Microb. Ecol.7:1-11(1981)
MICROBI,4L ECOLOGY
Quantitation of Microbial Growth on Surfaces Douglas E. Caldwell, J Daniel K. Brannan, 1 Marvin E. Morris, 2 and Michael R. Betlach 3 1Departmentof Biology, Universityof New Mexico, Albuquerque, New Mexico87131; 2AppliedBiology and IsotopeUtilizationDivision, Division4535, SandiaNationalLaboratories,Albuquerque, New Mexico 87185; and 3Extraterrestrial ResearchDivision, NASA AmesResearchCenter, MoffettField, California 94035
Abstract. An equation describing the initial phases of microbial surface colonization is presented. Simultaneous microbial attachment and growth are considered as the primary components of colonization. A table is given that permits determination of growth rate from the density and distribution of cells present on surfaces after incubation in situ. Other methods used to calculate microbial growth rate on surfaces are evaluated. The new procedure is more accurate and less time consuming than those used previously. Published data on microbial surface colonization more closely follow the proposed colonization equation than the exponential growth equation, which overestimates the growth rate.
Introduction Although microbial surface growth is important, many assumptions concerning microbial activity in the environment are based solely on studies of planktonic unicells. The attachment of bacteria to surfaces often reduces predation, permits use of adsorbed substrates, and positions cells in favorable environments. Attachment to plant and animal surfaces can result in the shift of diffusion gradients due to the formation of microbial films. This increases the concentration of nutrients within the microenvironment of attached bacteria. Studies of these phenomena in continuous or batch culture are usually difficult or inappropriate, and thus direct studies of surface growth are needed. However, many theories concerning microbial growth and activity in the environment are based solely on batch or continuous culture experiments (6). This is due, in part, to the lack of adequate kinetic data describing microbial growth on surfaces. Continuous culture studies require that isolated populations of free-floating unicells be used. Such studies have provided facts concerning the growth capabilities of many bacteria. However, they have not contributed directly to knowledge of microbial activities in most environments except to define a range of possibilities. Observation of microbial surface growth has been improved using incidence 0095-3628/81/0007-0001 $02.20 (~)1981 Springer-VerlagNew York Inc.
2
D, E. Caldwetl et al,
fluorescence microscopy and electron microscopy (Figs. 1 and 2). As a result, the colonization of numerous natural and artificial surfaces has been studied using these methods (7-9). However, the kinetics of in situ microbial surface colonization have not yet been subjected to the same degree of mathematical analysis as have the kinetics of growth in liquids. This type of analysis is needed if quantitative studies of microbial growth are to be extended to surface environments. Attempts to quantitate microbial growth rates on surfaces have been discussed previously (4). The methods being used result largely from the observation of mierocolonies on glass slides and electron microscope grids (Fig. 1). These show that during the initial phases of colonization the size of colonies tends to cluster around values of 2, 4, 8, 16, 32, and 64 cells. This indicates exponential growth and has resulted in the use of the exponential growth equation to describe microbial surface colonization. This equation is used although exponential growth and linear attachment must simultaneously determine the density of bacteria on surfaces. It has also been observed that most colonies grow at least until they reach 64 cells (6 generations) before emigration or deliquescence occurs (2-4). However, organisms such as Hyphoraicrobium, Hyphoraonas, Caulobacter (Fig. 2), Pedomicrobium, Asticcacaulis, and other stalked and budding genera may not form microcolonies. Their offspring are frequently lost as flagellated cells that colonize sites on other surfaces (1, 4, 9). These genera can be recognized by cell morphology and are largely excluded from studies of in situ growth rate. The size of a single microcolony can be followed as a function of time by using a partially submerged microscope to continuously observe the growth of the colony on a submerged glass slide (10). The growth rate can then be accurately determined (assuming exponential growth) because the incubation period and both the initial and final size of the colony are known. However, this is a difficult procedure that does not readily permit identification using fluorescein-conjugated antibodies or electron microscopy because the cells must be observed continuously as they grow. As a result, this and similar procedures are infrequently used (2). In most investigations, growth rate is determined by plotting the log of the average colony size (or mean number of organisms per colony) versus time (2). The resulting slope is used to obtain #, the specific growth rate. In studies by Bott (3), "the counts on irradiated slides exposed to germicidal U.V. at regular intervals [to allow attachment but not growth] were subtracted from those on unirradiated slides for an estimate of cell numbers resulting from growth alone .... Generation times were determined from plots of the data on semilog paper." The irradiation control assures that the attachment of dead and moribund cells is not mistaken for growth. However, it fails to account for the cells that attach and commence exponential growth after the incubation period has already begun. It is thus assumed that all growing ceils attach at the beginning of the incubation and grow exponentially. The question that remains is' whether estimates of growth obtained in this way suffer seriously from the unstated assumption that the exponential growth equation applies equally well to batch cultures inoculated at time zero and to in situ surfaces that are continuously reinoculated. In an effort to eliminate the error inherent in this assumption, Caldwell et al. (5) embedded microbial populations in thin agar gels. This permitted determination of growth rate without the complicating effects of simultaneous attachment, emigration, and predation. The results of this method are more accurately described by the exponential growth equation than are results obtained from the colonization of slides. However, the environment in an artificial gel is too far removed from most natural situations to be very useful.
Quantitation of Microbial Growth on Surfaces
3
Fig. 1. A microcolony attached to a Formvar-coated electron microscope grid submerged in Vermillion Creek (Rose Lake Recreation Area, Michigan) for 5 days. There are 16 (2 4) cells, indicating that 4 generations have passed since the first cell in the colony attached to the surface. Because the age of the colony (time of attachment) is unknown, the growth rate can not be determined using the exponential growth equation. Transmission electron micrograph. Bar equals 1/zm.
To overcome these problems, a mathematical model is developed in this paper that applies to the colonization of surfaces briefly exposed in situ. It accounts for simultaneous growth and attachment and was devised to permit evaluation of the error inherent in previous estimates of growth rate as well as to provide a more accurate method for use in future studies.
4
D.E. Caldwell et al.
