITTER-O DO 5 I81.NP Bi(I)-P(I) 82(I)-P(I) T(I)IP(I) S(I)-STEP(I)*IO. INITIAL BOUNDARY CHECK AND COST EVALUATION CALL BOUNDS(P.COST) IF (IOUT.LE.O) GOTO 10 ° IF (IO.LE.0) GOTO 6 WRITE (05,1605) WRITE (65,1000) (J.P(J),J=1.NP) IF (IO.LE.O) GOTO 11 WRITE (05,1001) ITTER,C1 WRITE (05,1000) (J.P(J),Js1,NP) BEGINNING OF PATERN SEARCH STRATEGY DO 99 INRD-1,NRD DO 12 I-1.NP S(I)-S(I)I10; IF (IO.LE.O) GOTO 20 - WRITE (05.1003) ' WRITE (05.1600) (J,S(J),J=1,NP) IFAILaO.o PRETURBATION ABOUT T DO so I-1.NP ICsO P(I)-T(I)+S(I) IC-IC+1 CALL BOUNDS(P.IOUT) IF (IOUT.GT.0) GOTO 23 CALL PROC(P,CZ) L-L+1 IF (IO.LT.3) GOTO 22 WRITE (05,1002) L,CZ WRITE (05.1000) (J.P(J),Js1,NP) IF (C1-C2) 23,23,25 160 EROGRAM I (cont.) 23 24 25 30 31 33 34 35 IF (IC.GE.2) GOTO 24 S(I)=-$(I) GOTO 21 IFAIL=IFAIL+1 P(I)-T(I) GOTO 30 T(I)-P(I) CI-CZ CONTINUE' IF (IFAIL.LT.NP) GOTO 85 IF (ICK.EO.2) GOTO 90 IF (ICK.EO.1) GOTO 35 CALL PROC(T,C2) L=L+1 . IF (IO.LT.2) GOTO_31 WRITE (05,1002) L.CZ WRITE (05.1000) (J,T(J).J=1,NP) IF (C1-C2) 32.3%.34 ICK=1 DO 33 I-1.NP BI(I)-BZ(I) P(I)-82(I) T(I)-BZ(I) GOTO 20 CIBCZ 181-0 00 39 181.NP _ BZ(I)=T(I) 39 IF‘(ABS(B1(I)-82(I)).LTJ1.0E-20) 1818I81+1 CONTINUE IF (IB1.EO.NP) GOTO 90 'ICK-0 42 45 46 .47 90 91 99 ITTERcITTER+1 IF (IO.LT.2) GOTO 40 WRITE (05,1001) ITTER.C1 ‘WRITE (05.1000) (J.T(J).J-1.NP) ACCELERATION STEP DO 4s,11=1}11 DO 42 1:1,NP T(I)-sz(1)+sau(82(I)-31(1)) P(I)-T(I) sa-sa-.1 CALL BOUNDS(T,IOUT) IF (IOUT.LT.1) COTo 45 IF (11.50.11) ICK-1 CONTINUE DO 47 I-1.NP 81(I)-B2(I) GOTO «20 ' DO 91 I-I.NP T(I)-82(I) CONTINUE 161 ERQQBAM I (cont.) DO 100 I-1.Np 1oz P(I)-T(I) COSTICI IF (IO.LE.0) RETURN WRITE (05.1004) L.C1 WRITE (05.1000) (J.P(J).J-1.NP) RETURN IOOO FORMAT (3(35X.I7.5X.EI$.61)) 1001 FORMAT (411X13HITERATION NO. ,ISISX.5HCOST= . 1815.6.20X. 1OHRARANsTsRs1 1002°FORMAT (1OX3HNO..14. aXSHCOST=.a1s.51 1093 FORMAT (I1X28HSTEP 5128 FOR EACH RARANETER 1 1004 FORMAT (1H113HANSWERS AFTER .13.2X.23HFUNCTIONAL 1 EVALUATIONS II SXSNCOST-.s1s.6.2ox.18HORT1N IAL PARAMETERS 1 1005 FORMAT (1H135HINITIAL PARAMETERS OUT OF BOUNDS 1 END 162 PROGRAM I (cont.) SUBROUTINE CALC(P,COST) PERFORM AN ERROR ANALYSIS BETWEEN THE EXPERIMENTALLY OBSERVED LYSINE CONCENTRATIONS (SEXP) AND THE PREDICTED MODEL VALUE (8) AT VARIOUS TIMES. 0000000 DIMENSION S(150),P(100),C(10) OPEN (60,FILE-'CONC.DAT.',STATUS-‘OLD') INITIALIZE VARIABLES 0000 EVMAX - P(l) EKm - P(2) DS - 1.76E-7 VRES - 120.0 S(l) - 5.0 Vm - EVMAX/VRES COST - 0.0 CALCULATE THIELE MODULUS 000 D0 10 1 - 1,36 DO 20 J - 1,120 vc - 0.844 SA - 7.75 EL - VC/SA (S(J)*EL)/(S(J) + EKm))*(Vm/(2*60*DS))* * 0.5 S(J) - (EKm * ALOG(EKm + S(J))) * * 0.5 TM - X/Y x—< Y-< C CALCULATE EFFECTIVENESS FACTOR IF (TM.GE.O.AND.TM.LE.1)THEN E - 1.0 ELSE E - 1/TM END IF B - EKm/S(J) EFF - (E + B * TANH(TM)/TM)/(l + B) CALCULATE LYSINE CONCENTRATION VS. TIME USING RUNGE-KUTTA-GILL METHOD FOR SOLVING EQUATION FOR REACTION RATE (dS/dt - (E Vm S)/(S + Km)). DELTA TIME IS THIRTY SECONDS. 