THE RELATIONSHiP BETWEEN SUBSTRATE“
concammncm, RESPIRAYif-JN RATE, AND
GROWTH RATE: m: Escuemmmcou
m commueous new CULTURE

Thesis fer the 0&9:an cf Ph. D.
MICHEGAN STATE UNIVERSWY
Rober? S. Lipe
E961

II Ll! mu; min !! mm 9! ii i ll Il7llilllfllflllli mm

93 1 82

This is to certify that the

thesis entitled

The Relationship between Substrate Concentration,
Respiration Rate, and Growth Rate of Escherichia
coli in Continuous Flow Culture

 

presented by

Robert S. Lipe

has been accepted towards fulfillment
of the requirements for

Ph.D. degteem Microbiology and
Public Health

\ l
til L J

7 Mail):

\\ f ) 1 . _ A / ‘ ‘
hrofessor
\

Date May 2, 1961

 

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ABSTRACT

THE RELATIONSHIP BETWEEN SUBSTRATE CONCENTRATION,
RESPIRATION RATE, AND GROWTH RATE OF ESCHERICHIA

COLI IN CONTINUOUS FLOW CULTURE

By Robert S. Lipe

A continuous flow unit was constructed and satisfactorily
operated at dilution rates ranging from 0.01 to 0.85. Steady-
state conditions existed between dilution rate values of
D equal to 0.02 and 0.69. A non-steady-state condition
existed at D values below 0.02 and above 0.69 which resulted
in a wash-out of organisms from the unit at a rate faster
than replacement by growth. The actual wash-out rate was
found to be less than the wash—out rate predicted by theoretical
equations.

A maximum growth rate of km of 0.69 was established.
This value was obtained by both batch culture and continuous
flow procedures. In addition km was calculated by the method
of Reed and Theriault from a series of experimental data. The
value of 0.69 obtained by this method was in full agreement
with the experimentally obtained maximum growth rate.

The relationship between substrate concentration and
the specific growth rate R during the steady—state was

established, not as a linear relationship, but as a curve

Robert S. Lipe

that reaches a maximum asymptotically. Theoretical equations
proposed by Mondo, Novick and Szilard, and Herbert gt El: did
not agree with the experimental relationship obtained between
substrate concentration and k. Furthermore, values for km

and Sa obtained by a Lineweaver_Burke plot did not agree with
experimental data. In contrast the results obtained from the
use of a monomolecular type of equation, such as proposed by
Teissier, indicated that this type of equation more correctly
expresses the relationship between substrate concentration and
k. Data were presented which indicated that at a substrate
concentration of 1 mg/l or below k approaches zero. The data
also indicate that the specific growth rate k becomes
independent of substrate concentration at glucose concentrations
above 180 mg/l.

A linear relationship was established between k and
the respiration rate of the organism. The maximum oxygen
uptake rate was obtained at km and did not increase further
at D values greater than km. The data indicate that under
these conditions approximately 37 percent of the assimilated
substrate was oxidized independently of k.

The economic coefficient of the organism was found,
not to be constant, but to increase from 44 percent at the

lower k values to 55 percent at the higher k values.

Robert S. Lipe

The theoretical steady-state equations, proposed
by Monod and Herbert 23 gl. were found to be inadequate in

expressing the experimentally obtained relationships.

THE RELATIONSHIP BETWEEN SUBSTRATE CONCENTRATION:
RESPIRATION RATE, AND GROWTH RATE OF ESCHERICHIA

COLI IN CONTINUOUS FLOW CULTURE

BY

Robert St Lipe

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Microbiology and Public Health

1961

ii

ACKNOWLEDGEMENTS

I wish to express my sincere gratitude to Dr. Karl
Schulze for stimulating my interest in the project reported
herein and for his daily advice and encouragement during the
course of this work.

A deep-felt thanks is expressed to Dr. Walter L.
Mallmann for his guidance, encouragement, and assistance
during the period of this study.

Acknowledgement is made also to the Division of
Engineering Research which supported the laboratory work.

A grateful appreciation is expressed to my wife for
her patience, aid, and understanding which made the many

years of my education possible.

Chapter
I.

gII.

III.

IV.

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . .

LITERATURE REVIEW . . . . . . . . . . . . . . .

A. Introduction

B. Application of Continuous Culture
Techniques as a Research Tool

C. Industrial Applicatidn of Continuous
Culture

THEORETICAL CONSIDERATIONS . . . . . . . . . .

A. Kinetics of Bacterial Growth

B. Kinetics of Growth in Continuous Culture

C. Effect of Contamination

D. Effect of Mutation

EXPERIMENTAL APPARATUS, CULTURE AND METHODS . .

A. Description of Apparatus

B. Medium

C. Culture

D. Analytical Techniques

iii

14
23
27
3o
36
37
39
39
53
54

57

iv

Chapter Page
V. RESULTS . . . . . . . . . . . . . . ... . . . . 71

A. Experiment No. l 73

B. Experiment No. 2 74

C. Experiment No. 3 74

D. Establishment of the Steady-State 75

E. Establishment of km 80

F. Relationship between Substrate

Concentration Experimental k and

Calculated k values 82
G. Relationship between D and Substrate

Concentration at Low D Values 85
H. Relationship between k and Respiration

Rate During Steady State Conditions 86
I. Calculation of the Economic Coefficient

During Steady-State Conditions 88

J. Application of Experimentat Data to

Theoretical Steady-State Equations 89
K. Nitrogen, Ash, and Moisture Determinations 92
L. Viable Cell Count 92

VI. DISCUSSION . . . . . . . . . . . . . . . . . . 131

VII. CONCLUSIONS . . . . . . . . . . . . . . . . . . 151

VIII. APPENDIX . . . . . . . . . . . . . . . . . . . 154

IX. BIBLIOGRAPHY . . . . . . . . . . . . . . . . . 156

Table

10.

11.

Data

obtained

LIST OF TABLES

from the continuous flow unit

a D value of 0.059 during experiment No.

Data

obtained

from the continuous flow unit

a D value of 0.091 during experiment No.

Data

D

Data

Data

Data

Data

Data

Data

Data

Data

obtained

value of

obtained

value of

obtained

value of

obtained

value of

obtained

value of

obtained

value of

obtained

value of

obtained

value of

obtained

value of

from the continuous flow unit
0.124 during experiment No. 1
from the continuous flow unit
0.178 during experiment No. 1
from the continuous flow unit
0.240 during experiment No. 1
from the continuous flow unit
0.301 during experiment No. 1
from the continuous flow unit
0.360 during experiment No. 1
from the continuous flow unit
0.425 during experiment No. 1
from the continuous flow unit
0.485 during experiment No. 1
from the continuous flow unit
0.546 during experiment No. 1
from the continuous flow unit

0.610 during experiment No. l

Page

94

95

96

97

98

99

100

101

102

103

104

Table

12.

13.

14.

15.

16.

17.

18.

19.

20.

21,

Data obtained from the continuous flow unit at a
D value of 0.660 during experiment No. l . .
Data obtained from the continuous flow unit at a
D value of 0.730 during experiment No. 1 . .
Data obtained from the Continuous flow unit at a
D value of 7.94 during experiment No. l . .
Data obtained from the continuous flow unit at a
D value of 0.850 during experiment No. 1 .
Data obtained from the continuous flow unit
during experiment No. 2 . . . . . . . . .
Summary of averages of data taken during
experiments Nos. 1 and 2 . . . . . . . . .
Data obtained from the continuous flow unit
during experiment No. 3 . . . . . . . . . .
Concentration of organisms at D values greater
than 0.694 . . . . . . . . . . . . . . . . .
Relationship between substrate concentration and
experimental anc calculated k values . . . .
Comparison of the actual amount of oxygen used
with the theoretical amount of oxygen
required for complete.oxidation of sugar used

during the steady-state . . . . . . . . . .

vi

Page

L105

106

107

108

109

110

111

112

113

114

Table

22.

23.

24.

25.

vii
Page
Relationship between economic coefficient and k
during the steady-state . . . . . . . . . . 115
Comparison of experimental and calculated
g values . . . . . . . . . . . . . . . . . . . 116

Comparions of experimental x and i calculated

using the expression R Y(SR — E) . . . . ll7

.Comparison of experimental x and x calculated

D
YISR - sa(km do ) 118

using the expression 3

10.

11.

12.

13.

14.

viii

LIST OF FIGURES

Page

Continuous flow apparatus . . . . . . . . . . . 40
One liter reaction chamber . . . . . . . . . . 42
System for sampling and inoculation . . . . . . 43
System for aeration of culture in reaction

chamber . . . . . . . . . . . . . . . . . . 47
System for feeding substrate to reactidn

chamber . . . . . . . . . . . . . . . . . . 49
System for the discharge of culture from the

reaction chamber . . . . . . ... ... .,. . . 52
Standard glucose curve . . . . . . . . . . . . 61
Standard cell dry weight curve . . . . . . . . 63
Relationship between cell concentration and D . 119
Wash—out rate from the unit . . . . . . . . . . 120
Relationship between D and substrate

concentration over a D range of 0.059 to

0.855 . . . . . . . . . . . . . . . . . . . 121
Batch culture determination of k before and

after growth in the continuous flow unit . . 122
Relationship between substrate concentration.

experimental and calculated k values . . . . 123

Lineweaver-Burke plot of steady-state data . . 124

Figure

15.

16.

17.

18.

19.

20.

21.

Relationship between cell concentration and
D at low D values . . . . . . .'. . . .
Relationship between respiration rate and k
during the steady-state . . . . . . . .
Actual ul oxygen used vs theoretical oxygen
needed for complete oxidation of the
sugar consumed during the steady—state .
Percent of theoretical oxygen utilized vs k

during the steady—state . . . . . . . .

Relationship between economic coefficient and

k during the steady—state . . . . . . .
Comparison of experimental and calculated

E values . . . . . . . . . . . . . . . .
Quantitative divergences from the theory of

Monod . . . . . . . . . . . . . . . . .

ix

Page

125

126

127

128

129

130

135

I. INTRODUCTION

In the past few years a great deal of interest has been
stimulated in the possibility of conducting continuous flow
operations. By definition, continuous flow entails the
maintenance of constant operating conditions, including
organism concentration, in one or a series of vessels while
fixed volumes of nutrients and continuous flow reactor contents
are respectively added and removed at the same continuous rate.

From an industrial standpoint, prolonging the useful
time of fermentation such a system would result in fewer un—
productive periods, more uniform products, and reduced labor
costs. A continuous production would also be more adaptable
to instrumental control, and the effect obtained by varying
experimental conditions could be evaluated more readily and
accurately. In addition the yield might be increased by
better control of pH and other substrate variables.

On the other hand, continuous flow operation involves
certain disadvantages, such as complexity, relatively high
initial cost and the need for stringent control. In addition,
the benefits of continuous operation might easily be offset
by mechanical failure, contamination, or selective growth of
undesirable strains. However, it is possible that proper

design of equipment might minimize mechanical failures and

sources of contamination, and that the selective growth of
undesirable strains might be prevented by nutrient adjustment
to favor the growth of the parental type. Moreover, the
Iproblem of strain degeneration might turn out to be of little
importance, since the constant environment maintained by a
continuous operation might tend to reduce the risk of
degeneration that may occur, for example, during serial trans-
fers between batch growth periods.

The essential feature of this technique is that
microbial growth in a continuous culture takes place under
steady-state conditions; that is, growth occurs at a constant
rate and in a constant environment. Such factors as pH,
concentrations of nutrients, metabolic products, and oxygen
may be independently controlled by the experimenter. These
features of the continuous culture technique make it a
valuable research tool. In spite of this the technique has
so far been comparatively little used. The reasons for this
lack of use are, in general, twofold: first, the lack of a
generally accepted theoretical background and second, the
widespread belief that the technique is impracticable for
industrial application.

The theoretical considerations, which are actually the
basic factors that determine the relative advantages of

continuous flow operation, have been studied in some detail

and are now sufficiently well advanced to provide a good
foundation for experimental studies.

The foregoing considerations led to the design and
assembly of a small laboratory continuous flow unit; the main
purpose of which was to provide experimental data to test
mathematical equations which have been developed to explain
the kinetics of continuous flow operation. Of particular
interest to this work was the relationship between substrate
concentration inside the continuous flow unit and the specific
growth rate k. Very little data are to be found in the
literature on this relationship, especially at the very low k
values. There is also a need for data concerning the relation-
ship between k and respiration rate during the steady-state

operation of a continuous flow unit.

II. LITERATURE REVIEW

A. Introduction

 

The continuous culture of microorganisms is a technique
that is of increasing importance in microbiology both from
the standpoint of its use as a research tool and its enormous
potential in industrial application. Although it has been only
in the past twenty years that this technique has been subjected
to a more detailed investigation the technique itself has been
used in limited areas for hundreds of years. The first con-
tinuous generators for vinegar production have reportedly
been in operation since 1670 (Mitchell, 1926). Yeast has been
produced using continuous culture techniques since about 1879
(Rainier, 1879) and sewage has been so treated since before
1890 (Massachusetts State Board of Health, 1890). In fact,
these processes have been developed to such a high degree over
the years that future developments will probably consist merely
of advancements based on newer technology and improved equipment.

In other areas, such as the continuous propagation of
fungi for producing antibiotic drugs, and the continuous
propagation of algae for food and fodder, the possibilities
are only just beginning to be realized. In the past ten
years research emphasis has shifted to more difficult processes,

which in turn involve greater susceptibility to contamination,

instability of the organisms, and biochemical complexity.

The increasing urgency of the "population explosion" has led
to the initiation of a number of projects for the continuous
propagation of aglae and yeast for food (Brunol gt a1., 1950;

Burlew, 1953; Tamiya, 1957).

B. Application 2; Continuous Culture

 

Techniques a

‘3 Research Tool

The potential application of the continuous culture
technique for research purposes is almost endless. It is
fair to state that the limits of such application exist only
in the imagination of the investigator. Continuous culture
techniques of the single unit type, with some exceptions
(Cekan, 1939; Dyr and Protiva, 1958: Malek , 1952a, b, 1955;
Malek 23 al., 1953a, b, 1957, 1958; Protiva and Dyr, 1958),
have become established in research laboratories as a means
of studying microbial physiology and metabolism (Anderson,
1953, 1956; Andreev, 1955; Barnes and Dewey, 1947; Castor
and Stier, 1947; Cekan, 1939; Cleary et a1,, 1935; Cohn and
Torriani, 1953; Contois, 1959; Davies, 1956; Drobnica, 1959:
DeHaan and Winkler, 1954a, b; Dyr and Protiva, 1958; Gorini,
1958: Harris-Smith‘g£‘§1., 1958; Heden g£.§l., 1955a, b;

Holme, 1957, 1958, 1959; Horodko gt a1., 1958; Hotchkiss, 1954:

6

Jacob, 1953; Jordon and Jacobs, 1944, 194 , 1948; Kalyuzhniyi,
1955, 1957; Kalyuzhniyi gt 21,, 1955b; Kautsky and Kautsky,
1951; Kuska, 1958; Lark and Maaloe, 1954; Maaloe et 31., 1958;
Macura and Kotkova, 1953; Malek, 1950, 1952a, b, 1953, 1956,
1958; Malek gt 21., 1953a, b, 1957, 1958; Myers and Clark,
1944; Novick and Weiner, 1957; Ogburn gt 21., 1958; Oswald
Ig§.§1., 1953b; Perret, 1953; Pirt, 1957; Protiva and Dyr,
1958; Raper and Alexander, 1945; Rosenberger, 1958; Rosenberger
and Kogut, 1958; Rotman, 1958; Savage and Florey, 1950; Schulze,
1956; Sevcik, 1952; Svachulova and Rushka, 1956; Utenkov,
1941, 1944; Vavra, 1958; Wean and Young, 1939; Yerusalimsky,
1958 a, b, c; Zubrzycki and Spaulding, 1957, 1958) and genetics
(Bryson 1952, 1959; Cocito and Bryson, 1958; Cocito and Vogel,
1958; Fox and Szilard, 1955; Graziosi, 1959; Labrum, 1953;
Lee, 1953; Malek, 1955; Moser, 1957a, b, 1958; Northrop,
1954; Northrop and Kknitz, 1957; Novick, 1955, 1958; Novick
and Szilard, 1950a, 1951, 1952, 1953; Saenko, 1950;
Scherbaum and Zeuthen, 1954; Verbina, 1955).

In 1924 Felton and Dougherty (1924) reported the

continuous cultivation of Pneumococcus. Since that time this

 

technique has been used in cultivating a number of organisms.
Representative genera of the organisms that have been cultivated
by continuous flow techniques are as follows:

Algae - Ankistrodesmus (Kautsky and Kautsky, 1951),

 

Chlorella (Myers, 1946; Myers and Clark, 1944; Myers and

 

Johnston, 1949), Enqlena (Logotkin, 1937; Vavra, 1958),

Nitzchia (Ketchum and Redfield, 1938).

