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thesis entitled

Application of an automated stopped-

flow system in clinical analysis

presented by

Wai Tak Law

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PhD Chemistry

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APPLICATION OF AN AUTOMATED STOPPED-FLOW SYSTEM
IN CLINICAL ANALYSIS

By

Wai Tak Law

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1978

ABSTRACT

APPLICATION OF AN AUTOMATED STOPPED-FLOW SYSTEM
IN CLINICAL ANALYSIS

By

Wai Tak Law

Stopped-flow mixing with speetrophotometrie detec-
tion has several desirable features that makes it a suit-
able technique for fast clinical analysis. Mixing times
are as low as a few ms, which enables analysis to be done
in very short times by fast reaction-rate methods. A
typical application is the reaction-rate determination of
serum total protein by the biuret method. With the
stopped-flow method reported here, the analysis time was
10 s for each sample, which is a lOO-fold decrease when
compared with the normal equilibrium method. Preliminary
kinetics studies of the biuret reaction were performed
with a vidicon detector and the results provide a starting
point for future mechanistic investigations.

The short mixing time of stopped-flow systems is also
advantageous for equilibrium-based applications. Serum
albumin reacts very rapidly with bromcresol green. By
taking the equilibrium measurements early (2-6 s after

mixing), interferences from other slower reacting components

Wai Tak Law

are greatly reduced. 0

The automated stopped-flow system was also adapted
for serum lipid analysis. Highly specific enzymatic
methods of analysis for serum triglyceride and cholesterol
were used, and the results obtained compared to other
standard methods. Serum lipoprotein analyses were also
performed. The complete serum lipid profile, including
the increasingly popular serum high density lipoprotein
(HDL) analysis, can be completed in about half an hour.
Again the analysis time is reduced, in this case by at

least lO-fold,in comparison to other prevalent methods.

ACKNOWLEDGMENT

"And we know that all things work together
for good to them that love God . . . . ."

Romans 8:26.

As one goes through the disciplinary process of formal
education, it is sometimes hard to remain convinced of this.
These last five years have not been altogether smooth sail-
ing. The days spent grinding out problem sets, the nights
lost debugging programs, the hours spent brooding over me-
chanical problems and experimental failures, not to mention
all the despair, expasparation and frustration that accom-
pany these. But through it all, this particular knowledge
has been my mainstay, bouying me up between those scattered
moments of eurekas, making it possible for me to culminate
my schooling in this volume.

Through all this, I am most thankful to my advisor,

Dr. Stanley R. Crouch for his guidance. His willingness

to give me the freedom to do what I want, but offering help
when needed, built my confidence and independence in doing
research. His sincere concern for my career and the pat—
ience he showed me during the writing of this thesis are
deeply appreciated.

I would also like to thank the other members of my
Ph.D. Committee: Dr. J. L. Dye, who served as my second

11

reader, Dr. J. Holland and Dr. A. Timnick, for their com-
bined effort in seeing me through this project. I am also
most obliged to Dr. Hans Lillevik for introducing me to the
fascinating field of clinical chemistry.

Then I wish to thank Dr. Roy Gall, who has been an
excellent research partner all these years; always there
to help when the stopped-flow system failed, and providing
supportive comradeship when all else fails.

Next I would like to acknowledge Michigan State Uni-
versity and NSF for their financial support, Mr. Wai Kin
Law and Ms. Elite Wong in preparing the manuscript, and
Mrs. Peri-Anne Warstler for typing the final copy.

Then, my most grateful thanks go to my parents; not
only for their unswerving emotional and financial support,
but most of all for all the years of their lives poured
into mine, helping me become me.

I also want to thank my brothers and sisters of the
MSU Chinese Christian Fellowship for all their prayers
and concern. And finally, I thank God, my Heavenly Father,
for being my help and stay, and for reminding me time and
again that all things do work together for good to them
that love Him . . .

111

TABLE OF CONTENTS

Chapter Page

LIST OF TABLES. . . . . . . . . . . . . . . . . . .vii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . x
I. INTRODUCTION. . . . . . . . . . . . . . . . . . 1
II. BACKGROUND . . . . . . . . . . . . . . . . . . A

A. Clinical Analysis and
Instrumentation . . . . . . . . . . . . . . A

1. Common Clinical Tests . . . . . . . . . 5
2. Automated Systems . . . . . . . . . . . 7

B. The Discrete Stopped-flow System
and Kinetic Methods . . . . . . . . . . . . 12

l. The Automated Stopped-Flow
system. 0 O O O O O O 0 O O O O O O O O 15

2. Reaction-Rate Method of
Analysis. . . . . . . k . . . . . . . . 17

3. Differential Reaction-
rate Methods. . . . . . . . . . . . . . 2A

C. Application of the Stopped-Flow System
in Clinical Analysis. . . . . . . . . . . . 29

1. Experimental Criteria and
PPOblemS. o o o I o o o o o o o o o o o 29

2. Analyses Reported . . . . . . . . . . . 32
III. SERUM PROTEIN ANALYSIS. . . . . . . . . . . . 35
A. Introduction. . . . . . . . . . . . . . . . 35

l. The Biuret Reaction . . . . . . . . . . 36

2. Preliminary Observations. . . . . . . . 39

3. Protein Analysis Using Re-
action-Rate Method. . . . . . . . . . . A2

B. Stopped-flow Method . . . . . . . . . . . . A2

iv

Chapter Page

1. Reagents and Sample
Preparation . . . . . . . . . . . . . .A2

2. Automated Stopped-flow
System. . . . . . . . . . . . . . . . A3

3. Initial Rate Studies. . . . . . . . . AA

A. Experiments with Human
Control Lyophilized Sera. . . . . . . A8

5. Comparison with the Equilibrium
MGLhOd. o o o o o o o o o o o o o o o 52

6. Choice of Protein Standards . . . . . 5A
7. Studies with a Vidicon Detector . . . 63

Co COHClUSiODS o o o o o o o o o o o o o o o 75
IV. SERUM ALBUMIN ANALYSIS . . . . . . . . . . . 77
A. Introduction. 0 o o o o o o o o o o c O o 77

l. Bromcresol Green Dye-
binding Method. . . . . . . . . . . . 78

2. Proposed Solutions. . . . . . . . . . 79
B. StOpped-flow Method . . . . . . . . . . . 80

1. Reagent and Sample Preparation. . . . 80
2. Rate Studies I O O C O C O C C O O O O 81

3. Experiments with Human Control
Lyophilized Sera. . . . . . . . . . . 83

C. Conclusions . . . . . . . . . . . . . . . 89
V. SERUM TRIGLYCERIDE ANALYSIS . . . . . . . . . 91
A. Methods of Analysis . . . . . . . . . . . 91
B. Stopped-flow Method . . . . . . . . . . . 95

l. Reagent Preparations. . . . ... . . . 96
2. Rate Studies 0 O O O O O O O O O O O O 96
3. Experiments with Human Serum. . . . . 101

C. Conclusions . . . . . . . . . . . . . . . 103

Chapter

Page

VI. SERUM CHOLESTEROL ANALYSIS . . . . . . . . . 10A

A. Introduction. . . . . . . . . . . . . . . 10A

B. The Stopped-flow Method . . . . . . . . . 107

1.
2.

Reagent Preparation . . . . . . . . . 107
Rate Studies. . . . . . . . . . . . . 109

C. Conclusions . . . . . . . . . . . . . . . 116

VII. SERUM LIPOPROTEIN ANALYSIS. . . . . . . . . 119

A. Introduction. . . . . . . . . . . . . . . 119

1.

2.

Lipoprotein Profile and
Hyperlipoproteinemia. . . . . . . . . 119

Methods of Analysis . . . . . . . . . 122

Be StOppEd-flow MGthOd o o o o o o o o o o o 123

l.
2.
3.

A.

5.

General Scheme. . . . . . . . . . . . 123

Choice of Precipitation Agent . . . . 126

Separation of the Lipoprotein
Fractions . . . . . . . . . . . . . . 129

The Ultrafiltration
MethOdOOOOOOOOOOOOIOOOOOOOOOOOO O I .132

Experiment with Fresh Human
Serum . . . . . . . . . . . . . . . . 136

C. Conclusions . . . . . . . . . . . . . . . 1A0

VIII. FUTURE DIRECTIONS. . . . . . . . . . . . . 1A3

APPENDIX A.
APPENDIX B.
APPENDIX C.
REFERENCES.

. . . . . . . . . . . . . . . . . . 1A7
. . . . . . . . . . . . . . . . . . . 176
. . . . . . . . . . . . . . . . . . 193
. . . . . . . . . . . . . . . . . . . 195

vi

Table

2-1

2-A

3-1

3-2

3-3

3-5

3-6

3-7

LIST OF TABLES

Routinely Performed Clinical Tests.

Popular Models of Discrete
Chemical Analyzers. . . . . . . .
Important Properties of the
Stopped-Flow System . . . . . . .
Clinical Applications of the
Stopped-flow System . . . . . . .
Methods for the Determination

of Total Serum Protein. . . . . .
Results for Total Serum Protein
Standards (At - 0.1 s). . . . . .
Results for Total Serum Protein
Standards (At - 10 s) . . . . . .
Results of Determination of Total
Human Serum Protein . . . . . .
Comparison of the Reaction Rate
Method with the Equilibrium
Method. . . . . . . . . . . . . .
Comparison of Rates of Reaction
of Albumin from Different Sources
Biuret Reaction with Different

Albumin Compositions. . . . . . .

vii

Page

13

18

33

37

A9

51

53

56

69

61

Table Page

3-8 Biuret Reaction with Albumin
from Different Sources. . . . . . . . . . 62
A-l Determination of Human Serum

Albumin . . . . . . . . . . . . . . . . . 87
A-2 Serum Albumin Determination with

Different Methods . . . . . . . . . . . . 88
5—1 Determination of Serum Tri-

glyceride . . . . . . . . . . . . . . . . 100
5-2 Serum Triglyceride Determina-

tion with Different Methods . . . . . . . 102

6-1 Cholesterol by Reaction-rate
MGthOd. o o o o o o o o o o o o o o o o o 113
6-2 Cholesterol by Equilibrium

MGthOd. o a o o o o o o o o o o o o o o o 115

7-1 Physical Properties of Serum
Lipoproteins. . . . . . . . . . . . . . . 131
7-2 Comparison of the Centrifugation

Method with the Ultrafiltration

MethOdo o o o o o o o o o c o o o o o o o 135

7-3 Lipid Analysis on Three Human
Sera. . . . . . . . . . . . . . . . . . . 138
7-A Lipoprotein Analysis on 3 Human

Sera. . . . . . . . . . . . . . . . . . . 139

A-l Basic Moves of a Simplex. . . . . . . . . 151

viii

Table

Page

Regression Analysis with the

Simplex Method. . . . . . . . . . . . . . 165
Weighing by Variable Data

Acquisition Rates . . . . . . . . . . . . 172
Effect of Length of Sampling

Time on Error . . . . . . . . . . . . . . 17A

ix

Figure

2-1

3-1:

3-5

3-6

3-7

LIST OF FIGURES

The automated stopped—flow system . . . .
Classification of reaction-rate

method. . . . . . . . . . . . . . . . . .
The biuret reaction . . . . . . . . . . .
Preliminary observations of the

biuret reaction .

Initial rate studies of the biuret
reaction. (a) At = 1008; (b) At = 103. .
Standard curves for two reaction

rate methods used in the biuret

reaction. . . . . . . . . . . . . . . .
Standard curve for serum protein,

At = 108. . . . . . . . . . . . . .
Standard curve for serum protein

using the equilibrium method. . . . . . .
Comparison of rate of reaction between
BSA and human serum protein . . . . . . .
Time scan of the absorption spectra
during the human protein-biuret re-
action. . . . . . . . . . . . .'. . . .
Apparent wavelength shift of the

biuret reaction . . . . . . . . . . . .

Page

16

22
38

A1

A5

147

50

55

57

6A

65

Figure Page

3—10 Absorbance versus time for the

biuret reaction with human serum.

(a) 752 nm; (b) 829 nm. . . . . . . . . . 67
2-11 Absorption spectrum of the copper-

protein complex from the biuret

reaction with human serum after

about 25 minutes. . . . . . . . . . . . . 68
3-12 Absorption spectrum of the biuret

reagent . . . . . . . . . . . . . . . . . 69
3-13 Rate studies of the biuret

reaction. . . . . . . . . . . . . . . . . 70
3-1A Time scan of the bovine albumin-

biuret reaction with a vidicon

detector. . . . . . . . . . . . . . . . . 72
3-15 Time scan of the bovine globulin-

biuret reaction with a vidicon

detector. . . . . . . . . . . . . . . . . 73
3-16 Absorption spectrum of the copper-

protein complex from the biuret re-

action with bovine serum albumin

after about 25 minutes. . . . . . . . . . 7A
A-l Reaction of BCG with pure bovine

albumin . . . . . . . . . . . . . . . . . 82
A-2 Reaction of BCG with serum

albumin . . . . . . . . . . . . . . . . . 8A

xi

Figure Page

A-3 Reaction of BCG with serum

albumin of abnormally high

concentration . . . . . . . . . .'. . . . 85
5-1 Enzymatic reaction of serum

triglyceride. . . . . . . . . . . . . . . 97
5-2 Standard curve for enzymatic

analysis of serum triglycerides . . . . . 99
6-1 Enzymatic reaction of serum

cholesterol . . . . . . . . . . . . . . . 105
6-2 Enzymatic cholesterol reaction,

At=lOOs . . . . . . . . . . . . . . . . . 110
6-3 Reaction rate of enzymatic

cholesterol vs time (serum

cholesterol). . . . . . . . . . . . . . . 111
6-A Reaction rate of enzymatic

cholesterol vs. time (pure

cholesterol dissolved in an

aqueous solvent). . . . . . . . . . . . . 111
6-5 Standard curve for enzymatic

cholesterol analysis. . . . . . . . . . . 11A
7-1 Characteristic lipoprotein

fractions and electrophoretic

patterns. . . . . . . . . . . . . . . . . 121
7-2 Proposed serum lipoprotein analysis

procedure . . . . . . . . . . . . . . . . 125

xii

Figure Page

7-3 The complete filtration assembly. . . . . 13A
7-A Electrophoretic pattern for serum

sample. . . . . . . . . . . . . . . . . . 1A1
A-1 Basic moves of a simplex. . . . . . . . . 150
A-2 Procedure for the modified

simplex . . . . .p. . . . . . . . . . . . 153
A-3 Procedure for the super-

modified simplex. . . . . . . . . . . . . 15A

A-A Safety factor in SMS. . . . . . . . . . . 160
A-5 Boundary violation in SMS . . . . . . . . 160
A-6 Effects of rate differences and

noise on error. . . . . . . . . . . . . . 167
A-7 Effect of initial simplex size

on efficiency . . . . . . . . . . . . . . 169

xiii

I. INTRODUCTION

With the advancement of instrumentation and fast
analytical methods, the clinical sciences are becoming
more and more chemically orientated. Massive screening
chemical tests are being performed for individual patients
nowadays, as evidenced by the popularity of the Techni-
con continuous flow analyzers that can do six, twelve,
or even more tests on each sample. Because of the constant
demand for higher throughput and 'stat' analysis, together
with the increasing use of enzymatic methods, reaction-
rate methods of analysis are becoming more important than
ever in clinical chemistry. It is not impossible that
in the near future enough tests may be performed on each
individual so that everyone would have his or her own
normal ranges and no longer would it be necessary to com-
pare test results with the population's average. The large
volume of tests performed will certainly require a much
faster throughput rate than the typical 120 samples/hour
rate of most current instruments.

The stopped-flow mixing system, although used pri-
marily as a research tool until now, has the potential
of being a very fast and versatile analyzer. It can mea-
sure reaction half-lives from milliseconds to hours. Re-
quired reagent volumes are as low as 100 pl, and the instru-
mentation is easily automated. The only problem that has

prevented wider applications of it in clinical chemistry

1

is the lack of research in examining the applications of
this fast mixing system.

In this thesis, the stopped-flow system was applied
to routine analyses. Chapter 2 is a general discussion
on some basic concepts about fast kinetics and the
characteristics of several types of automated clinical
chemistry analyzers. Then the automated stopped-flow
system is described.

Chapter 3 presents a reaction-rate analysis of the
protein biuret reaction that cuts analysis time by more
than 100-fold when compared to conventional methods.

Chapter A describes an equilibrium method that allows
serum albumin to be determined with bromcresol green
within 2 8. Most of the interfering reactions are also
reduced simultaneously through the use of the rapid
equilibrium method.

Then we move on to the important area of lipid
analysis. Triglyceride analysis is described in Chapter
5, and cholesterol analysis in Chapter 6. These lipid
analyses use slow enzymatic reactions so some means of
treating the problem of the long analysis times had to
be devised in order to utilize stopped-flow mixing ad-
vantageously. Furthermore, the problems of formulating
suitable aqueous standard solutions were also investi-

gated.

Chapter 7 concentrates on lipid profiling and
analyses of lipoproteins. The analysis of high density
lipoprotein has generated increasing interest recently,
and its significance as an indicator of coronary heart
disease has created a large demand for this test. The
technique of getting a total lipid profile using serum
triglyceride, cholesterol, and lipoprotein concentrations
was investigated. We are able to report a rapid proced-
ure that cuts the normal analysis time six to forty fold.

Finally, in Appendix A, we report an application
of the simplex technique in regression analysis and dif-
ferential rate analysis. Although we have not applied
the technique to actual clinical tests, it appears to
have great potential in differential analysis of complex
mixtures, especially those involving enzymes. A well
documented super-modified version of the simplex program
written in FORTRAN IV language is also included in this
section.

We conclude that the stopped-flow system has great
potential in the field of clinical chemistry. Additional
comments on the future trend of research in methodology

may be found in the last chapter.

II. BACKGROUND

The first part of this chapter describes the commonly
performed clinical tests and the most used clinical-
chemical instruments. Next, a summary of kinetic methods
of analysis is presented, followed by a brief descrip-
tion of the automated stopped-flow system used in this

research and its role in clinical chemistry.

A. Clinical Analysis and Instrumentation

 

The clinical field offers many exciting research
opportunities for the analytical chemist who enjoys
making meaningful measurements. While some may still
regard quantitative chemical measurements merely as
tools, many physicians and scientists are sharing with
the analytical chemist a deep concern for accuracy,
precision, and speed. Undoubtedly, the most recent trend
is the increasing use of automated instruments to replace
manual methods of analysis, and a wide variety of auto-
mated analyzers and methods have been reported. But,
the emphasis of this dissertation is on automated wet
chemistry only, and instrumental techniques such as
automated flame spectrometry and chromatography are not

discussed.

1. Common Clinical Tests

The number of different chemical tests performed in
a clinical laboratory has risen from fewer than thirty
in 1950 to more than one hundred in the past few years
(23). The twelve most popular models of chemical analyzers
provide 27 different routine tests that they can perform
(See Table 2-1). Many factors determine what tests are
to be performed routinely. First, they must serve as
indicators of diseases, preferably with a one-to-one
correspondence. For example, the use of the enzyme
glucose oxidase for serum glucose analysis is a good
test for diabetes mellitus. Second, the analysis time
(both total work time and technician time) must be as
short as possible. Tests such as serum Na+ and K+
using flame photometry require less than one minute and
thus are performed routinely as stat tests. Third,
the tests should be simple. Excellent reference methods
such as the KJeldahl test for protein nitrogen involve
complicated distillation and multiple-step reactions
and, therefore, most laboratories prefer the simpler,
but less precise blood urea nitrogen (BUN) test. Finally,
low cost, availability, and sample size requirements are
also important factors that govern the choice of routine
methods.

Recent research and development of new clinical

chemical methods make increasing use of enzymes, which

 

Routinely Performed Clinical Tests.

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are very specific, as they become more available. With
the development of multi-test systems such as the Techni-
con SMAC, more laboratories conduct screening programs

as these systems allow much information to be gathered
from a small sample. Simultaneously there is increased
concern for greater precision in routine testing on a
day-to-day basis and between laboratories (23). More-
over, there is a growing recognition for the need of
referee methods, which would establish the "true" consti-
tuents of serum more exactly than is possible with the
present routine daily production methods (23). It is hoped
this will help to shift the emphasis from a concern for
more economic service to one for improved quality in
terms of proper standardization procedures and develop-

ment of meaningful quantitative measurements.

2. Automated Systems

Commercially available automated systems for wet
chemical methods have developed along three major direc-
tions. They are continuous-flow systems, centrifugal

analyzer systems, and discrete-sample systems.

a. Continuous-flow Analyzers - L. T. Skeggs (10)
conceived the continuous-flow princip1e_in 1957 and
Technicon Instruments Corporation later introduced

the first «AutoAnalyzer. This system received wide

 

acceptance in the clinical chemistry laboratory, and the
newest model (SMAC) is computerized to do multiple tests
simultaneously on the same sample within a few minutes.

The AutoAnalyzer uses a peristaltic pump and tubing
of various sizes to carry fixed-volume proportions of
samples and reagents continuously through the system.
This eliminates the operations of pipetting, weighing
and measuring of reagents. Air bubbles in the stream
physically separate samples into segments to minimize
the carry-over from the previous samples and to reduce
the wash time. Glass tubing coiled in different lengths
allows heavier liquids to fall through the lighter ones
to produce uniform mixing. And,to avoid manual deprotein-
ization of the samples, the AutoAnalyzer dialyses them
through a semipermeable membrane.

The AutoAnalyzer has a modular design, which makes
general maintenance and any necessary modifications rela-
tively simple (7). The major component modules are the
sampler, the proportioning pump and manifold, the dialyzer,
the heating bath, the flow cells, and the colorimeter.
Newer modules include a computer and detectors such as
the flame photometer, fluorometer, and ion-selective
electrodes. To change from one chemical test to another,
different cartridges can be plugged in, thus expanding
the system to run a maximum of A0 different tests if

desired (7). Finer tubing, smaller flow cells, and

electronic debubbling help to reduce the wash volume
tremendously, so that a sample volume of only A50 ul
is now needed for a 20 test run (70).

Despite the wide adoption of the continuous-flow
method, it still has its drawbacks. For example, the
construction of the flow system makes it inconvenient
to run single chemical tests, and often the laboratories
would therefore do 12 or 20 different unnecessary tests
on each sample. Then, because the system uses single-
point or two-point fixed time reaction-rate methods to
determine enzyme activities, blanks and the shape of the
reaction curve have to be ignored, which could be a major
source of error for abnormal samples. The system is also
not suitable for studying very fast and very slow reac-
tions. Finally, the initial cost of the system is high

so that smaller laboratories often cannot afford it.

b. Centrifugal Analyzers - The concept of using
centrifugal force to transfer and mix liquids in a
centrifuge and do multiple sample analyses was introduced
by N. G. Anderson at Oak Ridge National Laboratories
(21,71). This system, which also has a modular design,
consists of an analyzer, a control module, a rotoloader
and a digital computer with all its accessories. The
analyzer houses the spinning rotor, a monochromator, and

a photosensor. The control module, as the name suggests,

10

controls the reaction time, and the mixing, washing and
drying processes, while the rotoloader automates sample
preparation and makes additions.

The rotor consists of an outer ring containing a
number of cuvets formed by compressing the inert spacer
between two plates of optically transparent material,
and a removable central transfer disc of Teflon contain-
ing three concentric rows of cavities. Acceleration of
the rotor causes any sample and reagent placed in the
inner cavities to move outward, first to the outermost
row of cavities and then into the cuvet. The transfer
mixes the sample with the reagents. To monitor the re-
action, one only needs to measure the transmittance
change of the mixture inside the cuvet. Each rotor
usually has 16 channels and the first one normally holds
the reagent blank. The computer gathers the data and
processes it immediately. As a final step, the rotor
automatically cleans itself after each run (21,8).

The three commercial instruments currently avail-
able in the United States are the GeMSAEC by Electro-
nucleonics Inc., the Rotochem by American Instrument Co.,
and the CentrifiChem by Union Carbide Co. (8,22).

The centrifugalanalyzer can perform most of the
commonly requested clinical chemistry tests, and is
especially suitable for determining enzyme activities,

because of its multi-point continuous monitoring approach,

11

its highly sensitive temperature control, and its precise
metering of sample and reagents. No reagent blank is
necessary because the mixing only takes three seconds,
and by extrapolation, one can use the sample as its own
blank.

