The influence of growth rate and cell concentration on bacterial attachment to surfaces in a continuous
flow system
by Christopher Henry Nelson
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Environmental Engineering
Montana State University
© Copyright by Christopher Henry Nelson (1983)
Abstract:
Many factors influence the rate of bacterial attachment to surfaces. Two factors of interest in this study
were the growth rate and concentration of cells in the bulk water. A pure culture of Pseudomonas 224S
was used as the test organism. The experimental system consisted of smooth, hydrophilic (glass)
surfaces placed in a well-mixed continuous flow system. The results indicate attachment rate was
greatest with cells growing at approximately 1/2 their maximum growth rate and the surfaces became
saturated with cells at approximately 0.1% coverage. The cells tended toward a uniform distribution
when surface saturation occurred. The results of this study suggest that bacterial colonization of
surfaces occurs in two phases. Initially, cells are transported to a surface where attachment occurs until
the surface becomes saturated with cells. After the surface is saturated, the primary mechanism for cell
accumulation is growth of attached cells. THE INFLUENCE OF GROWTH RATE AND CELL CONCENTRATION
ON BACTERIAL ATTACHMENT TO SURFACES IN A
CONTINUOUS FLOW SYSTEM
by
Christopher Henry Nelson
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Environmental Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
December 1983
main ub
c o p . 3-
ii
APPROVAL
of a thesis submitted by
Christopher Henry Nelson
This thesis has been read by each member of the thesis committee and has been found
to be satisfactory regarding content, English usage, format, citation, bibliographic style,
and consistency, and is ready for submission to the College of Graduate Studies.
'O'
Chairperson, Graduate Committee
Approved for the Major Department
TT-
Date
Head, Major Department
Approved for the College of Graduate Studies
'(L
Date
Graduate Dean
iii
STATEMENT OF PERMISSION TO USE
In presenting this thesis is partial fulfillment of the requirements for a master’s degree
at Montana State University, I agree that the Library shall make it available to borrowers
under rules of the Library. Brief quotations from this thesis are allowable without special
permission, provided that accurate acknowledgment of source is made.
Permission for extensive quotation from or reproduction of this thesis may be granted
by my major professor, or in his absence, by the Dean of Libraries when, in the opinion of
either, the proposed use of the material is for scholarly purposes. Any copying or use of
the material in this thesis for financial gain shall not be allowed without my permission.
Signature
Date
A t,
/9%
iv
ACKNOWLEDGMENTS
I wish to express my appreciation to the following people:
Bill Characklis, for providing the encouragement and the environment which stimu­
lated me to realize the full potential of the graduate educational experience.
'
Dan Goodman, for helpful statistical advice and critical comments relating to my
\
thesis.
Gordon McFeters, for helpful microbiological advice.
Ted Williams, for his interest in my education.
Joe Robinson, for statistical analysis help and microbiological advice.
The IPA group; Keith and Barbara, Rich, Mukesh, Rune, Andy, Maarten, Nick, Frank,
and Ginger, for being an interesting group of people to work with and a great bunch of
people to interact with.
V
TABLE OF CONTENTS
Page
APPROVAL...........................................................................................................; ..........
ii
iii
STATEMENT OF PERMISSION TO USE...........................................................................
ACKNOWLEDGMENTS................................................................................................
TABLE OF CONTENTS................................
iv
v
LIST OF TABLES...................................................................................
LIST OF FIGURES...................................................... ; ............ .......................................
ABSTRACT..........................................................................................................
viii
ix
INTRODUCTION........................................................................
LITERATURE REVIEW...................................................................
Adsorption of Conditioning F ilm ...................................................................
. Transport to Surface.................
Reversible/Irreversible A ttachm ent..........................................................................
Factors Influencing A ttachm ent..............................................................................
Growth R ate...............................................................................................
Concentration......................................................................................................
2
2
3
3
4
5
EXPERIMENTAL APPARATUS AND METHODS.........; .............................................
6
Experimental S y stem .................
Cleaning Procedures..................................................................................................
Experimental Procedure............................
Staining Procedure.......................... : .......................................................................
Counting Procedure....................................
6
8
8
8
9
RESULTS......................: ........................................... ................... ....................................
11
Experimental R esults..................................................................................
Response Surface A nalysis.....................
Variance/Mean Ratio............................
11
11
13
vi
TABLE OF CONTENTS-Continued
Page
DISCUSSION.............................................................
Growth R ate...............................................................................................................
Surface Saturation......................................................................................................
Zones of Inhibition.........................................................................................
Surface Thermodynamics...............................................
Assumptions...............................................................................................................
M odel.........................................
16
16
16
21
21
23
24
CONCLUSIONS..................................................
27
LITERATURE C ITE D ........................................................
28
A P P E N D IC E S ................................
1 —Nutrients and Dilution W ater.......................... ............................................. '.
2 —Raw D ata...............................................................
3 —Chemostat Cell Counts.............................................................................. .. . ..
4 —Variance/Mean Analysis.................................................. i ............................
31
32
34
76
78
vii
LIST OF TABLES
Tables
Page
1.
Model and ANOVA Table..................................................................................
13
2.
Literature Comparisons. ; ...................................................................................
19
3.
Parameter Estimation Using Nonlinear Least Squares Analysis......................
25
viii
LIST OF FIGURES
Figures
Page
1.
Experimental design..........................................
2.
Octagon design...................................................................................; ...............
12
3.
Response surface.....................................................................
14
4.
Influence of bulk water cell growth rate on potential
colony forming units...........................................................................................
17
Predicted influence of bulk water cell concentration,
X, on attached cell concentration (X = 0.13 gm '3) .........................................
18
Influence of bulk water cell concentration on potential
colony forming units. .. .................................
20
Scale drawing of attached cells covering 0.1% of surface
area with a uniform distribution, suggesting “zones of
inhibition” concept..............................................................................................
22
5.
6.
7.
7
ix
ABSTRACT
Many factors influence the rate of bacterial attachment to surfaces. Two factors of
interest in this study were the growth rate and concentration of cells in the bulk water. A
pure culture o f Pseudomonas 224S was used as the test organism. The experimental system
consisted of smooth, hydrophilic (glass) surfaces placed in a well-mixed continuous flow
system. The results indicate attachment rate was greatest with cells growing at approxi­
mately 1/2 their maximum growth rate and the surfaces became saturated with cells at
approximately 0.1% coverage. The cells tended toward a uniform distribution when sur­
face saturation occurred. The results of this study suggest that bacterial colonization of
surfaces occurs in two phases. Initially, cells are transported to a surface where attachment
occurs until the surface becomes saturated with cells. After the surface is saturated, the pri­
mary mechanism for cell accumulation is growth of attached cells.
I
INTRODUCTION
Bacterial attachment to surfaces occurs in many diverse environments. Subsequent
growth of attached bacterial cells results in the formation of a biofilm. Biofilms have many
beneficial uses. For example, they are used in ,wastewater treatment (e.g., rotating biologi­
cal contactors). Biofilms also cause problems in many engineering systems. For example,
they increase heat transfer resistance in heat exchangers.