 

Bacteria - Aerobacter (Elsworth and Meakin, 1954;

 

Herbert 21 31., 1956; Pirt, 1957; Pirt and Callowf 1958),

Azotobacter (Macura and Kotkova, 1953; Malek, 1952a, b, 1956;

 

Owen and Johnson, 1955; Rotman, 1956), Bacillus (Harris-Smith

 

§£_§1,, 1958; Malek 33 al., 1953a; Monod, 1950; Northrop,
1954, 1957; Savage and Florey, 1950; Sevcik, 1952), Brevibacterium

(Finn and Wilson, 1954), Brucella (Gerhardt, 1946; Sterne, 1958),

 

Chlorobiom (Butlin, 1958), Chromatium (Butlin, 1958),

 

 

Clostridium (Malek, 1955; Dyr and Protiva, 1958; Dyr gt 1.,

m

 

1958; Protiva and Dyr, 1958; Yerusalimsky, 1958a, b, c),

Corynebacterium (Savage and Florey, 1950), Desulfovibrio

 

 

(Butlin, 1958; Maxon, 1955), Escherichia (Anderson, 1953, 1956;

 

Clearly gt 31., 1935; Fox, 1955; Fox and Szilard, 1955; Gorini
and Maas, 1957; Gorini, 1958; Holme, 1958, 1959; Jacobs, 1953;
Jordan and Jacobs, 1944, 1947, 1948; Marcura and Malek, 1958;.
Malek, 1950; Malek §t_§1,, 1953b; Novick, 1958; Novick and
Szilard, 1950b, 1951, 1952; Novick and Weiner, 1957; Rogers
and Whittier, 1930; Rotman, 1955, 1956, 1958; Savage and

Florey, 1950), Mycobacterium (Duche and Neu, 1950, Kuska,

 

1958; Savage and Florey, 1950; Svachulova and Rushka, 1956),

Penumococcus (Felton and Dougherty, 1924; Hotchkiss, 1954;

Pirt and Callow, 1958), Propionibacterium (Jerusalimsky,

 

1958a, b, c), Proteus (Savage and Florey, 1950), Pseudomonas

 

(Finn and Wilson, 1954; Rosenberg and Kogut, 1958), Salmonella

(Formal t al., 1956; Horodko §£_§1,, 1958; Lark and Maaloe,

1954; Maaloe gt al., 1958; Malek gt al,, 1953b), Serratia

(Guenther, 1957; Smith, 1954), Shigella (Barnes and Dewey,

 

1947), Staphylococcus (Rogers, 1957), Streptococcus (Karush

 

g£_31., 1956; Ogborn gt 1., 1958; Rogers and Whittier, 1930;

Rosenberger, 1958).

Fungi - Actinomyces (Kolesnikova, 1959), Qphiostoma

 

(Von Hofsten t 1., 1953), Penicillium (Bartlett, 1958;

 

Bartlett and Gerhardt, 1958; Gerhardt, 1959; Duche and Neu,
1950; Lewis and Lucas, 1945; Moor, 1945; Soltero and Johnson,
1954), Trichophyton (Duche and Neu, 1950, Schulze, 1951).
Protozoa - Tetrahymena (Scherbaum and Zeuthen, 1954;
Vavra, 1958).
Yeast - Monilia (Malek gt_ 1., 1957), Rhodotorula

(Kautsky and Kautsky, 1951), Saccharomyces (Beran, 1958;

 

Davies, 1956; Finn and Wilson, 1954; Malek 33 31., 1958;
Maxon and Johnson, 1953; Moor, 1945; Novick and Weiner, 1957;
Plevako 2; 31., 1958), Torula (Feustel and Humfeld, 1946),
quosaccharomycetes (Harris and Hajny, 1959; Peterson 23 El-r
1958).

In more recent years some very interesting applications

of the principles of continuous culture have appeared. Zubrzycki

{Ill-II I. ’III) ll‘lll..|..llj ‘
its!

 

 

.I}i i .\a| it! .I..|ii

 

9
and Spaulding (1957) have used a modified chemostat to study
norman human fecal microflora. The microflora composition was
found under certain conditions to be analogous to that present

.in vivo. Macura and Malek (1958) used the continuous method

 

to study microbiological processes in the soil. By their
method nitrification and transformation of glucose in soil
samples could be studied.

An especially interesting application of the principles
of continuous culture has been in the area of continuous
cultivation of animal cells. Bryson (1959) and Henderson
(1959) point out that the utmost care must be taken in con-
tinuous cultivation of neoplastic cells as the most able cells
are therein selected which need not be equivalent to the
inoculum and the results are therefore of limited significance
for normal biological systems. They also point out that cells
in continuous culture can change very rapidly. Cooper £3 31.,
(1958) used continuous culture techniques to study the
critical effect of oxygen tension on the growth rate of animal
cells. Greig (1958) grew kidney cells continuously from
bovine embryos for 45 passages without any changes in morphology.
Epithelial tissue from tonsils was grown in a continuous culture
by Evans (1957). The spontaneous occurrence of intranuclear
inclusion bodies was studied in continuous cultures of renal

cells by Larin (1958).

10

The possibility of applying continuous cultivation
techniques to cream souring during the production of butter
is suggested by Masek (1959) and Wilkovske and Fronte (1958).

In the field of waste water treatment Ware and Evans
(1959) carried out experiments with the treatment of phenol
waste waters in simple aerated vessels by continuous culture
techniques. Yeast waste waters were treated by using sulphate-
reducing bacteria in a continuous anaerobic fermentation on
a technical scale by Barta and Gregr (1956). A similar process
of sulphur fermentation of waste waters was described by
Butlin gt 31., (1956), Butlin (1958) and Burgess gt 31., (1958).

The wide range of published papers is an indication
that the continuous flow method is acquiring a more sound
position in theoretical research wherever investigators begin
to understand its value as a means for solving a number of
problems of microbial biochemistry, physiology and genetics
which could hardly be solved by any other method. It is still
true, however, that the majority of papers in this field is
concerned with the direct application of this method. It
should be stated in this connection that in the practical
application of the method success is ensured only by a sound
knowledge of the theoretical basis of continuous culture and
that the most valuable contribution of the last few years

consists in the fact that the empirical approach to the solution

11
of practical problems popular in the past, has been abandoned.

Rogers and Whittier (1930), followed by Cleary et 21,,
(1935), were the first to discover that the density of organisms
grown under continuous culture conditions could be determined
by the concentration of added nutrients. With this information
it soon became apparent that, in most, if not all, of these
cultures there existed actually only two different types of
experimental conditions. Novick (1955) has referred to these
types as being either internally or externally controlled.

The internally controlled continuous flow units may be
defined as those in which the growth rate of the organism
depends on the rate of some process occurring within the cell
in the presence of an excess of nutrients. In such systems
constant conditions are usually maintained by regulating the
nutrient feed rate to maintain a given turbidity of the
culture as measured by a photocell (Anderson, 1953, 1956;
Bryson, 1952, 1953; Myers, 1946; Myers and Clark, 1944; Myers
and Johnston, 1949). Northrop (1954) has described a
continuous culture device that substitutes a commercial
colorimeter for the photo-cell system. These techniques are
very useful for studying the rate of formation of a product of
bacterial metabolism and have also been adapted to large—scale
processes. The devices that have been used for experimental

work are basically similar and have been given various names
\

r‘.
S

12

such as "Auxanometer" (Anderson, 1953, 1956), "Turbidostat"
or "Turbidostatic selector" (Bryson, 1952, 1953) and "Breeder"
(Fox, 1955; Fox and Szilard, 1955). Characteristic features
of these various types of apparatus include the use of scrapers
or glass beads to prevent growth on the sides of the culture
tube. (Anderson, 1956; Northrop, 1954, 1957, 1958; Northrop
and Murphy, 1956), and the intermittent rather than continuous
measurement of cell density (Fox, 1955, Fox and Szilard, 1955).

The externally controlled continuous flow units are
those in which the growth rate is dependent on the concentration
of some nutrient in the medium. Among the controlling nutrients
that have been employed are a required amino acid such as
tryptophan (Novick and Szilard, 1950b), arginine, proline
and histidine (Novick and Szilard, 1954); an energy source
such as lactate (Novick and Szilard, 1951), glucose (Monod,
1950), maltose (Cohon and Torriani, 1953), glycerol (Herbert
‘g§.§1., 1956); the nitrogen source such as ammonia (Novick
and Szilard, 1950b); and phosphate (Novick and Szilard, 1951;
Novick, 1955). This principle has been especially valuable
in studying mutation, rates and other problems in genetics.
Monod's "Bactogen" (Monod, 1942, 1949, 1950) and Novick and
Szilard's "Chemostat" (Novick and Szilard, 1950a, b) are two
of the best known examples of equipment designed to provide
external control. The "Bactogen" probably gives better aeration

but the "Chemostat" is simpler to set up and operate, less

13

likely to become contaminated, and more accurately defined in
volume. The "Chemostat" has become more widely used than the
"Bactogen" and has undergone more modification (Browning and
Lockinger, 1953; Duche and Neu, 1950; Fox and Szilard, 1955;
Kubitschek, 1954; Novick and Szilard, 1950b; Rotman, 1955;
Zubrzycki and Spalding, 1957); however, the "Bactogen" also
has been applied and redesigned (Harrison, 1958; Heden 32
'31., 1955a; Rogers, 1957; Von Hofsten §t_§1,, 1953).

It may be stated that, in general, the vast number of
devices that have been reported are but modifications of the
"Chemostat" and the "Bactogen." The basic equipment is
represented by a continuous flow reactor vessel which is com-
plemented by a specific apparatus for continuous cultivation,
such as the continuous preparation and sterilization of media
(Begma gt al., 1956; Fremel, 1955; Fukimbara, 1956; Gallagher
t 21., 1942; Malchenko, 1947; Malchenko gt al., 1947; Petkov,

1957; Pfeiffer and Vognovich, 1952; Stark gt _1., 1943;
Watanabe, 1956), accurate dosing of medium volumes, an apparatus
for keeping the volume constant and another for continuous
treatment of the product. The apparatus has further been
equipped by a device for continuous measurement and regulation
of pH (Deindoerfer and Wilker, 1957; Nilsson, 1958), of the

redox potential (Squires and Hosler, 1958), of dissolved-

oxygen (Sawyer at al,, 1959), of turbidity and of gas composition

14
(Telling 23 al., 1958).

In the extensive literature dealing with equipment for
continuous cultivation a marked development may be observed
toward more perfect and frequently more complicated apparatus.
The more complicated the device the more difficult it is to
operate. This has been expressed very fittingly by Novick
(Malek and Hospodka, 1960) who said: "In my country I had
considerable difficulty because people began to use the
apparatus without properly understanding it and published
papers and made a bad name for the apparatus. The second kind
of person (I do not like) is a man who published his paper
describing a new cantinuous flow apparatus with which he does
no experiments because the apparatus is so complicated that
it requires five engineers in constant attendance to keep it

in operation. These people are what we call in English

'gadgeteers' and I think that such people should be scolded."

C. Industrial Application gf_Continuous Culture

The numerous attempts at the practical application of
continuous culture data back-to 1670 (Mitchell, 1926), but
have constantly encountered difficulties which may be ascribed
to the empirical appraoch to the problems as well as to inadequate

technical level. Only after a definite theory of homogeneous

15
continuous cultivations had been developed was it realized
that each application requires a certain suitable continuous
fermentation system. It is also important to realize that
continuous cultivation processes require Specifically designed
apparatus of a new type, in which a great deal of our knowledge
of microbiology and chemical engineering is taken into account.
The most attractive feature of continuous cultivation in
practical application is the possibility of a considerable
increase in productivity as compared to the batch process
(Herbert gt al.,_1956). The greatest drawback of the method
is the high probability of contamination during long-term
cultivations on an industrial scale. This problem will likely
be solved by further technical development.

The many applications of continuous cultivation all
have certain points of similarity by which they may be grouped
together. DeBecze and Rosenblatt (1943) have suggested a
classification according to basic design of the processes
that have been used in industry. Three types of design may
be recognized: single-stage, modified single-stage and
multiple-stage.

The single-stage continuous fermentations may be defined
as those in which the entire process is completed in one vessel,
nutrients being added and cells and products being removed at

the same rate. This type of apparatus is simple and has found

16
wide application, especially in the yeast industry. Before
1940 most of the information on its use in growing yeast,
usually either Torula or Saccharomyces, was in patent records
although a few references did appear in scientific and technical
journals (Bilford 3; al., 1942; Illes, 1938a, b; Unger §£“§1.,
1942). Since the fall of Germany a number of reports were
published on the significant advances made in that country
during the war, principally on the use of single-stage Waldhof
fermenters, with sulfite waste liquor as a starting raw
material (Schulze, 1956). It has been reported (Saeman gt
._1., 1945) that almost all of the sulfite liquor in Germany
had been used to produce yeast or alcohol. Since that time
a number of other papers have appeared (Harris‘gt.§1., 1948a,
b, c; Hidalgo Fernandeq—Cano and Cid, 1952a, b; Imhoff and
Fair, 1956; Krauss and Thomas, 1954; Leopold and Fencl, 1955:
Machenko, 1947; Negre, 1949; Nomura, 1956; Ruf 23 al., 1948;
Shichiji, 1956).

Another large-scale, industrially important, single-
stage continuous fermentation in operation at the present time
is the trickling filter used for treating sewage (Babbitt, 1953;
Halvorson $3.31., 1936; Imhoff and Fair, 1956; McCabe _t al.,
1956). This process is one in which sewage is applied to a

bed of rocks, on which a mixed culture of microorganisms is

maintained. Substances other than stone have also been used

17
as a support for the microorganisms (Schulze, 1957, 1960).
The trickling filter was first used in this country in 1890
and is still the method of choice for municipalities with a
population of less than 10,000 people.
Continuous fermentations of the single stage type have
also been developed for the large scale productiOn of algae,

such as Chlorella, Euglena or Scenedesmus, using shallow troughs

 

or tubes rather than the usual vertical fermenters, in order
to give better illumination of the cultures (Bryson, 1952;
Burlew, 1953; Cook, 1951; Krauss, 1955; Krauss and Thomas,
1954). Algae have also been used as a source of oxygen supply
in the continuous treatment of sewage (Gotaas e; 31., 1954;
Ludwig g; 31., 1951; Oswald g: al., 1953a, b).

Other applications of single-stage continuous fermenta-
tion include the continuous propagation of an Aspergillus for
use as a medium supplement (Ruf g; 31., 1948) and a lactic acid
process, using Lactobacillus (Whittier and Rogers, 1931).

This process was abandoned because side reactions could be
more easily avoided in a batch process (Olive, 1949).

The modified single-stage process is generally used
where a product other than the microorganisms themselves is
desired. Many single-stage fermenters have been designed to
permit the reuse of the cells by recirculation or by con-

structing the fermenters so that most of the cells are retained

18
in the reactor vessel. The activated sludge process, discovered
in 1914 (Ardern and Lockett, 1914), is an example of this type
(Babbitt, 1953; Imhoff and Fair, 1956; McCabe §§.§1., 1956:
Metcalf and Eddy, 1935). In this process, a biomass consisting
of a mixed culture of microorganisms, is recirculated from the
final settling tanks back to the aeration tanks to serve as a
massive inoculum for the incoming sewage. Such treatment loWers
the organic content of the sewage and there is some indication
that it may be an economical way of reducing the sulfates, which
are present, to sulfides, which would be of value in manufacturing
sulfuric acid (Butlin, 1958; Butlin §£_§1,, 1956). Yeast
processes might also be conducted in a similar way, with a
protion of the yeast being continually recirculated (Kalyuzhniyi
_§§_a1., 1955b).

Another example of the modified single-stage process

is the vinegar generator (Allgeier 33.31., 1952, 1953, 1954)
which reused the acetic acid-producing bacteria, except that
in this case the Acetgbacter organisms remain fixed to the
packing, while the medium, partially acidified by recirculating
some of the vinegar, flows continuously through the generator.
This operation permits the re-use of the microorganisms at
optimum conditions for vinegar formation rather than at
optimum conditions for growth. The "Fesselhefe" method of
making alcohol from sulfite waste liquor (DeBecze and Rosenblatt,

1943) as well as a few other systems (Powell, 1958a; Sarkov,

19
1950), uses a packed bed to which yeast is bound. A pulp
suspension has also been described which is used for binding
the yeast in much the same way as a packed bed (Andreev, 1955;
Kalyuzhniyi, 1955, 1957). Northrop gt 31,, (1919) described
acetone-ethyl alcohol fermentations in which a Bacillus used
as the fermenting organism was bound to a bed of wood shavings.
A fungus product, itaconic acid, has been made in much the
same way, with an intermittent feed replacing half the fermenter
contents with fresh medium at the conclusion of each fermen—
tation (Pfeiffer §t_§1,, 1952).