Newly designed transfer discs, improved sequences
of rotation (23), and disposable rotors (8) have eliminated
the cumbersome process of sample preparation and many of
the carry-over problems. But again, the relatively high
cost of centrifugal analyzers has prevented many labora-

tories from purchasing one.

c. Discrete Analyzers - Many other instruments have
been built for clinical chemical analyses. Some can
perform as many tests as a SMAC system, some only do
enzymatic analyses, and others can only run one or two
specific tests. Yet, they all have one thing in common:
each processes the specimen separately, generally by
steps mimicking the conventional manual procedures.

For all their simplicity and lack of elegance. dis-
crete sample analyzers have their distinct advantages.
First, one does not have to worry about cross-over con-
tamination and, since each step in the procedure is in-
dependent, one can easily trace the source of any trouble.
Finally, these analyzers generally require lower volumes

of reagents and samples. But, as a trade-off, one must

12

put up with a much lower throughput rate and a greater
probability of breakdown, due to the mechanical complexity
of discrete analyzers. ‘

Since many such systems are available, it is impos-
sible to review each one of them here. But, Table 2-2
does give a brief summary description of the larger
systems. For more detailed descriptions, reference
to the books (7-9) and reviews (15-18) listed in the

bibliography should be made.

B. The Discrete Stopped-flow System and Kinetic Methods

Chance pioneered the development of the stopped-flow
system in 19A0 (2A). Since then many sophisticated
elaborations of this system have appeared. Some examples
of these are the computer-controlled systems developed
by Crouch, _e_t_ a_l_. (25), by Dye, _e_§ g. (27), and Pardue's
fully automated system (19A) that can even prepare solu-
tion automatically. A recent review by Crouch £2.21-
(29) compares many of the home-made and commercial systems
and describes them in detail.

The stopped-flow technique for rapid mixing of
chemical reagents was originally designed to allow the
study of fast reactions with half-lives as short as a few
milliseconds. It has not been until recently that
scientists have investigated its potential for other

kinds of analyses. There are several advantages that

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1A

make the stopped-flow method an attractive tool. First,
it is a highly versatile system, for not only can it
provide analytical data on reactions that occur in a
matter of a few milliseconds, but it is also suitable
for studying slow reactions. For example, by using kine-
tic measurements one can use it to study the initial
stage of reactions. ’By waiting for the reaction to
go to completion, one can also use it to make equilibrium
measurements. Therefore, unlike the continuous-flow
systems that have a limited range of reaction half-lives
the stopped-flow analyzer features rapid throughput of
information and the study of reactions over a wide range
of half-lives. Secondly, the system can be fully auto-
mated. Using minicomputers or microprocessors to control
the processes of solution preparation, data acquisition
and data manipulation speeds data throughput, improves
accuracy and increases precision. And finally, the small
sample volume required (a few microliters) makes it attrac-
tive for routine clinical measurements where sample size
is often severely limited.

This section describes briefly the stopped-flow system
in our laboratory and some fundamentals of kinetic

analysis.

15

l. The Automated Stopped-flow System

Beckwith (A) first built the pneumatic driven stopped-
flow system, and Notz (5) interfaced it with a PDP 8/e
minicomputer.

Figure 2-1 shows a diagram of the automated stopped-
flow system. This system can be operated both manually
and automatically.

Operation begins by turning on the delivery valve
(A), which connects the reagent and sample reservoirs to
the delivery syringes, while closing off the remainder
of the flow system. The syringes then draw in reagent
and sample solutions, and the delivery valve then turns
to connect the syringes to the mixing chamber and the
observation cell. Air pressure is applied to the drive
syringe piston, when the waste valve (B) opens and con-
nects the flow system to the stopping syringe. The
syringe drive piston rapidly strokes forward and forces
the solutions through the mixing chamber, observation cell,
and stopping syringe. The flow stops when the spring-
1oaded stopping syringe comes to rest against a mechani-
cal stop. At the same time, an optical interrupter sends
out a pulse which signals the end of flow and triggers
the computer to begin gathering data. When the measure-

ment is finished, the waste valve opens to the drain and

l6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 2-1. The Automated Stopped-Flow System.

17

the stopping syringe forces the old solution out the drain
port (A). The valves then reset and run the next sample.
Interactive FORTRAN programs are available to analyze the
data. Results are stored on magnetic media, or the
printer types out a copy of the results. Circulating
water acts as the system's thermostat, keeping the tempera-
ture of the observation cell slightly above that of the
drive syringes and the mixing chamber, so that it will
match the temperature of the solution after mixing (6).

The design of the mixer and the flow rate ensure
turbulent flow and efficient mixing. The rapid stopping
of the solution completes the mixing and provides back
pressure which prevents cavitation (5). Table 2-3
lists some other important information about the system.
The dead time of the system (5:1 ms) dictates the practical
limit on the fastest reaction which can be observed.
However, for most clinically important reactions, the dead

time imposes no serious problem.

2. Reaction-Rate Method of Analysis

With the advancement of electronics and instrumen-
tation, reaction-rate methods, previously difficult to
do experimentally, are now becoming routine. Several
books (36-38), review articles (39-A1), and papers (A2-AA)

on the theory and application of these methods have been

18

Table 2-3. Important Properties of the Stopped-Flow

 

 

System.

Dead Time 511 ms
Mixing Time N5 ms
Stopping Time 3’1 ms
Volume of Sampling Syringe 2.35 ml
Volume of Each Push

(6 pushes/fill) 0.39 ml
Volume from Mixer Entrance
to Exit of Observation Cell 0.16 ml
Pathlength of Cell 1.9A 0.01 cm

 

 

19

published.

The biggest advantage of the reaction-rate method
compared to equilibrium methods is its greatly reduced
experimental time. It is possible to measure the rate
of change of the concentration of reactants or products
immediately after mixing without waiting for the reaction
to go to equilibrium. Since the measurement can be com-
pleted before significant side reactions occur, and be-
cause only relative rate measurements are made, many of
the interfering factors are thus eliminated. Stopped-
flow analyses often employ reaction-rate methods. By
simply adjusting the experimental conditions, one can
obtain first or pseudo-first order reaction conditions.
For example, consider a simple reaction:

kA
A+R+P

where kA is the rate constant, A is the substrate, R the
reagent in excess, and P the product. The rate of dis-

appearance of A can be expressed as

d[A _
71% " 'kAEA] (1)

If Equation (1) is integrated from time t = 0 to time

t = t, we have

[A] = [AJOexp(-kAt) (2)

20

If Equation (2) is substituted into (1),

9§%J-= -kA[AlOexp(-kAt) (3)

when t = 0, exp(-kAt) = 1

therefore,

‘3?’ = -kA[A30 <“)

Equation (2) suggests that the initial concentration
of the reagent [AJO can be obtained by measuring the
concentration of A at any time t. [AJO can also be ob-
tained by measuring the rate of change of A at time t,
[Equation (3)]. But Equation (A) is the basis of the
most commonly used rate method. By measuring the reac-
tion rate at the very beginning so that the time is ap-
proximately equal to zero, the exponential term approaches
unity and thus the reaction becomes pseudo-zero order
in time. This is known as the initial rate method, and
requires that the measurement be made while the reaction
curve (the exponential concentration Xi- time curve)
is still linear. For 1% accuracy in the initial rate
measurement, the measurement should be completed before
the relative concentration changes by 5% for the fixed

time method (31), and by 2% for the variable time

21

method (32).

In the last few years, more clinical chemists have
been using rate methods mainly due to the extensive use
of enzymes (33). At the same time however, this wide-
spread use of rate methods has also brought about am-
biguity in the terminology. Pardue has suggested a
comprehensive classification which has helped to clarify
the terms somewhat (3A).

Equilibrium methods were defined as those methods
based upon reactions that go to completion, and rate
methods as those based on measurements made while the
reaction is approaching completion.

The commonly used direct response rate methods can
be classified as in Figure 2-2. The simplest is the
one-point method wherein the signal is measured at some
predetermined time after the reaction has been initiated.
This method does not provide any information on the blank
or the shape of the response curve. For the two-point
method, there are two different approaches. The fixed-
time approach measures the total signal change over a
predetermined fixed time interval, while the variable-
time approach measures the total time required for the
signal to change a predetermined amount and relates it
to the analyte concentration. The two-point method has
an advantage over the one-point method in that it com-

pensates for sample and reagent blank, but errors due to

 

 

22

 

 

 

 

fl

 

 

 

 

 

 

 

 

all

 

A

 

Figure 2-2.

"A

10

One-Point Method
Simple. no information
on blank or shape of
curve

Two-Point.Method
Fixed-time or variable-
time, simple, no
information on curve
shape

Maggi-point Method

A) Delta Method
Suitable for 5-10
data points

B) Regression Method
Suitable for large
number of data
points

Classification of reaction-rate method.

23

non-linearity of reaction curves caused by induction
periods or substrate depletion still occur.

When three or more data points are collected either
in the fixed-time or the variable-time modes, it is de-
fined as the multiple-point method. At least two dif-
ferent approaches within this class can be identified.
The "delta method" takes multiple absorbance data at
fixed time intervals and computes values of A called
"deltas". Delta values of the same magnitude are used
to compute the substrate concentration. In the "regres-
sion method", one collects many data points and then uses
a mathematical algorithm, such as the linear least-squares
method, to obtain the slopes from the linear region.
An advantage of the regression method is its applicability
to both linear and nonlinear responses. The first and
second derivatives of A gs. t help to locate the linear
region of the response curve, and overlapping groups of
data will give many values of the slopes for averaging.
It appears that with the help of computerized data acquisi-
tion and analysis, the collection of large amounts of data
is no longer a laborious task, and the regression multiple-
point method, properly implemented with statistical analysis,
is the preferred method.

Reaction-rate methods can be very rapid and show a
high degree of freedom from interferences, which are im-

portant advantages in clinical analysis. The method is

2A

also more specific than the equilibrium method so that
separation steps can often be avoided. Differential
analysis of complex mixtures can also be performed by
taking advantage of the different reaction rates of two
or more reactants with a common reagent (A9-52).

But there are some rather complex problems in using
reaction-rate methods. Rate methods usually require
carefully controlled experimental conditions, such as
temperature, pH, ionic strength, size and shape of the
reaction vessels, etc. Minor changes in these condi-
tions can change the reaction rate and thus the result.
The half-life of the reaction must be greater than the
mixing time of the instrument, and the precision also
decreases with shorter observation time (A2). 0n the
other hand, reactions with half-lives longer than a few
hours are also not practical for routine analysis. For
selected procedure, however, the overall advantages of

rate methods can outweigh the disadvantages.

3. Differential Reaction-rate Methods

Rarely does one find the sample for analysis in pure
form, devoid of any other substances that might interfere
in the determination of the sought after substance. So
one must find some means to eliminate the interferences.

Separation of the target sample component from interfering

25

substances is often too time consuming, or even impracti-
cal. In some cases, by judiciously selecting the experi-
mental conditions, one can alter the reaction rates of
different components within the sample so that they are
sufficiently different from each other to allow one or
more of the closely related components in the mixture to
be analysed without prior separation (AS-A8).

Mark §t_a1. discussed the various methods for
analysing mixtures whose reactants have large rate
differences (A5), and Papa (36) and Mottola (A0) have
evaluated the more commonly employed methods.

In clinical analyses, we are mostly interested in
first and pseudo-first order reactions with respect to
total reactant concentration, or enzymatic activities.
Several differential rate methods exist for the study of
these reactions. The graphical extrapolation method (52)
and the method of Roberts and Regan (5A) are very useful,
but the method of proportional equation is of particular
interest here (53). Generally this method requires less
time than the other approaches, while it does not require
prior knowledge of the total initial concentration of
reactants. Most important of all, it is a mathematical
method which is therefore easily adaptable for automa-
tion (A0).

This method is based on the principle of constant
fractional life, which is applicable to most simple first

26

and pseudo-first order reactions. When a substance

reacts with constant fractional life, its initial con-
centration is directly proportional to that of the product
at any given time. Consider the following first or pseudo-

first order reaction:

A + R -+ P (5)

The concentration of the product at any given time t is

[PJt = kA(l — e‘kAt)[A]O (6)
or
[Plt = GAEAJO (7)
where
GA = kA(1 - e'kAt) (8)

The proportionality constant GA is dependent on the
rate constant kA and the time t. As long as the factors
that affect kA (such as temperature, pH, and ionic
strength) do not change and the time t is fixed, GA

remains constant. In Equation (7), the concentration of

the product at any given time is therefore proportional

27

to the initial concentration of A. Very often an elec-
trical signal St is observed instead of Pt' This signal
is proportional to Pt by a factor n, and Equation (7)

becomes

m
l

or

St = KAEAJO (10)

and KA becomes the new proportionality constant. If
there is a binary mixture (A + B) and the two different
components react by first order kinetics to give the same
product P, the concentration of the product at any time

tl can be given by

[Pjtl = GAlEAJO + GB1EBJO (11)

where GB is the proportionality constant for substance

B. At a different time t2,

[P3t2 = GA2EAJO I GsafBjo (12)

Thus, to determine the proportionality constants GAl

and GBl experimentally, one can measure the concentration

28

of the product at time t1 for known amounts of pure A
and pure B under the same experimental conditions as

that of the mixture.

[Pltl = GAllAlo (13>

[P]t1 = GB1EBJO (1“)

To find GA2 and GB2’ keep the experimental conditions
constant and change the observation time to t2. Substi-
tution of the four constants back into Equation(ll)znui
(12)will allow the concentrations [A10 and [B]O to be
obtained on an unknown sample.

The method is applicable to mixtures that contain
more than two substances (38).

With the help of a computerized on-line system, 100
or more data points can be obtained during the course
of reaction. One can set up 100 or more proportional
equations and solve for the unknown concentrations [A30
and [B]O. Appendix A of this thesis describes the use of
multiple proportional equations in some first and pseudo-

first order reactions found in clinical analyses.

29

C. Application of the Stopped-flow System in Clinical

Analysis

Traditionally, only the few scientists who study the
kinetics of rapid reactions use stopped-flow mixing
systems. It was not until 1969 that Pausch and Margerum
(A9), and Javier _p‘_1. (6A), first reported its use for
analytical purposes. And it was only after Pardue gp'gl.
had evaluated their discrete sampler stopped-flow mixer
system in 1977 (1) that its use in clinical analysis ap-
peared in a clinical journal. Two reasons account for
this. First, instrument companies have been slow to
realize the potential of this system as an analytical
instrument. Therefore, very few commercial instruments
are available. Also, the stopped-flow systems that are
on the market are so inconvenient to use, they are in
no way comparable to the "home-made" versions. Second,
not enough clinical methods have been developed for
recognition of the advantages of such a system and hence

its adoption as a routine analytical tool.

1. Experimental Criteria and Problems

An ideal clinical chemistry analyzer should be in-
expensive, simple to operate, have a high sample through-
put rate, and if possible, be portable. It should be

easily automated, with no carry-over problem. It should

30

give precise and accurate results, and be capable of

doing a wide variety of tests. The sample volume for
analysis should be as small as possible, and finally,
the reagents inexpensive.

The advantages of the stopped-flow system in monitor-
ing fast reactions, as discussed earlier, include high
throughput rate, high precision and accuracy, easy auto-
mation, good mixing and a large reaction time range.

In addition, it is also suitable for equilibrium (end-
point) analyses. In fact, Pardue 33 a1. (1) have just
reported that attaching a sample loop to the system faci-
litates further measurements for equilibrium methods.

Most of the instruments currently used for kinetic
analyses in clinical laboratories are designed for
relatively slow reactions, usually requiring anywhere
from a few seconds to a few minutes for a complete measure-
ment. Thus they may not be adequate for such tasks as
the.LHD isoenzymes determination by Everse _p{_1. (59),
or the biuret protein reaction which is reported later.
For the former, the first set of measurements must be
taken within 0.2 s,while the measurement time for the
latter is about 0.1 s. Pardue has already suggested that
instruments with mixing and measurement capabilities that
require approximately 0.01 5 would be highly applicable
in clinical chemistry (1).

To further reduce the sample size when using stopped-

31

flow systems, one can use new cells and mixer designs,

or add zero dead-volume valves and fittings to the system.
And, to cut reagent costs drastically, especially those
needed for enzymatic reactions, one can employ reusable
immobilized enzyme reaction loops such as those developed
in our laboratory (2). The tremendous improvements in
detection systems in recent years allow measurements with
high sensitivity. Dual-channel and multichannel systems,
such as the rapid scanning monochromator and vidicon have
already been useful for fundamental studies of bio-
chemical systems (67). For turbid samples, other non-
optical detectors based on thermal or electrical prin-
ciples can be used (68,67).

Since no system is perfect, there still remain some
problems in using the stopped-flow instrument described
here. One of the major criticisms made of this system
is the lack of sample preparation and initial separation,
like that found in the autoanalyzer. But with the pos-
sibility of adapting one of the recently reported auto-
matic solution makers onto the stopped-flow analyzer,
one of the most time consuming steps in the process would
no longer be a problem (1,29).

A second problem with using this system is that of
carry-over, which exists because at present the observa-
tion cell is not disposable. This makes repeated rinsings

between samples necessary. It seems, however, that by

32

incorporating Pardue's proposed sample loops, this prob-
lem too can be eliminated (l).

A third disadvantage of this system is its inability
to perform multiple tests in parallel due to its dis-
crete mixing characteristics. One must remember, however,
that a stopped-flow system is not designed for this, but
is rather a 'stat' analyzer.

And finally, sample and reagent are mixed in a 1:1
ratio in the stopped-flow system. Therefore dilutions
must be made to obtain favorable experimental conditions.
However, in some cases excessive dilution causes undesir-
able problems, such as turbidity or slow reaction rate.

Despite the above limitations, the stopped-flow
system can be made applicable to many kinds of wet
chemical analyses done in clinical laboratories, and as
is shown throughout this dissertation, it has uniquely
advantageous features when compared with other existing

systems.

2. Analyses Reported

Applications of the stopped-flow system in clinical
analysis to date have been few, and they are all listed
in Table 2-A. Most of these involve a reaction-rate
method with adjustment of the experimental conditions
so that the reactions occur under pseudo-first-order

conditions. Enzymatic reactions are especially suitable

33

 

 

 

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Hm.om HocosaoocHHoconQOAOHnoHarm.m QHo< OHmmoom< .:
mm.~m moCOCHSUONcomuo on COHmpo>coo mzHH<zmma< .m
mw oumnomonoleconaoppHclm mH< .m
mm ommnmmHoschHpoMHoSH szopHm meg .H
.mom meoEEoo COHuomom\mpcowwom HmOHEono mumppmnsm

 

 

.Eopmmm SOHMIUooQOpm on» no mCOHmeHHoQ« HooHcHHo

.zlm mHQMB

3A

for this system, because of the kinetic measurements
required. ‘The differential technique used to determine
isoenzymes is unique, and seems to be an interesting one
to apply in the investigation of other isoenzyme systems
(3,59). 80 little has been done in exploiting the stopped-
flow system for routine clinical tests, that the inherent
advantages of the system have not been exploited. But,
with increased use, these will gradually emerge to make
their contribution to the clinical sciences. The major
portion of this research deals with exploiting the po-
tential advantages of stopped-flow mixing for important

clinical analyses.

III. SERUM PROTEIN ANALYSIS

A. Introduction

One of the most often employed yet valuable clinical
tests is the determination of total blood serum protein.
The total protein and the ratio of individual protein
fractions of a patient may change independently of each
other, due to any one of three causes: impaired protein
synthesis, pathological loss or diminished intake of
fluid, or an absolute increase in protein content (8).
Consequently, the analysis of a patient's serum for
total protein is done routinely, and the results are
used to decide if any additional subfraction protein
analysis is necessary. This chapter describes a kinetic
biuret determination of total serum protein using the
stopped-flow mixing system, which has the advantages of
extremely short measurement times as well as small sample
volume requirements. Because the stopped-flow system can
obtain data almost instantaneously after mixing, a sig-
nificant improvement in precision over other methods is
obtained using the fixed-time rate method because of the

speed of the biuret reaction.

35

36

l. The Biuret Reaction

As Table 3-1 shows, there are many methods available
for the determination of serum protein. The physical
methods based on UV absorption or refractive index are
simple and non-destructive, but lack accuracy (8). The
Kjeldahl method has high precision and accuracy, but the
slow digestion and distillation processes involved make
it unsuitable for routine analysis of large numbers of
samples (8,76). Sensitive methods such as the Folin and
Ciocalteu method are either unnecessarily complex or are
based on estimation of a side chain such as tyrosine,
which may yield serious errors when the composition of
a serum sample is abnormal (77-79). In view of this, the

biuret method, which is not as sensitive as the Folin
and Ciocalteu method, is nevertheless sensitive enough
for serum protein analysis, and is least affected by
variations in protein compositions. Thus, it is the most
widely used method in clinical laboratories for protein
determinations.

All proteins contain a large number of peptide bonds.

2+

When a protein solution is treated with Cu ions in an

alkaline medium, a purple colored complex of unknown com-

2+

position is formed between the Cu ion, the carbonyl

and the imine group of the peptide bonds. An analogous

2+

reaction takes place between the Cu ions in alkaline

medium and the organic compound biuret (See Figure 3-1),

37

 

 

 

 

H cho whom UHQLSp mCOHpSHom
Icon .oopcoEmHolco: ousHHU CH opsHom mo .ocoo exp on
you oHnmuHSm .mommdoow HmCOprooopo szoopHo unsoEm cm xoocH
:H pouHeHH pan oHowm mp mommopocH xoch o>Hpommmom o>Hpompmom .m
H OHQEmm mo o>Hp E: 0mm pm mnpom
tongumoolcoc .momLSOom Inm ochopzu mo mwch oHmeopo
5 oofiefl use Boom .ea mam to moaoaoo meson ooaoooa 53383 >2 .m
m maowmsn
oEom an mopomaoch
.o.m can» oaaaooam
whoa AHo\Ew H.0Imo.ov
.pogdHn corp o>HuHmcom ucowmmp .o.m on» 29H;
opoe moEHp OOHuom pcommon poasHp map ocHnEoo mazoq .o .m .2
Hommav
m HmEpocnm mH Espom mH moonoEoo oSHp o>Hw ou COHpsHom
tonne .OHmHooam ocHmeHm :H opmoanoEOpmeSp
pom Ho\we m.HIm.o locomono anz cHopopo Eamon on» sopHMoOHo
mpH>HpHmcom @000 no wosopw Hocond map mo COHpowom ICHHom .m
Aozm<v moonQEoo man
m Ho\em m. concouo on wCOH +mso ocHmeHw ssz
um.o mpH>HpHmcom 30A meson ooHpooo :Hopono mo COHpomom poLSHm .m
w cospoe ppmocmpm wHoEwm mo
can no choEEoo pom: pcopcoo cowoppHc HopOp monummoz HnmoHonx .H
.mom pamesoo COHpomom compo:

 

 

.cHopopm

Esaom Hmpoe no COHpmcHEmmpoQ on» non moonpoz .Hlm oHnme

38

 

7"7
A? :9

HzN-EC-Nflg-C-NHZ + eu'H” alkali”, Cu-Biuret Complex
I
u--4
Bi ret

U Blue Amax(5AO nm)

r"l?

HZW'? :9-0H ++ alkaline

Rl-CAC-NHPC-H + Cu -——————%~Cu-Biuret Complex
L____:R2 Blue/Amax(5A0 nm)
Protein

Figure 3-1. The biuret reaction.

39

which gives the reaction its name. The biuret reaction
only takes place between the cupric ion and compounds
which have at least two NH2CO- groups, two NH2CH2-
groups, or two NHZCS- groups. These groups must be
directly joined to another similar group, or joined via
a carbon or nitrogen atom. Therefore any dipeptides or
amino acids present in the serum will not react and will
not interfere with the protein analysis. The actual
mechanism of the reaction is not known, but it is hypo-

2+ ion is coordinated to four to six

thesized that each Cu
nearby peptide linkages (8,72,85). The intensity of the
color produced is proportional to the number of peptide
bonds present, which is in turn proportional to the concen-

tration of the protein.

2. Preliminary Observations

The biuret method introduced by Kingsley in 1939 (72)
is well known, and many modifications of the method have
been published (73-75). In fact, quite often it is
taught to students in clinical biochemistry courses.