Fig, 2, Caulobacter Sp. attached to a Formvar-coated electron microscoPe grid submerged in Gull Lake (Kellogg Biological Station, Michigan) for 5 days. The parent cell divides by binary fission, leading to the production of flagellated offspring that may leave the surface and attach at other sites. In this genus and in other genera of stalked and budding bacteria, emigration complicates the determination of growth rate on surfaces. Transmission electron micrograph. Barequals 1/am.
Derivation of the Colonization Equation T h e c h a n g e in the density o f bacteria on surfaces is due to numerous factors including a t t a c h m e n t (immigration), emigration, predation, growth, death, interaction between colonies, and modification o f the m i c r o e n v i r o n m e n t within colonies. However, the
Quantitation of MicrobialGrowthon Surfaces
5
analysis of surface colonization can be simplified for initial growth (6 generations or less) on newly exposed surfaces. In this situation, most factors are relatively unimportant compared to the combined effect of attachment and growth. The colonization rate is equal to the growth rate plus the attachment rate. Since growth is exponential and attachment is linear, this gives the following differential equation: dN
--=pN+A
(1)
dt
where: N = number of cells on the surface (cells) /1 = specific growth rate (h- l ) A = attachment rate (cells h - 1) t = time of incubation (h) (N and A must be obtained from the same surface area or number of microscope fields) Integrating Eq. 1:
N
=
+
(eut)
-- --
(2)
/.t Because this equation is valid only during the initial stages of colonization on a newly exposed surface, the initial number of cells (No) is always equal to zero. Thus: N
=
eu t _
_
r~
)
Equation 3 was used to obtain Table 1. This table lists values of/a corresponding to known values of A and N for incubation periods of 24 and 48 h. The table is necessary because it is not possible to solve Eq. 3 for/~. Similar tables for other incubation periods or with smaller increments of A and N (for greater accuracy) can also be obtained using Eq. 3. Modification of Eq. 1 to account for emigration, predation, variable attachment rates, and variable growth rates is possible, but results in unnecessary complexity for studies of the initial phase of colonization. The kinetics of microbial growth in older microbial surface films have been studied extensively in thin-film fermentors and similar systems. Under these conditions the rate of growth is equal to the rate of cell loss due to the sloughing of cells from the surface (11). The kinetics of initial surface colonization in these artificial systems are not analogous to those developed here because the inoculum or " s e e d " is supplied initially but not during the incubation. As a result, initial colonization can be described adequately by assuming simple, exponential growth in these artificial systems (11). This assumption is not adequate for the description of in situ colonization. The validity of the table was confirmed using a computer model of colonization. This model determined values of N assuming that attachment by individual cells occurred at uniform time intervals and that growth occurred exponentially by all attached cells during these intervals. Figure 3 shows the cell number as a function of time predicted by Eq. 3. If growth is rapid compared to attachment, then colonization is nearly exponential (Fig. 4). However, if the reverse is true, then colonization becomes nearly linear (Fig. 3). When
A
0.9
14.2617 11.9327 10.2795 9.04750 8.09509 7.33816 4.02666 2.51476 2.06762 1.86160 1.74466 1.66970 1.61773 1.57961 1.55048
1.0
14.3075 11.9785 10.3253 9.09322 8.14085 7.38392 4.07242 2.56052 2.11338 1.90736 1.79042 1.71546 1.66349 1.62537 1.59624
#
1.38629 1.15524 0.99021 0.86644 0.77016 0.69315 0.34657 0.17328 0.11552 0.08664 0.06931 0.05776 0.04951 0.04332 0.03850
24 hours
Doubling time
0.5 0.6 0.7 0.8 0.9 1.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
14.2106 11.8815 10.2284 8.99631 8.04394 7.28701 3.97551 2.46361 2.01647 1.81045 1.69351 1.61855 1.56658 1.52846 1.49933
0.8 14.1526 11.8236 10.1704 8.93832 7.98595 7.22902 3.91752 2.40562 1.95848 1.75246 1.63552 1.56056 1.50858 1.47047 1.44134
0.7 14.0856 11.7566 10.1034 8.87137 7.91900 7.16207 3.85058 2.37147 1.89153 1.68551 1.56857 1.49361 1.44164 1.40352 1.37439
0.6 14.0065 11.6774 10.0243 8.79219 7.83982 7.08289 3.77139 2.25949 1.81235 1.60633 1.48939 1.41443 1.36246 1.32434 1.29521
0.5 13.9096 11.5805 9.9274 8.69528 7.74291 6.98598 3.67449 2.16258 1.71544 1.50942 1.39248 1.31752 1.26555 1.22743 1.19830
0.4 13.7847 11.4556 9.80242 8.57035 7.61797 6.86104 3.54955 2.03764 1.59050 1.38448 1.26754 1.19258 1.14061 1.10249 1.07336
0.3
Table 1~ Values of log N (after 24 and 48 h) corresponding to values of #(h - 1) and A (cells h - I) as predicted by the colonization equation (Eq. 3)
0.1 13.6086 13.3075 11.2795 10.9785 9.62633 9.3253 8.39425 8.09322 7.44188 7.14085 6.68495 6.38392 3.37346 3.07243 1.86155 1.56052 1.41441 1.11340 1.20839 0.907360 1.09145 0.790420 1.01649 0.715462 0 . 9 6 4 5 1 9 0.663490 0 . 9 2 6 4 0 4 0.625374 0 . 8 9 7 2 7 4 0.596244
0.2
~7 t-n t"3
1.38629 1.15524 0.99021 0.86644 0.77016 0.69315 0.34657 0.17328 0.11552 0,086643 0.069315 0,057762 0,049510 0.043322 0.038508
p
28.7569 24.0196 20.6463 18.1242 16.1683 14.6087 7.68485 4.37336 3.34379 2.86159 2.58825 2.41441 2.29507 2.20839 2.14276
1.0
28.7112 23.9738 20.6005 18.0784 16.1225 14.5629 7.63909 4.32760 3.29803 2.81584 2.54248 2.36865 2.24931 2.16264 2.09700
0.9
A
2K6601 23,9227 20.5494 18.0272 16.0714 14,51176 7.58794 4,27645 3,24688 2.76469 2.49133 2.31750 2,19815 2.11148 2.04585
