Colonization of a smooth surface by Pseudomanas aeruginosa : image analysis methods by Andreas R Escher A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering Montana State University © Copyright by Andreas R Escher (1986) Abstract: Primary adsorption of bacteria to a clean substratum has generally been described by measuring net accumulation. Thus, the independent processes that contribute to the overall accumulation of biofilm, such as adsorption, desorption, cell multiplication, and erosion, cannot be considered separately to help to elucidate mechanisms of early colonization. With the use of image analysis techniques and additional software, these individual processes at the substratum in a continuous flow system have been measured directly. Additional parameters, such as cell movement and direction, orientation of the colony forming units (CFU), spatial distribution at the surface, and shape are also quantified with this technique. With the continuous flow system, the influences of operational parameters such as fluid shear stress, the bulk properties of the fluid, and the characteristic of the substratum can also be delineated in a fundamental manner. Two experimental variables, bulk CFU concentration and shear stress have been used to investigate early colonization under different conditions and to determine the rate controlling factor in biomass accumulation. In addition, a novel method for quantitative analysis of spatial distribution has been developed. It was found that adsorption and desorption rates are independent of the surface concentration whereas growth and surface related processes are independent of bulk concentrations. At low surface concentration, P. aeruginosa tend to adsorb randomly. With increase in surface concentration the spatial distribution of adsorbing CFU becomes uniform indicating a formation of a repulsing area around adsorbed cells.  COLONIZATION OF A SMOOTH SURFACE BY PSEUDOMONAS AERUGINOSA: IMAGE ANALYSIS METHODS by Andreas R. Escher A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Civil Engineering Montana State University Bozeman, Montana December 1986 i D37% i - v s / f p ii APPROVAL of thesis submitted by Andreas R- Escher This thesis has been read by each member of the thesis committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and is ready for submission to the College of Graduate Studies. z Date Chairperson, Graduate Committee Approved for the Major Department Date r Approved for the College of Graduate Studies Date Graduate Dean ill STATEMENT OF PERMISSION TO USE In presenting this thesis in partial fulfillment of the requirements for a doctoral degree at Montana State University, I agree that the Library shall make it available to borrowers under the rule of the Library. I further agree that copying of the thesis is allowable only for scholarly purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. Requests for extensive copying or reproduction of this thesis should be referred to University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan 48106, to whom I have granted "the right to reproduce and distribute copies of the dissertation in and from microfilm and the right to reproduce and distribute by abstract in any format." Date: / 2 / Z 2 / Signature: TABLE OF CONTENTS Page LIST OF TABLES ........................................ . vii LIST OF FIGURES ..................... viii ABSTRACT.................... I ................. . . . . xii INTRODUCTION .......................................... I Relevance o£ Blofilma........... . I Previous Research . -.............. 3 Goal of Research.................... 5 Objectives of Research . . . . G BACKGROUND ...................................... 7 Process Analysis . . . . . . . . ........ . . . . 7 Transport ...................... 10 Transport and Adsorption to the Substratum . . 11 Diffusivity .................. . . . . . 11 Transport Rate to the Substratum . . . . 13 Assay for Substratum Properties.......... 14 Growth-Related Processes ..................... 16 Spatial Distribution . 18 Fluid Dynamics...................... 19 Turbulent F l o w ................................ 19 Laminar F l o w .................................. 21 CONCEPTUAL MODEL OF SURFACE COLONIZATION .............. 23 Population Balance in Terms of C F U ................ 23 Transport . . . . . 23 Adsorption........................ 25 • Reversible versus Irreversible Adsorption . . 25 Desorption .................... 27 CFU-Separation ...................... 28 Other Processes at the Substratum............ 28 Population Balance in Terms of Cells ............ 29 Multiplication and Erosion .................. 29 Kinetic Expressions in Terms of CFU '. . .............. 30 Transport from Bulk Flow to Substratum . . . . 31 Population Balance at Substratum . . 34 Kinetic Expressions in Terms of Cells ............ 37 Transport from Bulk to Substratum . . . . . . 38 Population Balance at Substratum ............ 39 Sticking Efficiency .............................. 42 Summary of the Conceptual Model ........ . . . . . 43 Table o£ Contents (continued) EXPERIMENTAL SYSTEM AND METHODS . . . . . . . 44 Experimental System .............................. 44 Image Analyzer............ 46 Modification of the Programs...................... 47 Data Collection and Analysis...................... 48 Image Collection . . 48 Fixpoint Calculation ........................ 50 Image Analysis................................ 50 Data Assembly................................ 51 Method of Analysis and Chemostat Operation . . . . 54 Direct Cell C o u n t .................... 54 Cell Size Distribution ............ 55 Mounting of Capillary Tube ..................... 56 Chemostat Operation .............................. 56 RESULTS .................... 58 Progression of Experiments . . . . . . . . . . . . 58 Kinetic Results ................ . . . . . . . . . 63 Directly Measured Results ............. . . . 63 Derived R e s u l t s ............. 74 Behavioral Distribution ̂ ...........78 Residence Time . . . . . . . . . . . 79 Orientation of CFU During Adsorption . . . . . 81 Motility at Substratum . . . . . . 82 Cell Number per CFU .................... 85 Spatial Distribution of CFU during Adsorption . . . 85 DISCUSSION .................................... . . . . . 89 Sorption-Related Processes ...................... 89 Offset Time of Desorption............ 95 Growth Related Processes ........................ 96 CFU-Separation . . . . . . . . . . 96 Multiplication Rates ........................ 97 Erosion ....................................... 98 Summary of Kinetic Results ...................... 100 Simulation with the Kinetic Results . . . . . 102 Spatial Distribution ............................ 105 CONCLUSION............................................. 108 NOMENCLATURE/SYMBOLS'. ............................ 109 Nomenclature..................................... H O Symbols .................................... Ill v Table o£ Contents (continued) Page LITERATURE CITED 113 Vi Table o£ Contents (continued) APPENDICES........................................ 117 APPENDIX A ...................................... .. THEORY OF SPATIAL DISTRIBUTION . ............ 118' SPATIAL DISTRIBUTION ......................... 119 No Influence.......................... 120 Positive Influence . .................... 120 Negative Influence . .................... 120 THEORY OF QUANTITATIVE SPATIAL DISTRIBUTION . 121 Spatial Interaction Indices ............. 122 Relative Nearest Neighbor Distance . 122 Relative Influence Number . . . . . 124 CALIBRATION OF SPATIAL DISTRIBUTION . . . . . 125 TEST OF THE SPATIAL DISTRIBUTION............. 131 Uniform Test Distribution ............... 132 Aggregated Test Distribution 1........ 133 Aggregated Test Distribution 2........ 135 Conclusion of the Test Distributions . . 137 APPENDIX B .................. •................ . 139 ORGANIZATION OF DATA FILES................... 139 Data Organization.................... 140 APPENDIX C . . . 144 TABLES OF DIRECTLY MEASURED RESULTS ...........144 APPENDIX D ........................................ 160 FIGURES OF KINETIC RESULTS . . . . 160 APPENDIX E ........................................ 191 TABLES OF DERIVED RESULTS . . . . . . . . . . 191 APPENDIX F .......................... . . . . . . 200 DISTRIBUTIONS OF "BEHAVIORAL" CHARACTERISTICS 200 APPENDIX G ............................. 215 . RESULTS OF SPATIAL DISTRIBUTIONS ............ 215 Page n] on vii 1. Summary o£ directly measured rates at 0.5 N m""2 shear stress........................................ 67 2. Summary of directly measured rates at 0.75 and 1.0 N m™2................. 68 3. Summary of directly measured rates at 1.25 N m-2. . 69 4. Summary of derived rates calculated for 0.5 N m"2. 74 5. Summary of derived rates calculated for 0.75 N m-2.......................................... 75 Summary of derived rates calculated for 1.0 N m~2. 75 Summary of derived rates calculated for 1.25 N m "2................. 75 8. Residence time probability for reversibly adsorbed CFU under different shear stresses. . . . . . . . . 94 9. Directly measured results of series AAl. . ........ 145 10. Directly measured results of series AA2. . . . . . 146 11. Directly measured results of series AA3............. 147 12. Directly measured results of series AA4............. 148 13. Directly measured results of series ABl. . . . . . 149 14. Directly measured results of series AB2........... 150 15. Directly measured results of series AB3............. 151 16. Directly measured results of series AB4............. 152 17. Directly measured results of series AB5. ........ 153 18. Directly measured results of series AB6............. 154 19. Directly measured results of series ACl............. 155 20. Directly measured results of series AC2............. 156 21. Directly measured results of series AC3J ........ 157 22. Directly measured results of series AC4............. 158 23. Directly measured results of series AC5............. 159 24. Derived results of series AAl................... . 192 25. Derived results of series AA2............. 