The standard procedure involves mixing blood serum
or a protein standard solution with the biuret reagents.
The color is allowed to develop for 30 minutes, and the
absorbance at equilibrium is then measured not later
than 60 minutes after mixing. No data points are taken

during the 30 minutes waiting period. Because of the

no

long waiting period in the usual equilibrium biuret
procedure, a preliminary investigation of the kinetics

of the reaction was undertaken in order to determine if

a reaction-rate method might be applicable. The standard
biuret procedure was repeated, with absorbance values
taken as a function of time during the 30 minute period
before equilibrium. Typical absorbance-time curves are
shown in Figure 3-2a. From this preliminary experiment
two important observations were made.

The first observation was that the reaction did not
follow first or pseudo-first order kinetics, so that the
log absorbance XE: time plot was a curve instead of a
straight line, as shown in Figure 3-2b. The second one
was even more interesting. Figure 3-2c shows that straight
lines were obtained when the absorbance of each standard
was divided by the first standard and plotted against
time. This suggests that one may obtain an analytical
curve long before the reaction reaches equilibrium.

Thus, the 30 minute wait may be eliminated by using a
reaction-rate method. Since the earliest time observable
using manual mixing and a conventional spectrophotometer
was 2 minutes, it was decided to study this reaction

further with a stopped-flow mixing system.

A1

4
.40—
.30—
3
g .20-
4

 

 

 

TlME(min)
(a)

01
O)
I

\
ABS RAND

 

LOG(ABS no -A)

9
l

\o

53

l

l?
l

 

 

l l l 1 4L_

 

5 '0 ngefigj 25 TIME(min)
(b) (C)

Figure 3-2. Preliminary observations of the biuret
reaction.

A2

3. Protein Analysis Using Reaction-Rate Method

A survey of the literature showed that Hatcher and
Anderson (83), then Koch, Johnson, and Chilcote (7A) have
all reported various reaction-rate methods for determining
total serum protein with the centrifugal analyzer. Ac-
cording to Koch g3 a1., their method was reasonably pre-
cise and rapid (90 s per run). But Savory 33,11. (75)
reported that the method was relatively imprecise in their
hands and was subject to errors in the analysis of sera
from patients with dysproteinemias. Thus, we decided to
try another kinetic approach, namely the stopped-flow
mixing method, hoping to develop a more reliable, pre-

cise and rapid procedure.

B. Stopped-flow Method

1. Reagents and Sample Preparation

 

The biuret reagent, which contains copper sulphate
and tartrate in alkaline solution, was prepared according

to a modified formulation of Cornell 32 a1. (8A).

Biuret reagent. The working reagent contained cupric

sulfate (2.A g L-l), sodium potassium tartrate (8 g L'l),

_1)

sodium hydroxide (A8 g L , and potassium iodide (l g L'l)
Blank reagent. The blank contained sodium potassium

tartrate (8 g L'l), sodium hydroxide (A8 g L'l), and

A3

potassium iodide (l g L'l).

Standards. Standards were dilutions of human serum
protein standards (Dade Division, American Hospital Sup-
ply Corp., Miami, FL 33152; Cat. No. B5158) in saline
solution (NaCl, 9 g L-l).

Quality Control Sera. Lyophilized control serum
samples (Moni-trol I, Cat. No. B5103; Moni-trol II, Cat.
No. B5113, Dade Division, American Hospital Supply Corp.,
Miami, FL 33152), were reconstituted according to the
manufacturer's instructions and diluted 30 fold with

saline solution before use.

All reagents were filtered through a 5.0 pm dispos-
able filter (Millipore Corp., Bedford, Mass., 01730)
before use. The biuret reagent was stored in plastic
bottles in the dark, and all protein solutions were
freshly prepared from vacuum sealed prepackaged bottles

stored at 2-8°C.

2. Automated Stopped-flow System

 

Reaction-rate measurements were made on the computer
controlled stopped-flow speetrophotometrie system des-
cribed in Chapter 2. All data were acquired and processed
by a PDP 8/e minicomputer (Digital Equipment Corp., May-
nard, MA 0175A). Iteractive computer programs are
written by Notz (PNSF3. PNF103)-and by Gall (RGMAIN)

in our group. Notz's programs control the sequencing

AA

of the stopped-flow mixing system and the filling

and rinsing of the drive syringes. They also

perform the tasks of data acquisition and processing.
Gall's program analyzes the data collected. It displays
absorbance and rate on the CRT as a function of time.
The slope of the absorbance-time curve as well as the
maximum rate can also be calculated and displayed.

The rates are obtained by 9 point first derivative,
quadratic, Savitsky and Golay smooth on the absorbance-
versus-time data. If the reaction is not pseudo-first
order, the maximum rate is obtained. If the reaction is
pseudo-first order, the initial portion of the rate curve
is linear and the operator can identify the linear portion
and obtain the average initial rate with the program.

The stopped-flow system was thermostated at 25°C. Spectro-

photometric measurements were made at 5A0 nm.

3. Initial Rate Studies

Figures 3-3a-c show the absorbance-time curves for
the formation of the biuret product from human serum
protein standards. It is apparent that the biuret-
protein reaction proceeds quite rapidly. The total ob-
servation times for the 3 runs shown in Figure 3-3 were
1003 (Figure 3-3a), 108 (Figure 3-3b), and 0.18 (Figure

3-3c). As can be seen from Figure 3-3c and 3-3d, the

A5

 

 

 

 

 

 

06-0 r-
w
u
z
d r—
A”
m
<1

0 . J l
0 L00
TIME (sec)
1 IO"
(a )

0.20 -

ms —
'9’
q
E o
0 “°”
In
(D
<1

ombi:_f"".~

o o: s
o 1 J A A I
O LOO
TIME (sec)
I IO

(0)

(a) At = 1008;

040 v-

030 —

assonsawce
S
O
I

OIOP

 

0.50

RATE

 

(b) At

 

A l l L

TIME (sec)
I I0"

(b)

LOO

TIME (sec)
xIO

(d)
Figure 3-3. Initial rate studies of the biuret reaction.

= 2103 .

A6

reaction rate reaches a maximum before 0.1 s. No other
instrument could be used for studying the biuret
reaction in so short a time scale. In fact, the desir-
able feature of obtaining A0 for the sample-reagent mix-
ture without running a separate blank, can be done by the
stopped-flow system. Although Koch 33 £1. (7A) did the
experiment under slightly different conditions (on a
CentrifiChem analyzer), they took their first data

point at 33 after the reaction began, and called that
their blank. But as can be seen in Figure 3-3b, the
reaction has proceeded to a substantial extent after 3 s.

Fixed-time reaction-rate analysis of compounds is
usually limited to those substances undergoing first-
order or a pseudo-first order reaction (32,82). The biuret
reaction, although not a simple first-order reaction, is
suitable for fixed-time reaction-rate analysis, as shown in
Figure 3-A. Here, a standard curve for human serum pro-
tein using a two point fixed time method is shown.

For the initial quantitative studies, we used two
approaches: the two-point method, and the maximum rate
method. In the two-point method we took data at time t0
and at 0.15, and used the difference in absorbance, AA,
in the standard curve. Then we also measured the maximum
rate and used it the with the other approach. Figure
3-A presents the resulting standard curves. As can be

seen, the two-point method yields more precise results.

A7

 

 

 

 

 

.050 LC
O40 — i -* 0.8
.030 - — 0.6
MAXIMUM
(I) RATE
<1
.0I0 — 0.2
l l
O 4 8
PROTEIN CONCENTRATION
(G/ DL)
Figure 3-A. Standard curves for two reaction—rate methods

used in the biuret reaction.

MAXIMUM RATE

 

A8

The statistics of the calibration curve are summarized
in Table.3-2. Note that the precision is only fair.
For the three different series of standard solutions,
the relative standard deviation was as high as 5.8%.
The maximum rate method was even less precise, as
can be seen in Figure 3-3d. The maximum rate does not
last for a very long time period, and the relatively high
noise level in the derivative curve causes imprecision.
Since the biuret reaction is rapid, a longer measure-
ment time, At, was used in subsequent trials. Longer
At values give greater absorbance changes and thus better
precision due to less instrumental noise and a smaller
error in AA. A measurement time of 105 was chosen as a
compromise between precision and analysis time. It was
found that the precision improved greatly with a 10 8
measurement interval. Figure 3-5 shows that the standard
curve is linear up to 8 g/dl serum protein concentration.
The statistics of the plot are shown in Table 3-3. Note
that the maximum relative standard deviation obtained was
l.A%, which is equal or better than any equilibrium
method.

A. Experiments with Human Control Lyophilized Sera

To test our method with actual serum samples, three

1yophilized sera (Moni—trol I, Patho-trol, and Moni-trol

A9

Table 3-2. Results for Total Serum Protein Standards.
(t - 0.1 sec)

 

 

Protein Concentration Absorbance Relative Std.

 

(gm/dL) (Average) Deviation %
8 0.0A5A 1.A
7 0.0381 2.6
6 0.0365 5.8
5 0.0329 5.1
A 0.02A6 2.2
3 0.0202 1.6
Slope = A.86 x 10-3

Intercept 6.22 x 10"3 A

1.57 x 10’3

Std. Error of Estimate

 

 

 

50

Me

0.30

ABSORBANCE
o
I“
o

O.IO

 

 

() l l l 1 J
O LOO

PROTEIN CONC.( G/DL)
xIO'|

Figure 3-5. Standard curve for serum protein, At = 10 s.

51

Table 3-3. Results for Total Serum Protein Standards.
(t = 10 sec).

 

 

Protein Concentration Absorbance Relative Std.
(gm/dL) (Average) Deviation %

 

.393
.3AA
.308
~235
.213

00000
Ol—‘OOH

0.151

NW-fimmflm
Jr-lrl-‘WF-‘Nw

I4 H

0.101

Slope = A.85 x 10'2

6.96 x 10‘3 A

Intercept

Std. Error of Estimate 9.57 x 10-3

 

 

 

52

II, DADE, Division American Hospital Supply 00., Miami, FL
33152) were used as controls. The manufacturer of these
sera gives assigned values of total protein obtained by
replicate analyses using well-established methods. A
comparison of the results obtained here by the fixed-
time rate method with those obtained by other methods

is presented in Table 3-A. Note that the other reported
rate method using the CentrifiChem analyzer gives rela-
tively low results when compared to results from equilib-
rium methods. The precision is also poorer, and is es-
pecially noticeable with the Moni-trol I serum. As
reported previously, the 0.1 s fixed-time method gave
relatively poor precision, but we found the values still
fell within the acceptable range provided by the manu-
facturer. The 10 s fixed-time method gave good accuracy
and precision. An abnormal serum (Patho-trol) was also
analyzed using the 10 s fixed-time method. As shown in
Table 3-A, the results we got were slightly higher than
the value reported by the manufacturers, but still within

the allowable range.

5. Comparison with the Equilibrium Method

To further confirm the reliability of the results,
the same control sera were analyzed using an equilibrium

biuret method. A Beckman DB-GT spectrophotometer with a

 

Table 3-A.

Protein.

53

Results of Determination of Total Human Serum

 

 

Moni-trol I

l.

2.

3.
A.

Improved
biuret

CentrifiChem
SMAC
Mark X

Moni-trol II

 

1. Improved
biuret

2. CentrifiChem

3. SMAC

A. Mark X

Patho-trol

1. Improved
biuret

2. Technicon

AA II

Repprted Values

 

Mean
(s/dL)

7.0:.06
6.5:.35
6.8:.10
7.3:.10

5.31.07
A.51.05
5.2i.08
5.61.10

5.3:.12
5.9i.05

Range

6.7-7.3
5.8-7.2
6.5-7.1
7.0-7.6

5.0-5.6
A.2-A.8
A.9-5.5
5.3-5.9

5.0-5.6
5.6-6.2

Observed Values

At=0.ls At=lOs

6.791.15 6.79:.01

5035:085 5.1“1.0u
5.85:.08

 

 

5A

1 cm path length cuvet was used. The reagents and samples
were mixed, and the color was allowed to develop for 30
minutes before the absorbances at 5A0 nm were measured.
Dilutions were necessary for the more concentrated samples
*to produce.a linear standard curve, which is shown in
Figure 3-6. The results obtained were compared with

the results from the rate method and are listed in Table
3-5. The equilibrium method gave practically the same
results as the rate method. The differences found for

the Moni-trol I and Moni-trol II samples were less than

1%, while the Patho-trol sample had about 7% difference.

6. Choice of Protein Standards

Human serum protein was used as the standard in the
stopped-flow biuret procedure. Bovine serum albumin is
often the preferred standard material in equilibrium
methods because it is much cheaper and readily available
in pure crystalline form (81). However, Koch gp_gl.

(7A) have reported that it reacts faster than human serum
protein with the biuret reagent. We repeated their experi-
ment with the stopped-flow analyzer and observed the same
result (Figure 3-7). However, careful analysis of the

data revealed one otherinsight. It was found that the
rate of reaction of the human serum protein was about 0.65
times as rapid as the BSA. The human serum protein

standard used contains 5‘g albumin and 3 g globulin per

 

55

 

(180-
lu<160-
Q)
2!
<1
00
' O:
O
8
<1<M40-
(120-
o l l I
OI 2E) .40 6‘) 8;)
PROTEIN CONCENTRATION
(G/D L)
Figure 3-6. Standard curve for serum protein using the

equilibrium method.

56

Table 3-5. Comparison of the Reaction Rate Method with
the Equilibrium Method.

 

 

 

a Equilibriumb
Rate Method Method Difference
Moni-trol I 6.79 i 0.01 6.77 t 0.06 0.02
Moni-trol II 5.1A 1 0.0A 5.05 i 0.0A 0.09
i 0.05 0.A5

Patho-trol 5.85 i 0.08 5.A0

 

 

aAverage of 6 determinations on the same sample with 10
second measuring time.

bAverage of 3 determinations on the same sample with 30
minutes waiting period.

57

   

 

 

fiesa
.03.-
HUMAN SERUM
g .02—
<1
.0l -
o / l l
o 4 s
PROTEIN CONCENTRATION

(G/DL)

Figure 3-7. Comparison of rate of reaction between BSA
and human serum protein.

58

100 ml solution, which means that albumin makes up 62.5%
(W/W) of the total protein in the solution. As can be
seen from Table 3-6, there is a consistent similarity
between the two ratios (0.625 and 0.65). Hence, we
wondered if the rate difference observed between the
human and the bovine proteins could be caused by the
percentage of albumin and, furthermore, if the rate were
dependent on the albumin concentration.

If albumin actually reacts much faster than globulin,
this fact might have been easily overlooked by other ex-
perimenters, because no one has studied the rapid kinetics
of the biuret reaction (<1 5 after mixing).

If this were true, differential rate analysis could
be done on a serum sample to determine albumin and total
protein simultaneously. One measurement could be taken
very early in time to determine albumin and a second mea-
surement could be made much later in time to determine
total protein.‘ Albumin is a clinically important sub-
stance and is determined routinely (See Table 2-1 in
Chapter 2). Thus, if a simultaneous determination of
both the total protein and the albumin concentration were
possible, it would be most valuable.

In the first experiment, bovine serum albumin was
added to bovine serum globulin in different proportions
and their reaction rates with the biuret reagent were

obtained. For all the mixtures, both albumin and globulin

59

Table 3-6. Comparison of Rates of Reaction of Albumin
From Different Sources.

 

 

Protein

 

Concentration Rate Ratioa % Albuminb
8 gm/dL 0.6A7
5 gm/dL 0.650 0.625
A gm/dL , 0.65A

 

 

a = Rate of Human Albumin (62.5% Albumin)
Rate Rat1° Rate of BSA (1007Albumin)

b

 

._ Albumin Concentration = 6 gm/dL a 0 625
Total Protein Concentration gm d ’

60

had original concentrations of 6 g/dL, but the two were
mixed in varying amounts, ranging from 0% albumin to 100%
albumin. Table 3-7 shows the results, from which one can
see that no significant difference in rate exists. This
indicates that bovine albumin reacts with essentially

the same rate as bovine globulin.

To double check these results, BSA, pure human serum
albumin, and 65% human serum albumin standard solutions
of the same total protein concentrations were studied,
and the results are shown in Table 3-8. These indicate
clearly that BSA reacts faster than the human serum
albumin, while the percent of albumin in human serum
does not affect the rate significantly.

Thus, the idea of simultaneous determination of total
serum protein and albumin is not feasible. The experi-
ments performed, however, indicate two important guide-
lines for the reaction-rate determination of total
protein. First, human serum protein should be used in
the rate method because of the faster reaction with BSA.
Second, since the protein composition of the human serum
does not affect the biuret reaction, one should be able
to use human serum protein of any composition as a

standard.

61

Table 3-7. Biuret Reaction with Different Albumin Com-

 

 

 

positions.
Albumin Contenta Abs. at 0.1 sec
100% 0.028
75% 0.025
50% 0.028
25% 0.028
0% 0.030

 

 

a6 gm/dL albumin + 6 gm/dL globulin.

62

Table 3-8. Biuret Reaction with Albumin From Different

 

 

 

Sources.
Albumin 0.1 sec 100 sec
1. 8 gm/dL BSA 0.0A0 0.065

2. 8 gm/dL Human Serum
(95% Albumin) 0.032 0.053

3. 8 gm/dL Human Serum
(62.5% Albumin) - 0.033 0.055

 

 

 

63

7. Studies with a Vidicon Detector

No attempt was made to determine the biuret reaction
mechanism. But we used the biuret reaction to test a
new micro-computer controlled vidicon rapid scanning
stopped-flow system. designed by Carlson and Enke

at Michigan State University (86). Several interest-

ing observations were made, that may be of help in future
studies of the mechanism of the biuret reaction.

Figure 3-8 shows the spectral changes with time for
the biuret reaction with human serum protein. The original
scan covered a range of 565 nm-8A5 nm recorded with the
vertical scan frequency at 25 kHz with 102 channels per
scan frame, which results in a scan time of A.08 msec/
frame. The spectral changes which occurred from the time of
mixing through 5 s were recorded.

The spectrum with the large peak centered at about
575 nm represents the Cu-protein complex, which has an
increasing absorbance with time. One interesting observa-
tion is shown in Figure 3-9. A slight wavelength shift
of the peak occurs very early in time. The absorbance
maximum shifts rapidly from 610 nm to 560 nm in the
first second after mixing, while the shift after 2 s
becomes quite insignificant. The same spectrum in Figure
3-8 shows two isosbestic points at about 690 nm and 802

nm. The existence of these isosbestic points indicates

 

 

6A

0.251- 9
4.63:1

2.738-

1313’

-0721!

ABSORBANCE

0.37:4

690 nm
0.13“ ’-

u \/ m...
.. ...... Ki” ......

550 700 350
WAVELENGTH I am)

\.
\

 

 

 

Figure 3-8. Time scan of the absorption spectra during
the human protein-biuret reaction.

 

560nm 600nm

2.0 - + A

O
2‘
In

ABSORBANCE X ‘0

 

 

 

 

 

.725
A
o , F \
500 600 700
WAVELENGTH (nm)

Figure 3-9. Apparent wavelength shift of the biuret
reaction.

66

that there is probably an interfering species that ab-
sorbs in the IR region. Figure 3-10 shows the absorbance
change with time of the 752 and 839 nm bands. The band

at 752 nm decreases with time, while the one at 839 nm
increases with time. In order to identify the interfer-
ing species, the biuret-human protein reaction was allowed
go to completion (about 25 min) and obtained the absorption
spectrum shown in Figure 3-11. A comparison of the
spectrum with Figure 3-8 indicates that the absorption band
of the Cu—protein complex extends well beyond 850 nm, and
the increase in absorbance with time of the 839 nm band

is thus due to the Cu-protein complex as well. Therefore,
the decrease in absorbance in time at 752 nm must be caused
by an interfering species.

We identified this species as the Cu-tartrate complex
present in the biuret reagent. Figure 3-12 shows the
absorption spectrum of the Cu-tartrate complex, with the
biuret blank used as a reference. The spectrum has its
maximum absorbance at 680 nm, but the absorbance diminishes
beyond 800 nm. The amount of Cu-tartrate complex de-
creases during the reaction, which causes the net decrease
in absorbance at 752 nm. Since the Cu-tartrate complex
does not interfere beyond 800 nm, the observed increase in
absorbance with time at 832 nm must be due to the Cu-protein
complex. One other interesting observation is shown in

Figure 3-13. The disappearance rate of the Cu-tartrate

AISOIIANCI

 

l

AISOIIANCI

 

 

67

(a)

  

it

A
r

--.
.-b
In

I
l
3

”-

TIM! (s)

 

A

 

Figure 3-10.

1
I
I

“-b
..I-
E.

I
r
2

mu (s)

Absorbance versus time for the biuret
reaction with human serum. (a) 752 nm;
(b) 839 nm.

 

68

0.3- I

g 0.2--

ABSORIANCE

O"--

 

 

 

550 700 050
mvslewcm (nm)

Figure 3-11. Absorption spectrum of the copper-protein
complex from the biuret reaction with
human serum after about 25 minutes.

69

AI 50! DANCE

 

 

A A A
I

I i

I I v

550 700 .50
WAVELENGTH (lull)

Figure 3-12. Absorption spectrum of the biuret reagent.

70

 

 

 

 

 

2.000
Cu-tartrate
at 756 nm 563 an
L11 x 100
o . /
Z A '
< -I-. 616 nm
CD ...
CE ..
o -I-
(I) . Cuigrotein
m ... x
( d-
.. /
1E _-_.—.- TA
0.000
0.000 5.000

TIME (SEC)

Figure 3-13. Rate studies of the biuret reaction.

 

71

complex is slightly faster than the appearance rate of the
Cu-protein complex, which may account for the rapid wave-
length shift observed at the 575 nm region during the
first second after mixing.

Earlier in this chapter it was seen that BSA reacts
more rapidly with the biuret reagent than does human
serum protein, but proteins from the same source react
with the same rate. We attempted to find out if there
was any difference in the time dependent spectra by making
up a bovine serum albumin and a bovine serum globulin
solution with similar concentrations. Figure 3-1A shows
the time dependent spectrum for BSA and Figure 3-15 for
B80. No significant differences can be found between
these two spectra, which again suggests that albumin and
globulin react similarly.

When these Spectra are compared to the spectrum
shown in Figure 3-8, it can be seen that the reaction
profiles are significantly different in appearance from
the human serum protein profile. Only one isosbestic
point is observed at 690 nm, and the decreasing absorption
band at about 775 nm extends beyond 800 nm. We checked
the equilibrium absorption spectrum of the Cu-BSA complex,
and Figure 3-16 shows that there is essentially no ab-
sorbance above 800 nm. This suggests that there is probably
an additional interfering species that has a wavelength

maximum at a longer wavelength than the Cu-tartrate

72

Ofi-F

“33‘

2.050 ‘

.lfih‘

0.9“ V

0.0.3 V

ABSORMNCE
l
I

' musa

0138 -

-- A / - 779 nm

586 am

 

 

550

 

WAVEIENGTH (m)

Figure 3-1A. Time scan of the bovine albumin-biuret
reaction with a vidicon detector.

73

0.35- F
“3 0\

0.04 .-

-I L-
0.4.0.1

41.25:-

ABSORIANCE

N38-

676 an
570 mu ' " /

 

775 um

 

 

550 700 050
WAVElENGfl-l (um)

Figure 3-15. Time scan of the bovine globulin-biuret
reaction with a vidicon detector.

7A

 

 

 

0.3-T
0.2- b
U
U
5 . J.
.
8
O
“
.
‘
0.1- -
O
J A A l L J A A A A A L l I. l
o E T I I l I I I I : I I 0 F : I I r I ‘1 ‘
550 700 ISO

WAVE lENGTH (mu)

Figure 3-16. Absorption spectrum of the copper-protein
complex from the biuret reaction with bovine
serum albumin after about 25 minutes.

 

75

complex. This may be an intermediate that appears quickly
after mixing and then disappears during the reaction. This
could account for the decreasing band beyond 800 nm and
at the same time off-setting the interference of Cu-
tartrate at 575 nm. This may also account for the fact
that the initial rate of the biuret-bovine protein reac-
tion is faster than that of the biuret-human protein
reaction.

Carlson suggested that the rate curve should
be investigated at wavelengths below 550 nm in the future
in order to identify the unknown interfering species
(86). Rate studies will help in understanding the re-
action rate difference between the different sources of
protein, and in this way perhaps the cheaper and more
readily available BSA can be used as a standard material

in the kinetic biuret method.

C. Conclusions

It has been demonstrated that the unique capabilities
of the automated stopped-flow analyzer enable the de-
termination of total serum protein by the biuret method
in 105. The reaction-rate method is found to be rapid,
simple, and precise. The method gave the same magnitude
of precision as the equilibrium method, but used less
sample volume (15 HR vs. 70 u£ undiluted serum), and was

considerably less time consuming (103 1g. 30 min).