00000000 I63 PROGRAM I (CONT.) 20 IO DT - 0.5 0(1) - (EFF * Vm * S(J))/(S(J) + EKm) FA - S(J) + 0(1) * DT/2 0(2) - (EFF * Vm * FA)/(FA + EKm) U - (1/2) * * 0.5 FB -S(J) + DT * 0(1) * (w - 0.5) + DT * 0(2) *(l-W) 0(3) - (EFF * Vm * FB)/(FB + EKm) F0 - S(J) - DT * 0(2) * w + DT * 0(3) * (1 + W) 0(4) -(EFF * Vm * F0)/(F0 + EKm) Z -(DT/6)*(C(1)+(2-(l/W))*C(2)+(2+(1/W))*C(3)+C(4)) S(J+1) - S(J) + z CONTINUE READ (60,*) SEXP COST - COST + ABS((S(J+1) - SEXP)**2) S(1) - S(J+1)) CONTINUE CLOSE (60) RETURN END 164 PROGRAM II 000000 000 0000 20 10 THIS FILE WAS USED TO CALCULATE THE DESIGN TIMES FOR THE PLOT SHOWN IN FIGURE 6.8. THE PROGRAM CALCULATES THE DESIGN TIME AT VARIOS CONVERSIONS OF LYSINE USING THE ANALYTICAL SOLUTION TO THE LEFT HAND SIDE OF EQUATION (6.20). OPEN (63,FILE- 'DTM.DAT.',STATUS- 'NEW') VmA -7.44 VMAX - 7.44 * 0.61 EKm - 0.688 DS - 1.76E-7 VRES - 120.0 S - 1.0 Vm - VMAX/VRES DTM - O CALCULATE THIELE MODULUS DO 10 I - 1,19 DO 20 J -1,50 v0 - 0.844 SA - 7.75 EL - VC/SA ((S*EL)/(S + EKm))*(Vm/(2*60*DS))* * 0.5 (s - (EKm * ALOG(EKm + 5)) * * 0.5 TM - X/Y X Y CALCULATE EFFECTIVENESS FACTOR IF (TM.GE.0.AND.TM.LE.1)THEN E - 1.0 ELSE - E - l/TM END IF B - EKm/S EFF - (E + B * TANH(TM)/TM)/(1 + B) CALCULATE DESIGN TIME SB - s - 0.001' D - (1/(EFF * VmA)) * (S - SB + Km * ALOG(S/SB)) DTM - DTM + D S - SB CONTINUE WRITE (63,*) DTM,S CONTINUE CLOSE (63) STOP END 00000 10 165 PROGRAM IIA THIS FILE WAS USED TO PREDICT LYSINE CONCENTRATION VERSUS TIME IN A HOLLOW FIBER CARTRIDGE USING THE DESIGN TIME FROM THE SFR. OPEN (63,FILE- 'DTM.DAT.',STATUS- ’OLD') OPEN (64,FILE- 'HFR.DAT.',STATUS- 'NEW') E - 0.0238 A - 12.59 VRES - 2000.0 DO 10 I - 1,19 READ (63,*) DTM,S T - (DTM * VRES)/(N * E * A) WRITE (64,*) S,T CONTINUE CLOSE (63) CLOSE (64) STOP END 000000 00000000000000 000 000 000 166 PROGRAM III THIS FILE IS THE MAIN PROGRAM WHICH INITIATES THE SEARCH ROUTINE BY CALLING PATTERN. IT ALSO CONTAINS THE INITIAL GUESES OF Pm AND Pa AND OTHER FORMATTING INSTRUCTIONS FOR PATTERN. DIMENSION P(1000), STEP(1000) SET INITIAL CONDITIONS AND SEARCH PARAMETERS P(l) - 1.0 E P(2) - 1.0 E STEP(l) - 0.0 STEP(Z) - 0.0 10 - 2 NP - 3 NRD - 3 -2 —2 1 1 CALL PATTERN CALL PATTERN (NP,P,STEP,NRD,IO,COST) STOP END THIS FILE IS A PAIR OF SUBROUTINES WRITTEN TO BE COMPATIBLE WITH THE PATTERN OPTIMIZATION SUBROUTINE. THEY SIMULATE A PROCESS AND COMPARE THE SIMULATION OUTPUT WITH THE EXPERIMENTAL OUTPUT (READ IN THROUGH A DATA FILE). THESE