0,8 28.6020 23.8647 20.4914 17.9693 16.0133 14.4538 7.52995 4.21846 3.18888 2.70669 2.43334 2.25951 2.14016 2.05349 1.98786
0.7 28.5351 23.7978 20.4248 17.9023 15.9464 14.3868 7.46300 4.22589 3.12194 2.63975 2.36639 2.19256 2.07321 1.98654 1.92091
0.6 28,4560 23.7186 20.3453 17.8232 15.8672 14.30764 7.38382 4.07233 3.04276 2.56056 2.28721 2.11338 1.99403 1.90736 1.84173
0.5 28.3590 23.6217 20.2484 17.7262 15.7703 14.2107 7.28691 3.97542 2.94585 2.46366 2.19031 2.01647 1.89712 1.81045 1.74483
0,4 28.2341 23.4967 20.1234 17.6013 15.6454 14.0858 7.16198 3.85049 2.82091 2.33874 2.06537 1.89153 1,77218 1.68551 1.61988
0.3
28.0580 23.3206 19.9474 17.4252 15.4693 13.9097 6.98588 3.67439 2.64482 2.16263 1.88928 1.71544 1,59609 1,50942 1.44379
0.2
27.7569 23.0196 19,6463 17.1242 15.1683 13.6086 6.68485 3.37336 2.34379 1.86159 1.58824 1.41441 1.29506 1.20839 1.14276
0.1
For ease of interpolation, values of log N are given rather than N. For values of A greater than 1.0 or Jessthan 0. I, the value of A may be multiplied or divided by I0 and the values of log N increased or decreased by 1.0 accordingly (compare values of log N forA = 1.0 and A = 0.1). The doubling time (h) is equal to ln2/~. The growth rate (generations h - 1) is equal to tHln 2.
0.5 0.6 0.7 0.8 0,9 1.0 2,0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
Doubling time
48 hours
Table 1 (continued)
,2
ra~
O
8
~r
,O
8
D.E. Caldweilet al.
////~ .//"
14
15 12
,,
/
/-1
I0
--
//////////
Ii)
~
5 4
/ per generat/on
/
'S O0
2
I
, ~ 1 3
I 5
4
I 6
I 7
I 8
I 9
I I0
Hours
Fig. 3.Plot of the predicted values for N as a function of time (from Eq. 3). The linear dashed line is for comparison to show that neitherof the curves is linear. the procedures of Bott and Brock (1-4) are used, # is equal to the slope of plots given in Fig. 4 (obtained after converting log N to In N). This assumes that exponential growth is solely responsible for colonization. The error that results from this assumption is given in Table 2. Taking the natural logarithm and rearranging Eq. 3 gives the equation below.
(4) 4
/ 5
~ _ /0hoursper generat/on Z O
._1
2 I
0 0
~* /
~'~..~_ I hourper generation / ce/lper hour
~
I
I
I
I
I
I
I
I
I
I
I
2
5
4
5
6
7
B
9
I0
Hours
Fig. 4. Plot of the predicted valuesfor log N (commonlog) as a functionof time from Eq. 3.
Quantitationof MicrobialGrowth on Surfaces
9
Table 2. Error resulting from the assumption that exponential growth is solely responsiblefor surface colonization Actual doubling time (h)
Apparent /.t (h - l)
Apparent growth rate (h)
Slope taken from 1 to 24 h 1.38629 2.0 0.69315 1.0 0.17328 0.25 0.08664 0.125 0.05776 0.083 0.03850 0.055
0.5 1.0 4.0 8.0 12.0 18.0
1.398 0.723 0.252 0.189 0.170 0.159
2.02 1.04 0.364 0.273 0.246 0.229
Slope taken from 24 to 48 h 1.3863 2.0 0.6932 1.0 0.1733 0.25 0.08664 0.125 0.05776 0.083 0.03850 0.055
0.5 1.0 4.0 8.0 12.0 18.0
1.3863 0.6932 0.1739 0.0915 0.0616 0.0524
2.0 1.0 0.25 0.132 0.0889 0.0756
Actual # (h - 1)
Actual growth rate (h - 1)
Apparent doubling time (h)
0.495 0.961 2.747 3.666 4.067 4.358 0.5 1.0 3.9 7.6 11.2 13.2
% Error of apparent growth rate
1.0 4.0 45.6 118.4 196.0 348.0 0.0 0.0 0.4 5.6 6.8 36.1
Actual growth rates were used to calculate the numberof cells on the surface at any point in time assuming simultaneousattachmentand growth (Eq. 3). The naturallogarithmsof these data wereplotted versustimeand the slope taken as the apparent growth rate constant, /.t. This latter step assumed that colonizationwas due solely to exponentialgrowth and that attachmentcould be ignored. Slopes were takenbetween 1 and 24 h as well as between 24 and 48 h. The attachmentrate had no effect on the apparent value of # and thus is not specified.
This shows that A affects the position of the plot of In N vs. t on the y axis but does not affect the slope. As a result, A does not affect the apparent value oftz and is not specified in Table 2. The main factors affecting the error are the magnitude of t~ and the time interval over which the slope was taken (Table 2). The error can thus be reduced to an acceptable level in ecological systems where # is high (approximately 1 h - t or greater) and where the slope is taken during time intervals between 24 and 48 h rather than between 0 and 24 or between 0 and 48 h. Unfortunately, this requires 48 generations of growth and would thus invalidate numerous assumptions that allow the investigator to ignore the effects of emigration, predation, death, interaction between colonies, and modification of the microenvironment within colonies. As a result, it is not possible to ignore the effects of attachment by assuming that exponential growth is solely responsible for microbial colonization of surfaces. If this assumption is made, estimates of ~u will be erroneous. The error is always an overestimate of # due to the attachment and growth of cells during the incubation period. These cells are assumed to be the progeny of the cells that attached at the beginning of incubation, thus inflating the growth rate. This explains why in situ growth rates on surfaces, determined using the exponential growth equation, have often exceeded the maximum growth rate obtained under optimum laboratory conditions (1). Comparison of Fig. 4 to results obtained in previous studies of microbial surface
10
D.E. Caldwell etaL
growth (1-3) shows that the colonization equation more closely fits the data than does the exponential growth equation:
N = JVo(e"')
(5)
Thus some of the previous studies of microbial growth rate on surfaces have an inherent error due to the method of calculation. However, it is possible to more accurately and conveniently determine growth rates on surfaces using Eq. 3 or Table 1.