In addition there are a number of processes which,
though based on the principles of the batch process, approach
the continuous process in actual operation. The Boinot alcohol
process (DeBecze and Rosenblatt, 1943) recovered all the
yeast left after fermentation and used it to initiate a new
alcoholic fermentation. Gluconic acid fermentations, in
which the fungi removed from the beer by contrifuging or
filtering are used to start a new fermentation, have also

t §_1_., 1940; Porges 3311., 1940, 1941);

been described (Moyer

A number of processes have been described in which the
fermentation is initiated in one vessel and finished in
others. For purposes of this discussion these processes have
been grouped together under the heading of multiple-stage

processes. This method generally results in either more

20

efficient use of the nutrient or better yield of product,
by permitting different conditions in each of the fermenters.
Many yeast fermentation processes have been reported.
(Altsheler §t_§1,, 1947; Andreev and Bolondz, 1955; Asai
gt al., 1952; Ashkinuzi 33 _l., 1953; Berenshtein, 1954; Cekan,
1939; DeBecze and Rosenblatt, 1943; Dyr gt 31,, 1958; Ericcson,
1947; Gladhii, 1946; Harris 33 al., 19483; International Yeast
Co., Ltd., 1926; Invention and Daranyi, 1932; Kazumov, 1957;
Keussler, 1943; Kuffner and Kuffner, 1933; Lebedev, 1936;
Logotkin, 1937, 1939, Malchenko and Christyakov, 1949; Malek
.SE.21-v 1957, 1953b; Olsen, 1927; Roseira de Mattos, 1951;
Savchenko, 1957; Smidrkal and Nejedley, 1956; Van Riju £3 31.,
1906; Yarovenko e; al., 1957; Zak and Dedkov, 1957), which are
designed to produce either yeast, alcohol, or glycerol, and
may use as many as eight fermenters in series. In many of
the small and medium-sized European distilleries, this system
is reported to be quite popular (DeBecze and Rosenblatt, 1943).

A complex study of the continuous fermentation of starch
raw materials to alcohol was taken up by Yarovenko g; 31., (1957).
In this case the situation was complicated by the subsequent
hyrolysis of dextrins to sugars during fermentation. A
Japanese worker (Ueda, 1956) described the conditions of

continuous fermentation of sugar and starch substrates from a

theoretical and practical point of view. The optimum conditions

21

for yeast growth in a multi—stage system of tanks according
to the utilization of nitrogen were discussed by Konovalov
(1959). The problem of utilization of poorly assimilable
sugars and of adaptation to these sugars and toxic substances
in sulphite liquors was studied by Fencl and Burger (1958).

Other papers dealing with continuous multi-stage
fermentation describe a system for the production of baker's
yeast (Rost, 1957); the pilot—plant production of glycerol

by using Zygosaccharomyces (Harris and Hajny, 1959); the

 

culture of Saccharomyces rouxii (Dawson, 1959); the production

 

of fruit wines (Krawczyk, 1958); the continuous production of
acetone-butanol (Yerusalimsky, 1958a, b, c); the long-term
vegetative transfer and continuous culture of Clostridium

acetobutylicum (Dyr and Protiva, 1958; Dyr t al., 1958) and

 

the production of 2,3-buty1englycol by bacteria (Pirt and
Callow, 1958). Beer and yeast yield was studied in relation
to the rate of dilution, temperature and number of fermenters
by Hough and Rudin (1958).

The continuous production of antibiotics is potentially
the single most important application of continuous culture
techniques. Although a number of commercial organizations are
known to have carried steady-state fermentations for antibiotics
production through varying degrees of development, the published

literature shows very little indication of the progress in

22

this area. In 1950 and 1951 patents were awarded to the
Distillers Co., Ltd. for single-stage continuous fermentation
processes to be used in making streptomycin (Distillers Co.,
Ltd., 1951, 1953). A fermenter with a 30 liter operating
capacity has also been described (Kroll,§t_§l,, 1956) which

was used for continuous fermentation of unspecified anti-
biotics. Subtilin has been made by a modified single-stage
fermentation where a small portion of the preceding run is

left in the fermenter as inoculum for the next run (Garibaldi,
1949). With the exception of these brief references, penicillin
and chloramphenicol are the only antibibtics which the literature
indicates as being produced by continuous fermentation (Abrahm,
1941; Clifton, 1943; Ehrlich §t_§1,, 1948; Gerhardt, 1959;

Lewis and Lucas, 1945; Moor, 1945; Stice and Pratt, 1946).

23

III; THEORETICAL CONSIDERATIONS

The various types of processes used for the continuous
cultivation of microorganisms described in Section II of this
dissertation are governed by certain mathematical principles
which are common to all. Monod (1942, 1949, 1950) was the
first to develop in a satisfactory manner the fundamental
equations which define the behavior of a continuous culture.
These fundamental concepts were later elaborated upon by Novick
and Szilard (1958, 1954, 1951). Since the appearance of these
papers a number of other authors (Contois, 1959; Drobnica,
1959; Elsworth £3 21., 1957; Herbert, 1958a, b, 1959a; Herbert
._£.21-v 1956; Ludwig gt 21,, 1951; Luedeking and Piret, 1958a,
b; Maaloe gg_al., 1958; Maxon, 1955; Moser, 1957a, 1958;
Northam, 1958; Pasynskii, 1957; Powell, 1954, 1955, 1956, 1958;
Rosenberger, 1958; SpiCer, 1955; Ueda, 1956; Yerusalimsky,
1958a, b, c, 1959a, b) have published further information con-
cerning the theory of continuous cultivation of microorganisms.

The theory of continuous cuIture, as well as the
application of the method, has been the subject of several
reviews (Bartlett, 1958; Herbert, 1958b; Malek and Hospodka,
1960; Maxon, 1955; Monod, 1950; Novick, 1955; Serfontein and

Weyland, 1959). Malek and Hospodka (1960) list a number of

symposia (Beran, 1958; Tunevall, 1959; Yerusalimsky, 1959a;

24
Symposia, 1954, 1958a, b, 1959) concerning the theory of
continuous cultivation of microorganisms.

Continuous flow systems generally consist of a reactor
into which nutrients flow at a steady rate and from which
products emerge. The factors governing the operation of such
a continuous flow system are (1) the way in which materials
pass through the reactor and (2) the kinetics of the reaction
taking place in the reactor. As Danckwerts (1954) pointed
out the first may be characterized by the distribution of
residence-times of molecules or minute particles passing through
the system.

In general two types of reactors are listed in the
literature. These are the completely-mixed tank and the ideal
tubular type with piston flow and no mixing. In the ideal
piston flow type all of the particles have the same residence-
time, equal to the mean residence-time While complete mixing
generally produces a wide spread of residence-times about the
mean. The piston flow reactor will be the more efficient for
chemical reactions whose rates fall off as the reaction proceeds.
but the completely-mixed reactor will be more efficient for
reactions of the "autocatalytic" type’whose rates increase with
time (Danckwerts, 1954). Since bacterial growth is an auto-
catalytic process, the completely-mixed reactor should be

the most efficient type for continuous bacterial culture

25
(Herbert et al., 1956) and will be the only type considered
in this discussion.

The reactor used in the experiments described later in
this thesis consisted of a one or three liter culture vessel
in which the organism could be grown under controlled
conditions. Sterile growth medium was fed into the vessel at
a controlled flow rate and culture emerged from it at the
same rate. The volume of the liquid in the reactor remained
constant. The contents of the reactor were sufficiently well
stirred, via the aeration system, to approximate the ideal of
complete mixing and the entering growth medium was instantaneously
and uniformly dispersed throughout the vessel.

The assumption of "perfect mixing"--of instantaneous
and homogeneous dispersal of the ingoing medium--great1y
simplifies the theoretical analysis of continuous cultures.

It is obvious that for purposes of study, at least, the degree
of mixing should be well defined in some sense, but it is not

at all obvious that an adequate approximation to "perfect
mixing" is practically attainable (Powell, 1956). A con-
tinuous culture is particularly sensitive to lack of homogeneity,
because of the steep fall in output near the critical dilution
rate. Moreover, the growth rate is not strictly equal to the
dilution rate unless the mixing is perfect.

Average residence-times in a vessle, such as used in

26
these experiments, will be determined not by the absolute
values of the flow-rate and culture volume but by their ratio
which may be called the dilution rate, D, defined as the
number of complete volume-changes per unit time. Expressed
mathematically D is equal to f/v where f is the flow rate
into the culture vessel and v is the volume of the vessel.
The mean residence-time of a particle in the culture vessel
is equal to 1/D (Herbert et_al,, 1956).

Herbert $3.31., (1956) developed equations which define
the behavior of a continuous culture. These equations are
essentially identical to those developed by Monod (1942,
1949, 1950) although their derivation is different and some-
what simpler than Monods. The derivation of the fundamental
mathematical relationships of continuous culture presented
here follows closely that given by Herbert g: 31., (1956).
The symbols used in this derivation are as follows:

x = cell concentration, mg cell dry wt/liter,

§'= steady-state value of x,

x0 = beginning cell concentration,
Ax = increase in cell concentration,

t = time, hours,

t'= mean residence time, hours,

td = doubling time, i.e., the time required for the

concentration of organisms to double, hours,

. At

ml

27

-change in time.

substrate concentration inside the reactor, mg/l,
steady-state value of 5,

concentration of substrate entering react r, mg/l,
constant equal to the substrate concentration at
Which k = 1/2 km,

dilution rate = f/v = number of complete volume
changes/hour,

critical value of the dilution rate D above which
complete "wash out" occurs,

rate of flow of feed solution into reactor, ml/hr,
volume of reactor, ml,

yield constant which is equal to weight of
bacteria formed/weight of substrate used,

growth constant or the specific growth rate =
rate of increase/unit of organism concentration
which is equal to 1/x ' dx/dt.

maximum rate of growth = the maximum value of k

at saturation levels of substrate.

A. Kinetics 2; Bacterial Growth

1. Derivation pf the specific growth rate ky—The specific

 

growth rate k may be derived starting with the familiar exponential

28
growth formula
x = x e (1)
upon differentiation equation (1) beomes

935 = kAt (2)
x H v.

equation (2) may be expressed as

g; = kdt (3)
X

solving equation (3) for k

dx = 1 dx
dtx x dt

 

k (4)
The expression l/x - dx/dt is termed the specific growth

rate and defines the rate of increase in cell concentration
per unit 6f cell concentration per unit time. The actual
rate of increase of concentration of organisms, dx/dt, is
sometimes also called the growth rate but is obviously not a.
constant. It has also been shown (Herbert g; 21., 1956) that
the expression l/x - dx/dt is equal to logez/td where td
represents the doubling time, i.e., the time required for
the concentration of organisms to double. k then may be
expressed as

loge2

k='———= (5)
x dt td

 

In equation (5) k and td are generally assumed to be
constants. It should be pointed out that this assumption is

correct only when all substrates necessary for growth are

present in excess (Herbert pp 21., 1956).

29
2. Relationship between the specific growth rate and

the concentration pf pp essential growth substrate--Monod

 

(1942) was the first to show the relationship between the
specific growth rate, k, and the concentration of an essential
growth substrate. k is nearly proportional to the substrate
concentration when the substrate concentration is low but
reaches a maximum value at high substrate concentrations. To
formulate these conditions mathematically Monod proposed the

following equation:

 

). (6)

It follows from this equation that exponential growth can
occur at specific growth rates having any value between zero
and km, provided that the substrate concentration can be
held at the appropriate value (Monod, 1950; Novick and Szilard,
1950).

Monod (1942) was also the first to show that there is
a simple relationship between growth and utilization of sub-
strate. This may be demonstrated in a growth media containing
a single organic substrate; under these conditions the growth
rate is a constant fraction, Y, of the substrate utilization

rate:
-- = -Y-- (7)

where Y is known as the yield constant. Thus over any finite

 

 

 

 

.... {Sill

30
period of growth
weight of bacteria formed

Y = weight of substrate used ° (8)

If the values of the three constants km, Sa' and Y are known
equations (5), (6), and (7) provide a complete quantitative
description of the growth cycle of a batch culture (Monod,
1942). These same equations and constants are equally

applicable to the theoretical treatment of continuous culture.

B. Kinetics 9: Growth ip Continuous Culture

In the development of a theoretical basis for growth
in a continuous culture certain assumptions are usually made.
It is generally assumed that the bacteria are growing under
complete mixing; that the inflowing medium contains a single
organic substrate, such as glucose, at concentration SR;
that all other substrates are present in excess; and that the
culture vessel is so efficiently aerated that the oxygen
supply is always adequate. Under these conditions the supply
of organic substrate is the sole growth-limiting factor. The
variables within the control of the experimenter are then
the substrate concentration and flow rate of the incoming
culture medium. A complete theory must describe how variation
of these factors affects the growth rate and concentrations of

organisms and of substrate in the growth vessel.

31

1. Expression pf the wash-out rate-—If one makes the
assumption that the bacteria in the reactor are not growing
or dividing then every organism in the vessel having a
residence-time greater than t is e-Dt. The wash—out rate (the
rate at which organisms initially present in the vessel would
be washed out if growth ceased but flow continued) may be
expressed as

-231:- = Dx (9)

2. Changes ip concentration pf organisms--The organisms
in a continuous culture vessel are growing at a rate described
by equation (5) and at the same time are being waShed out of
the vessel at a rate determined by equation (9). The net
rate of increase of concentration of organisms is given by the

simple balance equation (the individual terms refer to rates

in each case):

increase = growth - output
or
dx
dt - kx - Dx (10)

It may be seen from equation (10) that if k is greater than
D, dx/dt is positive and the concentration of organisms will
increase, while if D is greater than k, dx/dt is negative and
the concentration of organisms will decrease, eventually to
zero. When k equals D, dx/dt equals zero and x is constant

then a steady-state exists in which the concentration of organisms

32
does not change with time. Under these steady-state conditions,
the specific growth rate, k, of the organisms in the culture
vessel is exactly equal to the dilution rate D. During the
steady-state condition k equals D.

3. Changes ip_substrate concentration-—In the continuous
culture vessel, substrate is entering at a concentration SR:
being consumed by the organisms and flowing out at a concen-
tration s. The net rate of change of substrate concentration

is obtained from the balance equation (the individual terms

refer to rates);

 

increase = input - output - consumption
or

. . growth

a = - - .

incre se input output yield constant
or

ds kx

dt sB Ds ‘Y (11)

4. Fundamental equations pf continuous culture--
Equations (10) and (11) both contain k, which is itself a
function of 3 (see equation 6). By substituting (6) in

equations (10) and (11) the following equations are obtained:

 

from (10)
dx
dt — kx-Dx
or
dx 3
dt - x (km ) - Dx (12)

S +s
a

33

and from (11)

 

 

 

is. __ 19$
dt — Ds Ds Y
or S
d5 X[km(sa+s)]
'5: = Ds - Ds — Y
or
ds kmX s
a = D(SR -S) - Y (Sa+3) (13)

Equations (12) and (13) define completely the behavior of a
continuous culture in which the fundamental growth relations
are given by equations (5), (6) and (7) (Herbert.gp.§1., 1956).
These equations are virtually identical to the equations
developed by Monod (1950), although their derivation is
different from and much simpler than Monods.

5. The steady-state system--Considering equations (12)
and (13) it is apparent that if SR and D are held at constant
values and D does not exceed a certain critical value Do then
steady-state values exist for x and s for which both dx/dt and

ds/dt are zero. Solving (12) and (13) for dx/dt and ds/dt

equal to zero these steady-state values of'x and 5 may be

given as
D
E = Sa (k -D) (14)
m
and
—-Y( )-Y[ s<——D—-—)1
' SR'S " SR" akm -D (15)

34
From these equations the steady-state concentrations of bacteria
and substrate in the culture vessel can be predicted for any
value of the dilution rate and concentration of inflowing sub-
strate, provided the values of the growth constants km, Sa' and
Y are known. These equations were also first derived by Monod
(1950).

The equations describe accurately the situation existing
once a steady-state has been established but there is no
evidence that starting from non-steady state conditions, a
steady-state must inevitably be reached. The proof of this
was provided by Powell (1956) who has shown that, starting
from any initial values of x and s, the system inevitably
adjusts itself to the steady-state defined by equations (14)
and (15), and that this is the only stable state of the system.
For example, consider a system Which has just been inoculated,

when x is very small, 5 is nearly equal to s and k is greater

R
than D. The concentration of organisms will increase but owing
to the resulting fall in substrate concentration the Specific
growth rate will decrease, until eventually k becomes equal to
D. At this point the combined rates of substrate consumption
and loss just balance the rate of substrate addition and the
system shows no further tendency to change. The system is

stable in the sense that small accidental fluctuations from

the steady-state values will set up opposing reactions which

35

will restore the status quo. It is this automatic self-
adjusting property of the system that makes continuous culture
such a valuable research tool.

As already stated, in the steady-state the specific

growth rate is equal to the dilution rate

 

log 2
e 'S
k - t — km (S +a') -—D (16)
d a

The doubling time t is therefore equal to 0.693/D; i.e., if

d
one volume per hour is flowing through the culture vessel,
the mass of organisms will be doubling every 42 minutes.

It is evident from equations (14) and (15) that the
steady-state values of the concentrations of organisms and
substrate depend solely on the values of sR and D (since km.

Sa, and Y are constant for a given organism and growth medium).
By varying sR and D an infinite number of steady-states can
be obtained.

A somewhat different mathematical approach than the
one just given to the fundamental concepts of continuous
culture has been presented by at least three authors (Finn
and Wilson, 1954; Golle, 1953; Northrop, 1954). Their tehoretical
treatments are quite different from that of Herbert g; 31., (1956)

and very little experimental data are presented in support of

their theoretical conclusions.