The goal of this study was to conduct fundamental research on the attachment pro­
cess. Specifically, the influence of growth rate and concentration of cells in the bulk water
on attachment rates was investigated.
The results of this study should increase a fundamental understanding of the attach­
ment process which may be extrapolated to either control or promote biofilm growth.
2
LITERATURE REVIEW
Bacterial attachment to surfaces is a common occurrence in aquatic environments.
This review will focus on attachment at solid/liquid interfaces, on clean and smooth sur­
faces, and in a turbulent flow regime.
Adsorption of Conditioning Film
Studies have shown that when a clean surface is immersed in water, an organic con­
ditioning film is adsorbed on the surface. The rate and extent of adsorption is influenced
by many factors including the organic content and relative turbulence of the bulk water
and the available free surface energy (Fletcher, 1980). The rate of adsorption of the con­
ditioning film is, in general, faster than bacterial attachment rates so most surfaces will
have conditioning films present when attachment occurs.
Transport to Surface
Many natural and industrial environments are open, turbulent flow systems. Yet,
most laboratory studies of bacterial attachment have been conducted under quiescent,
batch conditions. Fluid flow conditions must be taken into account because they will
influence bacterial cell transport from the bulk water to the surface. For example, gravity
may play an important role in transport under quiescent conditions but convective trans­
port (turbulent bursts) may be more important under turbulent flow conditions.
The concept of a viscous sublayer is important in the discussion of a turbulent flow
system. The viscous, sublayer is a thin film of water which is in contact with a surface
during turbulent bulk water flow. For example, water flowing through a pipe under turbu­
lent conditions will produce a viscous sublayer which is in contact with the inner pipe wall
3
and is typically measured in microns. Fluid forces under turbulent flow conditions trans­
port cells to the viscous sublayer but the sublay er acts as a barrier to transport and it causes
the cells to lose their momentum as they approach the surface. How, then, are cells transr
ported to the surface? Observations indicate that velocity fluctuations in the bulk water
(turbulent bursts) disrupt the viscous sublayer and penetrate to the wetted surface (Camp­
bell and Hanratty, 1983). These velocity fluctuations appear to provide a mode of trans­
port for the cells to contact the surface.
Reversible/Irreversible Attachment
Once the bacterial cells have been transported to the wetted surface, two types of
attachment are possible; reversible and irreversible. Reversible attachment is the initial
step in the attachment process. In this phase, cells exhibit random motion and can be
removed by gently rinsing the surface with water. Irreversible attachment is firm adhesion
to the surface at which point cells no longer exhibit random motion and cannot be removed
by gentle rinsing (Marshall et al., 1971). Irreversible attachment is usually associated with
the production of extracellular polymeric substances (EPS) (Fletcher, 1980). Regardless of
mechanism, after a cell has attached to a surface, subsequent growth and transport pro­
cesses lead to the formation of microcolonies and eventually to the formation of a mature
bio film.
Factors Influencing Attachment
There are many factors which may influence attachment including the relative rough­
ness and free energy of the surface, the fluid dynamics, nutrient concentration, cation
concentration, pH, and temperature of the bulk water, and bacterial species present and
their physiological state. Two factors tested in this study are the growth rate and the bulk
water concentration of the cells.
4
The quantity typically measured in most attachment studies is cell accumulation rate
on the surface. Cell accumulation is the result of several processes; transport of cells to the
surface, attachment of cells to the surface, detachment of cells from the surface, and
growth of attached cells. The attachment and detachment processes can be combined as
net attachment. In this study, net attachment will be referred to as simply attachment.
Attachment is the dominant mechanism for cell accumulation in most bacterial attachment
studies because the relatively short experimental times (e.g., 2-6 hours) limit growth of
attached cells. Growth becomes more important as the experimental time is increased (e.g.,
> 6 hours) as typically occurs in biofilm studies.
Growth Rate
The growth rate of bacterial cells used in attachment studies can influence the rate of
attachment. Fletcher (1977) reports that in batch studies, the rate of cell accumulation on
a surface is greatest with cells taken from log phase cultures after a 2 hour exposure time.
Molin et al. (1982) found that the rate of microcolony accumulation on a surface increases
as the growth rate of the cells in the bulk water is increased with maximum accumulation
occurring near the maximum specific growth rate. Trulear (1983) observed in chemostat
studies that the extent of EPS production decreases as the growth rate of the cells is
increased. All three studies used a pure culture of Pseudomonas as the test organism.
The results suggest that growth rate, which is a measure of physiological activity,
influences the attachment process. The rate of attachment appears to increase as growth
rate increases. These results also suggest the rate of attachment is increased wheh minimal
amounts of EPS are associated with the cells, i.e., EPS does not appear to have a direct role
in initial attachment. Another possibility is that the structure of the EPS produced by the
cells varies as the physiological state of the cell changes. Changes in the structure of EPS
may influence its relative adhesiveness.
5
Concentration
The concentration of cells in the bulk water and on the surface can influence attach­
ment rates. Bryers and Characklis (1982) found cell accumulation rates on the surface to
be proportional to the suspended biomass concentration in the bulk water. Fletcher (1977)
observed that surfaces become saturated with cells as the concentration of cells in the bulk
water is increased for a given exposure time. Brannan and Caldwell (1982) found cell
accumulation rates on the surface to increase continuously with time.
These observations can be interpreted as follows. The transport rate of the cells to the
surface is proportional to the cell concentration in the bulk water. Attachment rate is pro­
portional to transport rate until the surface becomes saturated with cells. After saturation,
accumulation rates continue to increase due mainly to growth of attached cells rather than
attachment of cells from the bulk water. In other words, surface saturation will not be
observed if growth contributes significantly to observed cell accumulation rates or if the
cell concentration in the bulk water (and therefore transport rate) is not sufficient for
saturation to occur.
Fletcher observed saturation because her relatively short exposure time (2 hours)
minimized attached cell growth and her relatively high concentration of cells in the b u lk .
water ('v IO9 cells ml-1) resulted in a relatively high cell transport rate to the surface.
Bryers and Characklis did not observe saturation because their relatively long exposure
time ('v 50 hours) and the addition of substrate into their system allowed attached cell
growth to be significant. Brannan and Caldwell did not observe saturation because their
relatively low concentration of cells in the bulk water (a natural hot springs) resulted in a
relatively small cell transport rate to the surface and nutrients in their natural system
allowed for attached cell growth.