Application of the Colonization Equation To obtain the growth rate, the incubation period must be known. In addition, the number of microcolonies and the total number of cells must be determined at the end of the incubation. The area counted is not needed for calculation if the colony and cell counts were obtained from the same number of microscope fields (from the same area). The number of microcolonies is divided by the incubation period to obtain A. Values of A and N are then used to obtain the corresponding value of ~t by interpolation. All ceils included in calculations should belong to one species population based on fluorescent antibody identification (12) or morphological identification (I). However, an " apparent p " for the entire microbial community might be of value in some studies of net microbial activity. Some cells in a population may attach but be unable to form a colony. Therefore, only colonies with two or more cells (assumed to be actively growing) should be included in the determination of both N and A. Unfortunately, this procedure will a/so exclude the cells that attached but have not had sufficient time to divide. This can be corrected by using "preliminary" values of N and A (obtained by excluding all uniceUs) to calculate the number of cells that attached but did not have sufficient time to divide (doubling time multiplied by the attachment rate). The value obtained, N ' , is added to the number of mierocolonies with two or more cells to obtain a corrected value forA, and added to the total number of cells in the microcolonies to obtain N. The new values for A and N are then used to obtain a final corrected value for/a. If the total number of unicells exceeds N ' , then the difference is due to cells that were able to attach but unable to divide. An irradiated control slide cannot be used to obtain A because there would be no way to distinguish these two types of unicells. The assumptions inherent in the proposed determination are that: 1. No emigration occurs (Caulobacter spp., Hyphomicrobium spp., and related organisms are excluded from counts). 2. Low prey densities during initial colonization discourage predation and reduce predation rates to an insignificant level. 3. Six generations after colonization begins, most microcolonies have not deliquesced or emigrated. The incubation is terminated when a colony size of 64 is obtained. 4. During the period of incubation, /a is constant. Thus at the termination of the incubation there must be no contiguous colonies to ensure that the metabolism of neighboring colonies does not cause a change in growth rate. 5. During the period of colonization, A is constant. Thus the number of available attachment sites must greatly exceed the number of organisms attaching. In the
Quantitation of Microbial Growth on Surfaces
1l
final stages of colonization, most of the sites are occupied and consequently the attachment rate is greatly reduced (1). Thus the final density of cells on the surface must be low at the end of incubation. This assumption also implies that the environment (both the surface and the liquid) is in a steady state with a constant density of attaching cells in the liquid, adhering to the surface at a constant rate. If the environment is not constant (non-steady-state), then this assumption may be false and a more complex attachment function required. Preincubation of the surface in sterile-filtered liquid taken from the environment might reduce physicochemical changes in the surface due to adsorption of solutes. 6. Microcolonies with two or more cells are assumed to be growing exponentially whereas those with only one cell are assumed to be either dead, moribund, or growing exponentially. The attachment of dead cell clumps has been shown to be insignificant previously (2, 4). The proposed method is less time consuming than earlier procedures. There is no need for an irradiated control. In addition, it is not necessary to follow the time course of colonization except to verify the proposed equations in new environments. Thus a surface can be submerged and the growth rate calculated from only the number and distribution of cells at the end of incubation. The procedure is more accurate than methods based on the exponential growth equation (4), which overestimates the maximum specific growth rate (1). Its accuracy is comparable to that of the method used by Staley (10). Acknowledgments. Fritz Taylor, Oswald Baca, Wolfgang Krumbein, and Gregory Schiefer are acknowledged for helpful discussions. Larry Belser is acknowledged for review of the manuscript.
References I. Bolt, T. L., and T. D. Brock: Growth rate of Sphaerotilus in a thermally polluted environment. Appl, Microbiol. 19, 100~102 (1970) 2. Bott, T. L., and T. D. Brock: Growth and metabolism of periphytic bacteria: methodology. Limnol. Oceanogr. 15, 333-342 (1970) 3. Bolt, T. L.: Bacterial growth rates and temperature optima in a stream with a fluctuating thermal regime. Limnol. Oceanogr. 20, 191-197 (1975) 4. Brock, T. D.: Microbial growth rates in nature. Bacteriol. Rev. 38, 39-58 (1971) 5. Caldwell, D. E., S. J. Caldwell, and J. M. Tiedje: An ecological study of the sulfur-oxidizing bacteria from the littoral zone of a Michigan Lake and a sulfur spring in Florida. Plant Soil. 43, 101-114 (1975) 6. Caldwell, D. E.: The planktonic microflora of lakes. CRC Crit. Rev. Microbiol. 5, 305-370 (1977) 7. Hirsch, P., and S. H. Pankratz: Study of bacterial populations in natural environments by use of submerged electron microscope grids, Z. Allg. Mikrobiol. 10, 589-605 (1970) 8. Hirsch, P.: New methods for observation and isolation Of unusual or little known water bacteria. In German. Z. Allg. Mikrobiol. 12, 203-218 (1972) 9. Jordan, T. L., and J. T. Staley: Electron microscopic study of succession in the periphyton community of Lake Washington. Microb. Ecol. 2, 241-251 (1976) 10. Staley, J'. M.: Growth rates of algae determined in situ using an immersed microscope. J. Phycol. 7, 13-17 (1971) 11. Sanders, W. M.: Oxygen utilization by slime organisms in continuous culture. Air Water Pollut. Int. J. 10, 253-276 (t966) 12. Schmidt, E. L.: Fluorescent antibody techniques for the study ofmicrobialecology. In: Modern Methods in the Study of Microbial Ecology, Bulletin 17. Ecological Research Committee (Swedish Natural Science Research Council), Stockholm (1973)
MICROBI,4L ECOLOGY
Quantitation of Microbial Growth on Surfaces Douglas E. Caldwell, J Daniel K. Brannan, 1 Marvin E. Morris, 2 and Michael R. Betlach 3 1Departmentof Biology, Universityof New Mexico, Albuquerque, New Mexico87131; 2AppliedBiology and IsotopeUtilizationDivision, Division4535, SandiaNationalLaboratories,Albuquerque, New Mexico 87185; and 3Extraterrestrial ResearchDivision, NASA AmesResearchCenter, MoffettField, California 94035
Abstract. An equation describing the initial phases of microbial surface colonization is presented. Simultaneous microbial attachment and growth are considered as the primary components of colonization. A table is given that permits determination of growth rate from the density and distribution of cells present on surfaces after incubation in situ. Other methods used to calculate microbial growth rate on surfaces are evaluated. The new procedure is more accurate and less time consuming than those used previously. Published data on microbial surface colonization more closely follow the proposed colonization equation than the exponential growth equation, which overestimates the growth rate.