76

Because it is a relative measurement, the reaction-rate
approach should decrease greatly any interferences caused
by turbidity, hemolysis, or other background noises.

The highly automated system simplifies sample and data
handling, and the continuous monitoring of the reaction
enables the operator to detect any abnormal errors that
may occur during the reaction.

A vidicon detector has been used to show that some
kind of an intermediate is probably involved in the biuret
reaction, and any future studies concerning the mechanism
of the reaction should be performed in the early phase
of the reaction. The stopped-flow system is undoubtedly

a good instrument for studies of this kind.

IV. SERUM ALBUMIN ANALYSIS

A. Introduction

Albumins are water soluble proteins which are also
soluble in dilute and moderately concentrated salt solu-
tions. They are carbohydrate-free molecules with a
molecular weight of 65,000. Normal serum from a healthy
adult contains about 3.5-5.0 gm of albumin per 100 ml.

A low serum albumin level is an important cause of edema.

In most infectious diseases, liver problems, carbinomatosis,
and congestive heart failures, albumin levels as low as

2.3 to 3.2 g/100 ml are common (8).

Currently there are four major types of procedures
in serum albumin determination: the biuret method after
precipitation of globulin by salt (92); the dye-binding
method with bromcresol green, methyl orange, or 2-(A'-
hydroxyazobenzene)-benzoic acid (HABA); electrophoresis
(93); and the immunochemical method (9A). The dye-binding
method with bromcresol green (BCG) is most popular because
it is simple to use and easily automated (87). However,
it tends to give overestimations of the serum albumin,
especially when the concentration is low (88-90). Con-
sequently, the IFCC* expert panel on protein recommends

its use should be limited to screening (91). We looked

 

i
International Federation of Clinical Chemistry.

77

78

into this problem and have now presented a possible solu-

tion in this chapter.

1. Bromcresol Green Dye-binding Method

All proteins, especially albumins, tend to react with
many chemical Species by means of electrostatic or
Van der Wall's forces, and by hydrogen bonding. In fact,
most hormones, bilirubin, fatty acids, and many drugs
are first bonded to the albumin and then transported
through the body. Many anionic colored dyes also have
this protein-binding property. Bromcresol green is cur-
rently the most popular method for determining serum
albumin. The method was first introduced by Rodkey in
1965 (95), and then modified by Doumas gt al. (96), who
used a nonionic surfactant BriJ-35, and reduced the ab-
sorbancy of the dye blank. This immediately raised the
sensitivity of the method, prevented turbidity and made
the standard curve linear (96). Doumas and Straumfjord
have summarized the advantages and disadvantages of this
method (97). The advantages are the small sample size,
the availability and stability of the bromcresol green,
the high precision, the lack of interference from bili-
rubin, salicylate, or hemoglobin, the ease of automation,
and the negligible interference from globulins. The
disadvantages are the increase of color produced by the

serum with time (pure albumin produces color

79

instantaneously) and the yet undetermined specificity of

bromcresol green.

2. Proposed Solutions

Because proteins other than albumin also react with
BCG, considerable overestimation occurs, particularly
when the concentration of albumin is low. In fact this
has been one of the major criticisms of the method (98).
Gustafsson (99) postulated that BCG reacts with serum
proteins in two steps. The first is an immediate reac-
tion within the first minute which is mainly due to the
albumin present. This is followed by a slower reaction of
some 30 minutes, which is caused by some "acute phase
reactants", probably due to the presence of other pro-
teins or reactants in the serum whichhave a slower reac-
tion rate with BCG (99). Webster (100) investigated the
immediate reaction ( 305) using a conventional spectro-
photometer, and found that his results were 0.3 g/100
ml higher than those obtained by electrophoresis. This
difference was independent of the albumin content of the
serum. Therefore, he suggested that 0.3 g/100 ml albu-
min concentration should be subtracted from the raw data
to make them reliable (100). Both Gustafsson and Webster
tried to get estimates of the absorbance contributed by
the fast reacting albumin, by taking data as near to

the initial mixing time as possible. Gustafsson also

80

tried to estimate the absorbance at 0 min by extrapolating
the recorder curve to the time of mixing (99).

In this work, the albumin-BCG reaction was investi-
gated with the stopped-flow system. We took advantage
of the fast mixing feature of the stopped-flow system
and took data as near to the initial mixing time as
possible. By doing so the rapid albumin-BOG reaction could
be monitored and the approach to equilibrium observed.
Also, it was found possible to ascertain when other slower
reacting proteins began to interfere significantly. We
then compared our results with data from other conventional

methods.

B. Stopped-flow Method
1. Reagent and Sample Preparation

The reagents described by Doumas 32 31. (96) were
adapted to fit the stopped-flow system. The constituents

of the reagents are listed as follows:

Succinate buffer. Dissolve 11.9 g of succinic acid
in 800 m1 of water, adjust pH to ".0, dilute to 1 liter
with water, store at A°C.

BCG stock solution. Dissolve 0.fll9 g BCG (Sigma
Co., St. Louis, MO 63178) in 10 ml 0.1 N NaOH, dilute to
1 liter, store at H°C.

81

BriJ-BS solution (30%). Dissolve 3 g Brij-35 (poly-
oxyethylene lauryl ether, Sigma Co., St. Louis, MO 63178)
in 10 ml water with warming.

BCG working solution. Dilute 100 ml sotck BCG with
300 ml succinate buffer, add 1.6 ml 30% BriJ-35 solution,
adjust pH to “.20, store at 9°C.

Standards. Standards were dilutions of human serum
albumin (7.9 g/dl, diluted 200 fold with saline) obtained
from Dade (American Hospital Supply Corp., Miami, FL 33152).
Quality control sera (Moni-trol I and Moni-trol II) were
obtained from the same source, reconstituted according to
the manufacturer's instructions and diluted 200 fold with

saline solution before use.

2. Rate Studies

Pure human serum albumin was mixed with BCG reagent,
and the reaction at 25°C was monitored at 632 nm. Figure
4-1 shows the absorbance-time curves. The reaction
proceeds rapidly and reaches equilibrium in less than
0.5 s for a 16 g/dl albumin standard solution and less
than 2 s for the least concentrated albumin preparation.
The reaction was monitored for another 200 s, but no ap-
parent changes in absorbance occurred.

Next, a control serum (Moni-trol I) was prepared, for
reaction under the same experimental conditions. This

reaction proceeded rapidly at first, but slowed down after

82.

M/u
11mm MWflWWM

L

lllLLllllllllllllll'lllllllLllllllllJ
TI I ITI I I I l l l I I I I I'I'I'l ITI'I'I I'I I I I pr! I.I I I I I T]
o 0 o

o

ABSORBANCE

IIIIIIII'IIIIIIIIS'
O

LlIILJJII

 

9- 999 WWW
0.000 1.
TIME<SEC>

m0'1

Figure 4-1. Reaction of BCG with pure bovine albumin.

83

2 s (Figure 4-2). The second slower phase of the reaction
continued for about 30 min.

Finally, the reaction of a serum whose albumin con-
centration was beyond the linear range was also observed,
and Figure “-3 shows the results of this experiment. From
this figure it can be seen that the reaction approached
equilibrium very rapidly, and there is also a rather
evident breaking point, which demarks a slower reaction
about 6 s after mixing.

These rate studies indicate that there is indeed a
second slower reaction in the overall serum-BCG reaction.
This means that measurements must be made early in time
if error is to be avoided. Prior to 1976, most procedures
employed a reaction time of 5 to 30 min. Webster later
tried to measure the "immediate reaction" within 30 s,
but found that there was still a small positive differ-
ence between his results and those obtained from electro-
phoresis (100). Our results indicate that for the work-
ing concentration range of serum albumin (1.0 g/dl-6.0
g/dl) an observation time of 2-5 s after mixing should be

used to minimize interference from non-albumin materials.

3. Experiments with Human Control_Lyophilized Sera

A standard curve was prepared with diluted human
albumin standard solutions (7.9 g/dl, Sigma, St. Louis,

MO). At first we prepared the ECG reagent as before,

0.5001

0.000

Figure “-2.

ABSOR BANCE
'lUllLlllLUlilJlLLllllllLllLl_LlllIlLlJllLllllll

8A

IIIIIIII'TFIIIIIIrlII‘IIIIIII'IIloTTFIjIIIIIIIIIIIIIIIIIWIFT‘1
O

lllllllll

 

0.00 .000

0T1ME<_s-31Ec>

X10

Reaction of 800 with serum albumin.

85

1.200

oooooooooooooooooooooooooooo

ABSORBANCE

0.000

0.000 3.000

TIME(SEC)
x10 '1

Figure “-3. Reaction of BCG with serum albumin of ab-
normally high concentration.

86

but the Brij-35 caused minor mixing problems in the stopped-
flow system. Thus, we decided to dilute all the solutions by
a factor of two with saline solution. The sensitivity was un-
affected and a linear standard curve up to an albumin
concentration of 5.9 g/dl. was obtained. Table “-1 gives

the relative standard deviation of the data and the standard
error of estimate of the curve.

We then followed the manufacturer's instructions and
prepared 1:200 dilutions of three 1yophilized sera:
Moni-trol I, Moni-trol II, and Patho-trol from Dade. A
fixed-time equilibrium method was used for the determina-
tions with a 2 8 measurement time. The measurement time
of 2 s was chosen because our rate studies had shown that
the BCG albumin reaction for the most dilute solution is
completed in less than 2 s after mixing, while no sig-
nificant amount of interference began until 6 s after
mixing.

The results of our analyses are compared with the
values provided by the manufacturer in Table h-2, and it
can be seen that our estimates of albumin concentrations
within the normal range (3.5-5.9 g/dl) are lower than
those obtained by other methods. For Moni-trol I, our
results were 0.29 g/dl lower, and for the less concentrated
Monitrol II, the difference was even greater (=0.52 g/dl).
This is consistent with the fact that a decrease in serum

albumin concentration is often accompanied by an increase

87

Table 9-1. Determination of Human Serum Albumin.

 

 

 

Concentration A
(g/loo ml) (At=2 sec) RSD
1.38 0.118 3.0%
2.06 ' o.1u7 2.0%
3.16 0.197 1.9%
9.10 0.230 2.9%
9.51 0.255 2.0%
5.90 0.312 1.2%
Slope = 0.0928
Intercept =0.059

Std. Error of Est. = 3.78 x 10'3

 

 

88

Table 9-2. Serum Albumin Determination with Different
Methods.

 

 

Stopped-Flow
Method Other Methodsa

Mean RSD 1 2 3 9 5

Moni-trol I 9.11b 3.0% 9.9 9.7 9.9 9.9 ---
Moni-trol II 2.58 1.3% 3.0 3.1 3.3 3.1 3.2

 

 

Pathotrol 9.19 2.7% --- --- 9.7 --- 9.1
a1 = DUPONT ACA

2 = CentrifiChem

3 = Technicon SMAC, or AAII

9 = Hycel Mark X

5 = Salt Fractionation, biuret method

O‘
>
H
H

concentrations expressed in mg/100 ml.

89

in globulin concentration, which further increases the
magnitude of the slower reaction.

In fact, all our results were lower than those from
other automated BCG methods, which seems to indicate that
our method is less susceptible to overestimations of
albumin concentrations. Webster (98) reported that his
results were consistently higher than those from electro-
phoresis by 0.3 g/dl. Ferreria and Price said their
analysis using bromcresol green gave results that were
on the order of 0.5 g/dl higher than those obtained
through immunoprecipitation (99). Thus based on these,
one can safely assume that the manufacturer's reported
values should be about 0.3-0.5 g/dL higher than the actual
value, especially when their data are gathered from dis-
crete and continuous-flow systems, some of which were

measured 30 min after mixing.

C. Conclusions

We took advantage of the fast mixing feature of the
stopped-flow system and were able to find conditions for
determining serum albumin concentrations with bromcresol
green, with the least amount of overestimation. Our rate
studies suggest that a fixed-time equilibrium method
with a measurement time of 2 3 gives the most precise
results with least interference from other proteins in

the serum. Studies with 1yophilized control sera show

90

that our method consistently gives lower values than the
other automated techniques which use BCG. Electrophoresis
experiments should now be done on the same samples
whenever the necessary equipment is available. This would

further validate our results from the stopped-flow method.

V. SERUM TRIGLYCERIDE ANALYSIS

It is known that serum triglyceride levels increase
in patients with atherosclerosis (119) and diabetes
meilitus (115). Thus the assay of serum triglyceride is
an important clinical test for detecting these diseases.
Serum triglyceride is also determined routinely in lipo-
protein phenotyping, which is described in Chapter VII.
In this chapter, the stopped-flow system is shown to be
useful in the determination of serum triglyceride. By
monitoring the initial rate of an enzymatic reaction,
results are obtained rapidly, and an early absorbance

reading A can be determined without the problems ex-

0
perienced in adapting the enzymatic procedure for the cen-

trifugal fast analyzer (106).

A. Methods of Analysis

Many of the natural lipids are glyceryl esters of
fatty acids, and triglycerides are the most common.
Complete hydrolysis by strong acids, alkalis, or enzymes
yields free glycerols and fatty acids as shown below for

triolein.

91

92

 

 

O
CH200(CH2)7CH=CH(CH2)7CH3 HZC-OH
? H20 I
CH0C(CH2)7CH=CH(CH2)7CH3 :; HC-OH +
9
I
CH20C(CH2)7CH=CH(CH2)7CH3 H2C-0H
Triolein
(Triglyceride) Glycerol
3 CH3(CH2)7CH=CH(CH2)7COOH
Oleic Acid

The triglyceride level in blood rises to its maximum
within 9 to 6 hours after digestion of food. For reliable
results, blood specimens should be drawn after the patient
has fasted for 12 hours.

Two colorimetric methods have been used extensively
for serum triglyceride determination. Van Handel and
Zilvermit (101) extracted the serum sample with chloro-
formmethanol, removed the phospholipids, hydrolyzed the
triglycerides in alkaline solutions, and then oxidized
the glycerol to formaldehyde. The final product is pink,
with a visible absorbance proportional to the original
triglyceride concentration. The Hantzsch condensation
method (102) uses similar extraction and hydrolysis steps,
but the final product is the yellow diacetyl lutidine

species. This same product is also the basis of

93

fluorometric procedures (109).

These methods yield precise and accurate results,
but they are cumbersome and time consuming because of the
extraction and the chemical hydrblysis. 0n the other
hand, hydrolysis of triglyceride by enzymes eliminates
many of these complexities.

Currently there are two such methods. Bucolo and
David's lipase hydrolysis of triglyceride (105) is at
present the preferred method. It involves the following

sequence of reactions:

1. Triglyceride hydrolysis
Lipase
Triglycerides —————e.Glycerol + FFA

2. Glycerol reaction sequence

GK
Glycerol + ATP———’a-GP + ADP

PK
ADP + PEP-——>ATP + Pyruvate

LDH
Pyruvate + NADH-———>Lactate + NAD

where
ADP = Adenosine diphosphate,
ATP = Adenosine triphosphate,
FFA = Free fatty acids,
GK

Glycerol Kinase,

a-GP

c-Glycerol phosphate,

99

LDH = Lactate dehydrogenase,

NAD = Nicotinamide - adenine dinucleotide,

NADH= Nicotinamide-adenine dinucleotide, reduced,
PEP - Phosphoenolpyruvate, and

PK = Pyruvate Kinase.

Lipase has been shown to hydrolyze preferentially
the esters of the primary hydroxyl groups of glycerol
(112). Thus, in order to complete the hydrolysis, a non-
specific esterase (a-chymotrypsin) was added. When both
enzymes are present, the hydrolysis is completed after
10 minutes at 30°C. The free glycerol then reacts as
shown in the above equations resulting in the oxidation
of NADH. The total decrease in absorbance at 390 nm is
proportional to the concentratin of glycerol liberated
from triglycerides and the free glycerol in the sample
(free glycerol is usually subtracted as a blank).

The method has been used on the centrifugal analyzer
(106,107), and on the Gilford 3500 (110). Previous serum
extraction is not needed. Thus, the analysis is much
simpler than those techniques which require an extraction
step. However, phosphatase contamination by the enzymes
introduces a competing reaction that makes the final
value appear higher than what it is, and a "reagent blank"
run is necessary (105). Free glycerol present in the
sample also requires a sample blank determination.

Stinshoff gt a; (109) prescribed a correction factor

95

for free glycerol that follows a normal distribution:100
mg/l can be subtracted from each total triglyceride value
instead of running a sample blank. A less empirical way
to avoid running a blank is to use kinetic methods.
Lehnus and Smith (110) reported using a Gilford 3500
system to measure the change in absorbance during a 19
second measuring time after a lag time of 30 seconds.

The result was as good as the manual "end-point" method
(110). Chong-Kit (106) and Tiffany g£_al. (107) used

the centrifugal analyzer and made determinations by rate

methods in less than 3 minutes.

B. Stopped-flow Method

Although the centrifugal analyzer can determine serum
triglyceride rapidly, Chong-Kit reported that the inabi-
lity to take an early absorbance reading AO was a principal
problem in adapting the enzymatic procedure for the
GeMSAEC (106). The mixing time for the GeMSAES is about
20 3, during this time, there is an appreciable amount
of réaction, and the authors had to extrapolate back to
zero time to correct for this. The stopped-flow system
with its ability to obtain absorbance data very earily

in time, should eliminate this problem.

96

l. Reagent Preparations

1. "Stat—Pack" Triglyceride Kit (Calbiochem,
Post Office Box 12087, San Diego, CA 92112).
Vial A was reconstituted with 80 ml of dis-
tilled water, and 0.25 ml of undiluted serum
or standard glycerol was added to this solu-
tion. The contents were then mixed with
Lipase in Vial C, and incubated at 30°C for
10 min. The Glycerol Kinase in Vial B was
also reconstituted with 15.0 ml of distilled
water.

2. Stock glycerol standard.

Carefully weigh out 1.091 g of 99.8% pure
glycerol (Drake Brothers, Menomonee Falls,
WI 53051), and dilute to 1 liter. This is
equivalent to 1000 mg triolein per liter.

3. Working standard solution.

Dilute the stock glycerol standard with saline

to make working standard solutions.

2. Rate Studies

 

The enzymatic reaction was adjusted to follow pseudo-
first order kinetics. All analyses were carried out at
30°C, and the reactions were monitored at 390 nm for 60 s.
Figure 5-1 shows the absorbance-time curves. There is

a lag phase of N15 3, followed by a linear decrease in

97

db

LL
u u

b

lllLlLllll

llllllllll

II‘TIIIIII

TIMECSEC)

llllllllll
IIIIITIIII

lllllllllll

OITIIIIIIII

lllllJllll
rIrIIII

111111]!
IIII’IIIIII.
. 000

0

 

 

2. 000-”"°°"

.moz<mmomm<

- 1

1.600

am;

III‘III

'1

X10

Enzymatic reaction of serum triglyceride.

Figure 5-1.

98

absorbance that lasts from 20-90 3. After this, the
rate of reaction begins to decrease.

A standard curve can therefore be prepared in two
different ways. By measuring the constant rate in the
initial linear portion of the reaction, one can easily
get the initial reaction rate for each glycerol stan-
dard. Alternately, if the analyzer can give early ab-
sorbance readings - 3.5;, less than 1 s after the reaction
has begun - then these may be considered as the initial
absorbance reading A0 in a fixed-time rate method.

Standard curves were prepared with both methods, and
it was found that they produce similar results with ex-
cellent linearity up to 200 mg/dl. Figure 5-2 shows the
calibration curve by the initial rate method. Table 5-1
gives the statistics of the standard curve using actual
rate, as well as the precision of the stOpped-flow rate
method. In particular, it was found that being able to
monitor the reaction in more than one way can minimize
error caused by unsual samples. For example, in one
case, the serum sample used had an exceptionally large
amount of suspended particles, which caused excessive
noise in the initial rate measurement. The fixed-time
method saved us from repeating the analysis.

For both methods, there was no need to run separate
serum blanks, nor was there any need to obtain A0, as

the first data point was taken 10 ms after mixing. The

99

0.300“

Li I l J 1_L l l_l
I I I I l I I I Iir I

l l l L l l .1

INITIAL RATE

1 l 1 l
r I I I

l l L L I l
I I I I

 

0.000
0.00 .000

TGGCONC.(MG/DE>
X10 '2

Figure 5-2. Standard curve for enzymatic analysis of
serum triglyceride.

100

Table 5—1. Determination of Serum Triglyceride.

 

 

 

Concentration
(mg/dL) Rate RSD
50 0.70 9.1%
100 0.15 2.9%
200 0.30 3.8%
Slope = 1.53 x 10'3
Intercept = -0.005

Corr. Coeff.

0.9997

 

 

101

reaction times, and lag phases for the reactions are
determined by the concentration of the coupling enzymes.
For a general discussion of this, the article by Scopes

(116) should be consulted.

3. Experiments with Human Serum

The accuracy of the stopped-flow initial rate method
was assessed by comparing the results obtained with re-
ported values of a control 1yophilized human serum
(Moni-trol I). This comparison is shown in Table 5-2.
Our results appear to be comparable with those of the
reported values, and since we did not run a separate
serum blank sample, 10 mg/dL should be subtracted from
the results to correct for the presence of free glycerol
as suggested by Stinshoff gt El. (109). The 129 mg/dL
triglyceride concentration is consistent with the average
value obtained by the other methods.

The imprecision of the triglyceride analysis as
can be seen from Table 5-2, may also be dependent on the
dynamic blank caused by phosphatase contamination of the
lipase in the commercially prepared reagent, as reported
by Tiffany e§_al. (107). We tested this with a blank
reaction without glycerol, and found its contribution

insignificant for the batch of reagent we used.

102

 

 

 

Table 5-2. Serum Triglyceride Determination with Dif-
ferent Methods.
Mean Concentration
Method (mg/dL) S.D.
DUPONT ACA 129 16.82
BIODYNAMIC 133 ° 3.61
GEMINI 130 2.80
SMAC 93 9.81
HYCEL MARK X 190 (150)* 2.80
Ave. = 129
Stopped-Flow 129 (139)* 9.95

 

 

*Values not corrected for serum blank (free glycerol),

all other values are corrected for free glycerol.

103

C. Conclusions

The enzymatic triglyceride reaction is relatively slow
but has proved to be satisfactory with manual methods.
Although our adaptation of it for the stopped-flow
system did not improve the sample throughput rate, or
decrease the sample volume requirements significantly,
we were able to determine A0 at an early time period,
which allowed more effective use of the fixed-time rate
method. Furthermore, it was found that the stopped-flow
method is at least as efficient and viable as other methods

for the routine analysis of triglyceride.

VI. SERUM CHLOESTEROL ANALYSIS

A. Introduction

The importance of cholesterol (and cholesterol esters)
has long been recognized in clinical medicine. Serum
cholesterol levels and their dietary intake have often
been related to altherosclerosis, resultant strokes,
cardiovascular diseases, etc. (8,117). New diagnostic
approaches, such as hyperlipoprotein phenotyping, have
considerably increased the interest in cholesterol de-
terminations (118).

A host of different methods to determine serum choles-
terol fills the literature. These have been reviewed so
that even the interferences and sources of variation to
which these methods are prone have also been reported
(119-121). In the last 90 years, most analysts have
preferred the iron-surfuric acid reaction and the Lieber-
mann-Burchard reaction as the methods of analysis (8,122,
129). However, the recent introduction of enzymes as
reagents to determine cholesterol has focused attention
on the limitations of the strong acid approach (129).

The principle of the enzymatic procedure is presented
in Figure 6—1. Cholesterol esters are first converted
to free cholesterol by the enzyme cholesterol esterase.
The free cholesterol is then oxidized by cholesterol

oxidase, and the H202 produced is reacted with

109

105

 

PHENOL é-AMINOANTIPYRINE

qumonsmms DYE

Figure 6-1. Enzymatic reaction of serum cholesterol.

106

9—aminoantipyrine and phenol to form a quinoneimine dye
that absorbs at 510 nm.

The specificity of the enzymatic procedure is un—
doubtedly an important reason for its popularity. The
enzymatic procedure is much simpler to implement when
compared with the other reference methods (122,125).
Furthermore, results are as precise and accurate as
those obtained with other methods. All these factors
make it a good procedure to use for routine analysis.
The typical sample analysis time varies from 12 min. to
5 min.,_depending on whether a CentrifiChem analyzer
(128) or a DuPont ACA analyzer (129) is used.