SUBROUTINES THEN CALL CALC WHICH CALCULATES AN ERROR OR A COST ASSOCIATED WITH THE SIMULATION. PATTERN USES THE SUBROUTINES ITERATIVELY IN ORDER TO FIND THE OPTIMUM SET OF TRANSFER FUNCTIONS (Pm AND Pa) TO FIT THE DATA. SUBROUTINE PROC(P,COST) DIMENSION P(1000),STEP(1000) INITIALIZE ARRAY COST - 0.0 PERFORM SIMULATION AND CALCULATE ERROR CALL PULSE(P,COST) RETURN END 167 PROGRAM 111 (CONT.) SUBROUTINE BOUNDS (P.IOUT) DIMENSION P(1000).STEP(1000) IOUT80 IF (P(1).LT.0.) IOUTI1 IF (P(2).LT.0.) IOUT81 IF (P(3).LT.0;) IOUT¢1 RETURN ' END SUBROUTINE PATERN(NP. P. STEP. NRD. IO. COST) DIMENSION P(1000), STEP(1000). 81(100) .82(100). XT(100). S(100) 0-5--- STARTING POINT L81 ICK-Z ITTER80 DO 5 II1.NP 81(I)8P(I) 82(I)8P(I) T(I)'P(I) S(I)-STEP(I)N10. INITIAL BOUNDARY CHECK AND COST EVALUATION CALL BOUNDS(P. COST) IF (IOUT. LE. 0) GOTO 10 IF (IO. LE. 0) GOTO 6 WRITE (05.1005) WRITE (05.1000) (J.P(J).J=1.NP) ' RETURN CALL PROC(P,C1) IF (I0.LE.0) GOTO 11 WRITE (05.1001) ITTER.C1 WRITE (05.1000) (J.P(J).J81.NP) BEGINNING OF PATERN SEARCH STRATEGY DO 99 INRDI1.NRD DO 12 II1.NP S(I)-S(I)I10L IF (I0. LE. 0) GOTO 20 WRITE (05.1003) WRITE (05.1000) (J. S(J). J81. NP) IFAIL80.0 PRETURBATION ABOUT T DO 30 I-1.NP IC80 P(I)IT(I)+S(I) ICcIC+1 CALL BOUNDSCP.IOUT) IF (IOUT.GT.0) GOTO 23 CALL PROC(P,CZ) LILOI IF (IO.LT.3) GOTO 22 WRITE (05.1002) L.C2 WRITE (05.1000) (J.P(J).J81.NP) IF (Ci-C2) 23.23.25 168 'PRocRAM 111 (CONT.) 23 24 25 30 31 32 33 34 35 39 42 45 46 47 90 91 99 IF (IC.GE.2) GOTO 24 S(I)8-S(I)- GOTO 21 IFAILIIFAIL+1 P(I)8T(I) GOTO 30 T(I)SP(I) CIICZ CONTINUE . IF (IFAIL.LT.NP) GOTO 35 IF (ICK.EO.2) GOTO 90 IF (ICK.EO.1)-GOTO 35 CALL PROC(T.C2) L8L+1 IF (IO.LT.2) GOTO.31 WRITE (05.1002) L.C2 WRITE (05.1000) (J.T(J).J81.NP) IF (C1-C2) 32.34.34 ICK'I DO 33 I31.NP 31(I)8BZ(I) P(I)IBZ(I) T(I)832(I) GOTO 20 CIICZ IB1¢0 00 39 I31.NP 82(I)8T(I) . IF'(ABS(81(I)-82(I)).LT{1.0E-20) IBI‘IBI‘1 CONTINUE IF (IBI.EO.NP) GOTO 90 ICKI0 ITTER'ITTER+1 IF (IO.LT.2) GOTO 40 WRITE (05.1001) ITTER.C1 WRITE (05.1000) (J.T(J).J81.NP) ACCELERATION STEP ~SJI1.0 DO 45.II=1.11 DO 42 I-1,NR TII1-sch1+SJu(sch1-EIII11 P(I)-T(I) SJ-SJ-.1 CALL BOUNDS(T.IOUT) IF (IOUT.UT.11 COTO 45 IF (II.EO.111 ICKsI CONTINUE DO 47 I-1.NF BI(I)-BZ(I) COTO ~20 ' DO 91 I-1.NF T(I)-82(I) CONTINUE 169 EROGRAM 111 (CONT.) ‘DO 100 It1.NP 100 P(I)-T(I) COSTIC1 IF (IO.LE.0) RETURN WRITE (05.1004) L.C1 WRITE (05.1000) (J.P(J),J-1.NP) RETURN 1000 FORMAT (3(35x.17.5x.E13.61)) 1001 FORMAT (411X13HITERATION NO. .ISISX.SHCOST= . 1E15.6.2Ox. 10HPARAHETERS) 1OO2-FORMAT (10X3HNO..I4. 8X5HCOST-.EIS.6) 1003 FORMAT (IIXZBHSTEP SIZE FOR EACH FARAMETER ) 1004 FORMAT (1H113HANswERs AFTER .I3.2X.23HFUNCTIONAL 1 EVALUATIONs ll SXSHCOST-.E15.6.2Ox.1EHOFTIM 1AL pARAMETERs ) . 