Introduction Although microbial surface growth is important, many assumptions concerning microbial activity in the environment are based solely on studies of planktonic unicells. The attachment of bacteria to surfaces often reduces predation, permits use of adsorbed substrates, and positions cells in favorable environments. Attachment to plant and animal surfaces can result in the shift of diffusion gradients due to the formation of microbial films. This increases the concentration of nutrients within the microenvironment of attached bacteria. Studies of these phenomena in continuous or batch culture are usually difficult or inappropriate, and thus direct studies of surface growth are needed. However, many theories concerning microbial growth and activity in the environment are based solely on batch or continuous culture experiments (6). This is due, in part, to the lack of adequate kinetic data describing microbial growth on surfaces. Continuous culture studies require that isolated populations of free-floating unicells be used. Such studies have provided facts concerning the growth capabilities of many bacteria. However, they have not contributed directly to knowledge of microbial activities in most environments except to define a range of possibilities. Observation of microbial surface growth has been improved using incidence 0095-3628/81/0007-0001 $02.20 (~)1981 Springer-VerlagNew York Inc.
2
D, E. Caldwetl et al,
fluorescence microscopy and electron microscopy (Figs. 1 and 2). As a result, the colonization of numerous natural and artificial surfaces has been studied using these methods (7-9). However, the kinetics of in situ microbial surface colonization have not yet been subjected to the same degree of mathematical analysis as have the kinetics of growth in liquids. This type of analysis is needed if quantitative studies of microbial growth are to be extended to surface environments. Attempts to quantitate microbial growth rates on surfaces have been discussed previously (4). The methods being used result largely from the observation of mierocolonies on glass slides and electron microscope grids (Fig. 1). These show that during the initial phases of colonization the size of colonies tends to cluster around values of 2, 4, 8, 16, 32, and 64 cells. This indicates exponential growth and has resulted in the use of the exponential growth equation to describe microbial surface colonization. This equation is used although exponential growth and linear attachment must simultaneously determine the density of bacteria on surfaces. It has also been observed that most colonies grow at least until they reach 64 cells (6 generations) before emigration or deliquescence occurs (2-4). However, organisms such as Hyphoraicrobium, Hyphoraonas, Caulobacter (Fig. 2), Pedomicrobium, Asticcacaulis, and other stalked and budding genera may not form microcolonies. Their offspring are frequently lost as flagellated cells that colonize sites on other surfaces (1, 4, 9). These genera can be recognized by cell morphology and are largely excluded from studies of in situ growth rate. The size of a single microcolony can be followed as a function of time by using a partially submerged microscope to continuously observe the growth of the colony on a submerged glass slide (10). The growth rate can then be accurately determined (assuming exponential growth) because the incubation period and both the initial and final size of the colony are known. However, this is a difficult procedure that does not readily permit identification using fluorescein-conjugated antibodies or electron microscopy because the cells must be observed continuously as they grow. As a result, this and similar procedures are infrequently used (2). In most investigations, growth rate is determined by plotting the log of the average colony size (or mean number of organisms per colony) versus time (2). The resulting slope is used to obtain #, the specific growth rate. In studies by Bott (3), "the counts on irradiated slides exposed to germicidal U.V. at regular intervals [to allow attachment but not growth] were subtracted from those on unirradiated slides for an estimate of cell numbers resulting from growth alone .... Generation times were determined from plots of the data on semilog paper." The irradiation control assures that the attachment of dead and moribund cells is not mistaken for growth. However, it fails to account for the cells that attach and commence exponential growth after the incubation period has already begun. It is thus assumed that all growing ceils attach at the beginning of the incubation and grow exponentially. The question that remains is' whether estimates of growth obtained in this way suffer seriously from the unstated assumption that the exponential growth equation applies equally well to batch cultures inoculated at time zero and to in situ surfaces that are continuously reinoculated. In an effort to eliminate the error inherent in this assumption, Caldwell et al. (5) embedded microbial populations in thin agar gels. This permitted determination of growth rate without the complicating effects of simultaneous attachment, emigration, and predation. The results of this method are more accurately described by the exponential growth equation than are results obtained from the colonization of slides. However, the environment in an artificial gel is too far removed from most natural situations to be very useful.
Quantitation of Microbial Growth on Surfaces
3
Fig. 1. A microcolony attached to a Formvar-coated electron microscope grid submerged in Vermillion Creek (Rose Lake Recreation Area, Michigan) for 5 days. There are 16 (2 4) cells, indicating that 4 generations have passed since the first cell in the colony attached to the surface. Because the age of the colony (time of attachment) is unknown, the growth rate can not be determined using the exponential growth equation. Transmission electron micrograph. Bar equals 1/zm.
To overcome these problems, a mathematical model is developed in this paper that applies to the colonization of surfaces briefly exposed in situ. It accounts for simultaneous growth and attachment and was devised to permit evaluation of the error inherent in previous estimates of growth rate as well as to provide a more accurate method for use in future studies.
4
D.E. Caldwell et al.