36

C. Effect 9: Contamination

The possibility of contamination is one of the major
objections generally raised (Warner pp 21., 1954a, b) to the
use of continuous flow techniques on a large scale. This
objection has been answered by Dawson and Pirt (1954) as
based solely on conjecture. It will have to be admitted how-
ever that contamination is potentially a serious problem in
continuous culture work since the long operating periods make
them particularly liable to the occasional introduction of
undesirable organisms. Mathematical equations (Golle, 1953;
Bartlett, 1958) have been developed which show that the mere
entry of a foreign organism into a continuous culture does
not necessarily mean that the process will fail.

Assume that a continuous culture unit has been con-
taminated by a foreign organism. There are three possibilities
with respect to the growth rate of the foreign organisms in
the contaminated unit. Their growth rate can becgreater than,
equal to, or less than the dilution rate. If the growth rate
is greater than the dilution rate then the concentration of
the contaminant will increase exponentially with time until
the steady—state concentration of the limiting substrate: is
reduced to the point where the growth rate equals the dilution

rate. Under these conditions, the growth rate of the original

37
organism will be less than the dilution rate and its concentration
decrease to zero exponentially. An infection by an organism
with this type of growth rate will cause a complete failure of
the process.

If, on the other hand, the growth rate of the contaminant
is less than the dilution rate then its concentration will
approach a limit under the point where the growth rate equals
the dilution rate. A contamination by such an organism will
become serious only if its rate of entry is extremely high
and its growth rate only slightly less or equal to that of the

desired organism.

D. Effect pf Mutation

When mutation occurs in a continuous culture unit in
operation it is governed by the same principles that have
been applied in the discussion of contamination. By the same
line of reasoning that was applied in the treatment of
contamination, if the growth rate of the mutant, is greater
than the dilution rate, the entire culture will be replaced
by the mutant form. If the growth rate of the mutant is
equal to the dilution rate, the concentration of the mutant
will increase linearly and if the growth rate of the mutant

is less than the dilution rate, the concentration of the mutant

38
will approach a limit under the point where the growth rate
equals the dilution rate.

Two general conclusions may be drawn with respect to
mutation. Regardless of the growth rate of the mutant, the
continuous culture unit cannot be entirely free of variant
organisms, and if the growth rate of the mutant is greater
than the dilution rate a steadily increasing number of mutants
will be encountered. This was used to advantage by Novick and
Szilard (1950, 1951) to study mutation rates and to obtain
large populations of a desirable mutant.

In the case where the growth rate of the mutant equals
the dilution rate, the concentration of the mutant would
probably increase very slowly. However, if selective growth
in favor of an undesired type should occur in this case the
continuous culture unit would have to be stopped. The only
condition that will permit uninterrupted operation requires
that the growth rate constant of the undesired variant be

less than that of the parent organism.

39

IV. EXPERIMENTAL APPARATUS, CULTURE AND METHODS

A. Description pf Apparatus

An experimental apparatus was developed which consisted
of a continuous flow reaction chamber in which a constant
volume of a growing pure culture of bacteria was maintained.
Techniques were developed for the continuous feeding of
medium to this culture, continuous aeration of the culture,
sampling of the culture and continuous discharge of the culture
from the reaction chamber at a constant rate. This apparatus
is shown in Figure 1.

1. Reaction Chamber--Due to the wide range of k values
investigated it was necessary to use two separate reaction
chambers. In one of these a constant culture volume of one
liter was maintained and in the other.a Constant culture
volume of three liters was maintained. The three liter
reaction chamber was used for the very small k values while
the one liter reaction chamber was used for the higher k
values.

The reaction chambers were identical except for the
position of the discharge opening. The discharge opening was
positioned so that the contents of the chamber would flow out

when the volume reached one liter in one reaction chamber and

40

.moumnmmmm 30H“ mooscflucou

.H wuomflm

 

41
chamber and three liters in the other. The one liter reaction
chamber is shown in Figure 2.

Each reaction chamber consisted of a pyrex glass con-
tainer 12.5 cm wide and 32 cm deep. The top of the reaction
chamber was also of pyrex glass with three 2.5 cm openings
positioned around a 3.5 cm center opening. The top was
fastened to the reaction chamber by means of a metal ring with
three spring clamps. In order to prevent contamination at the
union between the top and the reaction chamber Lubriseal

r‘
(Arthur H. Thomas Co.) was placed between the two and the
union was in turn wrapped tightly with one inch masking tape.
This arrangement proved to be very satisfactory throughout
these experiments. Lubriseal was also used on all the glass
fittings and stopcocks of this apparatus.

The temperature of the reaction chamber was regulated
by immersing the chamber in a water bath (30 cm high, 30 cm
deep and 60 cm long). The temperature of the water bath was
maintained at 30C.: 0.5C throughout these experiments by
means of a Fenwal thermoregulator and heater. The water in the
bath was kept in constant agitation by means of a metal stirring
rod attached to a small motor.

2. System for inoculation and sampling pf the reaction
chamber--A schematic diagram of the system used for sampling

and inoculation of the reaction chamber is shown in Figure 3.

Figure 2.

 

One Liter Reaction Chamber.

42

 

43

 

Opening
for
Inoculation

Clamp A

Culture
Reaction
Chamber

 

 

 

\

Clamp B

 

 

 

/

 

/////d

Cotton Filter
‘ “#1

  

Clamp C

 

 

 

" b /////

Cotton Filter
#2

 

 

 

I z \ Two-way stopcock

 

 

Tube containing
70% alcohol

 

 

 

 

L/i

 

 

Figure 3. System for Sampling and Inoculation.

44
The procedure used for inoculation was as follows: A pipette
containing five m1 of a 48 hour culture of E, gpli_was inserted
in the opening for inoculation in the system. Clamp B was
closed and Clamp A was opened. Clamps B and C were then opened
and the inoculum entered the reaction chamber. Clamp A was
then closed for the remainder of the experiment.

The tubing used in this sytem, as with the aeration
and pumping systems, was a thick walled rubber tubing (I D -
0.40 cm, 0 D — 1.50 cm). An attempt was made to use plastic
tubing for the connections in this apparatus but this proved
to be very unsuccessful due to the fact that the tubing
would expand during autoclaving and would not contract upon
cooling. Numerous attempts to run the unit with plastic
tubing failed due to contamination at the union of the plastic
tubing with the glass tubing. The use of thick walled rubber
tubing, along with metal screw type clamps at the union of
the rubber tubing with the glass tubing, was found to be very
satisfactory in the prevention of contamination.

3. System for the sampling.p£ culture ip the reaction
chamber--Referring again to Figure 3, the technique for the
removal of samples for analytical purposes from the reaction
chamber was as follows: The tube containing 70 percent ethyl
alcohol (this tube was used to prevent contamination while

the sampling system was not in use) was removed. The two-way

45
stopcock was then adjusted so as to open the system containing
cotton filter II. This allowed the alcohol to drain from the
end of the sampling system. Clamp C was then closed and
Clamp B was opened. The two-way stopcock was adjusted so as
to allow liquid to flow from the reaction chamber. Suction
was then applied to the end of the sampling tube and an
appropriate amount (usually 50 m1) of sample was drawn into a
flask.

After the desired amount of sample was taken the two-
way stopcock was closed. Clamp C was then opened thus allowing
the sample in the sampling system between the reaction chamber
and the T to re-enter the reaction chamber. Clamp B was
then closed again sealing off the reaction chamber. The two-
way stopcock was again adjusted allowing the rest of the sample
in the sampling system to drain into the sample flask. The
two-way stopcock was closed and the tube containing 70 percent
alcohol was then placed over the end of the sampling system.
The two-way stopcock was then adjusted so as to open the
system containing cotton Filter II. This allowed the alcohol
to fill the end of the sampling tube from the two-way stopcock
down.

The cotton filters used in this system consisted of
glass tubes 25 cm long and 1.5 cm in diameter which were packed

with absorbent cotton. This size filter proved to be very

46
satisfactory throughout the experiments. These filters were
removed every two or three weeks and new filters put in their
place.

4. System for the aeration p§_£h§_cul§ure ip_£h§_reaction
chamber--A schematic diagram of the system used for the
aeration of the culture in the reaction chamber is given in
Figure 4. Due to the fact that the pressure of the laboratory
air supply was extremely variable (between 80 and 120 psi)

a system was developed to insure a steady and reproducible
air supply. The air from the compressed air line was passed
first through a pressure reducing valve which reduced the air
pressure from 80 - 120 psi to l - 15 psi. From the pressure
reducing valve the air passed through a pressure gauge and then
through a needle valve. The air flow was controlled by setting
the needle valve at a constant position and adjusting the
pressure reducing valve to the desired pressure. As long as
the needle valve setting remained constant a given reading
on the pressure gauge would always give the same rate of air
flow. This system was found to be very reliable and varied
from day to day by only a very small amount.

Next the air passed through a Wet test meter (Precision
Scientific Co.). Daily readings from this meter gave information
on the rate of air flow to the reaction chamber. The wet

test meter was followed by a large sterile cotton filter

47

 

 

Wet
Test

F—J//////////IT—l Meter "r‘

Cotton Filter

r1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘1
4, Needle valve
Pressure gauge
Pressure
reducing
valve
‘L ‘9
O
c 1t 8
u ure .
Reactiofl O Compressed air
Chamber 0 1ne
O
O
O
O
0
, 8
\ == /

 

Figure 4. System for Aeration of Culture in Reaction
Chamber.'

48
(26 cm long and 3.5 cm in diameter). This filter was replaced
at least once a week by another sterile filter of the same
size.

The sterile air then passed into the reaction chamber
and was dispersed into small bubbles by fritted glass dispersion
tubes. The three liter reaction chamber contained one large
fritted glass dispersion tube while the one liter chamber
contained two smaller glass dispersion tubes. Besides supplying
the needed oxygen to the culture this air supply also served
another purpose. The rate of air passing through the unit
was always high enough to keep the culture in a state of constant
agitation. This helped to keep the culture in a uniform state
and to prevent the bacterial cells from settling to the bottom
of the reaction changer and as a mixing device to thoroughly
mix the incoming substrate supply with that already present in
the reaction chamber.

The air left the reaction chamber by way of the sub-
strate overflow line. This constant flow of air out the sub-
strate overflow line helped to prevent a back-up of contamination
into the reaction chamber through this line.

5. System for providing the reaction chamber with g constant

supply pf substrate—-A schematic diagram of the system used

 

for the constant feeding of substrate to the reaction chamber

is shown in Figure 5. The substrate used in these experiments

49

.H0QEM£O cofluommm ou mumuumnom mcflcwmm now Ewume

.m magmas

 

 

 

 

 

mfidm
At

 

 

 

 

 

 

 

 

L
I

/

//////

 

 

 

nmuaam
aouuoo

 

 

mousse aouuoo

\

l L
l
l
I

mean some
ca xmmnm

Hmnfimnu
COHuummm

mHSDHSU

/

ldlll
D
O
O

 

 

mo

 

 

 

 

 

 

 

 

 

 

Illm osmao .... \

 

 

\

. Kinsman

 

 

50
was made up in batches of twenty liters. The container was a
twenty liter pyrex bottle and was protected from contamination
by a rubber stopper, covered at all times by a thick layer
of cotton, and a cotton filter placed in the air intake line.

The feed solution was pumped from the twenty liter
bottle to the reaction chamber by means of a Sigmamotor Model
T65 pump. With this pump the flow rate could be adjusted by
two methods; first, by varying the rpm of the motor and second,
by varying the size of the rubber tubing passing through the
pump. Both methods were used in these experiments. This
pump proved to be entirely satisfactory and was far superior
to roller action pumps or to a gravitational feed system.

It was found necessary to provide a break in the feed
line inside the reaction chamber in order to prevent growth
of the E, gpli_from backing up into the feed line. The
device shown in Figure 5 was found to be very satisfactory in
preventing the aerosol, which formed as a result of the
aeration of the culture, from contaminating the feed line.
Once the feed line was contaminated with the culture from the
reaction chamber it was not possible to prevent contamination
of the twenty liter bottle of feed solution.

A long stem graduated separatory funnel was inserted
in the feed line for the purpose of determining the feed rate

of the substrate entering the reaction chamber. As may be seen

51

in Figure 5 this feed rate determination was made as follows:
Clamp A (normally open) was closed and Clamp B (normally
closed) was opened. This directed the flow of feed solution
down into the graduated separatory funnel and the feed rate
was determined as ml/min with the aid of a stopwatch. A
small air line connected to a cotton filter was inserted in
this system in order to prevent a build-up of air inside the
closed graduated separatory funnel.

6. System for the discharge pf effluent from the reaction
chamber--A schematic diagram of the system used for the dis-
charge of culture from the reaction chamber is given in Figure
6. This system served two purposes. First, it acted as the
culture overflow system (thereby maintaining a constant volume
in the reaction chamber) and second, it served as the air
exit line.

As with the substrate supply system it was found
necessary to have a break in the overflow line in order to
prevent contamination from growing back up the line. Con-
tamination of various types was always present in the twenty
liter collection bottle at the end of the system but at no
time did the contamination grow past the break in the overflow
line. Two factors helped in preventing a back-up of contamination
into the reaction chamber. First, there was a constant flow

of air out this line and second, the walls of the flask were

52

 

Reaction
Chamber

4
1" Culture
/
/

 

 

 

 

’/
//

 

 

 

‘ IHH Water bath
la’l l
W“ i -)

Flask

 

 

Break in over-
flow line

Be aker*- «b

 

 

 

‘0
0’
0'
O
0'
C)
C)
C)

 

 

 

Twenty liter collectisn
bottle

 

 

 

Figure 6. System for the Discharge of Culture from the

Reaction Chamber.

53
dry at all times. All attempts to run the apparatus without
this break in the line failed due to the back-up of contamination
in the overflow line.

7. Sterilization pf the apparatus-—All parts of this

 

apparatus were sterilized in a gas autoclave at 15 lbs
pressure and 125 C for at least 30 minutes. The reaction
chamber, aeration system, sampling system, and feed system
(without the twenty liter bottle) were sterilized together.
The other parts of the apparatus were sterilized separately
and connected to the rest of the system by means of three inch

pieces of sterile, heavy rubber tubing.
B. Medium

The medium used for an aerobic continuous flow system
must meet at least three requirements. First, it must supply
all of the essential growth requirements for the organism used.
Second, all constituents, except the one being studied, must
be present in excess to insure only one growth limiting sub-
stance in the media. Third, the growth of the organism in
the medium must not equal or surpass the available oxygen
supply and thereby making oxygen a growth limiting factor.

1. Composition--The medium used in these experiments was

a modification of that used by Garrett and Sawyer (1952). This

54

medium had the following composition:

 

Substance gm/liter
Glucose 1.0
Urea 0.5
KH2P04 0.14
MgSO4 0.03
FeSO4 0.005
CaCl2 0.01
Yeast extract 0.01

 

In addition to the above constituents 100 m1 of 0.106 N
sulfuric acid was added to each 20 liters of the medium for
the initial pH adjustment.

The amount of each constituent in the medium is such
that the amounts of nitrogen, phosphorus, magnesium, iron,
calcium and nutriles (supplied by the yeast extract) are
present in excess. The amount of growth of the E, 99;; in
this medium was limited only by the amount of glucose present.

During preliminary experiments, using the above medium
containing 2 grams of glucose per liter, the efficiency of
the aeration system was found to be a limiting factor in the
amount of growth produced. Under these conditions the amount
of dissolved oxygen in the reaction chamber soon reached zero
and remained there. No such difficulty was found with the

medium containing a glucose concentration of 1 gram per liter

55
,as dissolved oxygen was always present in the reaction chamber.

2. Preparation--The medium was prepared in batches of 20

 

liters. In order to prevent caramelization of the glucose
during sterilization the glucose was sterilized in 100 m1

of 0.106 N sulfuric acid. This was then added to the rest

of the medium after the sterilization was complete. Each batch
of medium was sterilized in a gas autoclave for at least one

hour at 15 lbs pressure.

C. Culture

A number of different organisms were tried in the
continuous flow unit before a suitable one was found. Many
of the organisms tested were unsuitable for use in the system
because of clumping, sticking to the sides of the reaction
chamber, inconsistent growth or a tendency to settle to the
bottom of the reaction chamber. An accurate determination of
growth was not possible using an organism with any of these
characteristics.

The organism selected for these studies was a strain
of Escherichia coli (obtained from Dr. E. D. Devereux,
Department of Microbiology and Public Health, Michigan State
University). After a short adaptation period this organism

was found to have the ideal characteristics for use in the

56
Continuous flow system. Its growth was evenly dispersed with
no tendency to clump or to stick to the sides of the reaction
chamber.

The physiological characteristics of this strain were
tested both before and after its prolonged use in the continuous
flow system. With the exception of sucrose fermentation the
physiological characteristics of the organism at the end of
its use in the continuous flow system were identical to those
found before its adaptation to this system. This strain of
E, 29;; apparently lost its ability to ferment sucrose during
its use in the continuous flow system.

The physiological and morphological characteristics

of this strain were as follows:

Characteristic' Strain of E. coli used

Morphology Small rod, usually occurring

' singly, a few pairs always
present, non-motile, non-
encapsulated, non-spore
forming, gram negative.

Fermentation Glucose - acid with gas
reactions Lactose - acid with gas
Maltose - acid with gas
Mannitol - acid with gas
Sucrose - acid with gas
before use in the' ,
continuous flow system;
No acid or gas after
use in the continuous
flow system.