1005 FORMAT (1H135HINITIAL PARAMETERS OUT OF BOUNDS ) ENO 170 PROGRAM III (CONT.) 0 0000000 0000 000000000 SUBROUTINE PULSE(P,COST) PERFORM AN ERROR ANALYSIS BETWEEN THE EXPERIMENTALLY OBSERVED LYSINE CONCENTRATIONS (SEXP) AND THE PREDICTED MODEL VALUE (5) AT VARIOUS TIMES. DIMENSION 81(100),SII(100),P(IOO),CI(10),CII(10) OPEN (65,FILE-’PULS.DAT.',STATUS-‘OLD') INITIALIZE VARIABLES Pm - P(l) Pa - P(2) VI - 120.0 VII - 0.844 81(1) - 1.0 SII(1) - 0.0 A - 7.75 VMAX - 7.44 * 0.61 EKm - 0.688 X - A * Pm Y - A * Pa COST - 0.0 CALCULATE LYSINE CONCENTRATION VS. TIME USING RUNGE-KUTTA-GILL METHOD FOR SOLVING EQUATIONS (6.17) AND (6.18). THE PERIOD OF THE PULSE IS FOUR MINUTES AND DELTA TIME IS TWENTY SECONDS. RUNGE-KUTTA SCHEME FOR HIGH FLOW RATE HALF CYCLE DO 5 N - 1,8 DO 10 1 - 1,8 DO 20 J - 1,6 31 - 2/6 01(1) - - x * (51(J) - 511(1)) - Y * 51(1) 011(1) - - 01(1) - ((VMAX * SII(J))/(EKm + SII(J)) FIA - 31(1) + 01(1) * 31/2 F11A - SII(J) + 011(1) *31/2 01(2) - - x * (FIA - F11A) - Y * FIA 011(2) - - 01(2) -((VMAX * FIIA)/(EKm + FIIA) w - (1/2) * * 0.5 F13 - 51(1) + 31* 01(1)* (w-o.5) + 31* CI(2)*(1-W) F113 -511(1)+ 31* 011(1)*(w-o.5) + 31* CII(2)*(1-W) 01(3) - - x * (F13 - F113) - Y * FIB 011(3) - - 01(3) -((VMAX * FIIB)/(EKm + F113) 171 PROGRAM III (CONT.) 0000 20 30 FIG - 81(1) - DT * 01(2) * w + DT * 61(3) * (1 + W) FIIC - 811(1) - DT * 011(2) * w + DT* CII(3)* (1+W) 01(4) - - X * (PIC - FIIC) - Y * FIC 611(4) - - CI(4) -((VMAX * FIIC)/(EKm + FIIC) ZI- (CI(1) + (2-(l/W))*C1(2)+(2+(1/W))*C1(3)+C1(4)) 211- ((2-(1/W))*CII(2) + (2+(1/W))*CII(3) + CII(4)) SI(J+1) - (S(J) + (UT/6) * ZI)/VI SII(J+1) - (SII(J) + (DT/6) * (211 + CII(1)))/VII CONTINUE 81(1) - SI(J+1) 811(1) - SII(J+1) RUNGE-KUTTA SCHEME FOR LOW FLOW RATE HALF CYCLE 30 30 K -1,6 31 - 2/6 01(1) - x * (SI(K) - SII(K)) + Y * 511(3) 011(1) - - 01(1) - ((VMAX * SII(K))/(EKm + SII(K)) 11A - 51(1) + 01(1) * 31/2 FIIA - 511(1) + 011(1) *31/2 01(2) - x * (11A - FIIA) + Y * FIIA 011(2) - - 01(2) -((VMAx * FIIA)/(EKm + FIIA) w - (1/2) * * 0.5 113 - 51(1) + 31* 01(1)* (w-O.5) + 31* CI(2)*(l-W) 1113- 511(1)+ 31* 011(1)*(w-O.5) + 31* CII(2)*(l-W) 01(3) - x * (F13 - 1113) + Y * 1113 011(3) - - 01(3) -((VMAX * FIIB)/(EKm + F113) F10 - 51(1) - 31 * 01(2) * w + 31 * 01(3) * (1 + u) F110 - 511(1) - 31 * 011(2) * w + 31* 011(3)* (1+W) 01(4) - x * (110 - 1110) + Y * 1110 011(4) - - 01(4) -((VMAX * FIIC)/(EKm + 1110) 21- (01(1) + (2-(1/w))*01(2)+(2+(1/W))*01(3)+01(4)) 211- ((2-(1/W))*CII(2) + (2+(1/W))*CII(3) + 011(4)) SI(K+1) - (5(3) + (DT/6) * 21)/v1 SII(K+1) - (511(x) + (DT/6) * (211 + 011(1)))/v11 CONTINUE COMPARE THE CALCULATED AND EXPERIMENTAL LYSINE CONCENTRATIONS IN THE RESERVOIR. READ (65,*) SPUL