Fig, 2, Caulobacter Sp. attached to a Formvar-coated electron microscoPe grid submerged in Gull Lake (Kellogg Biological Station, Michigan) for 5 days. The parent cell divides by binary fission, leading to the production of flagellated offspring that may leave the surface and attach at other sites. In this genus and in other genera of stalked and budding bacteria, emigration complicates the determination of growth rate on surfaces. Transmission electron micrograph. Barequals 1/am.
Derivation of the Colonization Equation T h e c h a n g e in the density o f bacteria on surfaces is due to numerous factors including a t t a c h m e n t (immigration), emigration, predation, growth, death, interaction between colonies, and modification o f the m i c r o e n v i r o n m e n t within colonies. However, the
Quantitation of MicrobialGrowthon Surfaces
5
analysis of surface colonization can be simplified for initial growth (6 generations or less) on newly exposed surfaces. In this situation, most factors are relatively unimportant compared to the combined effect of attachment and growth. The colonization rate is equal to the growth rate plus the attachment rate. Since growth is exponential and attachment is linear, this gives the following differential equation: dN
--=pN+A
(1)
dt
where: N = number of cells on the surface (cells) /1 = specific growth rate (h- l ) A = attachment rate (cells h - 1) t = time of incubation (h) (N and A must be obtained from the same surface area or number of microscope fields) Integrating Eq. 1:
N
=
+
(eut)
-- --
(2)
/.t Because this equation is valid only during the initial stages of colonization on a newly exposed surface, the initial number of cells (No) is always equal to zero. Thus: N
=
eu t _
_
r~
)
Equation 3 was used to obtain Table 1. This table lists values of/a corresponding to known values of A and N for incubation periods of 24 and 48 h. The table is necessary because it is not possible to solve Eq. 3 for/~. Similar tables for other incubation periods or with smaller increments of A and N (for greater accuracy) can also be obtained using Eq. 3. Modification of Eq. 1 to account for emigration, predation, variable attachment rates, and variable growth rates is possible, but results in unnecessary complexity for studies of the initial phase of colonization. The kinetics of microbial growth in older microbial surface films have been studied extensively in thin-film fermentors and similar systems. Under these conditions the rate of growth is equal to the rate of cell loss due to the sloughing of cells from the surface (11). The kinetics of initial surface colonization in these artificial systems are not analogous to those developed here because the inoculum or " s e e d " is supplied initially but not during the incubation. As a result, initial colonization can be described adequately by assuming simple, exponential growth in these artificial systems (11). This assumption is not adequate for the description of in situ colonization. The validity of the table was confirmed using a computer model of colonization. This model determined values of N assuming that attachment by individual cells occurred at uniform time intervals and that growth occurred exponentially by all attached cells during these intervals. Figure 3 shows the cell number as a function of time predicted by Eq. 3. If growth is rapid compared to attachment, then colonization is nearly exponential (Fig. 4). However, if the reverse is true, then colonization becomes nearly linear (Fig. 3). When
A
0.9
14.2617 11.9327 10.2795 9.04750 8.09509 7.33816 4.02666 2.51476 2.06762 1.86160 1.74466 1.66970 1.61773 1.57961 1.55048
1.0
14.3075 11.9785 10.3253 9.09322 8.14085 7.38392 4.07242 2.56052 2.11338 1.90736 1.79042 1.71546 1.66349 1.62537 1.59624
#
1.38629 1.15524 0.99021 0.86644 0.77016 0.69315 0.34657 0.17328 0.11552 0.08664 0.06931 0.05776 0.04951 0.04332 0.03850
24 hours
Doubling time
0.5 0.6 0.7 0.8 0.9 1.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
14.2106 11.8815 10.2284 8.99631 8.04394 7.28701 3.97551 2.46361 2.01647 1.81045 1.69351 1.61855 1.56658 1.52846 1.49933
0.8 14.1526 11.8236 10.1704 8.93832 7.98595 7.22902 3.91752 2.40562 1.95848 1.75246 1.63552 1.56056 1.50858 1.47047 1.44134
0.7 14.0856 11.7566 10.1034 8.87137 7.91900 7.16207 3.85058 2.37147 1.89153 1.68551 1.56857 1.49361 1.44164 1.40352 1.37439
0.6 14.0065 11.6774 10.0243 8.79219 7.83982 7.08289 3.77139 2.25949 1.81235 1.60633 1.48939 1.41443 1.36246 1.32434 1.29521
0.5 13.9096 11.5805 9.9274 8.69528 7.74291 6.98598 3.67449 2.16258 1.71544 1.50942 1.39248 1.31752 1.26555 1.22743 1.19830
0.4 13.7847 11.4556 9.80242 8.57035 7.61797 6.86104 3.54955 2.03764 1.59050 1.38448 1.26754 1.19258 1.14061 1.10249 1.07336
0.3
Table 1~ Values of log N (after 24 and 48 h) corresponding to values of #(h - 1) and A (cells h - I) as predicted by the colonization equation (Eq. 3)
0.1 13.6086 13.3075 11.2795 10.9785 9.62633 9.3253 8.39425 8.09322 7.44188 7.14085 6.68495 6.38392 3.37346 3.07243 1.86155 1.56052 1.41441 1.11340 1.20839 0.907360 1.09145 0.790420 1.01649 0.715462 0 . 9 6 4 5 1 9 0.663490 0 . 9 2 6 4 0 4 0.625374 0 . 8 9 7 2 7 4 0.596244
0.2
~7 t-n t"3
1.38629 1.15524 0.99021 0.86644 0.77016 0.69315 0.34657 0.17328 0.11552 0,086643 0.069315 0,057762 0,049510 0.043322 0.038508
p
28.7569 24.0196 20.6463 18.1242 16.1683 14.6087 7.68485 4.37336 3.34379 2.86159 2.58825 2.41441 2.29507 2.20839 2.14276
1.0
28.7112 23.9738 20.6005 18.0784 16.1225 14.5629 7.63909 4.32760 3.29803 2.81584 2.54248 2.36865 2.24931 2.16264 2.09700
0.9
A
2K6601 23,9227 20.5494 18.0272 16.0714 14,51176 7.58794 4,27645 3,24688 2.76469 2.49133 2.31750 2,19815 2.11148 2.04585