Hydrogen sulfide Negative
production

57

Characteristic Strain of E, coli used

 

Citric acid or Negative
salts utilized

Methyl red test Positive
Voges-Proskauer test Negative
Indol production Positive
Fecal odor Negative
Gelatin liquefaction Negative

 

D. Analytical Techniques

 

l. Glucose determination-~The procedure used for the
determination of glucose was a modification of the method
used by Nelson (1944). Nelson's procedure consists of a
photometric adaptation of the Somogyi method (Somogyi, 1937)
for the determination of glucose. This method is based on
the autoreduction of copper in the presence of glucose
followed by the development of a blue color with a
arsenomolybdate reagent. The optical density of the color
developed is proportional to the glucose concentration and is
stable over long periods of time (Woods and Mellon, 1941).
The composition of the reagents used in this test is listed
in the appendix.

The optical density was determined using a Bausch and

58

Lomb Spectronic 20 colorimeter connected to a Raytheon Voltage
Stabilizer. The optical density for this procedure was
determined at the following wave lengths: 350, 400, 450,
500, 550, 600, and 650 u. The widest optical density spread
was obtained at a wave length of 650 u and this was used for
all determinations.

The procedure used for the determination of glucose
was as follows:

(1) To 20 m1 of the solution containing the glucose to
be determined,

(2) Add 1 ml of Ba(OH)2 and 1 m1 of ZnSO4 solutions to
precipitate the bacterial cells. Several different volumes
(from 0.5 to 10 ml) of these two reagents were tried. The
volume found necessary to precipitate the bacterial cells in
20 ml of suspension from the reaction chamber was 1 ml.

(3) Filter.

(4) To 10 m1 of the filtrate add 5 m1 of copper reagent.
This was made up daily by adding 1 part or copper solution B
to 25 parts of copper solution A.

(5) Place the tubes in boiling water for 20 minutes.

(6) Place tubes in cold water to cool.

(7) Add 5 ml Arsenomolybdate color reagent.

(8) Mix thoroughly.until all carbon dioxide has evolved.

(9) Read optical density in Spectronic 20 at 650 u.

59

Several different ratios of glucose filtrate to the
copper reagents and the Arsenomolybdate were treid to find
which would give the best results in the very low (1-10_ppm)
glucose concentration range. The best results were obtained
with the ratios given above.

Determination 92 standard glucose curve--Eight different
concentrations of glucose were made up by dilution from a
solution containing 1000 mg/l glucose. The optical density
of the color formed by the arsenomolybdate color reagent was
determined on each of these solutions. The results obtained

were as follows:

 

Tube No Glucose con mg/l Optical density
Blank -- 0

1 50 2

2 40 2

3 30 2

4 20 1.49

5 10 0.71

6 5 0.29

7 3 0.26

8 1 0.04

 

By using the method of least squares a line was obtained
from these data with a slope of 0.073. The equation for the

line was y = 0.073x. The standard deviation of the slope

60
was : 0.0159. The graphic relationship between glucose
'concentration and optical density is given in Figure 7.

2. Dry weight determinations--The relationship between
optical density and mg/l cell dry weight was determined by
using a Bausch and Lomb Spectronic 20 colorimeter connected
to a Raytheon Voltage Stabilizer. The optical density for
this procedure was determined at the following wave lengths:
350, 400, 450, 500, 550, 600, and 650 u. The widest optical
density spread was obtained at a wave length of 350 u. This
wave length was used for all cell dry weight determinations.

The mg/l cell dry weight was determined by passing a
known volume of cell suspension through a millipore filter
which had been previously weighed. The filter and cells were
then dried at 103 C for 24 hours. The mg/l cell dry weight
was obtained from the difference in these two weights. A
weight determination on the millipore filter indicated no
appreciable loss of weight of the filter due to the heating
at 103 C for 24 hours.

Determination p: the standarddensity curve--A flask
containing 1000 ml of nutrient medium was inoculated with E,
92;; and aerated for 48 hours. Three 25 ml samples of the
resulting suspension were passed through previously weighed
millipore filters. The cell dry weights obtained from these

samples were 8.8, 8.7, and 8.7 mg. This corresponds to 349.2

61

ON

mmOUSHm H\mE

.Q>HDU OmOUUHU UHMUCQUM

.h musmflh

 

 

 

AIISNSG TVDIldO

62
mg/l of E, 39;; suspension. Optical density determinations
'were made on the suspension containing 349.2 mg/l cell dry
weight and dilutions of this suspension. The following table

shows the results of these determinations:

 

Tube No. mg/l cell dry wt. Optical density
1 349.2 0.64
2 232.8 0.44
3 155.2 0.28
4 103.5 0.15
5 69.0 0.065

 

By using the method of least squares a line was
obtained from these data with a slope of 0.0018. The
equation for the line was y = 0.018x. The standard deviation
of the slope was : 0.00036. The graphic relationship between
mg/l cell dry weight and optical density is shown in Figure 8.

3. Dissolved oxygen determinations¢~The procedure used
for the determination of dissolved oxygen in the reaction
chamber was a modification of the standard Winkler method
(Standard Methods for the Examination of Water, Sewage and
Industrial Wastes, 1955). This method is based on the oxidation
of manganous hydroxide in a highly alkaline solution. The
solution was then acidified in the presence of an iodide and

free iodine was liberated in an amount equivalent to the oxygen

63

Xmaoo.o

.m>uso .uB who Hamo cnmccmum

.us sue Hamo H\ms

.m wusmflm

OON OOH cm 00 ow ON

a - q - q d - n W A

 

 

 

W

    
 

     

d 4

  

 

 

Katsueo TESTldO

64
originally dissovled in the sample. The free iodine was
then titrated with a sodium thiosulfate solution, using starch
as an indicator after most of the iodine had been reduced.

The composition of the reagents used in this test is
given in the appendix. The procedure used for this test was
as follows:

(1) To 50 ml of the sample from the reaction chamber,

(2) Add 0.5 m1 of manganous sulfate solution and 0.5 ml
of alkaline-iodide reagent,

(3) Shake and allow to stand for 1 minute,

(4) Add 0.5 m1 concentrated sulfuric acid, shake and
allow to stand for five minutes,

(5) Titrate with 0.025 N sodium thiosulfate solution
using starch as an internal indicator after most of the iodine
had been reduced.

The above test was carried out in a tube specially
made for this purpose. This tube had a total volume of 51.0 ml
in order to prevent aeration of the sample during shaking.

4. Oxygen uptake determinations-~Determination of the
osygen uptake rates, at the different k values studied, were
conducted in a circular 20 unit Warburg constant volume
respirometer. The procedure used in the determination of the
respiration rates was as follows:

Five ml of E. coli suspension taken from.the reaction

65
chamber was placed in each of six Warburg flasks. A‘2 cm
square piece of folded filter paper was placed in the center
well of each flask in addition to 0.2 ml of a ten percent
solution of potassium hydroxide to absorb the carbon diOxide
that was produced. The flasks were then attached to their
respective manometers and immersed in a water bath. The
flasks were then allowed to equilibrate, with shaking, for ten
to fifteen minutes before the manometer stopcocks were closed
and readings started. The shaking rate used in all of the
experiments was 116 strokes per minute. ‘

The time interval between manometer readings varied
during the experiments. At the very small k values it was
necessary to use a time interval of at least 1 hour between
each reading. At the higher k values manometer readings
could be taken every five or ten minutes. Care was taken
not to use any data in which there was a significant decrease
in the respiration rate between manometer readings.

Most of the oxygen uptake rates reported represent an
average of at least 18 separate determinations for each k
value studied. These 18 determinations represent six-separate
determinations each day at least three days for each k value.
All oxygen uptake data were calculated in terms of ulOZ/mg
cell dry weight/hour.

(The following two equations, as given by Umbreit pp.§l.,

66

(1957), were used in calculating the oxygen uptake rates:

273

 

. V ——T__ + Vf O
(l) Flask constant K = g
P
o
where V = Volume of gas phase in flask,
T = absolute temperature,
Vf = volume of fluid in flask, \
o = Bunsed Coefficient = 0.0260 (ml oxygen in
solution per ml liquid at 1 atm pressure
at 30 C,
P0 = 10,035 (standard pressure of mercury in terms

of manometer fluid).

(2) Amount of gas exchanged X = h x K,

where h alteration in reading on open arm of manometer,

k flask constant.

The composition of the Brodie's solution used in the

manometers is given in the appendix.
5. _pH determination p: control--pH determinations were

made three or four times daily using a Beckman Model H-2
pH meter. Twenty m1 of sample was taken from the reaction
chamber, placed in a 50 ml beaker, and the pH determined at
room temperature.

The pH of the feed solution was adjusted so that after
sterilization the pH was between 7.8 and 8.2. Due to the

production of acid by the organisms the pH of the material

67
inside the reaction chamber would drop to 5.2-5.6 if allowed
(to go unadjusted. For this reason a 500 ml container of
sterile 0.1 N sodium hydroxide was inserted in the system.

By addition of sodium hydroxide three or four times daily

the pH of the material in the reaction chamber was maintained
between 6.4 and 7.0. The average pH value obtained during
the experiments was 6.7. If the unit was running at very

low k values only small amounts of sodium hydroxide were
needed but at higher k values it was necessary to add as much
as 10 to 30 ml of the sodium hydroxide solution three or

four times daily in order to maintain the pH at approximately
6.7.

6. Microscopic examination--Daily samples were taken from

 

the reaction chamber and examined under the oil objective lens
of the microscope. Both wet mounts and gram stained pre-
parations were routinely examined. When contamination did
occur it was usually detected by the microscopic examinations.
In such cases the unit was shut down, cleaned, sterilized,
and inoculated again with a culture known to be free of
contamination.

7. Nitrogen determination--Total nitrogen determinations
made on organisms taken from the reaction chamber served two
purposes. First, to characterize the strain of E, gpll_used

and second, to determine if nitrogen was present in the

68
medium in excess so that it did not constitute a growth limiting
factor.

The procedure used for the total nitrogen determinations
was essentially the same as that listed by the A.0.A.C
Official Methods of Ananysis (1950). This procedure was as
follows:

(1) Six one gram samples of dried organisms were placed
in Kjeldahl flasks,

(2) Two grams of copper sulfate, 4 grams of potassium
sulfate along with 30 ml of concentrated sulfuric acid were
added to the flasks,

(3) The mixture was digested for 1.5 hours and then
allowed to cool,

'(4) 200 ml of amonia free distilled water was added to
each flask along with two or three pieces of granulated zinc
(to decrease bumping) and 60 m1 of sodium hydroxide solution
(450 gm sodium hydroxide/l water) to make the mixture
alkaline,

(5) The mixture was again heated and approximately 150
ml was distilled into 25 ml of 0.106 N sulfuric acid,

(6) The amount of acid used up was determined by titration
with 0.115 N sodium hydroxide using methyl red as an indicator,

(7) The percent nitrogen in the sample was calculated as

follows:

69

1.4 x N acid
gms of sample X ml acid used by NH

 

Percent nitrogen =
3

M1 acid used bY NH = (m1 acid used .E_2§§§

3 . — N acid x ml base)

8. Ash determination--Ash determinations were made on

 

samples of E, gpll_taken from the reaction chamber. The
procedure used for these determinations was as follows:

(1) One gram of dry cell material was placed in an
electric muffle furnace heated to a low red heat (650 C),

(2) After at least three hours in the furnace the
sample was removed, allowed to cool in a desiccator and
weighed,

(3) The percent ash was then calculated using the
following formula:

wt of ash

Percent ash wt of sample x 100

 

9. Viable cell count—-In order to obtain an estimate of

 

the relationship between mg/l cell dry weight and the number

of viable cells present per liter in the reaction chamber a
technique similar to the drop plate technique first reported

by Miles and Misra (1938) and later modified by Tomales-Lebron
and Fernandos (1952) and Mallmann and Broitman (1956) was

used. This procedure is predicated on the premise that colonies
will appear on a suitable medium from each single culturable

cell placed on the medium. The procedure used was as follows:

70

(1) Medium was prepared consisting of the same composition
.as the feed solution and containing two percent agar. The
medium was poured into standard size plastic Petri dishes and
allowed to stand in an inverted position over night at room
temperature in order to allow the surface of the plates to
become dry,

(2) Six equidistant circles approximately 2 cm in diameter
were drawn on the bottom of each Petri dish,

(3) Appropriate dilutions were made from samples taken
from the reaction chamber. Using a 0.2 ml.pipette, 0.1 ml
of each dilution was delivered to each of the six spots.
Duplicate plates were set up giving a total of 12 counts for
each dilution,

(4) To prevent the drops from running together the plates
were not moved for at least one hour,

(5) After the drop had been completely absorbed by the
agar the plates were incubated at 37 C for 48 hours and then

counted.

71

V. RESULTS

The data presented in this section were taken daily
from the continuous flow unit during three separate experiments.
The first experiment lasted for a period of 64 days. The
purpose of this experiment was to establish the relationship
between substrate concentration in the unit and k and to obtain
the approximate value for the maximum growth rate km. Oxygen
uptake data were also taken in order to determine the relation-
ship between k and the respiration rate. The first experiment
covered a D range of 0.059 to 0.85.

The second experiment lasted for a period of 33 days.
The main purpose of this experiment was to evaluate km as
close as possible and also to confirm the data from the first
experiment. The D range of the second experiment was 0.061 to
0.717.

The third experiment lasted for a period of 37 days and
its purpose was to establish the relationship between k and
substrate concentration in the unit at extremely low k values.
The D range of this experiment was between 0.011 and 0.081.

At the beginning of each of these three experiments
the unit was sterilized and filled with medium. The unit was
then allowed to stand for a period of three or four days in

order to determine if any contamination were present. If the

72

medium remained clear five ml of a 48 hour culture of E, 22;;
was added for inoculation. The unit was then allowed to stand
for another period of two or three days until heavy growth
was visible in the unit. The flow of nutrient solution was
then started and maintained for at least seven days at a
low flow rate (1 ml/min) in order to allow the unit to
stabilize itself.

Data were obtained daily from the continuous flow unit
as follows:

1. Glucose determinations--Two glucose determinations
were made on the influent medium and two more on samples
taken from the unit,

2. Dry weight—-mg/1 cell dry weight was determined at
least once each day,

3. Dissolved oxygen--Dissolved oxygen measurements were
made once daily during the investigation of the low D values
and 3 to 5 times daily while the unit was operated at the
higher D values. The dissolved oxygen range obtained during
the three experiments was 0.5 to 4.8 ppm, in other words,
the dissolved oxygen concentration did not decrease below
0.5 mg/l at any time. The rate of air supply, as measured
by a Wet-test Meter, varied from 1.0 l per min at small D
values to 3.1 1 per min at the higher D values. The dissolved

oxygen figures indicate that at no time during the operation

73
of the unit was dissolved oxygen a limiting factor.

4. Oxygen uptake--Six Warburg flasks were set up each
day in order to determine the respiration rate,

5. pH—-pH determinations were made at least once a day
during the investigation of the low D values and 4 to 8 times
daily while the unit was running at the higher D values,

6. Microscopic examinations--At least one wet mount and

one gram stain preparation were examined each day.

A. Experiment E9. E

 

The one liter continuous flow unit was operated at the
following D values for a period of three consecutive days
for each D value: 0.059, 0.091, 0.124, 0.178, 0.240, 0.301,
0.360, 0.425, 0.485, 0.546, 0.610, 0.660, and 0.730. In
addition to these values the unit was also operated for two
days at a D value of 0.794 and one day at a D value of 0.847.
After data were obtained over a three day period for one of
the D values listed, the flow rate of medium into the unit was
changed, thus adjusting the unit to a new D value. The unit
was then allowed to run at the new D value for at least 24
hours before any additional data were taken. When the D
value at which the unit was being operated reached 0.730
the cell concentration in the unit dropped below the steady-

state average.

74
The data obtained from the continuous flow unit during
experiment No. 1 are given in Tables 1-15. Averages of these
data, along with the averages of data obtained from experiment

No. 2 are given in Table 17.

B. Experiment E2. g

 

In order to confirm the data from experiment No. 1 and
'UDpinpmfint more exactly the value of km the one liter
continuous flow unit was operated for a period of 33 days at
the following D values: 0.061, 0.119, 0.238, 0.307, 0.427,
0.529, 0.599, 0.658, 0.662, 0.668, 0.658, and 0.725 for a
period of two days; one day at D values ranging from 0.689
to 0.717; and 4 days at a D value of 0.694. The same
procedure was used as in experiment No. l. The data obtained
from the unit during this experiment are given in Table 16.
Averages of these data, along with the averages of the data

obtained from experiment No. l are given in Table 17.

 

C. Experiment E2-.§

In order to establish the relationship between k and
substrate concentration at low concentration values the three

liter unit was operated for a period of 37 days at the following

75
D values: 0.081, 0.062, 0.052, 0.020, and 0.011. The larger
unit capacity was necessary in order to obtain the very small
D values. The data obtained during this experiment are given

in Table 18.