6
EXPERIMENTAL APPARATUS AND METHODS
Experimental System
Figure I is a schematic drawing of the experimental system used in this study. The
reactor is enlarged to show detail. The reactor consisted of a glass beaker, 9 cm in diameter
by 18.5 cm tall. The capacity of the reactor was 450 ml. The reactor was a continuous
flow system with cells and dilution water as the influent. Four glass microscope slides were
suspended in the reactor by a fixture consisting of silicon tubing and plastic support struc­
tures. The chemostat is identical to the reactor except it does not have removable glass
microscope slides. The variables of interest in this study were the bulk water cell concen­
tration in the reactor, X, and the growth rate of these cells, p. Growth rate was varied by
varying the flow of nutrients through the chemostat after steady state was reached. Cell
concentration was varied by varying the flow of dilution water through the reactor. Cells
were pumped from the chemostat to the reactor at a constant flow rate (0.3 ml m in'1) for
all experiments. The relative turbulence of the reactor bulk water was kept constant in all
experiments by maintaining the same stirring rate setting on the magnetic stirrer. Dye tests,
indicated that this stirring rate was adequate to assume complete mixing of fluids inside
the reactor. The temperature, T, of the chemostat was controlled by a water bath (T =
20°C). A single species of bacteria, Pseudomonas 224S, was used in this study. 224S had
a maximum growth rate, pm = 0.45 h r '1 (J. A. Robinson, personal communication). Nutri­
ent and dilution water compositions are listed in Appendix I. Growth was glucose limited.
Nutrient and dilution water solutions were autoclaved prior to use.
7
dilution
water bath
reactor
cede
dilution water
rubber etopper
effluent
r e m o v ab l e elldea
bul k w a t e r
Insulation
s t i r bar
magnetic stirrer
Figure I . Experimental design.
y
8
Cleaning Procedures
The glass microscope slides used in the reactor were cleaned in a consistent manner in
order to insure relatively uniform surfaces were used in all experiments. First, the slides
were immersed in tetra chlorethylene (TCE) for 2 minutes. Next, the slides were immersed
in 10% hydrochloric acid (HCl) for 2 minutes and rinsed with distilled water.
The reactor was washed with 10% HCl and then rinsed with distilled water. Clean
slides were mounted inside the reactor and the reactor was autoclaved.
The pipets used for staining were washed with 10% HCl and then rinsed with distilled
water. The pipets were autoclaved with the reactor.
The chemostat and all associated tubing were autoclaved prior to the start of the
experiments.
Experimental Procedure
The chemostat was innoculated with Pseudomonas 224S and allowed to run in batch
mode for 12 hours. Then, the dilution rate was adjusted for the desired growth rate, ju. The
chemostat was allowed to run for 6 detention times to reach steady state. Experiments
were begun after steady state was reached.
The dilution water flow rate was adjusted to give the desired cell concentration in the
reactor, X. The duration of exposure in each experiment was 6 hours. After 6 hours, the
slides were removed from the reactor and stained.
Staining Procedure
The reagents used in staining the slides from the reactor were as follows:
1. distilled water
2. 70% ethanol
3. acridine orange solution
9
The acridine orange solution consisted of I mg acridine orange per I ml of 2% formalde­
hyde. All three reagents were filtered through 0.22 jum filters. The same glass pipets were
used for staining in each experiment, in order to minimize potential differences in delivery
velocities between pipets. Ten ml pipets were used to deliver the distilled water and the
70% ethanol, and a 5 ml pipet was used to deliver the acridine orange solution.
A staining procedure was developed in order to observe cells attached to the glass
slides with minimum surface alteration. After the slides were removed from the reactor,
they were rinsed with 10 ml of distilled water per slide in a reproducible pattern. Next, the
slides were stained with I ml of acridine orange solution per slide for 15 minutes. Next, the
slides were rinsed with 10 ml of 70% ethanol per slide in a reproducible pattern and allowed
to dry for approximately 10 minutes. Finally, approximately 0.1 pi of immersion oil was
applied to each slide and a cover slip was placed on top of the oil in preparation for cell
counting.
Counting Procedure
Attached cells were counted using epifluorescence microscopy. Ten fields of IXlO4
pm2 size were counted per slide. Additional counts were made if the initial counts appeared
to be erratic in order to minimize the standard deviation of the data. The counts were
made in the same relative location on each slide. Both cell numbers and potential colony
forming units (PCFU) were counted. PCFU were defined as any group of cells in physical
contact with each other, a cell in the process of division, or a single cell attached to the
microscope slide surface after the 6 hour exposure time. The differentiation between cell
numbers and PCFU was deemed necessary in order to minimize the effect of surface cell
growth on the determination of attachment fates. This differentiation was especially
important since cell growth rate in the bulk water, p, was one of the variables tested. A
PCFU is assumed to originate from a single cell (possibly in the process of division) which
10
.
attaches to a surface and has the potential for subsequent growth. The data were analyzed
in terms of PCFU although most PCFU consisted of either I or 2 cells (refer to Appendix
2). An average PCFU value per IXIO4 /xm2 was determined for each experiment by taking
an average of counts made from approximately 40 fields from 4 slides.
Chemostat cell counts were determined by epifluorescence microscopy according to
the procedure proposed by Hobbie et al. (1977). The results are documented in Appendix
3.
11
RESULTS
Experimental Results
Experiments were statistically designed according to Hunter (1960). Twelve experi­
ments were arranged in an octagon design (Figure 2). The limits on each variable were
determined by preliminary experiments and the capability of the experimental system. A
second order polynomial was proposed as a model to approximate the results as suggested
by Hunter (1960) although other models could have been proposed. The second order
polynomial model is shown in Table I. The model was tested to determine if the approxi­
mation was reasonable. The resulting analysis of variance table (Table I) indicates the lack
of fit of the model to be insignificant at the 5% rejection level and the second-order terms
in the model to be significant at the 5% rejection level. In other words, the response
surface generated by the proposed second order polynomial model is a statistically valid
description o f the observed results. Figure 3 compares the response surface generated by
the model and the experimentally determined points. The response surface can be described
as a “rising ridge” and the experimental points are in good agreement with the response
surface.
Response Surface Analysis
In order to observe the response of each variable more closely, cross sections of the
response surface were taken at the midpoint of each axis (p = 0.17 hr-1, F d = 16 ml
min-1). The resultant graphs (Figures 4 and 5) illustrate the response o f one variable over
the experimental range while the other variable is held constant. In both figures, the lines
12
C E L L G R O W T H R A T E , Ji ( h r -*)
I
I
I
I
r
0.30
0.26
0.17
0.08
0.04
6
2 6
16
26 30
R E A C T O R D I L U T I O N R A T E , F0 ( m l I t i l n l
Figure 2. Octagon design.
13
Table I. Model and ANOVA Table.
Proposed Model
y = 2.35 + 0.43 x, - 0.77 X2 - 0.53
where:
X 21
- 0.004
X2
- 0.24 X 1 X 2
y = .predicted response
X 1 = relative values (-> /2 ,-1 , 0, I , >/2) on vertical scale of octagon design
x2 =. relative values ( - > /2 ,- 1 ,0 , I , V 2 ) on horizontal scale of octagon design
Analysis of Variance Table
(2nd Order Model, K = 2)
Sum of Squares
Crude
b0
bi
b2
bn , b22
b 12
residual = 2 (y - y )2
Lack of fit
Error
S
S0
d.o.f.
56.95 12
47.60
I
Mean Squares
F Ratios
0 70
F353 = l l . l K F . o s =9.28)
(significant)
S 1.0
6,24
2
S2 1 Q
2.11 • 3
Sr
1.00
6
0.81
3
q
Sr ' s e
SE
0.19
3
0.063
27
F3, 3 =4.28 (F.os =9.28)
(nonsignificant)
were generated by the model and the points and error bars were determined experimen­
tally.