192 26. Derived results of series, AA3............. 193 27. Derived results of series AA4..................... 193 28. Derived results of series ABl....................... 194 29. Derived results of series AB2.- 194 30. Derived results of series AB3. . 195 31. Derived results of series AB4. . . . . . . 195 32. Derived results of series AB5........... 196 33. Derived results of series AB6. .................... 196 34. Derived results of series ACl. 197 35. Derived results of series AC2..................... 197 36. Derived results of series AC3....................... 198 37. Derived results of series AC4..................... 198 38. Derived results of series AC5....................... 199 LIST OF TABLES Table Page N) H viii Experimental data from Powell and Slater (1983) . . 4 Definition of processes during early colonization of a substratum. ................................. 8 3. Schematic of the system. 45 4. Tracking Image. 1.0 N m™2 , IOe- cells/ml........ 49 5. Tracking Image: 0.5 N m~2 , !.I-IOs CFU ml-"1 . . . . 59 6. Tracking Image: 0.5 N m™2, IO-IOs CFU ml"1 . . . . 60 7. Tracking Image: 1.25 N m”2, 12.2-10® CFU ml"1 . . . 61 8. Typical progression of colonization .............. 64 9. Adsorption rates plotted against cell concentration in the bulk f l o w .................. 70 10. Desorption rates plotted against cell concentration.................................... 71 11. CFU-separation as a first order rate plotted against cell concentration ......................... 72 12. First order rate coefficient for cell multiplication (12a) and cell erosion (12b) . . . . 73 13. Correlation between desorption and adsorption at 0.5 N/m2 .......................................... 76 14. Correlation between erosion and multiplication at 0.5 N/m2 ........................................... 76 15. Correlation between offset time and bulk CFU concentration .................................... 77 16. Residence time distribution Series AA (0.5 N m”2) . 80 17. Orientation of adsorbing CFU . . . . . 82 18. Integrated movement at substratum ................ 83 19. Cells per CFU (Series AA) .......................... 84 20. Spatial distribution of adsorbing CFU ............ 88 21. Sticking efficiency $ .............................. 90 22. Surface-particle capture factor € for CFU . . . . . 92 23. Surface-particle capture factor € for cells . . . . 92 24. Probability of desorption of C F U ........ 93 25. Probability of desorption in terms of cell . . . . 93 26. Comparison of residence time of reversibly1 adsorbed CFU as a function of shear stress . . . . 94 27. CFU-separation rates ............................ 97 28. Multiplication rates of cells............ 99 29. Erosion rates of cells within colonies .......... 99 30. Probability of erosion of cells................. 100 31. Simulation of accumulation of cells under constant shear s t r e s s ................ 103 32. Simulation of accumulation of cells under constant CFU concentration.................... 104 LIST OF FIGURES Figure Page Figure Page 33. Example of a true random distribution for calibration ........................................ 127 34. Example of a uniform distribution for calibration . 127 35. Example of aggregated distribution for calibration 128 35. Frequency contour plot of the calibration distributions . ................................ . . 129 36. Frequency contour plot (Figure 35) displayed in linear scaling ................................... 130 37. Example of a uniform test distribution........... 132 38. Frequency contour plot of the uniform test distribution .................................... 133 39. Example of aggregated test distribution I ......... 134 40. Frequency contour plot of aggregated test distribution I ................................... 135 41. Example of aggregated test distribution 2 . . . . . 136 42. Frequency contour plot of aggregated test distribution 2 ............. .................... 137 43. Progression of colonization (Series AM) in terms of CFU (a) and area coverage (b)..................161 44. Progression in terms of cells (Series AM) . . . . 162 45. Progression of colonization (Series AA2) in terms of CFU (a) and area coverage ( b ) ................. 163 46. Progression in terms of cells (Series AA2) . . . . 164 47. Progression of colonization (Series AA3) in terms of CFU (a) and area coverage (b) ................ 165 48. Progression in terms of cells (Series AA3) . . . . 166 49. Progression of colonization (Series AA4) in terms of CFU (a) and area coverage ( b ) .......... .. 167 50. Progression in terms of cells (Series AA4) . . . . 168 51. Progression of colonization (Series ABl) in terms of CFU (a) and area coverage (b) ................. 169 52. Progression in terms of cells (Series ABl) . . . . 170 53. Progression of colonization (Series AB2) in terms of CFU (a) and area coverage (b) .................171 54. Progression in terms of cells (Series AB2) . . . . 172 55. Progression of colonization (Series AB3) in terms of CFU (a) and area coverage ( b ) ................ 