0,8 28.6020 23.8647 20.4914 17.9693 16.0133 14.4538 7.52995 4.21846 3.18888 2.70669 2.43334 2.25951 2.14016 2.05349 1.98786
0.7 28.5351 23.7978 20.4248 17.9023 15.9464 14.3868 7.46300 4.22589 3.12194 2.63975 2.36639 2.19256 2.07321 1.98654 1.92091
0.6 28,4560 23.7186 20.3453 17.8232 15.8672 14.30764 7.38382 4.07233 3.04276 2.56056 2.28721 2.11338 1.99403 1.90736 1.84173
0.5 28.3590 23.6217 20.2484 17.7262 15.7703 14.2107 7.28691 3.97542 2.94585 2.46366 2.19031 2.01647 1.89712 1.81045 1.74483
0,4 28.2341 23.4967 20.1234 17.6013 15.6454 14.0858 7.16198 3.85049 2.82091 2.33874 2.06537 1.89153 1,77218 1.68551 1.61988
0.3
28.0580 23.3206 19.9474 17.4252 15.4693 13.9097 6.98588 3.67439 2.64482 2.16263 1.88928 1.71544 1,59609 1,50942 1.44379
0.2
27.7569 23.0196 19,6463 17.1242 15.1683 13.6086 6.68485 3.37336 2.34379 1.86159 1.58824 1.41441 1.29506 1.20839 1.14276
0.1
For ease of interpolation, values of log N are given rather than N. For values of A greater than 1.0 or Jessthan 0. I, the value of A may be multiplied or divided by I0 and the values of log N increased or decreased by 1.0 accordingly (compare values of log N forA = 1.0 and A = 0.1). The doubling time (h) is equal to ln2/~. The growth rate (generations h - 1) is equal to tHln 2.
0.5 0.6 0.7 0.8 0,9 1.0 2,0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0
Doubling time
48 hours
Table 1 (continued)
,2
ra~
O
8
~r
,O
8
D.E. Caldweilet al.
////~ .//"
14
15 12
,,
/
/-1
I0
--
//////////
Ii)
~
5 4
/ per generat/on
/
'S O0
2
I
, ~ 1 3
I 5
4
I 6
I 7
I 8
I 9
I I0
Hours
Fig. 3.Plot of the predicted values for N as a function of time (from Eq. 3). The linear dashed line is for comparison to show that neitherof the curves is linear. the procedures of Bott and Brock (1-4) are used, # is equal to the slope of plots given in Fig. 4 (obtained after converting log N to In N). This assumes that exponential growth is solely responsible for colonization. The error that results from this assumption is given in Table 2. Taking the natural logarithm and rearranging Eq. 3 gives the equation below.
(4) 4
/ 5
~ _ /0hoursper generat/on Z O
._1
2 I
0 0
~* /
~'~..~_ I hourper generation / ce/lper hour
~
I
I
I
I
I
I
I
I
I
I
I
2
5
4
5
6
7
B
9
I0
Hours
Fig. 4. Plot of the predicted valuesfor log N (commonlog) as a functionof time from Eq. 3.
Quantitationof MicrobialGrowth on Surfaces
9
Table 2. Error resulting from the assumption that exponential growth is solely responsiblefor surface colonization Actual doubling time (h)
Apparent /.t (h - l)
Apparent growth rate (h)
Slope taken from 1 to 24 h 1.38629 2.0 0.69315 1.0 0.17328 0.25 0.08664 0.125 0.05776 0.083 0.03850 0.055
0.5 1.0 4.0 8.0 12.0 18.0
1.398 0.723 0.252 0.189 0.170 0.159
2.02 1.04 0.364 0.273 0.246 0.229
Slope taken from 24 to 48 h 1.3863 2.0 0.6932 1.0 0.1733 0.25 0.08664 0.125 0.05776 0.083 0.03850 0.055
0.5 1.0 4.0 8.0 12.0 18.0
1.3863 0.6932 0.1739 0.0915 0.0616 0.0524
2.0 1.0 0.25 0.132 0.0889 0.0756
Actual # (h - 1)
Actual growth rate (h - 1)
Apparent doubling time (h)
0.495 0.961 2.747 3.666 4.067 4.358 0.5 1.0 3.9 7.6 11.2 13.2
% Error of apparent growth rate
1.0 4.0 45.6 118.4 196.0 348.0 0.0 0.0 0.4 5.6 6.8 36.1
Actual growth rates were used to calculate the numberof cells on the surface at any point in time assuming simultaneousattachmentand growth (Eq. 3). The naturallogarithmsof these data wereplotted versustimeand the slope taken as the apparent growth rate constant, /.t. This latter step assumed that colonizationwas due solely to exponentialgrowth and that attachmentcould be ignored. Slopes were takenbetween 1 and 24 h as well as between 24 and 48 h. The attachmentrate had no effect on the apparent value of # and thus is not specified.
This shows that A affects the position of the plot of In N vs. t on the y axis but does not affect the slope. As a result, A does not affect the apparent value oftz and is not specified in Table 2. The main factors affecting the error are the magnitude of t~ and the time interval over which the slope was taken (Table 2). The error can thus be reduced to an acceptable level in ecological systems where # is high (approximately 1 h - t or greater) and where the slope is taken during time intervals between 24 and 48 h rather than between 0 and 24 or between 0 and 48 h. Unfortunately, this requires 48 generations of growth and would thus invalidate numerous assumptions that allow the investigator to ignore the effects of emigration, predation, death, interaction between colonies, and modification of the microenvironment within colonies. As a result, it is not possible to ignore the effects of attachment by assuming that exponential growth is solely responsible for microbial colonization of surfaces. If this assumption is made, estimates of ~u will be erroneous. The error is always an overestimate of # due to the attachment and growth of cells during the incubation period. These cells are assumed to be the progeny of the cells that attached at the beginning of incubation, thus inflating the growth rate. This explains why in situ growth rates on surfaces, determined using the exponential growth equation, have often exceeded the maximum growth rate obtained under optimum laboratory conditions (1). Comparison of Fig. 4 to results obtained in previous studies of microbial surface
10
D.E. Caldwell etaL
growth (1-3) shows that the colonization equation more closely fits the data than does the exponential growth equation:
N = JVo(e"')
(5)
Thus some of the previous studies of microbial growth rate on surfaces have an inherent error due to the method of calculation. However, it is possible to more accurately and conveniently determine growth rates on surfaces using Eq. 3 or Table 1.