Figure 4 shows the influence of cell concentration in the bulk water, X, on PCFU on
the surface. The growth fate of the cells used for this figure is /i =0.17 hr-1. Figure 5
shows the influence of specific growth rate of cells in the bulk water, p, on PCFU on the
surface. The cell concentration used in this figure is X = 1.3X105 cells ml-1 .
Variance/Mean Ratio
To help in the analysis of Figure 5, a variance/mean ratio analysis was conducted. The
variance/mean ratio provides a test of a population distribution on a surface. If the ratio
equals one, the population has a random distribution. If the ratio is greater than one, the
14
1.10
CELL GROWTH RATE, Ji ( h r ' )
• 0.75
1.75
0.1 7
3.73#
• 1.87
3.20
0.04
RE ACT OR
Figure 3. Response surface.
DI LUTI ON R A T E l Fb (ml m i n ' )
15
population has a contagious or clustered distribution. If the ratio is less than one, the
population has a more uniform distribution (Zar, 1974). The details and results of the
variance/mean analysis as applied to the experimental data from this study are presented in
Appendix 4.
A variance/mean ratio was calculated from the mean PCFU values from each experi­
ment. The value of the variance/mean ratio was calculated to be less than one, suggesting a
relatively uniform distribution. The null hypothesis tested was that the calculated variance/
mean ratio is not significantly different from 1.00. The results of the test indicated that
the null hypothesis could be rejected at the 7.5% rejection level. In other words, the
probability of the calculated variance/mean ratio being less than 1.00 is 92.5%. This sug­
gests the PCFU are more uniformly distributed rather than randomly distributed or con­
tagiously distributed (clustered).
X
16
DISCUSSION
Interpretations of the experimental results are presented in this section with empha­
sis on interpetations of the observed responses in Figures 4 and 5. The response in Figure 5
will be interpreted in terms of surface saturation, zones of inhibition, and surface thermo­
dynamics. A model is also proposed which describes bacterial accumulation on surfaces.
Growth Rate
Growth rate is a measure o f the physiological state of the cell. Figure 4 shows the
s
relationship between cell growth rate in the reactor bulk water, fi, and potential colony
forming units, PCFU. The resulting curve is “concave down” in shape with the maximum
number of PCFU occurring at approximately n = 0.2 hr"1. These results are consistent with
/
those of Fletcher and McEldowney (1983) who foupd maximum attachment rates for
Pseudomonas fluorescens to hydrophilic surfaces at (i =0.15 hr"1 in quiescent bulk water
conditions. In this study the maximum number of PCFU occurred at a growth rate which
is approximately 1/2 the maximum growth rate, pm, of Pseudomonas 224S . It is difficult
to speculate about the mechanism(s) responsible for promoting attachment from Figure 4.
In general, it can be concluded that the physiological state of the cell does influence its
attachment properties.
Surface Saturation
•'X
Initially clean surfaces appear to allow only a limited number o f cells to attach. This
phenomenon is termed surface saturation. Figure 5 is a conceptual representation o f sur­
face saturation at different cell concentrations in the bulk water. The surface is shown to
17
uirt n
I
/
Od Od
C E L L G R O W T H R A T E . i l ( h f 1)
Figure 4. Influence of bulk water cell growth rate on potential colony forming units.
A T T A C H E D C E L L C O NC E N T R ATI O N , Xa ( g m"1)
18
0.060
X/10
0.025
TI ME , I
Figure 5. Predicted influence of bulk water cell concentration, X, on attached cell concen­
tration (X = 0.13 gm"3).
19
become saturated with cells as the time of exposure is increased and the cell concentration
in the bulk water is held constant.
Figure 6 shows the relationship between cell concentration in the bulk water, X, and
potential colony forming units, PCFU. In this case, the surface appears to approach satu­
ration as the cell concentration in the bulk water is increased and the time of exposure is
held constant.
Surface saturation has been observed by other investigators. Fletcher (1977) observed
surface saturation to occur when approximately 40% of the surface was covered with cells.
Powell and Slater (1983) observed surface saturation to occur when approximately 1% or
5% of the surface was covered with cells depending on the experimental surface. In this
study, surface saturation occurred at approximately 0.1% coverage. The saturation cover­
age from each study and calculated transport and accumulation rates are included in Table
2. The reported saturation coverages decrease as the relative turbulence of the bulk water
increases. This response can be attributed to an increase in the detachment rate of cells
from the surface. The detachment rate can be approximated by subtracting the rate of
accumulation from the rate of transport. It is evident from this calculation that detach­
ment rate increases as the relative turbulence of the bulk water increases.
Table 2. Literature Comparisons.
Flow
Regime
quiescent
laminar
turbulent
% Coverage
at
Saturation
40
5
I
0.1
Rate of
Rate of
Transport Accumulation
(cells m'-2S-1XlO-4)
5000
167
472
—
4170
31
3
—
■
Presumed
Transport
Mechanism
Reference
sedimentation Fletcher (1977)
Powell and
diffusion
Slater (1982)
diffusion
—
this study
PCFU /
1 0 v unf
20
5.0
10.0
CELL C O N C E N T R A T I O N , X ( c e l l s m l ' x l O * )
Figure 6. Influence of bulk water cell concentration on potential colony forming units.
21
Zones of Inhibition
In order to investigate the surface saturation phenomenon further, a variance/mean
ratio analysis was performed qn the experimental data. The details of this analysis are pre­
sented in the Results section and in Appendix 4. The analysis indicates that the distribu­
tion of cells on the surface approaches a uniform distribution. The relatively small percent
surface coverage of cells at saturation (0.1%) and the relatively uniform distribution of
these cells suggest “ zones of inhibition” around each attached cell where subsequent
attachment of cells from the bulk water is prevented as long as the attached cell remains at
the surface. A conceptual representation of the “ zones of inhibition” is shown in Figure 7.
Microscopic observations made with a continuous flow system similar to the system
used by Powell and Slater (1983) support the “zones of inhibition” concept. Observations
of the surface revealed a very dynamic situation with cells constantly attaching and detach­
ing. However, cells preferentially attached to relatively unpopulated areas even if they were
initially transported to relatively colonized areas first.
!
Surface Thermodynamics
Surface thermodynamics provides a reasonable explanation of the “zones of inhi­
bition.” Surfaces can be characterized by the concept of surface free energy. Measure­
ments of surface free energy are made by immersing a solid in water and determining the
surface tension at the solid/liquid interface. Marshall (1976) observed a “marked lower­
ing” of the surface tension of germanium prisims exposed to pure cultures of bacteria
suspended in an artificial seawater medium. He suggests this response is due to the
adsorption of bacterial protein; presumably, cells and extracellular polymeric substances
(EPS). The decrease in surface tension corresponds to a decrease in surface free energy.