COST - COST + ABS((SI(K+1) - SPUL)**2) 31(1) - SI(K+1) SII(1) - SII(K+1) CONTINUE CLOSE (65) RETURN END 172 PROGRAM IV C THIS FILE WAS USED TO GENERATE DATA TO GENERATE A C COMPUTER SIMULATION THAT LINKS REACTOR PERFORMANCE C WITH THE EFFECT OF LYSINE DEPRIVATION ON LEUKEMIC C BLOOD CELL POPULATION BALANCES. C C 0000 0000000000 DIMENSION SI(100),SII(100),P(100),CI(10),CII(10) DIMENSION CAY(IO),WBC(10),PRO(10),EXPS(10) OPEN (67,FILE-'COMP.DAT.',STATUS-'NEW') INITIALIZE VARIABLES Pm - 6.94E-3 Pa - 9.19E-2 VI - 120.0 VII - 0.844 81(1) - 1.0 SII(1) - 0.0 SA - 7.75 VMAX - 7.44 * 0.30 EKm - 0.688 X - SA * Pm Y - SA * Pa aP - 0.0183 b? - 1.479 CAY(I) - 3.25E-3 CAY(2) - 8.98E-5 WB - 50.0 E3 PR - 1758.0 EXPO - 24.0 T - 20.0/3600.0 CALCULATE LYSINE CONCENTRATION VS. TIME USING RUNGE-KUTTA-GILL METHOD FOR SOLVING EQUATIONS (6.17) AND (6.18). THE PERIOD OF THE PULSE IS FOUR MINUTES AND DELTA TIME IS TWENTY SECONDS. RUNGE-KUTTA SCHEME FOR HIGH FLOW RATE HALF CYCLE 30 5 N - 1 8 30 10 1 - 30 20 3 - 31 - 2/6 01(1) - - x * (51(3) - 511(3)) - Y * 51(3) 011(1) - - 01(1) - ((VMAX * SII(J))/(EKm + 511(3)) 11A - 51(3) + 01(1) * 31/2 FIIA - 511(3) + 011(1) *31/2 01(2) - - x * (11A - FIIA) - Y * FIA 173 PROGRAM IV (CONT.) 000000 0000 20 011(2) - - 01(2) -((VMAx * FIIA)/(EKm + FIIA) w - (1/2) * * 0.5 113 - 51(1) + 31* 01(1)* (w-o.5) + 31* CI(2)*(1-W) 1113- 511(1)+ 31* 011(1)*(w-o.5) + 31* CII(2)*(1-W) 01(3) - - x * (113 - 1113) - Y * 113 011(3) - - 01(3) -((VMAX * FIIB)/(EKm + F113) 110 - 51(1) - 31 * 01(2) * w + 31 * 01(3) * (1 + W) 1110 - 511(1) - 31 * 011(2) * w + 31* 011(3)* (1+W) 01(4) - - x * (110 - 1110) - Y * 110 011(4) - - 01(4) -((VMAX * FIIC)/(EKm + 1110) 21- (01(1) + (2-(l/W))*CI(2)+(2+(1/W))*CI(3)+CI(4)) 211- ((2-(1/W))*CII(2) + (2+(1/W))*CII(3) + 011(4)) 51(3+1) - (5(3) + (31/6) * 21)/v1 511(3+1) - (511(3) + (DT/6) * (211 + 011(1)))/v11 CALCULATE NEW VALUES FOR THE TOTAL NUMBER OF WHITE CELLS (WB) AND THE NUMBER OF PROLIFERATING CELLS (PR) B - PR/(WB - PR) CAY(3) - aP/(bP + SI(J+1) NB - WB * EXP(-CAY(3) * T) A - CAY(2)/(CAY(3) + CAY(1)) C - CAY(S) + CAY(I) Q - A + (B - A) * EXP(-C * T) PR - (WB * Q)/(1 + Q) CONTINUE SI(1) - SI(J+1) 811(1) - SII(J+1) RUNGE-KUTTA SCHEME FOR LOW FLOW RATE HALF CYCLE 30 30 x -1,6 31 - 2/6 01(1) - x * (51(x) - 511(x)) + Y * 511(3) 011(1) - - 01(1) - ((VMAX * SII(K))/(EKm + 511(1)) FIA - 51(1) + 01(1) * 31/2 FIIA - 511(1) + 011(1) *31/2 01(2) - x * (FIA - FIIA) + Y * FIIA 011(2) - - 01(2) -((VMAX * FIIA)/(EKm + FIIA) w - (1/2) * * 0.5 113 - 51(1) + 31* 01(1)* (w—o.5) + 31* CI(2)*(1-W) 1113- 511(1)+ 31* 011(1)*(w-o.5) + 31* CII(2)*(1-W) 01(3) - x * (113 - 1113) + Y * 1113 011(3) - - 01(3) -((VMAX * FIIB)/(EKm + 1113) 110 - 51(1) - 31 * 01(2) * w + 31 * 01(3) * (1 + W) 1110 - 511(1) - 31 * 011(2) * w + 31* 011(3)* (1+W) 01(4) - x * (110 - 1110) + Y * 1110 174 PROGRAM IV (CONT.) 0000000 30 011(4) - - 01(4) -((VMAX * FIIC)/(EKm + 1110) 21- (01(1) + (2-(1/w))*01(2)+(2+(1/w))*01(3)+01(4)) 211- ((2-(1/w))*011(2) + (2+(1/W))*CII(3) + 011(4)) SI(K+1) - (S(K) + (DT/6) * 21)/V1 SII(K+1).