Application of the Colonization Equation To obtain the growth rate, the incubation period must be known. In addition, the number of microcolonies and the total number of cells must be determined at the end of the incubation. The area counted is not needed for calculation if the colony and cell counts were obtained from the same number of microscope fields (from the same area). The number of microcolonies is divided by the incubation period to obtain A. Values of A and N are then used to obtain the corresponding value of ~t by interpolation. All ceils included in calculations should belong to one species population based on fluorescent antibody identification (12) or morphological identification (I). However, an " apparent p " for the entire microbial community might be of value in some studies of net microbial activity. Some cells in a population may attach but be unable to form a colony. Therefore, only colonies with two or more cells (assumed to be actively growing) should be included in the determination of both N and A. Unfortunately, this procedure will a/so exclude the cells that attached but have not had sufficient time to divide. This can be corrected by using "preliminary" values of N and A (obtained by excluding all uniceUs) to calculate the number of cells that attached but did not have sufficient time to divide (doubling time multiplied by the attachment rate). The value obtained, N ' , is added to the number of mierocolonies with two or more cells to obtain a corrected value forA, and added to the total number of cells in the microcolonies to obtain N. The new values for A and N are then used to obtain a final corrected value for/a. If the total number of unicells exceeds N ' , then the difference is due to cells that were able to attach but unable to divide. An irradiated control slide cannot be used to obtain A because there would be no way to distinguish these two types of unicells. The assumptions inherent in the proposed determination are that: 1. No emigration occurs (Caulobacter spp., Hyphomicrobium spp., and related organisms are excluded from counts). 2. Low prey densities during initial colonization discourage predation and reduce predation rates to an insignificant level. 3. Six generations after colonization begins, most microcolonies have not deliquesced or emigrated. The incubation is terminated when a colony size of 64 is obtained. 4. During the period of incubation, /a is constant. Thus at the termination of the incubation there must be no contiguous colonies to ensure that the metabolism of neighboring colonies does not cause a change in growth rate. 5. During the period of colonization, A is constant. Thus the number of available attachment sites must greatly exceed the number of organisms attaching. In the
Quantitation of Microbial Growth on Surfaces
1l
final stages of colonization, most of the sites are occupied and consequently the attachment rate is greatly reduced (1). Thus the final density of cells on the surface must be low at the end of incubation. This assumption also implies that the environment (both the surface and the liquid) is in a steady state with a constant density of attaching cells in the liquid, adhering to the surface at a constant rate. If the environment is not constant (non-steady-state), then this assumption may be false and a more complex attachment function required. Preincubation of the surface in sterile-filtered liquid taken from the environment might reduce physicochemical changes in the surface due to adsorption of solutes. 6. Microcolonies with two or more cells are assumed to be growing exponentially whereas those with only one cell are assumed to be either dead, moribund, or growing exponentially. The attachment of dead cell clumps has been shown to be insignificant previously (2, 4). The proposed method is less time consuming than earlier procedures. There is no need for an irradiated control. In addition, it is not necessary to follow the time course of colonization except to verify the proposed equations in new environments. Thus a surface can be submerged and the growth rate calculated from only the number and distribution of cells at the end of incubation. The procedure is more accurate than methods based on the exponential growth equation (4), which overestimates the maximum specific growth rate (1). Its accuracy is comparable to that of the method used by Staley (10). Acknowledgments. Fritz Taylor, Oswald Baca, Wolfgang Krumbein, and Gregory Schiefer are acknowledged for helpful discussions. Larry Belser is acknowledged for review of the manuscript.
References I. Bolt, T. L., and T. D. Brock: Growth rate of Sphaerotilus in a thermally polluted environment. Appl, Microbiol. 19, 100~102 (1970) 2. Bott, T. L., and T. D. Brock: Growth and metabolism of periphytic bacteria: methodology. Limnol. Oceanogr. 15, 333-342 (1970) 3. Bolt, T. L.: Bacterial growth rates and temperature optima in a stream with a fluctuating thermal regime. Limnol. Oceanogr. 20, 191-197 (1975) 4. Brock, T. D.: Microbial growth rates in nature. Bacteriol. Rev. 38, 39-58 (1971) 5. Caldwell, D. E., S. J. Caldwell, and J. M. Tiedje: An ecological study of the sulfur-oxidizing bacteria from the littoral zone of a Michigan Lake and a sulfur spring in Florida. Plant Soil. 43, 101-114 (1975) 6. Caldwell, D. E.: The planktonic microflora of lakes. CRC Crit. Rev. Microbiol. 5, 305-370 (1977) 7. Hirsch, P., and S. H. Pankratz: Study of bacterial populations in natural environments by use of submerged electron microscope grids, Z. Allg. Mikrobiol. 10, 589-605 (1970) 8. Hirsch, P.: New methods for observation and isolation Of unusual or little known water bacteria. In German. Z. Allg. Mikrobiol. 12, 203-218 (1972) 9. Jordan, T. L., and J. T. Staley: Electron microscopic study of succession in the periphyton community of Lake Washington. Microb. Ecol. 2, 241-251 (1976) 10. Staley, J'. M.: Growth rates of algae determined in situ using an immersed microscope. J. Phycol. 7, 13-17 (1971) 11. Sanders, W. M.: Oxygen utilization by slime organisms in continuous culture. Air Water Pollut. Int. J. 10, 253-276 (t966) 12. Schmidt, E. L.: Fluorescent antibody techniques for the study ofmicrobialecology. In: Modern Methods in the Study of Microbial Ecology, Bulletin 17. Ecological Research Committee (Swedish Natural Science Research Council), Stockholm (1973)