According to the first law of thermodynamics, the energy within a defined system, must
be conserved. Thus, the decrease in surface free energy must be accounted for by a trans-
22
1 0 0 >im
Figure 7. Scale drawing of attached cells covering 0.1% of surface area with a uniform dis­
tribution, suggesting “zones of inhibition” concept.
23
fer of energy somewhere on the surface. It is proposed that the decrease in surface energy
is accounted for by the formation of adhesive bon(is between the cell (and possibly its
EPS) and the surface during the attachment process. Once the available bonding energy of
a localized area on the surface is utilized, energy required for attachment is no longer
available and the “zone of inhibition” is formed. The size of the “zone of inhibition” is
proportional to the bonding energy required for attachment to occur, the available bond­
ing energy per unit area of the surface and of the cell, and localized conditions at the
sufface/bulk water interface such as the relative turbulence of the bulk water. In these
experiments, the “zones of inhibition” were relatively large since approximately 99.9% of
the surface remained free of cells after saturation was reached. Regardless of the mecha­
nism of formation, the “zone of inhibition” could be advantageous to cells which attach to
surfaces because it would decrease competition for nutrients from other cells in the sur­
rounding micro-environment.
Assumptions
The following assumptions were made in the interpretation of the experimental
results:
1. The effect of attached cell growth on the determination of attachment rates was
assumed to be negligible because of the following reasons:
a. Nutrients were not added to the reactor.
b. Experiments were limited to 6 hours.
c. PCFU were used in the data analysis instead of cell numbers.
2. The cell concentration in the chemqstat was assumed to remain constant in all
experiments as indicated by chemostat cell counts (Appendix 3).
24
Model
A model is proposed in this section which describes bacterial accumulation on sur­
faces in terms of potential colony forming units, PCFU:
r X (I - - —)
k
Units
where:
X a = PCFU
[PCFU/L2 ]
t
= time
[t]
r
= rate constant
X
= bulk water cell concentration
[cells/L3 ] 1
k
= saturation density
[PCFU/L2 ]
' [L/t]
This particular saturation model was chosen because its behavior is consistent with
observations and conclusions made during this study. Initially, the model predicts bacterial
accumulation on surfaces, X a , is proportional to the concentration of cells in the bulk
water, X. As Xa begins to increase, the accumulation rate, dXA/dt, begins to decrease. The
decrease in dXA/dt is proportional to the decrease in the surface area available for attach­
ment as cells attach to the surface and form zones of inhibition. The accumulation rate,
dXA/dt, will continue to decrease until Xa equals the saturation density, k. At this point,
the accumulation of PCFU on the surface, dXA/dt, equals zero. Bacteria will continue to
accumulate on the surface, however, as the cells within the PCFU begin to grow and divide.
The differential form of the model was integrated in order to obtain estimates of r
and k:
- ( ~ )
k [l - e
I
Note: All cells in the bulk water are considered PCFU so the units are consistent.
25
The parameters, r and k, were estimated using the Gaussian method of non-linear least
squares. The exposure time, t, was set equal to the exposure time used in this study, i.e.,
t = 6 hours. The bulk water cell concentration, X, and the observed PCFU, X. , were set
i ■
v
•
.
A
equal Jq the values listed in Table 3. The X values correspond to the cell concentrations
tested in the study and the Xa values correspond to the resulting PCFU observations when
the bulk water cell growth rate, ju, was held constant at p = 0.17 hr-1. The sensitivity equa­
tions derived for the parameter estimations were evaluated numerically using finite differ­
ences. After estimates o f r and k were calculated, predicted PCFU values, Xp were gener­
ated (see Table 3).
Table 3. Parameter Estimation Using Nonlinear Least Squares Analysis.
Bulk Water Cell
Concentration, X
(cells/m3 X IO'11)
9.7
1.3
1.3
1.3
1.3
0.7
k = 3.27 X IO8 ± 6.10 X IO7
r = 2.92 X 10'3 ± 8.11 X 10'4
correlation = -0.54
RSS
,-=Vx = 7.86 X IO14
(n-1)
S2 = 4.86 X IO15
Sx2 = 5.81 X IO14
Observed PCFU,
XA
(PCFU/m2 X IO'8)
Predicted PCFU,
Xp
(PCFU/m2 X 10'8)
3.20
2.65
2.d9
2.25
2.49
1.10
(PCFU/m2)
(m/hr)
3.27
2.25
• 2.25
2.25 .
2.25
1.14
The errors associated with the estimates of r and k correspond to 95% confidence
intervals. The errors are acceptable since the error associated with k is approximately 19%
of the estimate and the error associated with r is approximately 28% of the estimate. The
absolute value of the correlation coefficient (0.54) falls between the absolute limits of the
correlation coefficient (0-1.0). Therefore, the parameters are not highly correlated. The
26
correlation coefficient (-0.54) also implies a substantial negative correlation between the
parameter estimate errors. However, since the errors are sufficiently small, the parameter
estimates are acceptable.
A goodness of fit test o f the model was performed using the residual sum of squares,
RSS, the number of observations minus one, n-1, the variance of the observed PCFU, S2 ,
and the variance of the observed PCFU at the replicated center point in the octagonal
design (X = 1.3 X IO11 cells m"3), Sx2 . Calculation of I - [(RSS/n-l)/S2 ] gives an esti­
mate of the fraction of the observed PCFU variance accounted for by the model. Using the
appropriate values in Table 3, this calculation implies that the model accounts for approx­
imately 84% of the observed PCFU variance. However, this estimate also includes the vari­
ance o f the observed PCFU due to experimental error. This can be accounted for by calcu­
lating Sx2/S2 since Sx2 corresponds, to the variance of the observed PCFU for replicated
experiments and S2 corresponds to the variance of the observed PCFU for all experiments
listed in Table 3. This calculation yields, Sx2ZS2 = 12%. In other words, 12% of the vari­
ance of the observed PCFU can be accounted for by experimental error. As a result,
approximately 75% of the observed variance not accounted for by the model, can be
attributed to experimental error. Therefore, approximately 4% of the total observed PCFU
variance cannot be accounted for by the model.
27
CONCLUSIONS
The following conclusions can be drawn from this experimental study within the
range of experimental conditions tested:
1. Growth rate, which is a measure of the physiological state of a bacterial cell, influ­
ences bacterial attachment rates to surfaces. In this study, attachment rates were
greatest with cells growing at approximately 1/2 their maximum specific growth
rate.
2. Bacterial attachment rates are proportional to the concentration o f cells in the
bulk water until the surface becomes saturated with cells and the number of
attached cells approaches a constant value. In this study, surfaces approached
saturation with a relatively uniform distribution of cells at approximately 0.1%
surface coverage.
The concept of “zones of inhibition” around each attached cell was proposed to
explain the surface saturation, uniform distribution, and 0.1% surface coverage observa­
tions. The results of this study suggest bacterial accumulation on surfaces occurs in two
phases. Initially, cells are transported to a surface where a certain percentage attach until
the surface becomes saturated with cells. After saturation occurs, the primary mechanism
o f surface accumulation is growth of attached cells..