- (SII(K) + (31/6) * (211 + 011(1)))/v11 CALCULATE NEW VALUES FOR THE TOTAL NUMBER OF WHITE CELLS (WB) AND THE NUMBER OF PROLIFERATING CELLS (PR) B - PR/(WB - PR) CAY(3) - aP/(bP + SI(J+1) WB - WB * EXP(-CAY(3) * T) A - CAY(2)/(CAY(3) + CAY(1)) C - CAY(3) + CAY(I) Q - A + (B - A) * EXP(-C * T) PR - (WB * Q)/(1 + Q) CONTINUE EXPS(N) - (8 - N)/2 + EXPO WBC(N) - WB * EXP(-CAY(3) * EXPS(N)) A - CAY(2)/(CAY(3) + CAY(1)) C - CAY(3) + CAY(I) Q - A + (B - A) * EXP(-C * EXPS(N)) PRO(N) - (WB * Q)/(1 + Q) WRITE (67,*) N,WBC(N),PRO(N) S(l) - S(K+1) CONTINUE CLOSE (66) RETURN END LIST OF REFERENCES List of References .Abellq C.W., W.J. Stith, and D.S. Hodgins, Cancer Res., 32: 285 (1972). .Abell. C.W., D.S. Hodgins, and W.J. Stith, Cancer Res., 33: 2529 (1973. .Alberts, B., D. Bray, J.Lewis, M. Raff, K. Roberts, and J.D. Watson, WW , Chapter 12, Garland Publishing, Inc., New .‘York (1983). .Ambrus, C.M., S. Anthone, C. Horvath, K. Kalghatgi, A.S. Lele, G. Eapen, .J.L. Ambrus, A.J. Ryan, and P. Li, Ann. Intern. Med., 106: 531 (1987). .Annetts, M. Biochem. J., 30: 1807 (1936). Bierman, H.R., K.H. Kelley, and P.A. Centero, in Ihg_Lgukgm1g§, pg 301, JW’Rebuck, FH Bethel, and RW Monto eds, Academic Press (1947). Box, G.E.P., W.G. Hunter, and J.S. Hunter, in Egpggimgngggg, Chapter 10, Wiley and Sons, New York (1978). Breslau, B.R. and B.M. Kilcullen, in Enzymg_finginggzing, pgs. 179-190, Vol 3, E.K. Pye and H.H. Weetall, eds., Plenum Press, New York (1978). Broome, J.D., Nature, 191: 1114 (1961). Cairo, M.S., Am. J. Pediatr. HematoI./Oncol., 4(3): 335 (1982). Chambers, R.P., W. Cohen, and W.H. Baricos, Methods in Ehzymology XLIV: Immobilized Enzymes, 291 (1976). Chance, B. and D. Herbert, Biochem. J., 46: 402 (1950). Chang, T.M.S., Methods Enzymol., 44: 201 (1976). Chang. T M S . C D Shu. and J Grunwald in W 2W3: M d' A Crawfurd. D A Gibbs. and R W.E Watts, eds. , John Wiley and Sons, New York 1982. Cohn. EJ. and Edsall. J.T in W lgn§_§ng_nipglgg_lgn§, pgs. 410- 412, Reinhold Publishing Corporation, New York (1943). Colton, C.K., Smith, K.A., Merrill, E.W. and Farrell, P.C. J. Biomed. Mater. Res., 5: 459 (1971). Cooney. D.0... in BMW. 13 39. Vol 2. Marcel Dekker, Inc., New York (1976). Creasey, W.A., in Angigggplggtic and 1mmunoggppre51vg Aggnts 11, pg 670, A.S. Sartorelli and D.E. Johns eds., Springer-Verlag, New York (1975). Cremer, P., M. Lakomec, W. Beck, and G. Prindull, Eur. J. Pediatr., 147(1): 64 (1988). Davis, M.E. and L. Watson, Biotechnol. Bioeng., 27: 182 (1985). 