In this chapter results of serum cholesterol determina-
tions with the stopped-flow system are presented. Two
rather significant problems which must be solved in order
to get satisfactory analytical results were discovered.
They are the slow rate of the enzymatic reaction, which
makes short analysis times difficult, and the difficulty
in preparing suitable aqueous cholesterol standard solu-
tions. We did not attempt to study the reported effect
of interference by bilirubin (131) because the serum
samples we worked with were all normal and contained

insignificant bilirubin concentrations.

107

B. The Stopped-flongethod
l. Reagent Prgparation

Cholesterol is not readily soluble in water, and as
a suitable aqueous primary standard for cholesterol is
lacking, we are seriously handicapped in our efforts to
make quantitative measurements of the steroid by non-
extracting procedures. The organic solvents, such as
ethanol or 2-propanol used for non-aqueous standard solu-
tion preparations (8) inhibit enzymatic activity and are
therefore unsuitable for our purposes (126).

As for the commercial aqueous cholesterol standards,
the "Presicet" standards produced by Boehringer Mannheim
Corp. (Indianapolis, IN 96250) are the most popular.

The kit contains cholesterol standard solutions of 50,
100, 150, 200, 300, and 900 mg/dl, combined with a
solubilizer and a preservative. Due to the unique 1:1
reagent to sample volume requirement of the stopped-flow
system, we had to dilute the cholesterol standards 50
fold with 0.2% phenol solution so that the reagent solu-
tion contains all the buffers and enzymes and the sample
solution contains the cholesterol sample. However, upon
.dilution, the solutions turned turbid, and thus a new
method to prepare aqueous standard solutions for stopped-
flow use was sought.

Solubilizer formulations that have been proposed

108

for aqueous standards are 25% Triton x-100, 12% Triton
x-100 with unique mixing, and 15% Triton x-100 with 7%
albumin (127). The 25% Triton x-100 preparation was found
to be too viscous for efficient stopped-flow mixing, and
several attempts to dissolve pure cholesterol in 15%

Triton solution failed. We experimented with an alcoholic-
aqueous mixture and prepared the standard solutions as

follows:

2-propanol, reagent grade (Fisher Scientific Co.,
Fair lane, NJ 07910)

Cholesterol (Sigma, St. Louis, MO 63178).

Triton x-100 (Research Products International Co.,

Elk Grove Village, IL 60007).

To prepare 25 m1 (500 mg/dl) cholesterol standard
solution, dissolve 0.125 g cholesterol in 1.0 ml 2-pro-
panol. Dilute to 25 ml with 15% Triton x-100, and warm
in a water-bath at 60°C until the solution turns clear.
Then prepare 50 to 900 mg/dl cholesterol standards by
proper dilutions with 15% Triton x-lOO. This preparation
procedure gave clear standard solutions in the normal
concentration range, and the final 2-propanol content
was small enough (N0.08%) that the enzymatic reaction was

not inhibited.

109

2. Rate Studies

We modified a commercial cholesterol Auto/STAT kit
(Pierce Chemical Co., Rockford, IL 61105) working reagent
preparation by carefully transferring 2 bottles (12.2
gm each) of enzyme reagent to a bottle containing 950
ml phenol reagent. After reconsitution, this solution
contains the enzymes peroxidase, cholesterol oxidase,
cholesterol esterase, 9-aminoantipyrine, phenol, a stabi-
lizer and a buffer. The substrate reagent was prepared
by diluting cholesterol standards or human serum samples
50-fold with the phenol reagent provided. The two solu-
tions were mixed in the stopped-flow system at 30°C, and
the absorbance was measured as a function of time at 510
nm.

Initially the reaction was monitored for 100 s, as
shown in Figure 6-2. There is a lag phase of about 20 s,
and from approximately 35 to 55 s, the reaction becomes
pseudo first-order. As can be seen in Figure 6-3, the
rate is constant during this period. All the sera behaved
similarly, and the rate was found to be proportional to
the serum cholesterol concentration. However, the reaction
with aqueous cholesterol standards was found to behave
quite differently. It has been reported earlier that
both alcohol and Triton x-100 retard the overall reaction
rate (126,127), and we confirmed this observation in our

studies. Figure 6-9 shows the rate of reaction with

110

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Figure 6-2.

 

 

 

8 r-
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x AA.
11‘ 4
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355 55s
I l I I
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TlME(sec)

Figure 6-3. Reaction rate of enzymatic cholesterol vs.
time (serum cholesterol).

 

 

 

 

l0 —
K)
9
)<
E
<1 5 “'
a:
1 T
0 so IOO
TIME (sec)

Figure 6-9. Reaction rate of enzymatic cholesterol vs.
time (pure cholesterol dissolved in an aqueous
solvent).

112

respect to time for a cholesterol standard. We noticed

a rapid increase in rate in the first 10 s, which then
decreased quickly. This is very different from the rate
of cholesterol reaction in the serum samples as shown in
Figure 6-3, and it was thus difficult to obtain a standard
curve for cholesterol using the reaction-rate method.

Table 6—1 shows a representation of the magnitude of
rate differences. Serum 3 is a fresh serum sample that
has a reported cholesterol value of 190 mg/dl. The 200
mg/dl standard solution was prepared in our laboratory,
while the Choles-trol was a commercially prepared
aqueous standard (Sigma Co., St. Louis, MO 63178). Both
aqueous standards gave a relative rate of 0.0031 absor-
bance unit per second, whereas the serum sample gave a
much faster rate. This makes standardization based on
the reaction-rate measurements of aqueous cholesterol
standards rather difficult.

It was found, however, that if data are collected
after the reaction reaches equilibrium (=15 min), a lin-
ear standard curve can be obtained with the same samples
as shown in Figure 6-5. Using the equilibrium method,

‘ we found that our observed values are on the average 3%
lower than the values reported in general. Table 6-2
shows some of the results obtained. Moni-trol II is a
control serum that has a normal cholesterol concentration

of 239 mg/dl, and samples 1, 2, and 3 are fresh serum

113.

Table 6-1. Cholesterol by Reaction-rate Method.

 

 

 

 

Concentration A
Sample (mg/6L) (1003)
Serum #3 190 .916
Standard 200 .318

Choles-trol 195 .310

 

 

119

10 '-

ABS.

 

 

 

() 1 1 1 11 I
O 500
CHOLESTEROL CONCENTRATION
(MG/DI.)

Figure 6-5. Standard curve for enzymatic cholesterol
analysis.

115

Table 6-2. Cholesterol by Equilibrium Method.

 

 

 

Re orted Observed
Sample (mg7dL) (mg7dL) % Diff.
Moni—trol II 239 230 3.8
Serum #1 225 219 2.7
Serum #2 260 251 3.5

Serum #3 193 190 1.6

 

 

116

samples obtained from Sparrow Hospital. The precision of
our equilibrium method was found to be 1.9% RSD, and the

maximum difference from the reported values was 3.8%.

0. Conclusions

What we have found about the reaction rate of aqueous
cholesterol standards helps to explain why most reported
cholesterol methods use the equilibrium approach. At
present, serum cholesterol can be determined with the
reaction-rate method in 100 s or less, but pooled sera
standardized against a reference method must be used as
standards. The problem with the aqueous cholesterol
standard has illustrated one of the disadvantages of the
stopped-flow system. Because sample and reagent are
mixed in a 1:1 ratio, dilutions must be made to obtain
favorable experimental conditions. In the case of the
cholesterol standards, excessive dilution causes the
undesirable problem of turbidity.

In order to use an aqueous cholesterol standard for
the reaction-rate method, a solubilizer for the cholesterol
must be found that does not affect the rate of the enzyme
reaction. Abele et_al. (126) used sodium deoxycholate
(SDC)'to stabilize cholesterol in an aqueous system.

They have shown that the SDC solution was free of inter-
ference with the enzymatic procedure, but like Pesce

33 al. (128), they measured the absorbance change of the

117

reaction after a 12 min waiting period. Thus, they in-
creased drastically the normally fast analysis times of
the CentrifiChem centrifugal analyzer. Furthermore, Abele
£2.21- did not mention any rate studies of the enzymatic
reaction using their solubilizer. Therefore, it may

be worthwhile to investigate this system further in the
future.

Because of the difficulties involved in obtaining
an aqueous standard solution for reaction-rate analysis,
more emphasis should be placed in the future on searching
for an enzymatic system that reacts faster. Rautela and
Liedtke (129) reported a new enzymatic system in 1978.
Instead of using phenol, they used N,N-Diethyaniline-
hydrochloride as part of their chromogen system. With
Triton x-100 as surfactant and sodium cholate as emulsi-
fier, they were able to decrease the time required for
complete reaction to 150 s.

There is still another approach to decrease the
sample analysis times with the kind of aqueous cholesterol
system we have available now. The immobilized enzyme
loop system developed in our laboratory (2) can be used
with the stopped-flow system. Dr. Marty Joseph (2)
has worked on developing an immobolized cholesterol oxi-
dase loop. Although the work needs further refinement,
the technology for immobilization is available (130).

If a multi-loop system can be developed for the serum

118

cholesterol analysis, one can first mix the sample and

the reagent, then draw the mixture into one of the many
immobilized enzyme loops with an inert solvent, so that
while waiting for the reaction to go to completion, one
simply has to switch to another loop for the next sample.
After the reaction reaches equilibrium, the final mixture
can be pushed to the mixing cell for reaction with the
chromogen and then into the observation cell for data col-
lection. The 15 min spent on waiting for the completion
of the reaction can therefore be eliminated by a multiple,

parallel immobilized-enzyme loop approach.

VII. SERUM LIPOPROTEIN ANALYSIS

A. Introduction

 

Numerous studies have demonstrated an association
between serum lipids and atherosclerosis (132,136-138).
Elevated levels of serum cholesterol and low density
lipoprotein have been shown to cause cholesterol ester
deposits in the artery walls, which eventually leads to
atherosclerosis (133). Fredrickson and his colleagues
separated serum lipoproteins by electrophoresis and worked
out a classification system for hyper-lipoproteinemias
(139) on which much of dietary management and drug therapy
depends.

Liquid profiles are obtained by quantitative tech-
niques. Standard methods, which use a preparative ultra-
centrifuge or electrophoresis, take 6 to 16 hours for
each analysis. The purpose of our work here was to
develop a reaction-rate method with the stopped-flow
system so that a complete lipid profile may be done in

less than half an hour.

1. Lipoprotein Profile and Hyperlipoproteinemia

There are three major components of serum lipids:
phospholipids comprise the largest fraction (70% phos-

phatidylcholine, 20% sphingomyellin), cholesterol is the

119

120

second largest group (about 75% esterfied to fatty acids),
and glycerides (almost all as triglycerides) comprise

the third fraction (135). Most of these lipids are
associated with lipoproteins. The serum lipoproteins

are a family of neutral lipids (primarily triglycerides
or cholesterol esters), surrounded by a layer of phos-
pholipid and protein. These particles can be divided
into four categories: chylomicrons, very low density
lipoproteins (VLDL), low density lipoproteins (LDL),

and high density lipoproteins (HDL). The function,
composition, and physical properties of each are summari-
zed in Table 7-1 (136,195,166). In general, the higher
the protein content, the higher the density of the lipo-
protein. The primary function of the lipoproteins is
lipid transportation. Abnormal concentration of any
fraction will create lipoproteinemias.

Fredrickson and coworkers (139) have classified
hyperlipoproteinemia into six phenotypes. The charac-
teristic lipoprotein fractions and electrophoretic pat-
terns are shown in Figure 7-1. A frequency study by
Jones (137) indicated that the bulk of hyperlipoprotein-
emias in medical practice are of types II and IV, while
the odd ones, types I, III, and IV, are sufficiently
rare to be of numerical importance.

High serum LDL or cholesterol levels have been used

as an indicator of hyperlipidemia for the past two

121

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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electrophoretic patterns.

122

decades. Meanwhile there was relatively little interest

in the role of the high density protein (HDL), which
ordinarily carries about 20% of the total plasma choles-
terol. In recent years, however, there has been an in-
creased interest in HDL levels and their significance in
the development of coronary heart diseases (139). Analysis
of HDL will certainly replace that of LDL as an indicator

of coronary heart diseases in the future.

2. Methods of Analysis

Lipid profiles are performed to determine serum or
plasma cholesterol and triglycerides, after which lipo-
proteins are then measured by an analytical ultracentri-
fuge or through electrophoresis (190—196). The former
is more quantitative but takes 8 to 16 hours for each
analysis (190). The most recently developed instrument
of this kind is the Beckman lipoprotein profiling system,
which uses a portable air driven ultracentrifuge with an
oxygen sensitive electrode as detector (193). Cholesterol
determinations in HDL, LDL, and VLDL can be made with 0.5
ml sample within 3 hours.

The second method involves electrophoresis of lipo-
proteins and is generally performed on paper or agarose
gel. When done on paper it takes about 10 hours (191),
but when agarose gel is used, the analysis time is reduced

to 3 hours (192). Because lipoprotein electrophoresis

123

is difficult to control, particularly with regard to
uniform sample application and irregular dye uptake by
lipids, it is only used in pattern recognition. In fact,
Iammarino (138) has suggested that the method be dis—
continued as a routine procedure due to its high cost
and because it offers no additional information to the
data generated by lipid analysis.

Helena Laboratories announced their new line of HDL
electrophoresis instruments early in 1978 and claimed
that their new method was both rapid and precise. They
used a specific enzyme reagent instead of the conventional
Oil Red 0 dye in developing the electrophoregrams, and
thus were able to reduce the total analysis time to 1
hour. But, a careful analysis of their data showed that
relative standard deviations as high as 25% were reported
in their quantitative analyses (199).

In this chapter, a stopped-flow method is reported
that requires only about 1/2 hour to perform and can
avoid the expense of using ultracentrifugation or electro-

phoresis equipment.

B. Stopped—flow Method

1. General Scheme

 

In order to use the stopped-flow mixing technique

for lipoprotein determinations, it was necessary to find

129

a method to separate the three different lipoprotein
fractions without using either ultracentrifugation or
electrophoresis. Thus, several procedures were investi-
gated.

Burstein and Scholnick (198,152) described several
useful chemical precipitation methods fortflmeseparation
of plasma lipoproteins. Fredrickson _£'a1. (156) used
a combined chemical precipitation and preparative ultra-
centrifugation method to separate the lipoproteins.

Later they reported a modified method which totally
eliminated the need for an ultracentrifuge (199). How-
ever, their method cannot be used for patients with sub-
stantial degrees of hyperglyceridemia (199). Wilson and
Spiger (151,155) reported a dual precipitation method as
an improvement of the above, but upon comparison with the
ultracentrifuge method, it was also found to be inapprop-
riate for serum with high level of triglycerides.

Our proposed method is shown in Figure 7-2. The goal
is to estimate the relative concentrations of VLDL, LDL,
and HDL along with the values for total cholesterol and
total triglycerides, such that the sample can be classi-
fied into different phenotypes. Precise quantitation of
the HDL fraction is important, especially in light of its
increasing significance as a correlative index of coronary
heart disease. The serum total cholesterol and total

triglyceride concentrations are first determined. If

I

125

 

chylomicro
HDL

LDL

VLDL

 

ns

 

 

 

Determi

Ctotal

1'18

 

Determi

TGtotal

Q
3

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I

 

ppt. with
ppt. agent

Detn. TGnet

 

 

 

ppt. with
ppt. agent

Detn. CHDL

 

 

 

 

 

ppt. with
ppt . agent

 

 

 

 

 

 

CVLDL= TGnet/ S
C

 

LDL ‘ Ctotal'CHDL'CVLDL

 

 

CVLDL= TGtotal/ 5
CLDL = Ctotal'CHDL'CVLDL

 

 

Type I; III,

V

Normal, Type 11, IV

Figure 7—2. Proposed serum lipoprotein analysis procedure.

 

126

the concentration of triglyceride is normal, precipitation
agents are added to completely precipitate chylomicrons,
LDL, and VLDL. The cholesterol level of the HDL fraction
left in the supernatant is determined, and the choles-
terol concentrations of VLDL and LDL can be estimated as
suggested by Fredrickson (199). If the triglyceride
level is high, one additional precipitation is performed
(198), and the estimation is done by a modified equa-
tion as shown in Figure 7-2.

The proposed method has several advantages over
other methods. First and most important, total serum
cholesterol, HDL, and triglyceride concentrations are
known quantitatively. This allows estimation of lipo-
protein concentrations without separation by electro-
phoresis or ultracentrifugation. Secondly, the total
analysis time is short. Finally, the whole procedure can

be easily automated.

2. Choice of Precipitation Agent

 

Serum lipoproteins are known to form insoluble com-
plexes with polyphosphates and detergents (152), with
polycations (161,150), and with polyanions (153-160).
The polyanions were first shown to give complete, im-
mediate, and selective precipitates by Burstein (198,

152), and the Lipid Research Clinic Program of the NIH

127

adapted a polyanion method (heparin—Mn++) that is currently
widely used in the United States. A mixture of LDL and
VLDL can be prepared by precipitation with heparin and
either MnC12 alone or MgCl2 plus sucrose. Other poly-
anions may also be used either with dextran sulfate and
MnClZ, or with sodium phosphotungstate and Mg012. It

was found that the lower the protein:1ipid ratio, the
easier is the formation of an insoluble lipoprotein-
polyanion-metal ion complex, but the nature of the lipid
moiety does not affect precipitation at all (198). The
nature of the lipoprotein-polyanion-metal ion interation
can be explained by assuming that the electrostatic
interaction between the positive charges of the proteins
and negative charges of the polyanion cause the poly-
anions to combine with the protein moiety of the lipo-
proteins to form soluble complexes. This is easily proved
by agarose electrophoresis (163). These compounds are
then precipitated by divalent cations.

The heparin-Mn++

precipitation process has been shown
to correlate well with the accurate but time consuming
ultracentrifugation method (153,155,159,160). However,

it has several undesirable problems. Not all heparin
preparations are equally efficient, and thus the complete-
ness of VLDL and LDL precipitation must be checked each
time a different lot of heparin is used (158). Also the

Mn++-heparin procedure requires that the sample be

128

placed in an ice-bath for 30 min. after the precipitating
reagents are added. Sera with triglyceride concentrations
of more than 900 mg/dL may require prior dilution before
precipitation (153,169). If an enzymatic technique is

++ sometimes forms

used to measure HDL cholesterol, the Mn
a visible precipitate with the enzyme reagents and also
contributes a variable and significant blank (157).

The application of Mg++-dextran sulfate as the
precipitation agent has recently been adapted for routine
lipoprotein quantification (158). There has not been
any further report on the reliability of the procedure,
and therefore this method was not studied here.

Lopes-Virella at 31. (157) described a routine
method using Mg++-sodium phosphotungstate. Values thus
obtained compared well with the ultracentrifugation method,
and the method does not have theproblems experienced with
the Mn++-heparin method described (157). Personal com-
munication with a local clinical laboratory confirmed
the reliability of the method (165). Pierce Chemical Co.
(Box 117, Rockford, IL 61105) manufactured a HDL-choles-
terol rapid STAT kit in 1977 that uses the phosphotung-
state-MgCl2 method. This kit also has unique features
that make it best suited for adaptation to the stopped-
flow system. Therefore, we chose this as our precipita-
tion agent. Details of the reagent have been presented

in the cholesterol chapter.

129

3. Separation of the Lipoprotein Fractions

The polyanion-metal precipitation method is very
efficient in separating HDL from the other fractions.
The HDL fraction remains in the supernatant while the
chylomicron, VLDL, and LDL fractions are precipitated.
Electrophoresis studies have shown that the precipitation
is selective and complete (198). In order to further
separate the remaining fractions quantitatively, ultra-
centrifugation must be used. In fact, the Lipid Research
Clinic program recommended using ultracentrifugation to
separate VLDL from LDL and HDL before separating the HDL
from the other fractions by precipitation (166).

Friedewald gt_al. (199) described a simple method
to estimate the concentration of VLDL and LDL. Their
procedure is very helpful in the interpretation of lipo-

protein profiles, and it is based on the following rela-

tionships:
CVLDL = TG/5
CLDL = Ctotal ' CHDL ' CVLDL
where T0 = serum triglyceride concentration, and
C = cholesterol concentration in the HDL,

LDL, and VLDL fraction

all units are expressed in mg/dL.

130

These equations are based on two observations: (1)
the ratio of the mass of triglyceride to that of cholesterol
in VLDL is apparently relatively constant and about 5:1
in normal subjects; and (2) when chylomicrons are not
detected, most of the serum or plasma triglycerides are
in the VLDL. The equations are fairly accurate when the
TG level of the serum is less than 900 mg/dL, making it
suitable for normal and type II patients (see Table 701).
But the use of the ultracentrifuge remains necessary with
the much rarer type I, III, and IV hyperlipoproteinemia.

Dual-precipitation methods have been proposed. De-
tergents such as sodium dodecyl sulfate were used to
separate the VLDL fraction (159,155). However, in-
complete aggregation of VLDL by sodium dodecyl sulfate
and the long incubation time reported do not justify the
adaptation of these methods in place of the ultracentri-
fuge.

A modified procedure, which was listed earlier in
Figure 7-2, is proposed in this work. The total choles-
terol and triglyceride levels are first determined. If
no elevation of the serum triglyceride level is observed,
the HDL and VLDL, LDL fractions are separated by the Mg++-
phosphotungstate method using Friedewald's equations to
calculate each concentration. If TG is larger than 350
mg/dL, an extra precipitation step is taken to determine

the net concentration of TG present in VLDL before

131

 

 

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132

calculating the concentration in the different fractions.
In our final lipoprotein profile, we will have total
cholesterol concentration, total triglyceride concentra-
tion, HDL cholesterol concentration, and an estimate of
the concentrations of all 9 different fractions of lipo-
proteins. This information combines the best of the old
(Fredrickson's phenotyping) and the new (CHDL) indices
for a complete profile.

Finally we have to consider the physical method of
separating the HDL in the supernatant from the VLDL and
LDL in the precipitate. Traditionally, the sample was
mixed and centrifuged in a table-top centrifuge (1500 x
g, 9°C) for 30 minutes. But, since Burstein reported
that the precipitation process is immediate (198), pre-
cious time is lost in the centrifugation process.

Warnick and Albers (160) used ultrafiltration in
their attempt to clear up the HDL containing supernatant
after centrifugation for 30 minutes. The flow rate was
quite acceptable (1 mL/min). We explored the possibility
of using ultrafiltration to replace centrifugation, thus

cutting the total analysis time by 30 minutes or more.

9. The Ultrafiltration Method

Fresh serum samples from fasting patients in Sparrow
Hospital were analyzed. To each 1.0 mL serum sample, 0.1

mL phosphotungstate-Mg++ precipitating reagent (Pierce,

133

Rockford, IL) was added, making the final concentration of
MgC12-6H20 1% (W/V) and phosphotungstic acid 0.9% (W/V).
Three samples were then centrifuged at 1000 x g for 20
minutes. The clear supernatants were aspirated out, and
the cholesterol contents of these HDL fractions obtained
by the Pierce manual method using an HDL/Cholesterol
Rapid STAT kit (product #99090,99002).

Another three samples were processed as follows:
a 0.22 um Millipore filter (Millipore Corp., Redford,
Mass. 07130), 25 mm in diameter, was placed on the lower
support of a Swinnex filter holder, and a silicone gasket
was put on the filter. Then an AP 15 and an AP 20 glass
depth prefilter (22 mm in diameter) were fitted into the
gasket. The upper unit of the Swinnex holder was tight-
ened over the lower support to form a complete filtration
assembly. Figure 7-3 shows the filtration assembly. The
1.0 mL precipitated suspension is then forced through the
filter assembly from a 10 mL Syringe, with a flow rate
of approximately 1 mL/min. The clear supernatant was
then collected for HDL cholesterol analysis.

The results obtained are presented in Table 7—2.
The difference in observed values between the two methods
is compatible within experimental error. From these
results, it seems reasonable to conclude that ultra-
filtration is a separation technique which is at least

comparable to centrifugation. The filtration process

139

 

 

 

*IOmI Syringe

 

 

 
  
  
    
  

Silicone

gasket
APIS

 

Swinnex_ ’W APZO Depth prefilter
filter . . .
holder 0.22pm Millipore filter

Figure 7—3. The Complete Filtration Assembly.

135

Table 7-2. Comparison of the centrifugation method with
the ultrafiltration method.