LITE RATURp CITED
29
LITERATURE CITED
Absolm, D. R., F. V. Lambert!, Z. Policova, W. Zingg, C. J. van Oss, and A. W. Neumann.
1983. Surface thermodynamics of bacterial adhesion. Applied and Environmental
Microbiology 4 6 : 90-97.
Brannan, D. K., and D: E. Caldwell. 1982. Evaluation o f a proposed surface colonization
equation using Thermothrix thiopara as a model organism. Microbial Ecology S: 15Bryers, J. D., and W. Q. Characklis. 1982. Processes governing primary biofilm formation.
Biotechnology and Bioengineering 24: 2451-2476.
Campbell, J. A., and T. J. Hanratty. 1983. Mechanism of turbulent mass transfer at a solid
boundary. AIChE Journal 29: 221-228.
Characklis, W. G. 1981. Fouling biofilm development: A process analysis. Biotechnology
and Bioengineering 22: 1923-1960.
Fletcher, M. 1977. The effects o f culture concentration and age, time, and temperature
on bacterial attachment to polystyrene. Canadian Journal of Microbiology 23: 1-6.
Fletcher, M. 1980. Adherence of micro-organisms to smooth surfaces, pp. 346-374. In
E. H. Beachey (ed.), Bacterial adherence. Chapman and Hall, London.
Fletcher, M., and S. McEldowney. 1983. Microbial attachment to non-biological surfaces.
In Proceedings of 3rd International Congress on Microbial Ecology, East Lansing,
Mich.
Gerhardt, P., R. G. E. Murray, R. N. Costilow, E. W. Nester, W. A. Wood, N. R. Krieg, and
G. B. Phillips. 1981. Manual of Methods for General Bacteriology. American Society
for Microbiology, Washington, D C.
Hobble, J. E., R. J. Daley, and S. Jasper. 1977. Use of nuclepore filters for counting bac­
teria by fluorescence microscopy. Applied and Environmental Microbiology 33: 12251228.
Hunter, J. S. 1960. Some application of statistics to experimentation. Chemical Engineer­
ing Progress Symposium Series #31 56: 1-17.
Marshall, K. C. 1976. Interfaces in microbial ecology. Harvard University Press, Cambridge,
Mass.
Marshall, K. C, 1980. Bacterial adhesion in natural environments, pp. 187-193. In R. C. W.
Berkeley, J. M. Lynch, J. Melling, and P. R. Rutter (eds.), Microbial adhesion to sur­
faces. Ellis Horwood, London.
30
Marshall, K. C., R. Stout, and R. Mitchell. 1971. Mechanism of the initial events in the
sorption o f marine bacteria to surfaces. Journal of General Microbiology 68: 337348.
Molin, G., I. Nilsson, and L. Stenson-Holst. Biofilm build-up of Pseudomonas putida in a
chemostat at different dilution rates. European Joum ti of Applied Microbiology and
Biotechnology 15: 2 \ 8-222.
Pielou, E. C. 1977. Mathematical ecology. John Wiley and Sons, New York.
Powell, M. S., and N. K. H. Slater. 1983. The deposition of bacterial cells to solid surfaces.
Biotechnology and Bioengineering 25: 891-900.
Robinson. J. A. 1983. Personal communication. ,
Robinson, J. A., M. G. Trulear, and W. G. Characklis. 1983. Cellular reproduction and
extracellular polymer formation by Pseudomonas aeruginosa in continuous culture.
Submitted for publication.
Trulear, M. G. 1983. Cellular reproduction and extracellular polymer formation in the
development of biofilms. Ph.D. Thesis. Montana State University.
Zar, j. H. 1974. Biostatistical analysis. Prentice-Hall, Inc., New Jersey.
31
I'
!
APPENDICES
32
APPENDIX I
NUTRIENTS AND DILUTION WATER
33
APPENDIX I
NUTRIENTS AND DILUTION WATER
Component
Concentration
Nutrients
C6 H12O6
0.01 g T1 distilled water
NH4Cl
0.1
Na2HPO4
0.56
KH2PO4
0.56
Trace Elements1
2.0 ml T1 distilled water
Vitamins1
0.1
pH
6.8
Dilution Water
Na2HPO4
0.56 g I-1 distilled water
KH2PO4
0.56
pH
.6.8
1 Refer to Gerhardt et al., Manual o f Methods for General Bacteriology, 1981,
p. 98(21C).
APPENDIX 2
RAW DATA
35
APPENDIX 2
RAW DATA
1.
EXP. # _____ refers to the experimental number listed in Figure 2.
2.
CELLS/FIELD and PCFU/FIELD are average values.
3.
S2 /x
4.
i.d. is the index of dispersion (see Appendix 4).
5.
Examples of cell and PCFU counts:
is the variance/mean ratio calculated from PCFU values.
C ELLS/PCFU
I
I
2
3
2
3
4
I
Z
O+
I
The count in microscope field I is I PCFU consisting of I cell.
The count in microscope field 2 is 3 PCFU. 2 PCFU consist of I cell and I PCFU con­
sists of 4 cells.
The count in microscope field 3 is 0 PCFU.
36
EXP. « /
CELL AND PCFU COUNTS
RESULTS:
C E L L S /F IE L D =
^ ' O t/
PC F U /F IE L D -
Z. L 7
s1 /
x =
i d. =
I ’ O tI
5% . S" I
DATA:
C ELLS/PCFU
I
I
Z
2
/
3
k
z.
6
I
/
/
7
I
8
O
Z
Z
9
10
I
2,
V
12
13
0
I
14
15
Z
16
17
4
j
/
5
ii
3
I
4
3
2
I
Z
O ^
Z
37
DATA (continued)
EXP. # /
CELLS/PCFU
1
2
I
/
3
Z
3
I
Z
if
Z
I
Z
(
I
/
(
H
(o
/
/
FIE L D
L
V
I
Z
I
/
(o
5'
I
L
I
/
I
I
I
4
38
DATA (continued)
EXP *
I
C ELLS/PCFU
I_______ ,
2________
I
/
/
I
3
Z
3
3
2.
/
I
)
FIE L D
3
I
/
I
3
Z
i
I
I
4
/
I
3
3
3________
Z
Z
39
CELL AND PCFU COUNTS
EXP
Z
RESULTS s
C E L L S /F IE L D
2.91
PC F U /F IE L D =
2 . 0 9
sV ; -
0 .9 1
i.d . =
70, 73
DATA:
C ELLS/PCFU
I
2
I
2
3
F IE L D #
O -^
/
I
4
I
5
I
6
I
7
4
3
8
XO
I
11
H
Z
13
3
14
/
15
O^
16
I
17
Z
I
I
9
12
3
2
I
2.
I
4
40
DATA ( c o n t i n u e d )
EX P. #
Z-
CELLS/PCFU
1_______ ,
2_______
/
3
/
/
/
Z
3
3
Z
I
I
3
F IE L D #
I
4
I
I
3
/
I
I
I
I
z.
Z.