175 176 Dimitrov, N.V., J. Hansz. M.A. Toth, and B. Bartolotta, Blood, 38: 638 (1971). Dimmock, C.K., R.J. Rogers, Y.S. Chung, A.R. McKenzie, and P.D. Waugh, Vet. Immunol. Immunopath., 11: 325 (1986). Edman, P., U. Nylen, and 1. Sjoholm, Methods Enzymol., 137: 491 (1988). Faguet, G.B., unpublished results, Medical College of Augusta, 1986. Farrell, P.C. and Babb, A.L. J. Biomed. Mater. Res., 7: 275(1973). Freese, E.G., J. Gerson, H. Taber, H.J. Rhaese, and E. Freese, Mutat. Res., 4: 517 (1967). Froment, G.F. and Bischoff, K.B. in Qhgm1g§1_Bg§g;g;_fingly§1§_§ng_ Design, pgs 178-355, John Wiley and Sons, New York (1979). Goodwin, T.W. and R.A. Morton, Biochem. J., 40: 628 (1946). Graf, T., Leukemia, 2: 127 (1988). Greaves, M.F., Leukemia, 2: 120 (1988). Greenberg, M.L., "Cellular Kinetics in the Leukemias," in Ihg_L§gkgng_ £211, Rubin, A.O. and S. Waxman, ed., CRC Press, Inc., (1979). Greenfield, R.S. and D. Wellner, Cancer Res., 37: 2523 (1977). Gross, L., Qnggg§n1§_ylxg§g§, Pergamon Press, NY, (1983). Grunwald, J., and T.M.S. Chang, Int. J. Art. Organs 4: 82 (1981). Hanefeld, F. and H. Riehm, Neuropediatrie, 11(1): 3 (1980). .Hardisty, R. M. and D.J.Weathera11,Blggg_§ng_1;§_91§91_g1§, Blackwell Scientific Publications, Oxford, (1974). Henderson, E.S. and T.A. Lister, Leukemia, 5th ed, T. Mackey, editor, W.B. Saunders Company, (1990). Holland, J.F. and T. Oknuma, Cancer Treat. Rep., 65(Suppl. 4): 123 (1981) Horowitz, B., B.K. Madras, A. Meister, L.J. 01d, E.A. Bovse, and E. Stockert, Science, 160: 533 (1968). Iyer, G.Y.N., J. Lab. Clin. Med., 54: 229 (1959). Kim, 8.8. and D.0. Cooney, Chem. Eng. Sci., 31: 289 (1976). Kim, I.H. and Chang, H.N. AIChE J., 1983, 29, 910 Kleinstreuer, C. and T. Poweigha, Advances in Biochemical Engineering/Biotechnology, 30: 91 (1984). 177 Knob, R.J., M.S. Thesis, Michigan State University, 1988. Kodama, K., H. Kusakabe, A. Kuninaka, H. Yoshino, H. Misono, and K. Soda, J. Biol. Chem., 255: 976 (1980). Kreis, W. and C. Hessian, cancer Res., 33: 1866 (1973). Kreis, W., Cancer Treatment Reports, 63: 1069 (1979). Kusakabe H., K. Kodama, A. Kuninaka, H. Yoshino, and K. Soda, Agric. Biol. Chem., 44: 387 (1980). Lewis, W. and S. Middleman, AIChE J., 20: 1012 (1974). Lowry, O.H., N.J. Rosebriogh, A.L. Farr, and R.J. Randall, J. Biol. Chem., 193: 265 (1951). Machida, H., H. Kusakabe, K. Kodama, Y. Midorikawa, A. Kuninaka, H. Misono, and K. Soda, Agric. Biol. Chem., 43: 337 (1979). Meschi, P., B. diNatale, G.F. Rondanini, C. Uderzo, M. Jankovic, G. Masera, and G. Chiumello, Harm. Res., 15(4): 