D. Establishment p£_the Steady-State

 

 

The relationship between cell concentration in the unit
and D is shown in Figure 9. The data used for this plot were
taken from Table 17. (Each of the points on this figure
represent an average of three days data (with the exception of
the D values above 0.694). As may be seen from Figure l and
Table 19 the cell concentration remained at a constant Value
between D values of 0.059 and 0.694. As the unit was operated
at D values above 0.694 the concentration of cells in the unit
decreased. This indicates that steady-state conditions existed
between D values of 0.059 and 0.694. Since, by definition,

D is equal to k during the steady-state, the D values cocurring
within the steady-state will be referred to as k values from
this point on. The average cell concentration during this
steady-state condition was found to be 427 mg dry cell Wt/l
with a standard deviation of 9mg/l.

The points above a D value of 0.69, shown in Figure l

and Table 19, represent a combination of data taken from

76
experiments Nos. 1 and 2. Points 1-7 were obtained from
, experiment No. 1 in the following manner: Prior to point 1
the unit had been running for two days at a D value of 0.69
and a cell concentration of 426 mg/l. The unit was then
adjusted to a_D value of 0.73 for a period of 32 hours. As
shown by points 1, 2, and 3 cell concentration values of 400,
394, and 394 mg/l were obtained at 7, 21, and 32 hours respectively.
The unit was then adjusted to a D value of 0.79 and allowed to
run at this value for 20 hours. The cell concentration at the
end of this 20 hour period was 311 mg/l indicating a wash-out
of cells from the unit (point 4, Figure 9). The unit was
then adjusted to a D value of 0.85 and allowed to run at this
rate for 23 hours. Cell concentrations of 202, 176, and 156
mg/l were obtained at 12, 16 and 23 hours respectively (points
5, 6, and 7, Figure 9). This indicates that at a D value of
0.85 cells are washed out of the unit faster than they are
replaced by growth, i.e., km must be below 0.85. Finally the
unit was adjusted to a D value of 0.69 and the cell concentra-
tion rose to the steady-state range value of 417 mg/l.

Points 8-11, Figure 9, were plotted from data obtained
from experiment No. 2 and were obtained in the following manner:
Prior to point 8 the unit had been running for two days at a
D value of 0.66 with a cell concentration of 422 mg/l. The

unit was then adjusted to a D value of 0.73 and allowed to

77
run at this rate for 2 days. At the end of this period the
cell concentration dropped to 370 again indicating wash-out
of cells from the unit (point 8, Figure 9). The D value of
the unit was then adjusted to 0.66 and allowed to run at
this rate for 6 days. At the end of this 6 day period the
cell concentration was 429 mg/l. Following this 6 day run
the unit was then operated for another 6 days at a D value
of 0.69I The cell concentration at the end of this period
was 430 mg/l. The D value of the unit was then adjusted to
0.71 and allowed to run at this rate for 3 days. The daily
cell concentrations were 400, 390 and 360 mg/l (points 9, 10,
11, Figure 9). This represents a slow but continuous decrease
over the 3 day period indicating that a D value of 0.71 is
slightly above km. Finally the unit was adjusted to a D
value of 0.69 and allowed to run at this rate for 4 days.

The cell concentration again rose to a steady-state range
value of 422 mg/l.

As mentioned before, from the experimental data
presented in Figure 9 and Table 19, it can be seen that the
cell concentration in the unit decreased, indicating non-
steady-state, as the D value increased beyond 0.69. As
illustrated by points 1-3, 5-7, and 9—11 (Figure 9), this
decrease in cell concentration was a function of time; i.e.,

as the unit was operated at a given D value above 0.69 the

78
unit did not adjust itself to a new steady-state, instead the
cell concentration continued to decrease even though the D
value was kept constant. This may also be seen from Table 19
which shows a summation of the data taken when the unit was
operated at D values above 0.69. This decrease in cell
concentration, at a particular D value above 0.69, indicates
that cells are washed out from the unit faster than they are
replaced.

Herbert g£_§l,, (1956) gave the following formula to
express the wash-out rate from a continuous flow unit:

525

- dt Dx (9)

This equation would express the wash-out rate under the condition
that k is equal to zero. It may be assumed that under conditions
where D is greater than km the organisms are still growing

at a rate equal to km. Equation (9) would then have to be
modified as follows:

as

-dt = D-km)x (17)

A similar equation has been proposed by Finn and Wilson (1954).

The theoretical concentration of cells in the unit
after the unit has been running at a D value above km for a
given period of time may then be calculated from the relation-
ship

-(D-k)
m

Y = xe (18)

where y equals the cell concentration after time t and x is

79
equal to the initial cell concentration. The theoretical cell
concentration was calculated using the data obtained at a
D value of 0.85. The cell concentration at the time the
unit was adjusted to this D value was 311 mg/l. After
operating at this D value for 23 hours eht cell concentration
was 156 mg/l. The theoretical cell concentration for the
unit running at a D value of 0.85 for 23 hours was calculated
to be 7.78 mg/l. This relationship between actual cell
concentration and calculated cell concentration is shown in
Figure 10. As may be seen from this figure the actual time
for complete wash—out at a D value of 0.85 would be
approximately 40 hours while the complete wash-out period
based on the calculated figures would be approximately 25
hours. In other words the actual wash-out rate from the unit
was less than the theoretical wash-out rate. One possible
reason for this is that the equations are based on the assumption
of complete and instaneous mixing. Actually the unit may not
have had complete mixing, therefore the difference. k was
also assumed to be constant under these conditions but there
was no way to prove this experimentally.

The relationship between D and substrate concentration
over a D range of 0.059 to 0.855 is shown in Figure 11. The
data used for this figure were taken from Table 17. Figure

11 shows that as D is increased the substrate concentration

80
also increases. It was shown in Figure 9 and Table 19 that the
non-steady-state begins at D values higher than 0.69. Since
km (0.69) corresponds to a substrate concentration of 180
mg/l it can be deducted that above 180 mg/l substrate concentra-
tion k is independent of the substrate concentration. Below
180 mg/l substrate concentration k is related to substrate

concentration in the manner shown by the curve in Figure 13.

 

E. Establishment of k
-—--m

km may be defined as the maximum rate of growth of a
culture or the maximum value of k at saturation levels of
nutrients. The value of km for this strain of E, 39;; grown
under these experimental conditions was determined by two
methods. The results obtained by these two methods were as

follows:

 

1. Continuous flow determination pE_Em--As already
indicated steady-state conditions existed between k values
of 0.059 and 0.694. When the unit was operated at D values
above 0.694 the concentration of cells in the unit decreased.
The higher the D value above 0.694 the faster the cell con-
centration decreased. The data shown in Figure 9 therefore
indicates that the km value for this strain of E, 2211' grown

under these experimental conditions, was between 0.69 and 0.71.

81

2. Batch culture determination pE_Em--In order to

 

determine km by the use of batch culture procedures and

also to determine if selective mutation occurred for different
growth rates, two batch culture determinations of km were

made. The first of these (listed as Flask A) was made

before the culture of E, gpii_was introduced into the continuous
flow unit. The second batch culture determination of km
(listed as Flask B) was made using organisms taken from the
continuous flow unit after the unit had been running for three
months. For each of these determinations a flask containing

1 liter of liquid medium was inoculated with a heavy inoculum
of the culture. Optical density determinations were made every
30 minutes on each flask for a period of seven hours. The
results of these determinations are shown in Figure 12. The
following table also shows a summation of the data obtained

from these two batch culture determinations.

 

Flask A Flask B
Slope by method of least
squares (km) 0.665 0.686
Slope by method of averages 0.66 i 0.11 0.69 i 0.076
Generation time (min) 62.4 60.6
pH range 6.5-6.8 6.4-7.0

 

The t test, according to the procedure given by Youden

(1951), gives a t value of 3.008 on a comparison of the two slopes.

82
The 1 percent critical value for t with 8 degrees of freedom
(n + n - 4) is 3.355. This indicates that there was no
significant difference in the slopes of the two lines and
therefore no significant difference in the growth rates of

the organisms in the two samples.

F. Relationship between Substrate Concentration,
Experimental E_and Calculated E_values

 

 

 

 

The data pertaining to the relationship between sub-
strate concentration and k obtained from the continuous flow
unit are given in Table 20 and Figure 13. From Figure 13 it
can be seen that, during the steady-state condition, as the
substrate concentration in the unit increases the k value
also increases.

Also given in Table 20 and Figure 13 are the k values
that have been calculated by two different methods. The
first method was by using the relationship

k=k(s) (6)

m Sa + s
as given by Monod (1942) and Herbert gp.EE.,(l956). The
values of km and Sa used in this calculation were obtained from
the experimental data and were 0.69 and 40 reSpectively. Sa

is defined as that substrate concentration at which k is equal

to l/2km and may be obtained, along with the value for km from

83
the data presented in either Table 17 or Figure 13. As may
be seen in Figure 13 the k values calculated by this method
follow the experimental values closely up to a k value of
about 0.4 and then fall considerably below the experimental
values at the higher 5 values.

Another method of obtaining the constants km and Sa
would be to employ the Lineweaver-Burke plot (Dixon and Webb,

1958), which is based on a modification of equation (6):

i’ - + ——— x ——- (19)
When l/k is plotted on the y axis and l/x on the x axis, the
y intercept is equal to l/kfi and the x intercept is equal to
l/Sa. The results obtained by plotting the experimental data
from experiment No. l in this manner are shown in Figure 14.
The values of km and Sa were calculated to be 1.20 and 120.5
respectively by the method of least squares. This indicates
that the experimental relationship between k, km, and s does
not follow this expression as the values for km and Sa are
much higher than the experimentally obtained values of 0.69
and 40 respectively.

The general shape of the experimental curve suggests
that the relationship between substrate concentration and k

may follow a unimolecular expression of the type given by

Teissier (1936).

84

k = k (1 - 6“") (20)
m
c in this case may be defined as a reaction velocity constant.
Here too there is a problem of calculating the values for km
and c. Reed and Theriault (1931) devised a method whereby

km and c can be caluclated from a series of experimental data

by three simulteneous equations:

 

2
Zle - AZfl - BZflf2 - CZflf3 - o
2
ZfZY - AZflf2 - BZf2 - CZf2f3 — o
2
Zf3Y - AZflf3 - B2f2f3 - CZf3 — o
where
- cls
fl = 1 - e
- cls
f2 = se
cls
f3 = e
A=k
m
Y = k
-Bzcn
c' = 2.302585c"
c = c' xh
B
h_k
m

Using the data presented in Table 17 (only the data
obtained during the steady-state condition were used) in the

solution of these three equations, km was calculated to be 0.69.

85
This is in full agreement with the experimental data. c
was calcualted to be 0.012 from these equations. The results
from the use of this method indicate that the equation for the

relationship between substrate concentration and k would be

k = 0.69 (1—e-O°0128) (21)

k values calculated according to this equation are given in
Table 20 and are shown graphically in Figure 13. Although
the calculated values are all lower than the experimental
values it can be seen that the general shape of the curve
shows good agreement with that obtained from the experimental

values.

G. Relationship between E and Substrate Concentration
25 Low 2 Values

The relationship between D and substrate concentration
at low D values was investigated in experiment No. 3. The
results of this experiment are given in Table 18. As may be
seen from this table, as the D value drops the substrate con-
centration in the unit also drops. The relationship between
D and substrate concentration obtained during experiment No. 3
is shown graphically in Figure 15. These data indicate that
steady-state conditions existed at D values as low as 0.02.

These figures also indicate that the k range at which this

86
strain of E, 39;; may be kept in a steady—state under these
(experimental conditions is 0.02-0.69. When the unit was
operated at a D value below 0.02 the cell concentration in the
unit decreased. At this point the substrate concentration in
the effluent or inside the unit was 1 mg/l or below and too
low to be measured. This indicates that at D values below
0.02 and at substrate concentrations below 1 mg/l k appraoches

zero so that the cells are washed out according to equation (9).

H. Relationship between E_and Respiration Rate
During SteadyeState Conditions

Respiration rate determinations were made during
experiment No. l. The summation of the oxygen uptake data
is presented in Table 17. The relationship between respiration
rate and k during the steady-state operation of the continuous
flow unit is presented in Figure 16. An examination of this
figure indicates that there is a direct linear relationship
between respiration rate and k during the steady-state operation.
A linear relationship was also obtained by Herbert (1959b)
measuring the oxygen uptake at different k values of Aerobacter '

aerogenes grown in continuous culture. The oxygen uptake

 

data presented in Table 17 also indicate that the reSpiration
rate increases with k until a maximum rate is reached. The

maximum respiration rate corresponds to the maximum k value

87
(km) at which the unit can be operated under steady-state
conditions. An increase in D above 0.69, the value corresponding
to km does not increase the respiration rate of the organisms.
The equation for the line shown in Figure 16, as
calculated by the method of least squares is

Q = 9.43 + 543.6 k
02

where 002 is the reSpiration rate in u l/mg cell dry wt/hr.
From this equation the respiration rate for any given k value
can be calculated. It is suggested that the value for the
constant a (9.43), is given in this equation, represents the
endogenous respiration rate of this organism under these
experimental conditions.

The average respiration rate obtained at a D value of
0.69 and higher was 347 u 102/mg cell dry wt/hr. This value
is higher than the respiration rate of 272 u 102/mg cell dry
wt/hr at 32 C given by Spector (1956) for £2.2211- In fact
such a respiration rate would correspond to a k value of
0.49 under the experimental conditions described here.

A linear relationship was obtained between the actual
amount of oxygen consumed and the theoretical amount of oxygen
needed for complete oxidation of the sugar used by the organisms.
The data used in the calculation of this relationship are

given in Table 21 and are shown graphically in Figure 17.

As may be seen from Table 21 only 33.8 to 38.9 percent of the

88
theoretical oxygen needed for complete oxidation of the amount
of glucose assimilated was actually consumed. The equation
for this relationship, as shown in Figure 21, was calculated
by the method of least squares and found to be

Y = 0.37X
Where Y is equal to the actual amount of oxygen consumed in
terms of u 102/mg cell dry wt/hr and X is equal to the
theoretical amount of oxygen needed for the complete oxidation
of the sugar assimilated. These data indicate that during
the steady-state operation of the unit, approximately 37 per—
cent of the assimilated substrate was oxidized.

The relationship between percent of theoretical oxygen
utilized and k during the steady—state operation of the unit
is given in Figure 18. The data shown in this figure also
demonstrate that regardless of the value of k 37 percent of

the theoretical oxygen needed are consumed.

I. Calculation pg the Economic Coefficient
During Steady+State Conditions

The economic coefficient was calculated for each of
the k values used during the steady-state operation of the unit.

The following formula was used for these calculations:

weight of Bacteria formed/unit time

' ff' ' t . ' '
Economic coe 1c1en weight of Substrate used/unit time

89
The data obtained from these calculations are given in Table
22. The graphic presentation of the relationship between the
economic coefficient and k may be seen in Figure 19. These
data indicate that the economic coefficient of the organism
during the steady-state operation of the unit was between 44.3
and 54.7 percent. These values agree well with a value of
53.0 percent reported by Herbert gp.§l., (1956) for the

steady-state growth of Aerobacter cloacae utilizing glycerol

 

as a carbon source. These data also indicate that there may

be a gradual rise in economic coefficient as the k value
increases. This rise in economic coefficient appears to be

of the order of ten percent, i.e., the organisms were converting
substrate into cell material at a ten percent higher efficiency
at the maximum k value than at the lowest k value. This may

be related to the problem of endogenous respiration and will

be discussed later in Section VI of this report.

J. Application 2: Experimental Data pp Theoretical
Steady-State Equations

 

The following relationship between'S, 88, D and km has

been proposed by Monod (1950) and Herbert §£_§l,, (1956):

) (l4)

90

The results obtained from the application of the experimental
data during the steady-state condition to this equation.are
presented in Table 23 and Figure 20. The values of Sa and km
used in these calculations were 40 and 0.69 respectively. As
may be seen from Table 23 and Figure 20 the calculated'§ values
follow the experimental E values closely until a k value of 0.4
is reached. From this point on the calculated E'values are
much higher than the experimental E values. It will be recalled
that a similar breaking point occurred when the experimental
data were applied to equation (6). There appears to be no
relationship between these calculated 5 values and reality since
for a k value of 0.69 the calculated § value is higher than
that for SR, the substrate concentration entering the unit.

Monod (1950) and Herbert pp p;., (1956) give the
following equation to show the relationship between R, Y, SR'
km,.Sa, and D:

- _ D
x - Y (SR — s) - Y [SR - Sa ( k _ D

m

)1 (15)

The experimental values obtained for Y, SR and Sa were
applied to the first part of this relationship
2 = Y (sR - E)
The results obtained for the calculation of the steady-state
cell concentrations are presented in Table 24. As may be seen

from this table the calculated steady-state cell concentrations

are in full agreement with the experimentally obtained values.