I
/
Z
/
Z
3________
4
41
DATA (continued)
EXP. #
Z
C ELLS/PCFU
I_____________2
3
Z
I
Z
3
Z
<
Z
I
I
I
I
I
FIE L D
Z
t
I
I
I
Z
I
I
I
I
I
Z
I
I
I
3
I
4
42
DATA (continued)
EXP. # 2.
CELLS/PCFU
I
2
3_______
Z
Z
O ^
/
L
V
0 ^
/
Z
Z
7
/
Z
FIE L D
/
•
4
43
CELL AND PCFU COUNTS
EXP. #
3
RESULTS;
C E L L S /F IE L D =
3 .^ 0
Z • VO
P C F U /F IE L D -
=V S -
0,3%
i d. -
//. 3 3
DATA:
CELLS/PCFU
2
I
Z
I
2
3
3
Z
4
F IE L D #
/
I
5
6
7
8
9
O
3
I
i
Z
2
3
I
(
I
4
3
/
Z
l5
l6
l7
Z
I
I
3
/
I
3
3
I
I
3
4
44
I
DATA (continued)
EXP.
CELLS/PCFU
I_______ ,
&
2_______
2.
Z
3
I
3
Z
L
/
/
F IE L D #
/
Z
Z
(
/
/
3________
4
45
EXP # y
CELL AND PCFU COUNTS
RESULTS:
C E L L S /F IE L D =
Z . Sf
P C F U /F IE L D -
2, Z 3
s1 /
X =
i.d . =
OO
/ ,
S 7 . /7
DATA:
C ELLS/PCFU
I
I
2
2
I
Z
3
ZL
4
5
6
3M
6k
/
o
•*>
7
I
8
(
9
3
2
I
O
LO
*
Z
2
LI
I
L2
3
L3
2
14
15
16
17
O
^
I
I
I
Z
I
I
4
46
DATA ( c o n t i n u e d )
EXP. #
C ELLS/PCFU
I
3
2
/
H
3
I
/
H
Z-
I
3
I
o
2.
I
FIE L D
I
I
3
z.
0 ^
/
I
/
S
S
/
ZI
3
I
4
47
DATA (continued)
EXP. #
CELLS/PCFU
I_______ ,
zZ
/
2.
2_______
Z
S
/
I
I
I
Z
Z
FIE L D
I
I
I
Z
Z
Z
I
Z
I
Z
/
5
3
3________
4
48
EXP
CELL AND PCFU COUNTS
#
RESULTS:
C E L L S /F IE L D =
/.$"3
P C F U /F IE L D =
sV i t -
/. I Q
0 , 1 S'
i-d- =
DATA:
C ELLS/PCFU
I
2
I
3
I
/
F IE L D #
2
3
o
4
O
->
^
5
Z
6
2.
7
O ^
8
O
9
I
0
I
I
I
2
I
3
i
Z
/
4
5
/
6
i
7
i
4
49
DATA (continued)
EXP. # 5"
C ELLS/PCFU
I________.
2________
/
O *
z.
I
I
I
I
I
0 ^
Z0
^
I
FIE L D
/
I
/
I
C v
I
Z
Z
O ^
Z
I
I
O ^
I
3________
4
50
DATA (continued)
EXP.
* S
CELLS/PCFU
I_______ .
2________
Z
I
I
I
I
I
I
o*>
O^
/
I
FIE L D
I
I
I
I
I
I
I
I
A
I
I
Z
%
I
I
3________
4
51
DATA ( c o n t i n u e d )
EX P.
#
C ELLS/PCFU
1
2
3
4
I
0 ^
i
O ^
Z
I
I
0 ^
O >
O ^
I
i
/
FIE L D
I
3
I
0 ^
O ^
I
I
^
6
I
0 ^
'2.
52
DATA ( c o n t i n u e d )
EXP.
CELLS/PCFU
I_______ ;
I
2________
I
I
Z
I
FIE L D
Z
3________
4
53
CELL AND PCFU COUNTS
EXP
RESULTS:
C E L L S /F IE L D ^ H . % L
i. IQ
P C F U /F IE L D s1 /
x -
C-cIO
i.d . = £ 0 . 3 3
DATA:
C ELLS/PCFU
I
S '
2
3
/
Z
3
4
5
2
6
I
I
I
Z
3
3
7
F IE L D #
8
2.
9
10
8
o
5
11
12
13
14
J
Z
/
3
15
16
17
4
3
/
/
I
54
DATA (continued)
EXP. # _A_
CELLS/PCFU
1
2
3
3
I
i
Z
3
I
I
zZ
5
/
/
i
3
Z
I
Z
I
FIE L D
3
3
I
(
I
I
I
V
Z
I
/
3
zV
Z
I
4
55
DATA (continued)
EXP. #
6
CELLS/P C F U
I_______
2
3
Z
->
D
/
/
i
/
I
H
I
I
Z
i
FIE L D
I
L
I
5
S
/
2
4
56
EXP. #
CELL AND PCFU COUNTS
RESULTS:
CELLS/FIELD =
Z
PCFU/FIELD =
l'(> (s
S1 /
2.
X =
i.d.
=
‘i'/.S%
DATA:
CELLS/PCFU
FIELD #
I
2
I
Z
2
O ^
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
3
Z
7
Z
I
O >
Z
/
z.
O>
O
Z
i
Z/
Z
I
I
I
I
4
57
DATA ( c o n t i n u e d )
EXP.
CELLS/PCFU
1
2
3
O^
Z
3
/
O
I
I
Z
I
Z
O *
I
FIE L D
*
O
Z
^
Z
/
o >
i
^
0
/
I
/
4
Z
I
2
>
0
Z
/
4
58
DATA (continued)
EXP. #
7
CELLS/PCFU
1
Z-
2
3
/
O •>
/
z.
/
0 ^
FIELD
I
/
I
/
I
4
59
EXP. #
CELL AND PCFU COUNTS
RESULTS:
CELLS/FIELD =
/,7 5 "
PCFU/FIELD =
i‘ if f
V
X =
0 . '7 (
i.d.
=
GO, 0%
S
DATA;
CELLS/PCFU
i
2
I
J
I
2
I
Z
3
4
5
3
3
6
I
I
7
8
9
^
9
4
z.
io
I
11
I
12
13
14
17
Z
/
2
/
I
I
Z
15
16
3
I
I
4
60
DATA (continued)
EXP. #
CELLS/PCFU
1
2
3
I
I
I
o
I
I
O
Z
I
->
o
/
FIELD
%
Z
I
I
~L
I
I
O-*
I
/
0
*
Z
I
I
I
4
61
DATA (continued)
EXP. # _ s _
CELLS/PCFU
3
2
I
/
/
/
I
Z
I
I
I
I
I
3
o
^
I
O ■*
I
I
Z
o
->
/
I
Z
0 ^
Z
I
Z
O *
O
^
4
62
DATA (continued)
EXP. #
3
CELLS/PCFU
I_______ ,
2_______
I
I
I
I
I
I
4
I
»
0
I
FIE L D
I
I
I
I
I
2
2
I
i
I
I
3________
4
63
CELL AND PCFU COUNTS
EXP
RESULTS:
CELLS/FIELD =
5 - t Z7
PCFU/FIELD -
73
=V x «
O - cIS
i-d. -
H
I’ ^
2
.