 

 

 

Centrifugation Ultrafiltration
HDL Conc.* RSD HDL Conc. RSD
(mg/dL) (mg/dL)
55.6 3.6% 59.8 9.3%

 

 

*Average of 3 runs, total serum cholesterol conc.=230 mg/dL.

136

takes 1 minute instead of 20 minutes, and the filtration
assembly is disposable if necessary. Ultrafiltration has
the additional benefit of eliminating possible turbid
supernatants that are sometimes found with the centrifuga-
tion method. Therefore, this separation technique was

used in all further studies.

5. Experiment with Fresh Human Serum

Lipoproteins are not stable complexes and therefore
fresh serum samples are required in serum lipoprotein
analysis. We obtained three fresh serum samples from
Sparrow Hospital for analysis. The total triglyceride
and cholesterol concentrations were determined as follows:

Glycerol standards for serum triglyceride analysis
were prepared as described in Chapter 5. A standard
curve was prepared by using the initial rate method.

All analyses were carried out at 30°C, and the reactions
were monitored at 390 nm for 60 s. For each sample,
0.25 mL human serum was added to vial A of the "Stat-
Pack" reagent kit and was reconstituted with 8.0 mL of
distilled water. Details of the procedure can be found
in Chapter 5.

Cholesterol was analyzed with the equilibrium
method. Aqueous cholesterol standards were prepared from
pure cholesterol as described in Chapter 6. The Pierce

cholesterol Auto/STAT kit was used for the working reagents.

137

Human serum samples were diluted 50-fold with the 2%
phenol reagent provided. The two solutions were mixed in
the stopped-flow system at 30°C, and the absorbance was
measured at 510 nm 15 minutes after mixing.

The results for the total cholesterol and total tri-
glyceride determinations are listed in Table 7-3. Since
all the triglyceride levels were found to be below 350
mg/dL, we proceeded to follow Scheme A of Figure 7-2
and added 0.1 mL phosphotungstate—Mg++ reagent to 1.0
mL of each serum sample.

The separation of the precipitate was then performed
by ultrafiltration, and the cholesterol content of the
filtrates were determined. The results are again shown
in Table 7-3.

Using Fredrickson's equation, discussed earlier, con-
centrations of cholesterol in the different fractions of
lipoprotein were calculated, and they are listed in Table
7—9. The three samples we obtained all showed values
that were within the normal range. If the serum were type

II abnormal, the C concentration should be very high,

LDL
whereas if the samples were type IV, CVLDL would be
elevated. We therefore conclude that all three serum
samples are normal. Using the same samples, a cellulose
acetate plate electrophoresis study was performed with

a procedure developed in cooperation with Dr. Hans

Lillevik of the Michigan State University Biochemistry

138

Table 7-3. Lipid Analysis on Three Human Sera.

 

 

Serum #1

HDL =

Chol

TG =

Serum #2

 

HDL =
Chol =

T0 =

Serum #3
HDL =

Chol

TG

RSD
98 (Norm = 90-75) 5%
215 (Norm = 150-250) 1.9%
81 (Norm = 30-150) 3.8%
62 (Norm = 90-75)
251 (Norm = 150-250)
115 (Norm = 30-150)

69 (Norm = 90-75)
190 (Norm = 150-250)
95 (Norm = 30-150)

 

 

139

Table 7-9. Lipoprotein Analysis on 3 Human Sera.

 

 

quation

CVLDL = TGtotal/S

CLDL = Ctotal ’ CHDL ‘ CVLDL

Regalia CVLDL CLDL CHDL
Serum #1 16 155 98
Serum #2 23 166 62
Serum #3 9 122 69

Normal range (0-90) (62-185) (90-75)
Type 11 range (0-78) (173-890) (18-82)
Type IV range (6-356) (28-231) (15-79)

 

 

190

Department (See Appendix C for details of the procedure).
The resultant electrophoretic pattern is shown in
Figure 779. The normal lipoprotein pattern confirmed
our stopped-flow results.
HDL analysis has become increasingly important in
the past two years. Unlike electrophoresis data, our
results give quantitative concentrations of serum HDL.
Since the normal range of HDL is not very large (90-75
mg/dL), a less precise method would create false positive
or negative results. The stopped-flow method gives
results with better than 9% RSD at this low concentration
range, which is comparable to the currently available

manual methodology.

C. Conclusions

Although we did not encounter any abnormal samples
in our limited sampling, we have shown that the stopped-
flow method is feasible for obtaining a total lipoprotein
profile (total cholesterol, total triglyceride, HDL, and
phenotype of serum) in about 30 minutes. Analysis time
can easily be reduced to 15 minutes if the reaction-
rate method of cholesterol analysis is used. At this moment,
we have to use commercially prepared enzyme reagents, and
the reagent cost for each complete analysis is almost
$3.00. This high cost can be reduced by developing

multiple—loop immobilized systems as described in the

191

 

 

I’m '73

 

 

Figure 7-9.

DENSITY

Electronhoretic pattern for serum sample.

ORIGIN

DISTANCE FROM THE ORIGIN

192

cholesterol chapter, because then the expensive enzymes
would be reusable. The sample throughput rate would also
be further increased with this arrangement. The whole
process can be totally automated when the solution prepa-
ration and the filtration procedures are brought under

computer control.

VIII. FUTURE DIRECTIONS

The experiments performed in this thesis have il-
lustrated several unique characteristics of the stopped-
flow system in clinical applications. We found the system
excellent for routine clinical analyses in many ways.

The throughput rate is generally increased using the
reaction-rate method. The fast mixing characteristic of

the system allowed investigation of the initial rates of

 

rapid reactions with ease. The same feature also enabled .
us to study fast reactions, such as the bromcresol green-
albumin reaction, and in the process devise a way to
eliminate most of the interfering reactions.

On the other hand, several undesirable problems were
encountered. Several tests became uneconomical because
of the necessity to rinse the stopped-flow system between
samples with expensive reagents. We also met with tur-
bidity and some mixing problems mainly due to the require-
ment of using a 1:1 sample to reagent volume ratio. While
the results presented demonstrated some of the analytical
capabilities of the stopped-flow system, there are
probably many more routine chemical analyses that have
not been investigated by reaction-rate methods but are
adaptable to the system.

Pinnell and Northam reported a bromcresol purple

(BCP) method for analyzing serum albumin. They claimed

193

199

that the dye is specific to albumin, thus eliminating the
interfering problem to which BCG is susceptible (190).
Furthermore, they reported that the BCP reaction with
serum is an instantaneous one, making it very worthwhile
for future investigations with the stopped-flow system.

Enzymatic analysis of uric acid was done with a centri-
fugal fast analyzer (189). The reaction is relatively
fast, and the use of an early reading blank-corrected
approach was found to be desirable(189). The uricase/
catalase/aldehyde dehydrogenase-coupled procedure is
also ideally suited for adaptation to the stopped-flow
system.

The Jaffe reaction for serum creatinine appears to
follow pseudo-first-order kinetics (192) and this
routinely determined substrate can be easily analyzed
by the reaction-rate method using the stopped-flow instru—
ment.

Another commonly determined substance is serum alcohol.
Jung and Ferard described a specific and precise enzymatic
reaction which reached equilibrium after only 9 min (193).
No stopped-flow method for serum alcohol has been reported
yet.

One may also try to apply the simplex method des-
cribed in Appendix A in differential rate analysis for
mixtures. Pelizzetti 23 al, reported a kinetic determina-

tion of adrenaline, L-dopa and their mixtures with a

195

stopped-flow system (191). The simplex technique should
be superior to the single-point method of Lee and Kolthoff
they were using.

Another approach in research should be directed
towards developing the immobilized enzyme loops as men-
tioned in Chapters 6 and 7. Successful adaptation of
these loops onto the stopped—flow system would mean an
increase in throughput rate and a decrease in cost per
analysis.

Referring back to Table l in Chapter 2, one can see
that we have only explored a small fraction of the clini-
cal tests routinely performed. The largest unexplored
area is the analysis of enzymes in serum. The stopped-
flow system is especially suited for this kind of analysis
because all procedures for serum enzyme analysis involve
reaction-rate measurements; and the amount of enzyme
present in serum can be measured only indirectly in terms
of its activity (or rate of reaction) with its substrate.
Commonly determined enzymes such as SGPT, SGOT, LDH,

CPK, ACP and ALP all fit into this category.

Another important area for further work is the de-
termination of isoenzymes. Kaplan et_al. (59) were the
first to apply the stopped-flow system in a differential
determination of LDH isoenzymes. They pinpointed the
exact source for abnormal levels of LDH enzyme and used

the result as a sensitive test for myocardial infraction.

196

Their method was superior to conventional separation
methods such as electrophoresis because analysis time
was drastically reduced. Bostick and Mrochek ( 58)
reported a procedure for creatine kinase MB isoenzyme
using differential kinetics with a centrifugal analyzer.
This should also be suitable for the stopped-flow system.
Pardue had demonstrated that the stopped-flow system
could have an attractive throughput rate even for conven-
tional types of equilibrium analyses (1). Thus, the
stopped-flow system seems to be applicable to virtually
all types of wet chemical analyses performed routinely
in clinical laboratories. And in addition, it has a
capability for making fast measurements that are not pos-
sible with any of the conventional instruments. We feel
the stopped-flow system would make an excellent 'stat'
analyzer in clinical chemistry. Further research would
be centered around methodological development, complete
automation of the system, and the decreasing of the dead
volume in the system to minimize carry-over problems.
Automated sample preparation, valve sequencing, and simple
data processing can be brought under microprocessor control.
Chemically inert and inexpensive high pressure liquid
chromatography valves and fittings that have small dead
volumes can be used in an improved design of the system.
The continuous development in analytical methods should
bring about wider acceptance of the system in the clinical

chemistry field.

APPENDICES

APPENDIX A

APPLICATION OF THE SIMPLEX METHOD IN DIFFERENTIAL
KINETIC ANALYSIS

A. Introduction

A clinical chemist is often faced with the difficult
task of determining the fastest way to handle several var-
iables which are often known to interact. Spendley gt al.
(171) introduced an idea in 1962 for tracking optimum
operation conditions called the simplex optimization
method. Essentially it searches for the optimum using
empirical feedback strategy. Compared to other optimiza-
tion methods, it requires fewer experiments for each move.
It is also more compact, involves simple computations, and
is particularly attractive for automation.

Nelder and Mead (172) modified the original fixed-
size simplex method. Later Long applied it to analytical
chemistry (17“). Recently it has been applied in clinical
chemistry (176). Several excellent reviews about the
simplex optimization method have been published (167,169,
175,195), and at least one paper has indicated its pos-
sibility in regression analysis (187).

With the advent of high speed computers, linear least
square analysis has been used in routine statistical

analysis of data (179,180). However, more complex problems

197

198

such as non-linear or arbitrary functions sometimes require
special constraints upon the data collections; or a user
may face miserable failure (when an exasperated computer
finally print out a message of defeat), or even disastrous
failure (when the computer and user think they have found
the answer) when improper procedures are employed. Matrix
inversion is usually required in the curve fitting process
and can lead to serious round-off errors in the calculation
if handled improperly (185,186).

A powerful general purpose curve fitting program called
'KINFIT' was designed by Dye and Nicely (182) and was
very successful using CDC 3600 and 6500 computers as well
as IBM 7099 and 360-75 computers. In the process of doing
differential kinetics analysis in our laboratory, the need
for a simple and computationally more compact program to
be used with a 16K PDP 8/e minicomputer became evident.
This need stimulated an investigation of the simplex
method in curve fitting. This idea is explored in this
chapter, and experiments with computer-simulated data are

reported to demonstrate the feasibility of the idea.

B. The Super-Modified Simplex

1. General Description

 

The Nelder and Mead modified simplex has been used

widely, but the procedure sometimes fails in stochastic

199

or noisy environments due to premature simplex contractions,
adherence to false ridges, or reluctance to approach the
boundary constraints (178). Denton gt al. (178) developed
a super-modified simplex (SMS) procedure that increased

the utility, reliability, and efficiency of the Nelder and
Mead version. We further modified the SMS and applied it
in least-square analysis as described later. The rules of
the Nelder and Mead modified simplex are briefly reviewed
below to facilitate the understanding of the SMS (169,

172).

A simplex is a n-dimensional geometric figure containing
n+1 vertices. For example, the initial figure of a two
dimensional simplex is a triangle with vertices VBVNVW’
as shown in Figure A-l. These three vertices were measured
and vertex VB was found to be the best response, Vw the
worst response, and VN the next-to-worst response. ‘P is
the centroid of the face remaining after the worst vertex
has been eliminated (169). The optimum in the response
surface can be found by one of several different moves
as listed in Table A-1. To eliminate the worst response
Vw, Table A-1 again provides us with several measures:
it can be replaced by VR through reflection, by VE through
expansion, or by VCR or VCW through contraction. A
failed contraction occurs when the response at either VCR
or VCw is worse than the response at VR or Vw, respectively.
When this happens, a "Massive Contraction" move is then

made, each leg of the simplex is contracted to one half

150

 

 

 

 

 

REFLECTION EXPANSION
/\

\
L
I

I

I

I

CONTRACTION

 

Figure A-l. Basic moves of a simplex.

151

Table A-1. Basic Moves of a Simplex.

 

 

VE = P + y(P - Vw) y = expansion coeff.=2
VCR: P'+ 8(P - Vw) B = contraction coeff.=0.5

<;
O
2
ll
“UI

-e@-vm

 

 

152

its present length towards VB, forming a smaller new
simplex VBVN'VW' or VBVN'VR" The responses are then
determined and the optimization process continued. Boun-
dary violations are handled by assigning a poor response

to the vertex that violates the boundary and the new

vertex is determined by a CW contraction. A flow chart

of the modified simplex is shown in Figure A-2. Reflection
is always the first move, followed by expansion or contrac-
tion, while massive contraction is used only when the

contraction has failed to give a better response than the

original worst response.

2. Procedure for the Super—Modified Simplex

The flow chart for the super-modified version is shown
in Figure A-3. The initial vertex and the responses are
determined as before. A reflection is made to determine
the new response RVR. Now, instead of expanding or contract-
ing with a fixed coefficient, a second order polynomial

2+Bx+C) is fitted through the responses at

curve (y=Ax
Vw, P, and VR' If the optimum sought for is a maximum,
and the slope A is negative (i;§;, the curve is concave
down), the maximum can be located within the interval by
evaluation of the derivative of the curve. The response
of this new vertex can then be determined, and after the

safety and boundary checks, the optimization process can

be continued. If the curve concaves up, no maximum can

153

 

 

@[mra

 

 

Reflection
No Yes No
7 7
Y No

es
NO
RVE<RVBT Vw ””9.
Yes
in.
<:::>--—--N found?

LJI

Figure A-2. Procedure for the modified simplex.

 

 

 

   

 

 
 

Iassive
ontractio

FE-

 

 

 

 

  

 

159

 

 

 

Reflection

Flt Rw, RP'RVR

through y-Ax2+Bx+C
determine A.B

Extend VW & VR by
theoretical response

Locate the mm‘xlo Pick direction

 

 

 

 

 

 

 

C811 this VR' of expansion

 

 

 

 

 

 

 

V Isafty
R! (Expansion )
factor '®

 

 

 

 

Va.-I

boundary

 

 

 

 

 

 

.Yes EXIT J

Figure A-3. Procedure for the super-modified simplex.

155

be located. The curve is then expanded a percentage of
(VWTE) and the extended interval boundary producing the
highest predicted response is chosen as the new vertex
location. Further expansion can be made by testing the
slopes at these extended boundaries, deciding upon the
direction of expansion, and expanding according to the
magnitude of the slope.

The SMS procedure thus allows the simplex to locate a
new vertex more freely and move much faster towards the
optimum by checking a larger response surface during each
move by curve fitting. Although additional calculations
are required, there is virtually no delay in experimental
time since all calculations are performed by the mini-
computer.

A subroutine SMSMPX.FU was written following the
algorithm described. It chains to other subroutines that
input parameters in an interactive mode, print out results
in several modes, and plot the simplex after each itera-
tion as desired. A detailed description of the program,
as well as the working program written in the FORTRAN IV

language, is listed in Appendix B.

3. Design of the SMS Algorithm

This section describes the basic factors considered

while designing the algorithm of the SMS subroutine.

156
i). Fitting a second degree_polynomial curve - Instead
of expanding or contracting with a fixed coefficient in each
move, 3 points (VR,VW,F) are fitted to the equation

y = Ax + Bx + C

therefore we have three equations as follows:

_ 2 O
yl Axl + Bxl + Cx1
y2 = Ax22 + Bx2 + ng

_ O
y3 - Ax3 + Bx3 + 0x3

Solving for the unknowns A, B, and C by matrix methods,

we have
A = (y1X2+le3+V2X3-Y3X2-X3yl-Y2Xl)/D
_ 2 2 2 2 2 2
B - (xly2+ylx3+x2y3-x3y2-y3x1 x2yl)/D
c = y -Ax2-Bx
l l l
where

157
We can simplify the equations by letting x1 = -1, x2 = O,
and x3 I l as the x coordinates for the 3 responses. The
resulting equations are

A = l/2(y1+y3-2y2) = 1/2(R+w-2C)

B = 1/2(yl-y3) = l/2(R-W)

where R - response at VR;

w a response at Vw;

C response at F.

Finding A and B in this manner, we can proceed to find

the shape of the curve as described in the next section.

ii) Determination of minimum and maximum - The second

derivative of the function Y = Ax2

+ Bx + C was calculated
to see if it is at a minimum or a maximum. If the second
derivative is positive, the function curves upward and
there is a minimum. If it is negative, the function curves
downward indicating a maximum. And if the value is zero,

it means that there is an inflection, which may be a maximum,

or a minimum, or neither.

iii) Expansion coefficient - The next step is to de-
cide how much further we are going to expand or contract

the vertex VR. Take the example of a maximization process.

158

If no maximum is found, the polynominal curve is then
expanded further by a factor in order to investigate more
portions of the response surface. The magnitude of this
factor can be decided by looking at the slope of the new
vertex at the extended boundary. Denton gt al. (12)
suggested that the greater the slope (indicating rapid ap-
proach to the optimum location), the smaller the required
expansion coefficient; and conversely, the smaller the
slope (indicating remoteness from the optimum location),
the larger the required expansion coefficient. We found
that there is a problem with this concept. It is difficult
to define a "large slope" as such, because the value of a
slope depends on the units one is using. An alternate

way to attack this problem is to look at the ratio of the
old and the new responses and decide upon the size of the
expansion coefficient accordingly. In an optimization
process for the maximum, if the ratio is large (indicating
rapid approach to the optimum location), use a small expan-
sion coefficient; but if the ratio is small or is close to
l, we want to expand more to explore new grounds. The

following equation was found to work quite well,

x = new response/old response

y = expansion coeff. = —2.75x + 6.75

159

iv) Safety factor - Due to the adaptation of the curve
fitting method, the new vertex may occur at or very near
the centroid. This will reduce the dimensionality of the
process and may terminate the progress of the simplex.
Therefore a small safety interval is placed between the
centroid and the new vertex at the beginning of the search.
We picked 0.2 out of 1.0 absolute scale to be this safety
factor. As illustrated in Figure A-H, when the new vertex
is located within this range, we set it equal to 0.2.

Use of the safety interval is unnecessary when approaching
the termination of the optimization search and can easily

be eliminated near the optimum.

v) Boundary violation - When VR is located outside
of the boundary constraint, we simply set the point at
the boundary which is intersected by the vector connecting
VW and VB as the effective VR, we call this new vertex
VR" The polynomial curve is then fitted through the
responses Of VW’ F, and VR" and the search continues.
This process is illustrated in Figure A-S. The method
prevented the old problem of reluctance to approach the
boundary constraint reported in the modified version of

simplex (178).

vi) Initializing a new simplex - Usually the first

question that confronts a user of the simplex method is

160

        
    
   

   

I
IV

 

 

-1.o -o.2 L; R 0.2 .0
VW I'Pl VRO

 

i
I

Figure A-h. Safety factor in SMS.

 

 

Boundary
I ,Constraint

 

Figure A-5. Boundary violation in SMS.

161

how to design the initial simplex. Long (17h) described
in detail the construction of initial simplexes of up to
ten factors. Instead of selecting the step size and the
initial vertex randomly, a systematic algorithm is used.

The following is an example of a two dimensional simplex.

1) Choose the initial vertex (V1);
2) Choose step size (Si);

3) Calculate p1 and q1 with N = number of factors;
p1 = (Si/(N*21/2))((N+l)1/2+N-l)
q1 = (Si/(N'2l/2>)(<N+1)1/2'1’

A) Calculate the 3 vertices using pi and q1.

'<
a

1 (x1,y1)
V2 3 (x1+pl’yl+q2)

.<
u)
I

' (x1+qlsyl+p2)

A subroutine called VERTEX is written to help automatic
calculation of the initial simplex. The user Just has to
type in the step size and the initial vertex to start the

simplex process. This program can be found in Appendix B.

vii), Convergence and global optimum - There are many
ways to check for convergence. Examples are methods based
on objective function, zero slope, quadratic fit, variance

of responses at simplex vertices, or predetermined number

162

of iteration steps (181). We found that using a small pre-
assigned residual value to stop the optimization process
provided satisfactory results. To assure that the optimum
is global, two or more different regions of the factor sur-
face are used as starting points. If the same optimum is

obtained, the optimum is indeed the global one.

C. Simplex as a Curve Fitting Method

A generalized equation we used in our experiment is:

where kA and kB are pseudo-first-order rate constants.
At any time ti’ the concentration of product in terms of

the initial concentration [AJO and [B]O is

-k t -k t
[P] = [A]O(l - e A 1) + [310(1 - e B 1)
In terms of observed absorbance,
-k t -k t
Y1 = eb{[A]0(1 — e A 1) + [810(1 - e B 1)}

The objective is to determine [A]O and [B10 by obtaining

the best fit of the observed Y1 values in response signal

163

and by using an optimum set of data points.

The data are n pairs of observations (Y1 and t1,
where i=1 to n) taken in a fixed period of time. The dif-
ference in the observed absorbance values and the calcu-
lated absorbance values are the residuals (pi). In random
data, pi will be centered about the average (E’= 0) with
a standard deviation 01‘ We want to minimize the sum of
the residual square with the least square method.

If all Oi are equal, we have the following equation:

n

pi - minimum
i-l

If the 01 are not equal, a weighting factor “1 is used.
One weighting method is shown in the following:
n 2
m u 8 minimum
1:21 11
where

m1 = 1/03

The effect of “i is to de-emphasize imprecise data
points. The detailed treatment concerning the principle
and application of linear-least square regression analysis
can be found in most statistics text books.

We have taken into account the fact that the simplex

16“

method is computationally compact because there are few
multiplications, no divisions, and no matrix calculations
at all. The super-modified simplex has also been shown

to be efficient and reliable.

D. Tests with Simulated Data

We proceeded to generate simulated data with the com-
puter and studied the factors that affect the speed, pre-
cision, and effectiveness of using the simplex method in

regression analysis.

1. Simple Mathematical Models

Least square regression analyses on 3 equations shown
in Table A-2 were performed. LLSQ is a general linear
least square method available from most statistical text
books. CRFIT is a non-linear curve fitting routine adapted
from Bevington's book (177). It uses a combination of
gradient search and linearization technique. Simplex per-
forms equally well as the traditional methods; in the non-
linear case in which there are 6 different unknown parameters
to fit, the simplex routine found the optimum faster than
the CRFIT method and in the case of poor initial estimates,
it has a lower rate of failure to find the global maximum
point. These initial studies with simulated data gave

encouraging evidence that simplex is suitable for simple

165

Table A-2. Regression Analysis with the Simplex Method.

 

 

Equation #1
y(x) = alx + b

 

Actual LLSQ Simplex
a1=20.0 20.0 20.0
Equation #2
y(t) = a1(l-e ) + a (l-e
Actual CRFIT Simplex
a1=0.100 0.099 0.100
a2=0.200 0.200 0.199
Equation #3
x-a 2 2
y(x)=a1exp -0.5( a3 ) +au+a5x+a6x
Actual CRFIT Simplex CRFIT Simplex
(good int. est) (poor int. est)
a1=208.2 207.99 210.70 “0.81 162.6
a2= 56.05 56.0“ 56.03 50.2 56.5
83: 3056 308“ 3056 1059 3055
au=l86.6 185.8 186.2 227.5 295.4
a5= -2.30 -2.27 -l.92 -h.2u -0.59
a6= 0.0096 0.0093 0.0098 0.025 0.051

 

 

166

regression analyses. We performed a series of tests on
Equation 2 in Table A-2 and used that as a guideline on
selecting optimum performance conditions and present them

in the following sections.