91
This was to be expected since Y has been calculated previously
in the same manner.
An entirely different picture was obtained when the
steady-state cell concentrations were calculated using the

last part of this relationship

_ D
X _ Y.[SR- Sa( km - D

)1

The results obtained from the application of the experimental
data during the steady-state condition to this equation are
presented in Table 25. The results were calculated using

both an average Y value of 47 percent and the actual experimental
Y values obtained during the operation of the unit. An

average value of 964 was used for SR and a value of 40 was

used for Sa. As may be seen from Table 25 the i values
calculated using the average Y value of 47 percent are higher
than the experimental values at the low k values and are much
lower than the experimental a values at the high k values. The
i values calculated using the actual Y values are in close
agreement with the experimental x values until a k value of

0.4 was reached. From this point the calculated i values
indicate that wash-out is occurring from the unit while the
experimental i values indicate that the steady-state condition
still exists. This breaking point again occurs at about the

same k value as in equations (6) and (14).

92

K. Nitrogen, Ash, and Moisture Determinations

Samples were taken from the unit while it was running
at a k value of 0.062.’ The cells from these samples were
obtained by high speed centrifugation. Nitrogen, ash, and
moisture determinations were made as described in Section IV.
The results of these determinations are summarized in the

following table:

 

Nitrogen Moisture Ash

% dry wt % %
12.6 72.5 8.5
12.0 72.0 8.3
11.9 72.8 8.3
12.7 72.6 8.7"
11.4 72.9 9.7*
11.7 70.6* 8.5

 

* not used in calculating average
The average values of 12.1 percent nitrogen, 72.6 percent
moisture and 8.5 percent ash are in agreement with the values
of 73 percent moisture, 8.6 percent ash and 9-13 percent

given by Spector (1956) for E, coli.

L. Culturable Cell Count

 

Culturable cell counts were made by the method described
in Section IV. The following data were obtained at a cell

concentration of 422 mg cell dry wt/l during steady-state

93
operation of the unit:

Count x 108 cells/ml

\l\l(DO\\lUI
le-thwb

The average of these data is 7.0 x 108. Each figure given
represents an average of 12 counts; i.e., two plates each
containing six counts. These figures indicate that 1 mg cell
dry wt represents approximately 16.6 x 108 viable cells and
that during steady-state conditions the unit was operated at

a concentration of approximately 7.0 x 108 cells/ml.

94

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109

Table 16. Data obtained from the continuous flow unit during
experiment No. 2.

 

 

 

Substrate con mg/l Cell con
D pH Influent Effluent mg/l

0.061 6.5 965 5.6 427
950 4.3

0.119 6.8 980 13.0 434
965 13.9

0.238 6.9 960 34.6 417
830* 31.0

0.307 6.4 975 42 438
960 38

0.427 6.0 960 68 422
950 61

0.529 6.5 955 98 427
980 106

0.599 6.7 945 124 434
975 120

0.658 6.3 980 159 422
900* 150

0.658 6.5 990 157 427
960 148

0.662 6.5 960 140 438
985 155

0.668 6.8 970 153 422
834* 148

0.689 6.7 980 175 434
950 168

0.689 6.4 630* 170 422
680* 165

0.694 6.5 975 178 434
960 171

0.694 6.7 965 176 422
970 179

0.694 6.4 980 168 434
955 164

0.709 6.4 965 210 400
960 196

0.714 6.8 990 217 390
970 224 '

0.717 6.5 965 237 360
840* 143*

0.725 6.8 960 200 352
970 220

 

*Data not used in calculations

110

 

 

 

Table 17. Summary of averages of data taken during
experiments 1 and 2.
Cell con Substrate con mg/l Oxygen uptake

D mg/l Influent Effluent 1/mg/hr
0.059 422 958 5.1 34
0.061 427 957 5.0 ---
0.091 429 961 8.3 52
0.119 434 973 13.5 --—
0.124 431 960 13.3 70
0.178 428 971 20.3 105
0.238 417 960 32.8 ---
0.240 421 969 30.4 141
0.301 433 961 37.0 188
0.307 438 968 40.0 ---
0.360 420 969 42.1 225
0.425 420 969 58.0 249
0.427 422 955 65.0 ---
0.485 413 962 74.4 265
0.529 427 968 102.0 ---
0.546 433 963 96.5 314
0.599 434 960 122.0 ---
0.610 426 963 112.0 335
0.658 422 980 155.0 ---
0.660 434 966 161.0 353
0.662 438 973 148.0 ---
0.668 422 970 151.0 ---
0.689 434 965 172.0 -——
0.689 422 --- 168.0 ---
0.694 434 968 175.0 ---
0.694 422 968 178.0 ---
0.694 434 967 166.0 -—-
0.709 400 963 203.0 -—-
0.714 390 980 221.0 ---
0.717 360 965 237.0 ---
0.725 352 965 210.0 ---
0.730 396 957 195.0 341
0.794 311 968 259.0 352
0.794 333 977 238.0 348
0.847 202 975 320.0 340
0.847 156 972 382.0 355
0.855 176 963 378.0 343

 

111

 

 

 

Table 18. Data obtained from the continuous flow unit
during experiment No.

Cell conc Substrate con mg/l

Day D mg/l Influent Effluent pH

1 0.081 438 950 6.3 6.5
975 6.0

3 0.062 422 960 5.4 6.4
840* 4.7

5 0.052 442 965 4.3 6.7
980 3.9

7 0.020 422 975 0-1 6.4
975 0-1

12 0.020 434 960 0-1 6.6
985 0-1

17 0.011 380 970 0-1 6.9
951 0-1

22 0.011 355 965 0-1 6.6
974 0-1

31 0.011 314 960 0-1 6.4
770* 0-1

37 0.011 293 965 0-1 6.7
950 0-1

 

*Data not used in calculations

112

Table 19. Concentration of organisms at D values greater
than 0.694.

 

 

Cell con Time unit
Experiment D mg/l running at Remarks
D value-hrs

 

2 0.66 422 48 Steady-state

l 0.69 426 48 Steady-state

2 0.71 400 24 Non-steady-state
2 0.71 390 48 Non-steady—state
2 0.71 360 72 Non-steady—state
1 0.73 400 7 Non-steady-state
l 0.73 394 21 Non-steady-state
l 0.73 394 32 Non-steady-state
2 0.73 370 48 Non-steady-state
1 0.79 311 20 Non-steady-state
l 0.85 202 12 Non-steady—state
l 0.85 176 16 Non-steady-state

l 0.85 156 23 Non-steady-state

 

113

Table 20. Relationship between substrate concentration and
experimental and calculated k values.

 

 

 

 

Substrate Experimental Calculated k Calculated k
con mg/l k 5 -ct
k = km (S +8) k = km (l—e )
a

5.1 0.059 0.078 0.040
5.0 0.061 0.077 0.040
8.3 0.091 0.119 0.066
13.5 0.119 0.174 0a102
13.3 0.124 0.173 0.102‘
20.3 0.178 0.233 0.153
32.8 0.238 0.311 0.228
30.3 0.240 0.298 0.213
37.0 0.301 0.332 0.250
40.0 0.307 0.345 0.267
42.1 0.360 0.354 0.276
58.0 0.425 0.408 0.347
65.0 0.427 0.427 0.377
74.5 0.485 0.449 0.409
102.0 0.529 0.495 0.490
96.5 0.546 0.489 0.476
122.0 0.599 0.519 0.533
112.0 0.610 0.509 0.513
155.0 0.658 0.549 0.586
161.0 0.660 0.553 0.592
148.0 0.662 0.543 0.576
151.0 0.668 0.546 0.579
172.0 0.689 0.565 0.605
168.0 0.689 0.558 0.600
175.0 0.694 0.562 0.608
178.0 0.694 0.564 0‘610

 

114

 

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115

 

 

 

Table 22. Relationship between economic coefficient and k
during the steady-state.
Cell conc Substrate used Economic
k mg/l mg/l coefficient
0,059 422 953 44.3
0.061 427 952 44.9
0.091 429 953 45.0
0.119 434 960 45.2
0.124 431 947 45.5
0.178 428 951 45.0
0.238 417 927 45.0
0.240 421 939 44.8
0.301 433 924 46.9
0.307 438 928 47.2
0.360 420 927 45.3
0.425 420 911 46.1
0.427 422 890 47.4
0.485 413 888 46.5
0.529 427 866 49.3
0.546 433 867 50.0
0.599 434 838 51.7
0.610 426 851 5031
0.658 422 825 51.1
0.660 434 805 53.9
0.662 438 825 53.1
0.668 422. 819 51.5
0.689 434 793 54.7
0.694 434 793 54.7
0.694 422 790 53.4
0.694 434 801 54.2

 

116

 

 

 

Table 23. Comparison of experimental and calculated 5 values.
k Experimental § Calculated §
0.059 5.1 3.8
0.061 5.0 3.9
0.091 8.3 6.0
0.119 13.5 8.3
0.124 13.3 8.8
0.178 20.3 13.9
0.238 32.8 21.1
0.240 30.4 21.3
0.301 37.0 31.0
0.307 40.0 32.1
0.360 42.1 43.6
0.425 58.0 64.2
0.427 65.0 65.0
0.485 74.5 94.4
0.529 102.0 131.4
0.546 96.5 151.7
0.599 122.0 263.0
0.610 112.0 305.0
0.658 155.0 822.5
0.660 161.0 880.0
0.662 148.0 945.7

0.668

151.0

 

117

Table 24. Comparison of experimental i and i calculated
using the expression R = Y (SR - 5)

 

 

 

Experimental 2 Calculated §*
422 419
429 428
431 418
428 428
421 422
433 434
420 417
420 419
413 414
433 433
426 426
434 434

 

*Calculated using experimental Y values.

118

 

 

 

Table 25. Comparison of experimental i and i calculated
using the expression i = Y [SR - Sa( k 3 D )]
m
k Experimental i Calculated §* Calculated §**
0.059 422 449 425
0.061 427 449 ---
0.091 429 450 431
0.119 434 449 --—
0.124 431 449 434
0.178 428 446 428
0.238 417 443 —--
0.240 421 443 422
0.301 433 438 438
0.307 438 438 ---
0.360 420 432 417
0.425 420 423 415
0.427 422 423 ---
0.485 413 409 405
0.529 427 391 ---
0.546 433, 382 405
0.599 434 329 ---
0.610 426 309 327
0.658 422 67 ---
0.660 434 --- 42

 

*Calculated using average Y value.
**Calculated using experimental Y values.

119

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122

  

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Time - hours

Figure 12. Batch Culture Determination of k before and
after growth in the continuous flow unit.

133

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131

VI. DISCUSSION

The primary object of this dissertation was to compare
the results obtained during the operation of a continuous
flow unit with those predicted by the theory originated by
Monod (1950) and elaborated on by Novick and Szilard (1950b)
and Herbert g: p;., (1956). It is also of interest to compare
the experimental results with the results that might be pre-
dicted by the theories of other workers.

A feature that is common to most theories of continuous
flow culture is that the net growth must be the resultant of
exponential growth minus exponential wash-out. This may be
expressed mathematically by re-writing equation (10) as follows:

d (loge x)
dt

 

= k - D (22)

It follows from this equation that when a steady-state
(d(1ogex)/dt = 0) exists, then k is equal to D, i.e., the
specific growth rate must be equal to the dilution rate.

An apparent error that has been made by a number of authors

in mathematical discussions of continuous culture is to confuse,
in equation (22), the specific growth rate k (which varies with
the substrate concentration) and the maximum growth rate km.

If, in the above equation k equals km equals a constant, it must

follow that a steady-state is possible only at one particular

132
flow rate, i.e., when D is equal to km. This is the assumption
that has been made by Golle (1953) and Finn and Wilson (1954).
The same idea appears to be implicit also in the writings of
Adams and Hungate (1950) and Northrop (1954). This is in
obvious disagreement with the results presented in Section V.
The experimental data show very conclusively that logarithmic
growth is possible at any k value below km and that a continuous
culture is an inherently stable system that will adjust itself
automatically to changes in dilution rate at dilution rates
below D = km. The data presented in Figure 9 and Tables 17
and 18 show that any number of steady—states can be obtained
at different dilution rates as the theories of Monod (1950),
Novick and Szilard (1950b) and Herbert pp 3;., (1956) predict.

The theories of Monod (1950) and Novick and Szilard
(1950b) predict that steady-states can be obtained at different
dilution rates anywhere between zero and km. Herbert g; 3E.,
(1956) also stress this point. The data presented in Figures
9 and 15 indicate that any number of steady-states may be
obtained at dilution rates varying from 0.02 to 0.69. As
may be seen in Figure 15 there is a decrease in cell con-
centration below dilution rates of 0.02. This indicates that
in the operation of a continuous flow unit there is a minimal
dilution rate below which the steady-state no longer exists.

The probable reason for this minimal dilution rate may be seen

133
in the data presented in Table 18. As the dilution rate
reached values of 0.02 and lower the substrate concentration
in the unit reached values of 1 mg/l or lower. It is possible
that at a substrate concentration of 1 mg/l or below k becomes
zero.

The essential feature of the theories given by Monod
(1950), Novick and Szilard (1950b) and Herbert gpfl§£., (1956)
is that thethakeinto account the observed facts that bacteria
can grow only at the expense of the substrate utilized, and
that their specific growth rate is a function of the substrate
concentration. It then becomes obvious that a continuous
culture unit is a device for controlling growth through control
of the substrate concentration; each dilution rate fixes the
substrate concentration at that value which makes k equal to
D. This important role of the substrate is not considered in
the mathematical papers of Golle (1953), Finn and Wilson (1954),
Adams and Hungate (1950) and Northrop (1954).

Herbert g; g;., (1956) state the following on the
relationship between substrate concentration and dilution rate:
"over the useful range of flow rates in a continuous culture,
the substrate is nearly completely utilized and the issuing
medium virtually exhausted; hence negligible growth could
occur in any subsequent culture vessels in series with the

first. Our experimental results confirm that almost complete

134

utilization of substrate does in fact occur." As may be seen
from the data presented in Figure 11 the amount of substrate
leaving the continuous flow unit over the useful range of
dilution rates cannot be considered negligible. It is probable
that this is relative and may depend on the type of organism
and type of media used. The substrate concentration in the
effluent increased with increasing D values and at D values
approaching km reached concentrations as high as 180 mg/l.
This represents approximately 18 percent of the substrate put
into the unit and cannot be considered as "almost complete
utilization of substrate” as stated by Herbert (1959b).

In consiiering the relationship between cell concentration
and D, as presented in Figure 9, a number of quantitative
divergences from the theory of Monod (1950) have been summarized
by Herbert (1959b). These are presented graphically in Figure
21.

In Figure 21, curve (a) is the usual theoretical plot
of cell concentration against dilution rate. One type of
divergence is illustrated by curve (b); here instead of the cell
concentration falling sharply to zero at a wash—out point
slightly higher than km the wash-out rate of organisms from
the unit is lower than theoretical considerations predict.

As may be seen from the data presented in Figure 9 this is

the type of curve that was obtained in these experiments. This

Steady-state Cell Concentration

135

 

 

 

 

 

 

K‘
\
\ (C)
'\
\x
‘x
\
\
'\
\.
a \
( ) \
,I \
a’ ‘\
/ \
1/ (d) \\
/ \ (b)
/ \
’ \
/ \
/ \
I \
\
I \
I \
\
k
m
Dilution Rate
Figure 21. Quantitative Divergences from the Theory of

Monod.

136

type of curve was explained by Herbert (1959b) as an artifact
due to imperfect mixing of the inflowing culture medium with
the contents of the continuous flow unit. It would appear
that under conditions where D is greater than km the organisms
present in the unit would continue to grow at a rate equal to
km. Equation 17 was presented in Section V to take into
account this continued growth. The actual wash-out rate
obtained from the use of this equation was still less than '
the predicted rated. Herbert g£.§;., (1956) and Herbert (1959b)
also found the actual wash-out rate to be less than the
predicted theoretical value.

A second type of deviation from the theoretical is
shown by curve (c) in Figure 21. Herbert (1959b) explains this
type of curve as being due to non—consistency of the yield
coefficient Y. In this case Y is said to increase as the
growth-rate decreases. This type of behavior was first ob-
served by Holme (1957) with E, 23;; growing in glucose-NH

3

medium with NH3 as the growth limiting substrate, and was
shown to be due to the accumulation of intracellular glycogen
at low growth rates. Herbert (1959b) also found similar
results with Torula utilis growing in an ammonia limiting
medium. In this case also the increased cell yield at low

growth rates can largely be accounted for by the increase in

cell carbohydrate.

137

The opposite type of behaviour is illustrated by curve
(d) in Figure 21; here the yield coefficient Y decreases at
low growth rates. Herbert (1959b) found this type of curve
with Torula utilis growing on a glucose-NH3 medium with the

carbon source as the growth limiting substrate and also with

.5. aerogenes growing on a glycerol-NH medium with glycerol

3
as the growth limiting substrate.
Similar results, to a limited degree, have been
obtained in these experiments. From the data shown in Figure
19 it may be seen that as the growth rate increases the economic
coefficient increases from 44 to 54 percent. This would
indicate that the organisms are converting substrate into cell
material at a ten percent higher efficiency at the high k values
than at the lower k values.
The most probably explanation of these results is that
in addition to anabolic metabolism of the organisms they also
have a constant endogenous metabolism, by which cell-substance

is oxidized to carbon dioxide. This has been expressed

mathematically by Herbert (1959b) by the following equation:

<12:

dt (k - E) x (23)

where E is a constant term representing the endogeneous

metabolism.