DATA;
C ELLS/PCFU
I
2________
I
4
3
2
3
7_
I
4
2.
2L
I
5
6
7
8
9U
b.
9
H
3
Z
2,
Z
2
I
L
I
H
10
11
I
H
3
12
13
3
H
3
14
15
5
16
I
17
I
H
L
3
3________
4
64
DATA ( c o n t i n u e d )
EX P.
#
CELLS/PCFU
I
j
2
3
Z
2
I
I
4
2
3
S
V
I
I
5
7
I
3
i
F IE L D
I
Z
Z
I
I
3
I
¥
I
Z
/
I
I
I
Z
3
I
Z
4
65
DATA ( c o n t i n u e d )
EX P.
#
CELLS/PCFU
I
2
3
I
S'
FIELD
sr
-
3
.
4
66
EXP
CELL AND PCFU COUNTS
/0
RESULTS:
CELLS/FIELD =
O -^ O
PCFU/FIELD =
sV
i-d .
0-75"
X =
=
(#1. It0
DATA:
CELLS/PCFU
2
I
I
I
2
C
^
3
O
4
O
^
5
2
6
I
7
O
8
FIELD #
>
9
O
>
I
O
O
Li
C
L2
I
L3
Z
L4
I
LS
2
Z
16
17
3
4
67
DATA ( c o n t i n u e d )
EX P.
#
C ELLS/PCFU
I
,
2
,
3
4
2
2
Z
Z
/
I
/
O -=>
Z
•
O ^
F IE L D
O ^
O ^
O
I
/
O »
Z
O ^
O ^
/
68
DATA (continued)
EXP. #
IO
CELLS/PCFU
2
I
3
I
Cj
-* >
I
I
I
i
I
O
I
2_
FIELD
O
^
I
O
>
O
I
Z
I
I
Q
O
4
69
DATA ( c o n t i n u e d )
EXP
CELLS/PC F U
I_______ ,
Z
I
FIE L D
O 1S>
2_______
3________
4
70
E X P.
CELL AND PCFU COUNTS
#
//
RESULTS:
C E L L S /F IE L D -
I
O ' ^ S'
PC F U /F IE L D s V
i.d .
X -
/-Ol
-
cZ / , 5 L
DATA:
CELLS/PCFU
I
2
I
I
(
2
/
3
4
FIE L D
*
o
5
Z
6
I
7
O
8
I
9
I
10
O
11
I
12
O
»
I
*
^
I
13
14
I
O
15
16
17
0^3>
I
3
4
71
DATA (continued)
EXP. #
Il
CELLS/PCFU
I
;
2
,
I
O >
I
O
I
Z
I
Z
/
O >
I
FIE L D
I
o
I
Z
I
Z
o
O
/
o^>
Z
o^>
3
4
72
DATA (continued)
EXP. # / /
FIE L D
C ELLS/PCFU
73
EXP
CELL AND PCFU COUNTS
#
ZZ
RESULTS:
Z ' 70
C E L L S /F IE L D =
PC F U /F IE L D =
sV
i.d.
X
-
=
O
. cI 7
S 7•
DATA:
CELLS/PCFU
I
3
2
I
2
2
I
Z
3
I
I
4
I
S
5
z.
FIE L D
6
I
7
I
8
I
9
Z
10
O
12
o
Z
14
15
I
Z
16
17
/
I
11
13
/
I
I
J
Z
4
74
DATA (continued)
EXP. # I Z
CELLS/PCFU
3
2
I
/
I
I
I
I
3
c ^ >
I
I
I
I
Z
I
I
*
aw
Z
H
Em
Z
I
3
3
Z
I
I
I
4
I
Z
5"
4
75
DATA (continued)
EXP. #
/ 2.
CELLS/PCFU
I
2_______
2.
I
O >
O -?>
3
i
I
/
I
I
I
Z_
I
I
I
4»
0
F IE L D
3
I
I
L
I
I
I
Z
3
._____ 4
76
APPENDIX 3
CHEMOSTAT CELL COUNTS
77
APPENDIX 3
CHEMOSTAT CELL COUNTS
Growth Rate, At (hr-1)
Cell Concentration, X (#/lX IO4 Atm 2 )
X1
S
0.30
22.4
18.5
6.19
5.92
0.26
15.4
12.5
6.70
4.48
0.17
21.4
5.64
0.08
Average
14.8
17.12
6.16
1 Each x represents an average of 10 fields.
78
APPENDIX 4
VARIANCE/MEAN ANALYSIS
79
APPENDIX 4
■*
.
'
5
VARIANCE/MEAN ANALYSIS
Calculate:
1.
v a r ia n c e /m e a n =
S12I x =
_
(1 /n x )
n
2
_
(x- - x ) 2
i
j=l
where:
x
n
i
= ( 2 x;)/n
J-1
n = number of observations per experiment
Xj = value of each observation
2.
in d e x o f d is p e r s io n
=
i.d .
=
n
2
_
(Xj - x ) 2 / x
i
j=l
Index is approximately xa distributed with n-1 degrees of freedom (d.o.f.) and pro­
vides test of whether calculated s2 /x exceeds I significantly (Pielou, 1977).
3. sum of i.d. from each experiment = 2 i.d. = 616.08
2
Sum of i.d. is approximately %2 distributed (the sum of several x 2 distributions is x 2
distributed) with d.o.f. equal to the summation of the d.o.f. calculated in 2. for each
experiment.
2 (n -1 ) = 668
4.
x2
s t a t i s t i c tr a n s f o r m e d t o s t a n d a r d n o r m a l d e v ia te b y :
z = (2 X2 )1/2 - (2n'-l)% (Hoel, 1971)
where:
x2
= Z i.d.
n' = d.o.f.
z = -1.44
(Used to test whether calculated s2 /x is significantly less than I )
1The values for each experiment are listed on the cell counts forms in Appendix 2.
2 Experiment #3 was omitted from the analysis because of an abnormally low s2 /x =
0.38 in comparison to the other experiments (refer to Appendix 2). It was thought that
the s2 /x from Experiment #3 would unfairly bias the results of this analysis towards rejec­
tion of the null hypothesis, H0 (see 6.).
80
5. weighted average of s2 /x for all experiments
( s2 /
x
)t
where:
%
= S [(s2/x )n ]i /nT = 0.92
i=l
k = number of experiments
n = number of observations per experiment
nT = total number of observations
6. null hypothesis, Hq : (s2 /x)T not significantly different from 1.00.
z = -1.44 (from 4.) => a = 0.075 (from normal distribution table)
Therefore, H q can be rejected at the 0.075 level.
MONTANA STATE UNIVERSITY LIBRARIES
3 1 762 10056641 1
MAIN LIB.
N 378
N 331
cop. 2
of growtf
r a t e and c e l l
c o n c e n tr a tio n
b a c te r ia l
on
a tta c h m e n t...
MAIN I H -
N 318
N 331
Co f>-3.