1) Effect of ratio of rates,_rate constants,_and
concentrations on error - We ran a series of tests which
contained ratios of rates from 0.006 to 250, rate constant
ratios from 1.2 to 10, and concentration ratios from 0.005
to 25. A total of 88 runs were made. The initial esti-
mates of concentrations A and B were up to M0 times dif-
ferent from the actual concentrations. Four different
starting points were used in each run to ensure that the
optimum obtained were global. Simulated noises, generated
by the computer, was added to study its effect on error.

The data are tabulated and presented in Figure A-6.
With the equations used, we found that the ratio of the
rate constants kA and kB should be larger than 1.2. Any
thing smaller produced a large error even with noise-free
data. In our example, reagent A reacts faster than re-
agent B, and the error on determining the concentration of
A is affected both by the rate constant kA as well as
the initial concentration of A. The product of the con-
centration and the rate constant gives rate A, and as
can be seen in Figure A-6, a small rate A/rate B ratio

gives large error.

167

  

0% Noise

    

% Error

   

 

 

4. :4 50
(Rate A/ Rate B)

0 i

20-

1% Noise

 

 

 

 

(Rate A/ Rate B)

    
   

 

 

100 -- B
5% Noise
as
8 S .L
I...
H
a:
*3 A
o i i % 2 50
(Rate A/ Rate B)
Figure A—6. Effects of rate differences and noise on

error.

168

An excessive noisy response surface sometimes causes
false convergence of a search at local optima. We found
that the simplex method worked well up to a 5% noise level.
The simplex method is less prone to the noise problem than
the conventional curve-fitting methods due to 2 reasons:
(1) if the differences in the responses are large compared
to the size of noise, the simplex will move in the proper
direction; and (2) if the difference in the responses are
smaller than the noise, the simplex may move in the wrong
direction. However, a wrong move will probably yield a
lower response that would cause the simplex to proceed

again towards the optimum.

ii) Effect of initial simplex step size on efficiengy
- There had been varied opinions on how to choose a suit-
able starting point for the simplex method. Long dis-
cussed the effect of step size on the efficiency of the
simplex method (17A). He pointed out that too large an
initial step could cause the simplex to miss the optimum;
but this would only apply to fixed-size samples. An
initial large step size is usually an advantage, since
the optimum is approached more rapidly.

We studied the same problem with the super-modified
simplex and found that it is indeed advantageous to start
with a large step size. Figure A-7 shows four randomly

selected initial simplex vertices. The smallest step size

169

 

 

 

 

 

.0004.”
qb
m
M
0 ur-
c:
O
.1
u
d
t:
8
0
8 ~+ *
C) optimum
W
0 i

l
.oboz
Concentration of A

Figure A-7. Effect of initial simplex size on ef-
ficiency.

170

needed “6 iterations to attain the optimum, while the lar-
gest needed only 8. It is apparent therefore that a large

initial simplex should be used for the SMS method.

iii) Weighting by variable data acquisition rates -
Weighting of data has been done traditionally by using
empirical weighting factors. Bidder and Margerum (188)
attempted to account for the difference in weight of the
data in terms of the magnitude of the signal and to offset
the overemphasis of the slower reacting component by using
variable data acquisition rates. They determined the ap-
propriate sampling rate by the following equations:

th

no. of data point taken at x rate

L Ix-Ix_l

th

and, rate of data acquisition for the x component

"Mt“

- N ;L_
r'x ' I i

i x

where N total no. of data points;

L

total no. of reacting components;
x = no. of the component as listed in order

from largest to smallest rate constant;

171

I = interval of time defined by A half-lives
of the designated components; and

= u(o.693)/k.

According to their calculation, one should obtain two
sets of equations that gives the rates of data acquisition
and the number of data points taken for both the faster
and the slower reacting components. These equations are
used to calculate the optimum sampling rates with the input
data shown in Table A-3.

The calculated optimum sampling rate is 51 points taken
in 5.59 s initially. We investigated this calculation using
simulated data with the simplex method, taking 50 data points
for the fast reaction initially and 50 data points for the
slower reaction. We varied the initial sampling periods
and obtained the total errors in estimating the initial
concentrations of substrates A and B. The results ob—
tained are listed in Table A-3. The optimum data acquisi-
tion rate found by simplex is taking 50 points for 5.7 s
for our reaction, which agrees quite well with the cal-
culated values. These results confirmed the prediction
made by the method of Ridder and Magerum and strongly sug—
gested that all differential rate analysis of multicom-
ponent mixtures should be performed in a variable data

acquisition rate mode.

172

Table A-3. Weighing by Variable Data Acquisition Rates.

 

 

 

Initial Sampling Perioda Total Error
M6.8 sec 0.A6%
25.2 0.32
17.6 0.30
10.6 0.32

7.8 0.32
6.7 0.17
6.2 0.12
5.7 0.10b
11.6 0.13
A.“ 0.13

 

 

aTotal sampling period = 270 3; total number of data
points = 100; number of data points taken in the initial
period = 50.
bInput parameters are kA=0.5, kB=0.01, [A]=0.0001,
[B]=0.0002, e=2000; theoretical optimum sampling rate
is taking 51 points in 5.59 s.

173

iv) Effect of length of samplinggtime on error -
Should we take data for the entire duration of the slower
reaction then? Ridder and Margerum suggested the time of
sampling should be four times the half-life of the slower
reaction. We checked this with the simplex method, and
expected to observe dramatic increase in error when the
total sampling time is reduced.

For the reaction we are studying, four half—lives of
the faster reactant equaled 1.38 s while that of the slower
reactant, four half-lives equaled 277.2 s. We proceeded
to reduce the total sampling time to find its effect on
error. The results are presented in Table A-h. The experi-
ments were performed with simulated data with 1% random
noise added. It is surprising to find that with a sampling
time as short as 35 3 (approximately one half-life of the
slower reactant), the error obtained was not much higher
than that of 280 3 (four half-lives). As the sampling time
is reduced further, the error increased dramatically. When
the total sampling time is smaller than one half—life of A,
the error becomes unacceptable. Our results indicate that
for very slow reactions, the total sampling time may be
reduced to about one half-life of the slower reactant in
order to increase the sample throughput rate as well as
to decrease interferences that may be caused by the

products.

 

179

Table A9. Effect of Length of Sampling Time on Error.

 

 

 

 

 

Total Sampling Period Total Error

280 sec 0.1%

210 0.1

190 0.15

703 0.10

35 0.16

20 0.67

10 1.50

5 3-55

1 16.30
a“(A-1.38 s
tB-69.3 s

RIB-277.28

175

E. Conclusions

We have shown that simplex is a useful tool for re-
gression analysis. Although we did not make any actual
applications with it, our studies with computer simulated
data have given us several insights in the application of
the super-modified simplex in numerical analysis.

We found that the super-modified version is superior
to the other versions in terms of speed and efficiency in
finding the true optimum. We have applied it in both
linear and non-linear least-square fits of simulated data,
and it worked better than at least one conventional method
on a small computer. The simplex method is less prone
to noise problems. We also found that one should start
the SMS with a large initial simplex and weight the data
by means of variable data acquisition rates. For very
slow reactions, the total sampling time may be reduced to
one half—life of the slower reacting species to increase
the sample throughput rate as well as to decrease any
interferences caused by the products.

Actual experiments should be performed in order to prove
the validity of the simplex method in regression analysis

and differential rate analysis.

APPENDIX B

176

PROGRAM PFIT06.P4

This is a curve-fitting program written in the fortran IV
language.

PROGRAMMERP- NA! TAX LAW
DEPT.OF CHEMISTRY
MSU, E. LANSING, MICE. 48824

PURPOSE-~This program uses the super-modified simplex procedure
to make a least-square fit to a linear or non-linear
function.

USAGE --Tb load and run PFITDG in fortran IV mode;

.R LOAD

*PFIT06<PFIT06.F4
*(FUNCO6,PARMIN,LIST,INPUT,SMSHPX,SPLOT,VERTEX(ALT MODE)
.R FRTS

*PFIT06.LD

.R PFITOé

SUBROUTINES AND FUNCTIONS REQUIRED --

FUNC06--evaluates function given
PARMIN--inputs parameters for the main program

LIST --Iists l)initial, 2)curret, or 3)final values
of parameters and variables
INPUT --input variables and initial simplex vertex value

SMSHPXF-the super-modified simplex subroutine

VERTEXP-(optional) inputs step sizes and initial vertex
estimates, will calculate(N+l) sets of initial
vertices by the method of Long.

SPLOT --(optlonal) plots simplex vertices on the
graphics terminal after each iteration.

DESCRIPTION OF TERMS:-

IDIIIa NO. OF FACTORS

V(I.J)=VALUE 0F FACTOR.J AT VERTEX I

ALIM(3,J)=LOWER, UPPER LIMITS, PRECISION IN EACH FACTOR J
R(I)=RESPONSE AT VERTEX I

IB=INDEX OF THE BEST POINT

stlNDEX OF THE WORST POINT

INWSINDEX OF THE NEXT T0 WORST POINT

DELII)=DISTANCE BETWEEN THE WORST POINT AND THE CENTROID
VTEM(1,I)=TEMPERARY NEW VERTEX FOR CENTROID
VTEM(2,I)=TEMPERARY NEW VERTEX FOR THE REFLECTED POINT
EVRSPOINT VR EXTENDED 20% , RVR IS THE RESPONSE
EVW=POINT VW EXTENDED 20% , RVW IS THE RESPONSE
ALMIT=HIGHER LIMIT IN THE SIMPLIFIED COORDINATE
BLMIT=LOWER LIMIT IN THE SIMPLIFIED COORDINATE
BINT.TINT=LOWER AND UPPER SAFTY INTERVAL FOR THE CENTROID
REP=RESPONSE OF THE POINT EP

MODIFICATION OF THE PROGRAM FOR GENERAL USES--

The subroutine SMSHPX can be adapted to other optimization
procedures with minor or no modification. The main program and
other subroutines can be changed according to one’s need in one
of the following ways:

1) Input all parameters by using DATA statements in the
beginning of the program PFITS6. Subroutines PARMIN
and INPUT can be omitted. Change FUNC06 and LIST
according to one's need.

2) Rewrite FUN006,INPUT.PARMIN. AND LIST.

177

 

SUBROUTINE SMPLX( IB)

noOOOOOCOODOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

GOO

10

FILENAME:

DATE: JAN 7.

178

SMPLEX. F4
1977

VERSION: E - GENERAL PURPOSE SIMPLEX
DESCRIPTION OF PARAMETERS:

IDIM DII-IENSIONALITY OF THE SPACE (NO. OF FACTORS)
V( 1..” VALUE OF FACTOR J AT VERTEX I
R( I) RESPONSE AT VERTEX I
ALIM(3,J) LOWER. UPPER LIMITS, PRECISION IN EACH FACTOR J
IRET( I) NO. OF MOVES VERTEX I RETAINED
IMV TYPE OI" MOVE:
l. BNR REFLECTION 5. BPTR TY l T.C.
2. ENE EXPANSION 6. BPTN TY 2 T.C.
3. BNCR CONTR TY l 7. BN’CR N-REFLCT
4. BNCV CONTR TY 2 8. BN’CW N-REFLCT
Im INDEX OF WORST POINT
IALGO SIMPLEX ALGORITHM TO BE USED:

’SQ' SEQUENTIAL (N0 SIZE CHANGES)

’NI‘I’ NELDER AND MEAD (KEEP FAILED CONTRACTIONS)
’TC’ TOTAL CONTRACTION ON FAILED CONTRACTION
'NR' N-REFLECTION ON FA’ILED CONTRACTION

THESE PARAMETERS MUST BE AVAILABLE TO THE SUBROUTINE. AS WRITTEN,

ALL ARE STORED IN BLOCK COMMON; THEY MAY. HOWEVER,

BE PASSED AS

ARGUMENT‘S IN THE CALL WITH APPROPRIATE CHANGES IN THE PROGRAM.

SUBROUTINE CALLED: FUNC (V.R.I)
VITH V( I.J) AS ABOVE
R( I) AS ABOVE

I INDEX OF VERTEX BEING EVALUATED
SUBROUTINE FUNC CALCULATES THE RESPONSE R FOR THE VERTEX I.

V AND R MUST BE DII‘IENSIONED IN THE SUBROUTINE.

COMMON /BLKl/V( 10,9) .VR( lO,9)/BLK2/R( lO)/BLK3/ALIM(3.9) . IDIM
COMMON lBLK4/IRET( lO)/BLK5/IMV. IWRST. IALGO.DEV, IFMOD. ITER

DIMENSION DEL(9) . SUMI9) , VTEM( 10,9) , RTEM(10)

DETERMINE BEST. WORST. NEXT-TO-VORST POINTS

D0 20 I=l.IDIM+l

D0 10 JIl,IDIM+l

IF (I .EQ. J) GO TO 10

IF (R(I) .LT. R(J)) GO TO 15
CONTINUE

IB=I

15

19

2O

24

DOOM
on

26

179

DO 19 K=l,IDIM+l

IF (I .EQ. K) GOTO 19

IF (R( 1) .GT. R(K)) GO TO 20
CONTINUE .

IWRST'I

IW=I

CONTINUE

DO 25 I=l.IDIM+l

IF (I .EQ. IV) GOTO25

DO 24 J=l.IDIM+l

IF (I .EQ. J) GO TO 24

IF (J .150. IV) GO TO 24

IF (R(I) .GT. R(J)) GO TO 25
CONTINUE

INW=I

CONTINUE

DETERMINE MOVEMENT IN EACH VARIABLE TO CENTROID

DO 26 I=l.IDIM

SUM( I)=O

DO 30 I=l,IDIM+l

IF (I .EQ. 1W) GO TO 30
D0 29 J=1.IDIM
SUM(J)=SUM(J)+V( I.J)
CONTINUE

DO 35 I=l.IDIM

DEL( I) =SUM( I)/IDIM-V( IN, I)

DETERMINE REFLECTION R, RESPONSE

DO 40 I'-'I.IDIM
VTEM( l . I)=V( IW. I)+2$DEL( I)
CALL FUNC (l.VT'EM. RTEM. 1)

IF (IALGO .EQ. 21150.) GO TO 46
IF (RTEIN 1) .LT. R( IB)) GO TO 100

TRY EXPANSION HERE

DO 45 I=I.IDIM
VTEM(2. I)=V( IW, I)+2.5*DEL( I)
CALL FUNC (I.VTEI‘I. RTE. , 2)

IF (RTEI-I(2) .GE. R( IB)) GO TO 60
EXPANSION FAILED - RETURN BNR

DO 50 I=l. IDIM

V( IN, I)=VTEI-l( l. I)
R( IW)=RTEM( l)
IMV=1

DO 51 I=l. IDIM+1
IRET( I)=IRET(I)+1
IRE'I'( IW)=l

RETURN

RETURN EXPANS ION

DO 63 I=1.IDIM
V( IN, I)=VTEM(2. I)
R( IW)=RTEM( 2)
IMV=2

DO 70 I31. IDIM-l-l
IRET( I)=IRET( I)+l
IRET( "031

RETURN

EXPANSION NOT ATTEMPTED

IF (RTEM(1) .GE. R( 1mm GO TO 125
IF (RTEM( 1) .GE. R( II") GO TO 150

000

105

000

106
107

108

I-t-OOO

113

000

269
2 IO

2 15
220

000

125
127

129

180

TYPE 2 CONTRACTION

DO 105 I=1.IDII‘I

VTEII(2.I)=V( IW,I)+DEL(I)/2

CALL FUNC (1,VT'EPI. RM. 2)

IF (RTEI‘I(2) .GE. R( IV) .OR. IALGO .NE. 2mm GO TO 110

TOTAL CONTRACTION (TYPE 2)

DO 788 I=1. IDII'I

V( IN, I)=VTE1‘I(2. I)

DO 107 I=1.IDIPI+1

DO 106 J=1.IDIM

V( I.J)=(V( I.J)+V( IB.J))/2
CONTINUE

IIIV=6

DO 108 I=I,IDIM+1

II" (I .EQ. IR) GO TO 108
CALL FUNC (1.1]. R, I)
IRET( I)'1

CONTINUE

IRET( IB)=IRET( IB)+I
RETURN

RETURN TYPE 2 CONTRACTION

DO 111 I91.IDIII+1

IRET(I)=IRET(1)+1

DO 113 I=I.IDIH

V( IN. I)=VTEI-1(2. I)

R( IW)=RTEI‘1(2)

IRET( IW)=1

IPIV=4

IF (RTEI‘I(2) .GE. R.( IN) .OR. IALGO .NE. 2HNR.) RETURN

N-REFLECTION (TYPE 2)

DO 205 I=1,IDIM

SUM(I)=O

DO 210 I=I,IDIN}1

IF (I .EQ. INN) GO TO 210
D0 209 J=I.IDIH
SUM(J)=SUM(J)+V(I.J)
CONTINUE

DO 215 I=1.IDIM
DEL(I)=SUM(I)/IDIM-V(INW.I)
DO 220 I=1.IDIN
V(INW.I)=V(INW.I)+2*DEL(I)
IMV=8

IRET(INW)=1

RETURN

REFLECTION

DO 127 I=I. IDIM
V( IN, I) =IVTEPN 1 . I)
R( IW)=RTEI'1( 1)
IMV=1

D0 129 I31. ID111+1
IRET( I)=IRET( I)+1
IRET( IW)=1

RETURN

 

 

000

150
155

I58

175
176

705

000

305

309
3 10

3 15
320

181

TRY TYPE 1 CONTRACTION

DO 155 I'LIDIH

VTEI‘I(2.I)'V( 1W.I)+1.5*DEL( I)

CALL FUNC (1.VT'EI‘I. RTEPI. 2)

IF (RTE1‘1(2) .GE. RTE!“ 1) .OR. IALGO .NE. 231!» GO TO 175

TOTAL CONTRACTION (TYPE 1)

DO 789 I81.IDI1‘I

V( IN. I)IVTEII(2. I)

DO 157 I'l.lDIl‘1+1

DO 156 J31.IDII‘I
V(I.J)=(V(I.J)+V( IB.J))/2
CONTINUE

IMV=5

DO 158 I'LIDII‘H-l

IF (I .EQ. IB) GO TO 158
CALL FUNC (1.V. R, I)
IRET(I)=1

CONTINUE

IRET( IR). IRET( IBM-1
RETURN

RETURN TYPE 1 CONTRACTION

DO 176 1'1.IDIII+I

IRET(I)=IRET(I)+1

DO 705 I31. IDIII

V( IW.I)'VTEI‘1(2.I)

R( IW)=RTEI‘1(2)

IRET( IV)!!!

IIIV'3

IF (RTEI‘R2) .GE. RTEIRI) .OR. IALGO .NE. 2RNR) RETURN

N-REFLECTION (TYPE 1)

DO 305 131, IDIH

SUI“ ”'0

DO 310 I'1,IDII‘B'1

1F ( I .130. IN) GO TO 310
D0 309 J=1. IDII'I
SUM(J)=SUI‘I(J)+V( I.J)
CONTINUE

DO 315 I31, IDII‘I

DEL( I)=SUM( I)/IDII‘I-V( INN. I)
DO 320 I31. IDIH

V( INW, I)=V( INN. I)+2*DEL( I)
II‘IV=7

IRET( INW)=1

RETURN

END

 

fl'angc‘.’ ”'1” VfiJ. fl
3.

 

‘rq

O0000000000OOOOOOOOOOOOOOOOO

000

220
230
240

1 10
1080
1 190

1 200
3500

182

PFITOG. F4

A PROGRAM To SOLVE POR.TEE PARAMETERS OF AN INTEGRATED

RATE EQUATION INVOLVING Two CONCENTRATION TERMS

AND EXERCISE TRE ALGORITHM FOR A SERIES OF PROBLEMS.

TRIS PROGRAM IS DESIGNED To FIND THE OPTIMUN SAMPLING RATE

WHEN KA AND KB ARE KNOWN. TEE USER.CAN CHOOSE UP TO

TWENTY SAMPLING RATES. AND TEE RATE TEAT GIVES THE MINIMUM

x ERROR WILL BE POUND. r“

DATE 9 MAY 1977 ‘
DESCRIPTION OP TERMS:

IALGO SIMPLEX ALGORITHM TO BE USED
’SO.’ SEQUENTIAL (NO SIZE CHANGE)
’NI‘I’ NELDER AND MEAD (KEEP FAILED CONTRACTION)
’TO' TOTAL CONTRACTION ON FAILED CONTRACTION
’NR’ N-REFLECTION 0N FAILED CONTRACTION Q .
IDIH NUMBER OF FACTORS ‘

 

VINIT INITIAL ESTIMATES OF VERTEXES
V( I .J) ONE OF THE VERTEXE
ALII‘I BOUNDARY PARAIIETERS

SWITOH( 6) IT'ERATION NO. WILL BE SHOWN ON KB
SWIT‘CH( 7) END TIIE PRESENT ITERATION
SWITCIN 8) RESTART

COMMON /BLK1/V( 10.9) .VR( 10.9)/BLK‘2/R( 10)

COMMON lBLK3/ALII‘I(3,9) , IDIII,TOTII1E,NUI‘1.FRAC
COPfl‘iON /BLK4/ IRET( IO)

COMMON /BLK5/Il*1V. IWRST‘. IALGO,DEV, IFI‘IOD, ITER
COMMON /BLK6/IPT. IDB. IDIMO,VINIT( 10,9) .EA,AK, BK
COMIION /BLK7/ACONC. BCONC, 1P1 , 1P2

DIMENSION ITII‘R 20) .ESUPN 100)

DATA QUIT/ 1HQ/, NQUIT/ 1110/, NO/lHN/, YES/IHY/

INITIALIZE

CALL RANG(-1,0. .0. ,1,0.)

WRITE(0,220)

F ORJ‘IAT( ' ENTER ANY INTEGER SMALLER THAN 500’)
READ(4,230) INT

FORI‘IAT( 13)

DO 240 I31, INT

CALL RANG(0.0. .0. .5,0.)

IOP=1

IFMOD=1

IDIM=2

ERSUPI=O.