More direct evidence for the existence of this constant

138
endogenous metabolism comes from the studies of Herbert (1959b)
on cell respiration at different growth rates. In this experi-
ment, which was done with 5. aerogenes, the respiratory carbon
dioxide output was found to be a linear function of the growth
rate. However, the straight line did not pass through the
origin but extrapolated back to a finite value when the growth
rate was zero. These results were explained by assuming the
total respiration to be the sum of an anabolic respiration
which is proportional to the growth rate and an endogenous
respiration independent of the growth rate. Further evidence
comes from carbon balance studies (Herbert, 1959b) which have
shown that, as the growth rate is reduced, a higher proportion
of the substrate carbon used is converted to carbon dioxide
and a lower proportion to cell carbon.

The results obtained from these experiments give
additional evidence for the existence of an independent
endogenous respiration rate. The data given in Figure 16
inidcate a linear relationship between the respiration rate of
the organism and k during the steady-state operation of the
unit. The equation for this linear relationship between
respiration rate and k was calculated by the method of least

squares and found to be

0 = 9.43 + 5436 k
02

139

The value 9.43 may be considered to represent the respiration
rate of the organism when k is equal to zero under these
experimental conditions.

Whether or not one should correct total observed
respiration values (exogenous values) by subtracting endogenous
rates has long been a debatable problem in various studies of
bacterial metabolism. With bacteria having low endogenous
and high exogenous rates of respiration, correction may not
markedly influence the values obtained. Wilner and Clifton
(1954) have reviewed earlier studies dealing with this problem
as it relates to oxidative assimilation. They found with g.
subtilis, a species exhibiting relatively high rates of
endogenous respiration and only several-fold increases in
rates of oxygen consumption in the presence of utilizable
substrates, that the percentages of assimilation varied markedly
with the concentration of substrate employed. On correction
for observed endogenous values the percentages of assimilation
agreed quite closely. They interpreted this as indicating that
endogenous respiration continues at about the same rate, in
either the presence or absence of an oxidizable foodstuff.
Santer and Ajl (1954) came to the same conclusion in studies
with Pasteurella pestis. They reported that washed cells
grown in the presence of labeled substrate evolved labeled

carbon dioxide at about the same rate irrespective of the

140

presence or absence of substrate.

The observations that endogenous respiration does
continue in many species, or in some may even be stimulated,
lend further support to the concept of the necessity for a
pool of intracellular organic matter needed by the organism,
not only for the maintenance of the status quo, but also for
use during growth.

To this writer's knowledge there are no published
figures on the percentage of oxidative assimilation of glucose
by Q. 99;; during the steady-state operation of a continuous
flow unit. As was noted in Section V, a linear relationship
‘was obtained between the actual amount of oxygen consumed
and the theoretical amount of oxygen needed for complete
oxidation of the sugar used by the organisms. Data pertaining
to this relationship are presented in Tabha 21 and are shown
graphically in Figure 17. These data indicate that 33.8 to
38.9 percent of the theoretical oxygen needed for complete
oxidation of the amount of glucose assimilated was actually
consumed. An equation for the linear relationship between
the actual amount of oxygen consumed and the theoretical amount
of oxygen needed for complete oxidation of the sugar used
by the organisms was given in Section V as

Y = 0.37X

where Y is equal to the actual amount of oxygen consumed in

141
terms of ulOZ/mg cell dry wt/hr and X is equal to the
theoretical amount of oxygen needed for the complete oxidation
of the sugar assimilated. This equation indicates that during
the steady-state operation of the unit, approximately 37 per-
cent of the assimilated substrate was oxidized. This value
is further substantiated by the relation between percent of
theoretical oxygen utilized and k during the steady-state
operation of the unit that is shown in Figure 18. The data
shown in this figure also indicate that, regardless of the
value of k, 37 percent of the theoretical oxygen needed are
consumed.

The only data available, for comparative purposes,
were obtained using batch culture techniques and washed suspended
cells. The values given for the percentage of glucose
assimilated that was oxidized ranged from 50 percent (Cook and
Stephenson, 1928; Clifton and Logan, 1939: and Siegel and
Clifton, 1950) to 70 percent (Krebs, 1937). The latter value
of 70 percent was obtained at a temperature of 40 C.

The data obtained during these experiments indicate
that the efficiency of conversion of substrate into cell
material increased approximately 10 percent as the k values,
during the steady£state operation of the unit, increased and
that at the same time the percentage of the glucose assimilated

that is oxidized remains at a constant value of 37 percent.

142

This would indicate that 44-54 percent of the substrate was
converted into cell material; 37 percent converted into carbon
dioxide and water; and 9-19 percent that might be accounted
for by the production of by-products.

It was noted in Section V that the dissolved oxygen
concentration in the unit varied between 0.5 and 4.8 ppm
during the steady-state operation of the unit. No investigation
of the effects of this varied dissolved oxygen concentration
on the activity of the organisms was made because it was felt
that sufficient evidence has been presented by Winzler (1941)
and Longmuir (1954) to indicate that the effect, if any, would
be negligible. The amount of available oxygen in a submerged
culture depends upon the rate of oxygen transfer from the gas
to the liquid phase and also on the rate of oxygen transfer
from the liquid to the cell. This later process, as has been
shown for yeast by Winzler (1941) and for bacteria by Longmuir
(1954), is independent of the concentration of dissolved oxygen
unless this is extremely small as compared with the saturation
concentration of oxygen.

The data from these experiments indicate that, especially
at the low k values, there was not enough sugar present in the
Warburg flasks to maintain the observed respiration rate. For
example, at a k value of 0.059 and a substrate concentration

of 5.1 mg/l each Warburg flask contained 0.026 mg of glucose.

143

In order to maintain a respiration rate of 34 ulOZ/mg cell

dry wt/hr for one hour the cells in the flask would require
0.11 mg glucose, assuming complete oxidation. At a k value

of 0.69 and a substrate concentration of 180 mg/l each Warburg
flask contained 0.9 mg of glucose. In order to maintain a
respiration rate of 350 ulOZ/mg cell dry wt/hr for one hour
the cells in the flask would require 1.1 mg of glucose. It
is suggested that, especially at the low k values, the cells
are utilizing stored substrate material in order to maintain
the observed respiration rates.

The single most important relationship to be considered
in the operation of a continuous flow unit is the relationship
between substrate concentration, 5, and the growth rate k.

The key to the modbcmf action of a continuous flow unit lies
in the way in which the growth-rate k depends on the con-
centration of a limiting growth substrate in the culture
medium. A number of different mathematical equations have
been proposed for the relationship between substrate concentration
and k. The concepts put forth by Golle (1953), Fin and
Wilson (1954), Adams and Hungate (1950), and Northrop (1954)
were discussed at the beginning of this section and require
no further diSCussion.
Garrett and Sawyer (1952) proposed a linear relation-

ship between substrate concentration and k. Working with mixed

144

cultures obtained from activated sludge they state "the
results that have been obtained indicate that the rate of
growth is directly proportional to the concentration of food
remaining up to a critical concentration above Which it is
constant and independent of the concentration of food." An
examination of their experimental data reveals that the k
range of their experiments was 0.03 to 0.16 and the substrate
determinations were made at only 3 k values (0.05, 0.10, and
0.16). Comparing this with the data presented in Figure 11
it may be seen that their data cover only a very small
portion of the total k range that might be expected. It

is doubtful that the results which they present are sufficient
to state "that the rate of growth is directly proportional to
the concentratbn of food" over a full range of k values.

The data presented in Figure 11 clearly show that the
relationship between substrate concentration and k is not a
linear relationship but is instead a curve that reaches a
maximum asymptotically.

The most widely accepted mathematical equation to express
the relationship between substrate concentration and k is the
one proposed by Monod (1950) (Equation 6). It should be pointed
out that, in Section III, the theoretical treatment of continuous
culture is based on a minimum number of simplified postulates.

It might well be objected that even under ideal conditions the

145

growth behavior of bacteria cannot be completely represented
by such equations as (5), (6), and (7). Such was found to be
the case in this series of experiments. As may be seen in
Figure 13 Monod's equation provides only partial fit to the
experimental data. In the comparison between the experimental
curve and that which is predicted by the equation agreement
exists only up to a k value of 0.4; from this point on, the
theoretical line is considerably lower than the experimental
line. One possible explanation for this lack of agreement
between experimental and predicted data may be found in one
of the basic assumptions made in the development of the theo-
retical equation. The relationship between growth of bacteria
and utilization of substrate is expressed as Y in Equation 7.
The assumption was made by Monod that the yield constant Y
is actually a constant and this was confirmed to his satis-
faction in batch culture studies (Monod, 1942). The data
presented in this study indicate that the yield constant Y
may not be constant under these conditions. From the data
presented in Figure 19 it can be seen that the yield constant
Y increased from 44 to 54 percent. Data presented by Herbert
(1959b) also indicate that the yield constant Y may be variable.
The experimental data obtained in these experiments
were plotted according to the Lineweaver-Burke plot which is

based on a modification of Equation (6). The results of this

146
plot are given in Figure 14. The values of km and Sa were
calculated from this plot to be 1.20 and 120.5 respectively
by the method of least squares. The values are clearly out
of line with the experimentally obtained values of 0.69 and
40 and indicate that the relationship between substrate
concentration and k does not follow an expression such as
Equation (19).

Powell (1959) in a summation of mathematical forms
which have been proposed for the relationship between sub-
strate concentration and k lists three additional expressions.
The first of these is the monomolecular type of equation used
by Teisseir (1936).

k = km (1 - e 'CS)
The second of these, listed as the Moser equation is the
expression

I“

s
k ‘ km (S + s
a

r )
where r represents a constant. This expression is clearly a
modification of the original equation used by Monod.

As an additional modification of Monod's original

education Powell (1959) rewrites Monod's equation in terms

of s as a function of k to give the following form

Powell then makes the hypothesis that Monod's original equation

147
applies to the concentration of substrate inside the organism,
but that the access of substrate to the interior is impeded by
the cell membrane and by diffusion. He then proposes that s,

the concentration outside the cell is given by the relation-

ship

 

k - k k
m m

Here the new constant A depends on diffusion coefficients
inside and outside the organism, on the permeability of the
membrane, and on the shape and surface:volume ration of the
organism.

The experimental data obtained in these experiments were
applied to the monomolecular type of equation. The method of
Reed and Theriault (1931) was used to calculate the constants
km and c from the exerpimental data. km was calculated to be
0.69. This is in complete agreement with km values obtained
by both continuous flow and batch culture procedures. The
value for c was calculated to be 0.012. The resulting equation
(Equation 21) was then plotted and compared with the experi—
mental values. This comparison is given in Figure 13. The
values obtained by this equation are somewhat lower than the
values obtained from the experimental data but the shapes of
the two curves are similar. As may be seen from Figure 13
the results obtained by use of the monomolecular type of

equation are in better agreement with the experimentally

148

obtained results than the values calculated by the use of
Monod's equation. An almost perfect fit of the experimental
curve may be obtained by changing the constant, c, from 0.012
to 0.016 in the momomolecular type of equation.

The values for the steady-state substrate concentrations
were calculated using equation 14. The results from these
calculations are presented in Table 23 and Figure 20 along
with the experimentally obtained values. As may be seen in
Figure 20 the calculated values follow the experimentally
obtained values closely for k values up to 0.4 then there
is a marked deviation between the two. There appears to be
no relationship between these very high calculated substrate
values and reality as in the case of a k value of 0.688 the
calculated substrate value indicates that there is more
substrate leaving the unit than is being put into it. It
will be recalled that a similar breaking point occurred when
the experimental data were applied to Monod's equation
(Equation 6). As equation (14) is based, in part, on the
relationship given by equation (6) this break at the same point
is to be expected.

The values for the steady-state organism concentrations
were calculated using equation 15. As may be seen in Table
25 the calculated values are in close agreement with the

experimental values for k values up to 0.4. From this point

149
on the calculated organism concentrations indicate that wash-
out is occurring from the unit while the experimentally
determined organism concentrations indicate that the steady-
state condition still exists. This breaking point again
occurs at about the same k value as in Equations (6) and (15).
This is again to be expected since equation (15) is based on
the fact that equation (6) represents the true relationship
between substrate concentration and k. As has already been
pointed out, equation (6) does not represent the true relation-
ship between the substrate concentration and k obtained in
these experiments.

It should also be pointed out that equations (14)
and (15) are based further on the assumption that Y is a
constant value and in addition that equation (9) represents
the wash-out of organisms from the unit. It has been shown
that neither of these assumptions was found to be true in
these experiments.

The problem of mutation is one that must always be
given consideration in experiments of this type. If a
mutation occurred that affected the growth rate of the
experimental organism it would seriously affect the results
of these experiments. With this possibility in mind the
growth rates of the organism were determined by batch culture
determinations both before and after its use in the continuous

flow unit. The results of these batch culture experiments

150
are shown in Figure 12. It may be seen from this figure that
the maximum growth rate, km, of the organism did not change
during the experiments. As was pointed out in Section III,
mutation would only become a serious problem if the growth
rate of the mutant were equal to or higher than the experimental

organism.

151

VII . CONCLUSIONS

A continuous flow unit was constructed and satisfactorily
operated over a D range of 0.01 to 0.85. Steady-state conditions
existed between D values of 0.02 and 0.69. A non—steady-state
condition existed at D values below 0.02 and above 0.69 Which
resulted in a wash—out of organisms from the unit at a rate
faster than they could be replaced by growth. The actual
wash-out rate was found to be less than the wash-out rate
predicted by theoretical equations.

A maximum growth rate of km of 0.69 was established
under these experimental conditions. This value was obtained
by both batch culture and continuous flow procedures. In
addition km was calculated by the method of Reed and Theriault
(1931) from a series of experimental data. The value of 0.69
obtained by this method was in full agreement with the experi-
mentally obtained maximum growth rate.

The relationship between substrate concentration and
the specific growth rate k during the steady-state was
established, not as a linear relationship, but as a curve
that reaches a maximum asymptotically. Theoretical equations
proposed by Monod (1950), Novick and Szilard (1950), and
Herbert gt al., (1956) did not agree with the experimental

relationship obtained between substrate concentration and k.

152

Furthermore, values for km and Sa obtained by a Lineweaver-
Burke plot did not agree with experimental data. In contrast
the results obtained from the use of a monomolecular type of
equation, such as proposed by Teissier (1936), indicateci that
this type of equation more correctly expresses the relation-
ship between substrate concentration and k. Data were presented
which indicatedthat at a substrate concentration of 1 mg/l
or below k approaches zero. The data also indicate that the
specific growth rate k becomes independent of substrate
concentration at glucose concentrations above 180 mg/l.

A linear relationship was established between k and
the respiration rate of the organism. The following equation
was found to express this relationship.

Q = 9.43 + 43.6k
O
2
The maximum oxygen uptake rate was obtained at km and did not
further increase at D values greater than km. A value of
9.43 ulOZ/mg cell dry wt/hr appears to be the endogenous
respiration rate of the organisms under these experimental
conditions. The data further indicated that under these
conditions approximately 37 percent of the assimilated sub-
strate was oxidized independently of k.
The economic coefficient of the organism was found,

not to be constant, but to increase from 44 percent at the lower

k values to 55 percent at the higher k values.

153
The theoretical steady-state equations, proposed by
Monod (1950) and Herbert et al., (1956) for the relationship

between a, x, Y, S Sa' D and km were found to be inadequate

RI

in expressing the experimentally obtained relationships.

154

VIII. APPENDIX

A. Composition 9; Reagents used in Glucose Determinations

 

 

(l)

(2)

Copper Reagent A

25 gm anhydrous sodium carbonate

'25 gm Rochelle salt

20 gm Sodium bicarbonate

200 gm anhydrous sodium sulfate

Dissolve reagents in 800 ml water and dilute to
1 liter.

Copper Reagent B

15% CuSO -5HéD containing one or two drops of con-

4

centrated sulfuric acid per 100 nd.

(3) Arsenomolybdate color reagent

(4)
(5)

Dissolve 25 gm of ammonium molybdate in 450 ml water
Add 21 ml of concentrated sulfuric acid

Add 3 gm of NaHAsO4'7H20 dissolved in 25 ml water
Place in an incubator at 37 C for 24 to 48 hours.

5% ZnSO4-6H20-

Approximately 0.3 N barium hydroxide. The zinc and
barium solutions should be adjusted so that 5 ml of

Zinc require between 4.7 and 4.8 ml of barium to

produce a definite pink to phenolphthalein.

B.

C.

.155

Composition of Reagents used in the Dissolved Oxygen

 

Determinations

 

(1)

(2)

(3)

(4)

Manganous sulfate solution

480 gm MnSO4-4H20 dissolved in 1 liter water
Alkaline-iodide reagent

500 gm sodium hydroxide

135 gm sodium iodide

Dissolve in 1 liter water

Starch solution

5 to 6 gms of soluble starch dissolved in 1 liter
boiling water

Sodium thiosulfate solution

6.205 gm sodium thiosulfate dissolved in 1 liter

freshly boiled water. This solution was standardized

against a standard potassium bi-iodate solution.

Composition 9£_Brodie's Solution

23 gm Sodium Chloride
5 gm Sodium choleate

5 gm Dreft

.500 ml distilled water

Colored with Safrain dye.

10.

156

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