237 (1981). Miller, J.M., L.D. Miller, C. Olsen, and K.G. Gillette, JNCI, 43: 1297 (1969). Moo-Young, M. and Kobayashi, T. Canadian J. Chem. Ehg., 50: 162 (1972). Nakatani, Y. and M. Fujioka, Eur. J; Biochem., 16: 180 (1970). Nakatani, Y., M. Fujioka, and K. Higashina, Anal. Biachem., 49: 225 (1972). Neuman, R.E. and T.A. McCoy, Science, 124: 124 (1956) Ogawa, H., and M. Fujioka, J. Biol. Chem., 220: 253 (1978). Ortega, J.A., M.E. Nesbit, and M.H. Donaldson, Cancer Res., 37: 535 (1977). Park, T.H., Kim, I.H. and Chang, H.N. Biotechnol. Bioeng., 27: 1185 (1985). Paulsen, J., Vet. Microbial., 1. 211 (1976). Polson, A. Biochem. J., 31: 1903 (1937). Popovic, M., P.S. Sarin, M. Robert-Guroff, Science, 219: 856 (1983). Powell, A., M.S. Thesis, Michigan State University, 1988. Regan, J.D., N. Vodopick, S. Takeda, W.H. Lee, and F.M. Faulcon, Science, 163: 1452 (1969). Reiken S.R., M.S. Thesis, Michigan State University, 1988. 178 Reiken, S.R., and D.M. Briedis, Biatechnal. Biaeng., 35: 260 (1990). Reiken, S.R., R.J. Knob, and D.M. Briedis, Enzyme Micrab. Technol., 12: 736 (1990). Reiken, S.R., and D.M. Briedis, Chem. Eng. Coum., 94: 1 (1990). Rosen, R. and R.J. Milholland, in AntigeopLgstig and 1mmugoguppgesive Agents 11, pg 85, A.S. Sartorelli and D.E. Johns eds., Springer-Verlag, New York (1975). Schiffer, L.M., H.L. Atkins, A.D. Chanana, E.P. Cronkite, M.L. Greenberg, H.A. Johnson, J.S. Robertson, and P.A. Stryckmans, Blood, 27: 831-843 (1966). Shu, C.D. and T.M.S. Chang, Int. J. Art. Organs 3(5): 287 (1980). Solbach, W., Blood, 64: 1022 (1984). Steel. K.G.D. and J.H. Torrie. W A_B12mggrig§1_522;g§gh, 2nd ed., Mcgraw-Hill Book Co., New York (1980). Stryer, L. in Biochemigggy, pgs 110-114, 2nd ed., W.H. Freeman and Company, New York (1981). Sugimura, T., S.M. Birnbaum, M. Winitz, and J.P. Greenstein, Arch. Biochem. Biophys., 81: 439-447 (1959). Suneya, M., M. Onuma, S. Yamamoto, K. Hamada, S. Watari, T. Mikami, and H. Izawa, J. Comp. Path., 94: 301 (1984). Thomas, E.D., R.B. Epstein, J.W. Eschbach, D. Prager, C.D. Buckner, and G.Marsaglia, New Eng. J. Med., 273: 6 (1965). Tivey, H., Acad. Sci, 60: 322 (1954) Wahn, V., U. Fabry, D. Korholz, D. Reinhardt, H. Jurgens, and U. Gobel, Pediatr. Pharmacal., 3(3-4): 303 (1983). Waterland, L.R., S. Michaels, and C.R Robertson, AIChE J., 20: 50 (1974). Waterland, L.R., C.R Robertson, and S. Michaels, Chem. Eng. COmmun., 2: 37 (1975). Webster, I.A. and M.L. Shuler, Biotechnol. Bioeng., 20: 1541 (1978). Webster, I.A., M.L. Shuler, and P.R. Rony, Biatechnal. Biaeng., 21: 447 (1979). Webster, I.A. and M.L. Shuler, Biatechnal. Biaeng., 23: 447 (1981). MIcHICAN STATE UNIV. LIBRARIES WWIIWIWIWIUIWll”lll‘INWIMIWII||| 31293010550766