WRITE(O.80)

FORMAT( ’ CALL SUBROUTINE INPUT TO CHANGE NUH. ACONC.ETC.?’/)
READ(4. 110)JANS

FORMA’NAI)

IF(JANS.NE.YFS)GO TO 108

CALL INPUT ,

WRITE(0, l 190)

FORMAT( ’ WANT TO LIST DETAIL OF EACH ITERAT‘ION?’/)
READ(4. 110)LI

WRITE(O,3500)

FORMAT( ’ WANT TO SPECIFY THE VALUE OF A FRACTION?’/)
READ“), 110)SPEC

IF(SPEC.EQ.N0)GO TO 3800

183

C

C SPECIFYING SPECIAL FRACTION

C
URITE(0.4500)

4500 FORMATT’ FRACTIGN=?'/)
READ(0,102)FRAC

102 FORMAT(E13.6)

103 FORMAT(I3)

IVARSI
ESUM(IVAR)=0.
CALL PARIN
GO TO 5001

3800 WRITE(0.4000)

4000 FORMAT(’ WHAT FRACTION TO START? DEFAULT=1’/)
READ(0,103)N
WRITE(0.5000)

5000 FORMAT(’ HOW MANY INTERVALS BETWEEN FRACTIONS? DEFAULT=1'/)
READ(0.103)INT
IF(INT.NE.1)GO TO 5002
M=NUH+N
GO TO 120

5002 M=NUN3INT¥N-INT

C

C

C

120 CALL PARIN
DO 350 IVAR!N.HAINT
ESUM(IVAR)=0.

FRAC=1./IVAR

5001 CALL FUNC(0.0..0..0)

IF (SWITCH(8.) .EQA 1) GO TO 380
IF(IVAR.NE.1)GO TO 705
IF( IDB.EQ.YES)CALL LIST( 1)

705 D0 329 131.3
DO 328 J81.2
V(I.J)8VINIT(I.J)

CALL FUNC(1.V,R.I)

328 CONTINUE

329 CONTINUE
ITERFO

C

3 ITERATE
CALL PLUIT V, IDIPI.ALIII,0)

100 ITERfilTERil
IF (SWITCH(6.) .E01 1) WRITE (0.735) ITER

735 FORMAT (’ ITERATION NO. ’13)
IF (SWITCH(7.) .E0. 1) GO TO 198
IF (ITER .GT. 250)GO TO 198
CALL PLOT(V.IDIM.ALIM.I)

0 CALL SMPLX

g CHECK FOR.CONVERGENCE
DO 40 131.1DIN
VMIN=V( I . I)

VMAX?VHIN

DO 39 J=2,IDIH+1
IF(V(J.I).GT.VMAX)VMAX#V(J.I)
IF( V(J. I) .LT.VHIN)VPIIN=V(J. I)

39 CONTINUE
VDEL= ABS( VMAX-VMIN)
RESID=.0001
IF(VDEL.GT.ALIMK3.I).OR.R(I).GT.RESID)GO TO 49

40 CONTINUE
GO TO 50

49 IF(LI.EQ.YES)CALL LIST(2)

GO TO 100

50
2000
198

1000

340
350
750
380
730

731

1814

WRITE(3,2000)IVAR.DEV

FORMAT(’ RUN NUMBER? 'I3I' NOISEg ’E13.2‘ X ’/3
AVGA=(V(1.1)+V(2.1)+V(3,1))/3.
RELACA=(ACONC-AVGA)*100./ACONC
AVGB=(V(1.2)+V(2.2)+V(3,2))/3.
RELACB=(BCONC-AVGB)*100./DCONC
ESUM(IVAR)=ESUM(IVAR)+ABS(RELACA)+ABS(RELACB)
WRITE(3.1000)FRAC.RELACA.RELACB,ESUM(IVAR)
FORMAT(’ FRAC= 'E13.6/’ % ERROR.OF A.B='2E13.6/‘ TOT ERR?’E13.6/)
IF(IDB.EQ.YES)CALL LIST(3)

NII=N+1

IF( IVAR. E0. NM) ERSUI‘F ESUM( NM)
IF(ESUM(IVAR).LT.ERSUM)GO TO 340

GO TO 350

ERSUM‘ESUM(IVAR)

IOP=IVAR

CONTINUE

WRITE(3.750)IOP

FORMAT(‘ OPTIMUM SAMPLING RATE IS RUN NUMBER ’I3/)
WRITE (0.730)

FORMAT (’ RESTART ?'0)

READ (0.731) IANS

FORMAT (A1)

IF (IANS .EQ. IHY) GO TO 1

END

an__4.1£-_r!'. 4'

 

l," I.-.‘ v

000000

000

20

40
100

200

220

DOOM

300

400
500

600

185

SUBROUTINE VERTEX
THIS PROGRAM WILL ASK FOR “STEP 81-. 2) INITIAL VERTEX
ESTIMATION, AND WILL CALCULATE (N+1) SETS OF INITIAL
VERTICES BY THE METHOD OF LONG FOR THE SIMPLEX OPERATION
UP TO TEN PARAMETERS CAN BE SPECIFIED.

COMMON IBLK3/ ALIM(3.9).IDIM.TOTIME, NUM, FRAC
COMMON lBLKfi/ IPT.IDB.IDIMO. VINIT(10.9).EA.AK,BK
DIMENSION SSIZE(10).P(10).Q(10)

SPECIFY STEP SIZES

DO 100 I=I.IDIM

WRITE(O.20)I

FORMAT(’ STEP SIZE FOR PARAMETER?I2‘=’8)
READ(4.40)SSIZE(I)

FORMAT(E13.6)

CONTINUE

INPUT INITIAL VERTEX

WRITE(0,200)

FORMAT(' ENTER INITIAL VERTEX’)
DO 280 J'I.IDIM

I31

WRITE(0.220)I,J

FORMAT(’ COOR('11’,'II’)=’0)
READ(4.40)VINITTI.J)

CONTINUE

CALCULATING INITIAL SIMPLEX COORDINATES

DO 300 I=1.IDIM
P(I)=SSIZE(I)/IDIM/1.1416*(SQRT(IDIM+1)+IDIM+1)
Q(I)=SSIZE(I)/IDIM/1.1416*(SORT(ID1M+l)-1)
CONTINUE

D0 500 J=I.IDIM

DO 400 I=2.IDIM}1

IF(I.EQ~J+1)GO TO 400
VINIT(I.J)=VINIT(1.J)+Q(J)

CONTINUE

CONTINUE

BO 600 I=2.IDIM}1

J=I-1

VINIT(I.J)=VINIT(1.J)+P(J)

CONTINUE

RETURN

END

186

SUBROUTINE FUNC (MODE,V,R,I)

DIMENSION V(10,9), R(10) . A( 100) , TIPIE(100)

COMMON /BLK3/ALIM(3,9) , IDIM.TOTIME.NUM.FRAC

COl‘flION /DLK3/IMV, IWRST, IALGO, DEV, IFMOD, ITER

COMMON /BLK6/IPT, IDB, IDIMO.VINIT( 10,9) .EA.AI(, BK

COMMON /BLK7/ACONC. BCONC. IP1. 1P2

IF (MODE .E0. 0) GO TO 200

SUM=0.

DO 5 J31. IDIM

IF (V( 1,.” .GT. ALIM(2.J) .OR. V( I,J) .LT. ALIM( 1,J)) GO TO 100
5 CONTINUE

DO 10 K=l,100

ACALC=EA*( V( I. 1)2=( 1.-EXP(-AK*TIME(K) ) )+

2 V( I , 2) :.‘:( 1 .-EXP(-BK=£€TIME( K) ) ))

10 SUM= SUM+( ACALC-A( K) ) 83:2
R( I)=—SUM
RETURN
C
C
100 R( I)=-10.E20
REI’URN
C
C INITIALIZE - CALCULATE THE ABSORBANCE VS TIME DATA
C
200 T=O.
TIIIEIN=TOTIME*FRAC
T1=TIMEIN/IPI

12=(TOTIME-TIMEIN)/IP2
D0 210 IVAR= 1.100
IF( T.CT.TIMEIN)T=T+T2
IF(T.LE.TIMEIN)T=T‘+T1
270 TIIIE( IVAR)'T
SU322=0.
DO 300 JPTS=I. 10
APT: EA?“ ACONC’N 1 . ~EXP( -AK$TIME( IVAR) ) )+
2 BCONC*( 1 .-EXP( -DK*TIME( IVAR) ) ))

c .
C ADD ON NOISE

C
IF (IFMOD .EQ. I) SDEV'ABSUIPTV‘DEV/IOO.)
IF (IFIIOD .EQ. 2) SDEV=SQRT( AI’T) *DEV/ICO.
IF ( IFMOD .E0. 3) SDEV=DEV
1“;;‘1:00
NUI‘I35
CALL RANG (O. SDEV, AVG, NUM, RANDC)
AP 1': APT-1' RANDG
309 SU§L=SUI13+APT
210 A( IVAR) =SUI'12/10.
RE'I'URN
END

 

187

SUBROUTINE PARIN

C
C INPUT PARAMETERS FOR MAIN (PARFIT.F4)

C

900
800

805
940

9 10
920
1200
39
700
710

.14

720

960
930

990
60
C

COMMON /BLK3/ALIM(3.9) . IDIM/BLKB/IMV. IWRST. IALGO. DEV. IFMOD, ITER
COMMON IBLK6/IPT, IDB. IDIMD.VINIT( 10,9) .EA,AK, BK

DATA NO/IHN/, YES/IHY/

WRITE (0,900)

FORMAT (IOX'SIMPLEX CURVEFIT ROUTINE’)

IDIM=2

WRITE (0,800) EA.AK.BK

FORMAT (’ MOLAR ABS 8 ’GlI.4/' RATE CONST A = 'Gll.4/
’ RATE CONST B 3 ’G11.4)

WRITE (0,8. 3)

FORMAT (’ CHANGES ?’8)

READ (4.940) IANS

FORIIA'I' (AI)

IF (IANS .EQ. NO) GO TO 5

WRITE (0,010)

FORMAT (’ MOLAR ABS 3 ’9)

READ (4,970) EA

FORMAT (011.4)

WRITE (0.830)

FORMAT (’ RATE CONSTANT A 3 ’8)

READ (4.970) AK

WRITE (0.840)

FORMAT (’ RATE CONSTANT B = ’8)

READ (4.970) BK

GO TO 2

WRITE (0.910)

FORMAT (’ ALGORITHM (SQ.NM.TO,NR) ?"3)

READ (4,920) IALGO

FORMAT (A2)

WRITE (0.1200)

FORMAT (’ LPT LIST EACH ITERATION ?’8)

READ (4.94:0) IDB

DO 40 I31. IDIM

PETITE (0,700) I,ALIM(1,I)

FORMAT (’ LOWER LIIIIT(’I1’) = ’G11.4)

WRITE (0.710) I.ALIM(2,I)

FORMAT (’ UPPER LIMIT (’Il’) = ’GII.4)

WRITE (0.720) I.ALIM(3. I)

FORMAT (' PRECISION ('I1’) = ’Gll.4v)

WRITE (0.805)

READ (4.940) IANS

IF (IANS .EQ. NO) GO TO 70

DO 60 I=1,IDIM

WRITE (0,960) I

FORMAT (’ LOWER LIMIT (’Il') = ’33)

READ (4.970) ALIM(1.I)
WRITE (0,980) I
FORMAT (’ UPPER LIMIT (’11')
READ (4,970) ALIM(2. I)
WRITE (0,990) I
FORMAT (' PRECISION (’11’) = ’8)
READ (4,970) ALIM(3. I)

II
:5
V

C INITIAL SIMPLEX

C
70

1000

850
2000

IF (IDIMO .NE. IDIM) GO TO 850

WRITE (0.1000)

FORMAT (’ USE SAME INITIAL SIMPLEX '.”$)

READ (4.940) IANS

IF (IANS .NE. N0) GO TO 100

WRITE'IO.2QOO)

FORMA'IT ’ USE SUBROUTINE VERTEX TO CALC. INITIAL SIMPLEX‘P’)
REA!“ 4.940) [ANS

IF( I.’1Ni).EQ.NO)GO TO 80

CALL VERTEX

188

GO TO 1001010)

WRITE (0, ’
T310 FORMAT (’ ENTER.COORDINATES OF INITIAL SIMPLEX )

DO 95 I=1.IDIM+1

WRITE (0.1320)
1020 FORMAT (1H )

D0 90 J=I.IDIM

WRITE (0.1030) I,J

FORMAT (’ COOR (’II’.’Il’) = ’8)
0330 READ (4.970) VINIT(I.J)
95 CONTINUE
100 RETURN

END

SUBROUTINE PLOT (V.IDIM.ALIM,MODE)
COMMON/BLKYIACONC,BCONC.IP1.1P2
DIMENSION V(10.9).ALIM(3.9)

IF (MODE .NE. 0) GO TO 100

CALL TPLINT (ALIM(1,1), ALIM12,1), ALIM(1,2), ALIM(2,2), 2, 1)
CALL TPLT(-1,ACONC,BCONC)

RETURN

100 CALL TPLT (0. V(3.1). V(3,2))
DO 110 I=I.3

110 CALL TPLT (I. V(I.1), V(I.2))
RETURN

END

189

SUBROUTINE LIST(MDDE)

MODE 1 INITIALIZE
2 CURRENT VALUES
3 CLOSE - FINAL VALUES

000000

COMMON /BLKl/V(10,9).VR(10,9)/BLK2/R(10)/BLKB/ALIM(3.9).IDIM
COMMON /BLK5/IMV.IWRST.IALGO.DEV,IFMOD,ITER

COMMON /BLK6/IPT,IDB.IDIMD.VINIT(10.9).EA.AK.BK

GO TO (10,100,200).MODE

C
C INITIALIZE

C
10 WRITE(3.900)IALGO
900 FORMAT(’ SIMPLEX OPTIMIZATION RESULTS’,5X,A2//)
WRITE(3,910)EA,AK.BK
910 FORMAT(’ INPUT CONSTANTS'//’ MOLAR ABS 3 'Gll.4/
2 ’ RATE CONSTANT A = ’Gll.4/
3 ’ RATE CONSTANT B 3 ’011.4)
WRITE(3.920)
920 FORMAT(1H0’LIMITS. DESIRED PRECISION’//’ UPPER LIM’2X3)
DO 12 I=1,IDIM
12 WRITE(3,930)ALIM(2.I)
930 FORMAT(1H+GII.4.2XB)
WRITE(3.940)
940 FORMAT(1H+)
WRITE(3,950)
950 FORMAT( ’ LOWER LIl‘I’ 2X.)
DO 14 131.1D1M
14 WRITE(3,930)ALIM(1.I)
WRITE(3,940)
WRITE(3.960)
960 FORMAT(’ PRECISION’2XB)
DO 16 131.1DIM
16 WRITE(3.930)ALIM(3.I)
WRITE(3.940)
WRITE(3.970)
970 FORMAT(1H0’INPUT INITIAL SIMPLEX PAR(1)...PAR(K)’/)
DO 20 I31.IDIM+1
WRITE(3,990)I
DO 18 J=1,IDIM
18 WRITE(3.930)V1NIT(I.J)
20 WRITE(3,940)
WRITE(3.975)
975 FORMAT(1H ’V’8X7PAR(1)...PAR(K)...RESID**2’/)
RETURN
C
C CURRENT VALUES
C
100 WRITE(3.980)ITER
980 FORMAT(1H0’ITERATION ’13)
DO 110 I=1,IDIM+1
WRITE(3.990)I
990 FORMAT(1H 13,2XB)
DO 105 J=I.IDIM
105 WRITE(3,930)V(I.J)
RI=-R( I)

WRITE(3,1000)RI
1000 FORMAT(1H+GII.49)
110 WRITE(3.940)
RETURN
C
C FINAL VALUES
C
200 WRITE(3.1010)ITER
1010 FORMAT(1H0’***$*****'/' CONVERGENCE OBTAINED

2 IN ’13' ITERATIONS’/’*********’/
3 ’ FINAL RESULTS’l)

210

1020

000

91

102
105
103
107

108

200

110

210

300

3000

310

340

400
500

190

D0 210 I=1.IDIM+1
WRITE(3.990)I

DO 203 J=I.IDIM
WRITE(3.930)V(I.J)
RJ=-R( I)
WRITE(3.1000)RJ
WRITE(3,940)
WRITE(3.1020)
FORMAT(1H1)
RETURN

END

SUBROUTINE INPUT
THIS SUBBOUTINE WILL INPUT CONTROL PARAMETERS FOR PFITO6.

DATE: 5/24/1977
COMMON/BLKS/IMV.IWRST.IALGO.DEV,IFMOD,ITER
COMMON/BLKQ/ALIM(3.9).IDIM3TOTIME,NUM.FRAC
COMMON/BLKY/ACONC,BCONC,IP1,IP2

DATA NO/lHN/,YES/1HY/

WRITE(0.91)

FORMAT(’ TOTAL LENGTH OF SAMPLING TIME IN SEC=?’)
READ(4,102)TOTIME

FORMAT(E13.6)

WRITE(0,105)

FORMAT(’ NUMBER OF SAMPLING RATES TO BE TRIED=?’)
READ(4.103)NUM

FORMAT( 13)

WRITE(0.107)

FORMAT(’ ACTUAL CONC OF A=?’)

READ(4.102)ACONC

WRITE(O.108)

FORMAT(’ ACTUAL CONC OF B =?’)

READ(4,102)BCONC

WRITE(0,200)

FORMAT(’ CHANGE NO. OF DATA POINTS IN INITIAL SAMPLING

2 PERIOD? DEFAUDT=50’/)

READ(4.110)JANS

FORMAT(A1)

IF(JANS.EQ.NO)GO TO 300
WRITE(0.210)

FORMAT(’ HOW MANY'DATA POINTS IN INITIAL SAMPLING PERIOD?’/)
READ(4.IO3)IP1

GO TO 3000

IP1=5O

IP2=100-IP1

WRITE(O,310)

FORMAT(’ ADD NOISE INTO DATA?’/)
READ(4.110)KANS
IF(KANS.EQ.NO)GO TO 400
WRITE(0,340)

FORMAT(' SPECIFY Z NOISE’l)
READ(4,102)DEV

GO TO 500

DEV=0.

CONTINUE

RETURN

END

000

10
15

19

191

SUBROUTINE SIBMPX

SUBROUTINE SMPLX
THIS IS THE SUPER MODIFIED VERSION FOR SIMPLEX. FOR
DEFINITION OF TERMS AND DESCRIPTION OF THIS PROGRAM. CALL
PROGRAM SMSMPX. 1N.

COINION/BLI(1/V( 10.9) ,VR( 10.9)lBLK2/R( 10) /BLK3/ALIM(3,9) . IDIM

COMMON / BLK‘I/ IILETT lO)

DIMENSION DEL(9).SUM(9).VTEM(10.9).RTEM(10)

DATA DINT/- . 2/ . TINT/ . 2/
DETERMINE BEST. WORST. NEXT-TO-WORST POINTS

II=0

JJ=0

DO 20 I=1.IDIM+1

DO 10 J=I.IDIM

IF(I.EQ.J)GO TO 10

IF(R( I) .LT.R(J))GO TO 15

CONTINUE

IBII

DO 19 K31. IDIM+I

IF(I.EQ.K)GO TO 19

IF(R( I) .GT.R(IO)GO TO 20

CONTINUE

IW=I

CONTINUE

DO 25 I'l.IDIM+1

IF (I.EO..IW)GO TO 25

DO 24 J=I.IDIM+1

IF( I.EQ.J)GO TO 24

IF(J.EQ. “000 TO 24

IF(R( I) .GT.R(J))GO TO 25

CONTINUE .

INW=I

CONTINUE
DETERMINE MOVEMENT FROM THE WORST POINT TO CENTROID FOR
EACH VARIABLE. (NW+B)/IDIM=COORDINATE OF THE CENTROID.

DO 26 I=1.IDIM

SUM( I)=0

CONTINUE

DO 30 I=1,IDIM+1

IF( LEO. IW)GO TO 30

DO 29 J=I.IDIM

SUM(J)=SUM( J)+V( I.J)

CONTINUE

DO 35 I=1. IDIM

DEL( I) =SUM( I)/IDIM-V( IW. I)

VTEM(1.I)=V( IW. I)+DEL( I)

CALL FUNC( 1.VTEM. RTEM. 1)
DETERMINE THE REFLECTION OF VW. CALL IT VTEM(2. I) AND FIND
IT‘S RESPONSE.

D0 4-0 I=1,IDIM

VTEM(2. I)=V( IW, I)+2*DEL( I)

CALL FUNC( 1.VTEM.RTEM,2)
FIT A SECOND ORDER POLYNOMIAL VURVE THROUGH VW.C. AND VR.
USING ONE OF THE FACTORS AND THE RESPONSE AS THE COORDINATES.
DETERMINE A AND B FOR THE CURVE Y=A*X**2+B*X+C BY USING THE
MATRIX METHOD. SETTING X(1)=-1. X(2)=0.AND X(3)=l. THE
COEFF. CAN BE SIMPLIFI- AS A30.5*(RR+W-2*C) AND B=0.5*(RR-W).

RR=RT'EM(2)

W=R( IW)

C=RTEM(1)

A=0 . 5*( RR+W-2*C)

B=0.5*(RR-W)

Pa-B/(2*A)

192

P IS THE DERIVATIVE OF THE EQUATION YEAXX3*2+B*X}C AND IT

SHOWS THE LOCATION OF THE MAXIMUM. GET THE MAX. BETVEEN

ALIM(1.1) AND ALIM(2.1) BUT NOT AT CENTROID. FIRST OF

ALL CHANGE ALIM(I.1) INTO THE SIMPLIFIED COORDINATES.
CF=1.0/ABS(VTEM(2.1)-VTEM(1.1))
ALMIT=(ALIM(2.1)-VTEM(I,1))*CF
BLMIT=(ALIM(1,1)-VTEM(1.1))*CF

C IF A<O. THERE IS A MAXIMUM AND THE CURVE IS CONCAVE DOWN.

IF(A.GE.O.)GO TO 300

IF(P.GT.ALMIT)GO TO 210

IF(P.LT.BLMIT)G0 TO 220

IF((P.GT.BINT).AND.(P.LT}O.))P=TINT

IF((P.GE.O.).AND.(P.LT.TINT))P=TINT

0000

GO TO 500
210 P=ALMIT

GO TO 500
220 P=BLMIT

GO TO 500

C CURVE IS CONCAVE UP. EXTEND VW AND VR BY'20%*(VVSP) AND
C GET THE THEORECTICAL RESPONSE.
300 EVR:I.20
EVW=-I.20
RVR=A*EVR#*2+B$EVR*C
RVWéA*EVW**2+B*EVW4C
DETERMINE THE NEWVOLD RESPONSE RATIO. PICK THE HIGHER
RATIO AS THE DIRECTION OF FUTHER EXPANSION. EXPAND THE CURVE
BY’Yh-2.75*x+6.75. WHERE XBRATIO 0F RESPONSES AND YHEXPANSION COEFF.
EP IS THE LOCATION OF THE REW'TREORETICAL EXPANDED VALUE.
RATIOI=RVR/RR
RAT102=RVWVW
IF(RATIOI.GT.RATIOB)GO T0 310
IF(RAT102.GT.RATIOI)GO T0 320
310 Yb-2.75*RATIOI+6.75
EP=Y*(I.0)
GO TO 350
320 =-2.75*RAT102+6.75
EP=Y*(-I.O)
350 REP=A$EP**2+B¥EP+C
C CHECK IF THE NEW RESPONSE REP IS IN BOUNCE. THEN CHECK
C IF IT IS BETTER THAN THE OLD ONE.
IF(EP.GT.ALMIT)GO TO 210
IF(EP.LT.BLMIT)GO TO 220
IF((REP.CT.R).AND.(REP.CT.W))GO TO 400
P=I.0
GO To 500
400 P=EP
C CHANGE P BACK TO THE TRUE COORDINATE AND SAMPLE ITS
C RESPONSE. SET P NOW AS THE NEW VERTEX.THAT REPLACES
C THE WORST POINT VW.

0000'

500 SLOPE= DEL( 2) /I)E.L( 1 )
V(IW,1)=P*(1./CF)+VTEM(1.1)
510 V(IW,2)=SLOPE*(V(IW.1)-VTEM(1.1))+VTEM(1.2)
550 CALL FUNC(1.V.R.IW)
IF(R(IW).LE.RRJGO TO 520
GO TO 560
520 V(IW,1)=VTEM(2.1)
V(IW,2)=VTEM(2.2)
R( IN) = RR
560 CONTINUE
RETURN

END

APPENDIX C

ELECTROPHORESIS OF SERUM LIPOPROTEINS ON CELLULOSE

ACETATE STRIPS

Equipment and Supplies:

1)

2)

3)
fl)

5)

Shandon "Celagram" cellulose acetate strips,
25 x 180 mm (Shandon Scientific Co., 515 Broad
St., Sewickley, PA 151H3).

Shandon electrophoresis apparatus, Model U77;
power supply, Model SAI 2761.

Whatman No. 3MM filter paper wicks.
Glasswares.

Sample applicators.

Reagents:

1)

2)

3)

Barbital buffer, pH 8.8, 0.1M

1.756 g barbital acid + 20.6 g sodium barbital
+ 0.37 g EDTA disodium salt in one liter of water.
011 Red 0 stain

0.“ g 011 Red 0 dye (Sigma Co., St. Louis, MO)
+ 380 mL acetone, add 300 mL water slowly, stir
at “5°C for 1 hour till 1 hour before use.

1.0 N NaOH solution.

193

19”

Procedures:

1)

2)

3)

4)

5)

6)

7)

Fill the buffer reservoirs of the electrophoresis
cells with 0.1M barbital buffer.

Load Whatman 3 MM paper wicks (1 inch wide) onto
support racks after soaking them in the barbital
buffer.

Carefully float the strip of cellulose acetate
with dull side up on top of a dishful of barbital
buffer. After it is thoroughly wetted, submerge
it into the buffer for several minutes.

Remove the strip and blot dry with filter paper.
Apply the sample on the dull side, then position
the dull side up on the wicks across a 10 cm bridge
gap inside the electrophoresis cells.

Set a constant current of 5 mA and allow the
electrophoresis to run for HS minutes.

Mix 35 mL 011 Red 0 stock solution with 10 mL

1.0 N NaOH solution, stain the cellulose acetate
strip in this bath for one hour. Wash with water
and apply a few drops of glycerol onto the surface
for storage.

Obtain a densitometric tracing of the slide when

an instrument is available.

 

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10.
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13.

1M.
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