173 56. Progression in terms of cells (Series AB3) . . . . . 174 57. Progression of colonization (Series AB4) in terms of CFU (a) and area coverage ( b ) ................ 175 58. Progression in terms of cells (Series AB4) . . . ,. 176 59. Progression of colonization (Series AB5) in terms of CFU (a) and area coverage (b) . . . . . . . . . 177 60. Progression in terms of cells (Series AB5) . . . . 178 61. Progression of colonization (Series AB6) in terms of CFU (a) and area coverage ( b ) ................ 179 ix List of Figures (continued) X Figure Page 62. Progression in terms of cells (Series AB6) . . . . 180 S3. Progression of colonization (Series ACl) in terms of CFU (a) and area coverage (b) ............ 181 64. Progression in terms of cells (Series ACl) . . . . 182 65. Progression of colonization (Series AC2) in terms of CFU (a) and area coverage (b) . . . . . . . . . 183 66. Progression in terms of ceils (Series AC2) . . . . 184 67. Progression of colonization (Series AC3) in terms of CFU (a) and area coverage ( b ) ............ 185 68. Progression in terms of cells (Series AC3J . . . . 186 69. Progression of colonization (Series AC4) in terms of CFU (a) and area coverage ( b ) ............ 187 70. Progression in terms of cells (Series AC4) . . . . 188 71. Progression of colonization (Series AC5) in terms of CFU (a) and area coverage (b) 189 72. Progression in terms of cells (Series AC5) . . . . 190 73. Residence time distribution Series AA (0.5 N m™-8 ) . 201 74. Residence time distribution (0.75 N m-2 ) .... 202 75. Residence time distribution (1.0 N m"2 ) ...... 203 76. Residence time distribution (1.25 N m""2 ) . . . . . 204 77. Orientation of CFU after adsorption. Shear, stress: 0.5 N/m2 ................................. 205 78. Orientation of CFU after adsorption. Shear stress: 0.75 N/m2 ................................. 205 79. Orientation of CFU after adsorption. Shear stress: 1.0 N/m2 ................................. 206 80. Orientation of CFU after adsorption. Shear stress: 1.25 N/m2 ................................. 206 SI. Integrated movement at substratum (Series AA, 0.5 N m--2 > ...................... ,...............207 82. Integrated movement at substratum (0.75 N m-"2 ) . . 208 83. Integrated movement at substratum (1.0 N m"-2 ) . . . 209 84. Integrated movement at substratum (1.25 N m"2) . . 210 85. Cells per CFU (Series AAr 0.5 N m™2 ) 211 86. Cells per CFU ( 0.75 N, m"2 ) .............. 212 87. Cells per CFU ( I .0 N m"2 ) 213 88. Cells per CFU ( 1.25 N m~-2> .............. 214 89. Spatial distribution of adsorbing CFUr Series AAl . 216 90. Spatial distribution of adsorbing CFUr Series AB3 . 217 91. Spatial distribution of adsorbing CFU, Series AA4 . 218 92. Spatial distribution of adsorbing CFUr Series AB2 . 219 93. Spatial distribution of adsorbing CFUr Series AA3 . 220 94. Spatial distribution of adsorbing CFUr Series AC2 . 221' 95. Spatial distribution of adsorbing CFU, Series ACl . 222 96. Spatial distribution of adsorbing CFUr Series ABl . 223 97. Spatial distribution of adsorbing CFUr Series AA2 . 224 List of Figures (continued) xi List of Figures (continued) Figure 98. Spatial distribution of adsorbing CFU, Series AB4 Page 22599. Spatial distribution of adsorbing CFU, Series AC3 226100. Spatial distribution distribution of adsorbing CFU, Series AB5 227101 . Spatial of adsorbing CFU, Series AC4 228102. Spatial distribution of adsorbing CFU, Series ABG 229103. Spatial distribution of adsorbing CFU, Series AC5 230 xii ABSTRACT Primary adsorption of bacteria to a clean substratum has generally been described by measuring net accumulation. Thus, the independent processes that contribute to the overall accumulation of biofilm, such as adsorption, desorption, cell multiplication, and erosion, cannot be considered separately to help to elucidate mechanisms of early colonization. ■ With the use of image analysis techniques and additional software, these individual processes at the substratum in a continuous flow system have been measured directly. Additional parameters, such as cell movement and direction, orientation of the colony forming units (CFU), spatial distribution at the surface, and shape are also quantified with this technique. With the continuous flow system, . the influences of operational parameters such as fluid shear stress, the bulk properties of the fluid, and the characteristic of the substratum can also be delineated in a fundamental manner. Two experimental variables, bulk CFU concentration . and shear stress have been used to investigate early colonization under different conditions and to determine the rate controlling factor in biomass accumulation. In addition, a novel method for quantitative analysis of spatial distribution has been developed. It was found that adsorption and desorption rates are independent of the surface concentration whereas growth and surface related processes are independent of bulk concentrations. At low surface concentration, P. aeruginosa tend to adsorb randomly. With increase in surface concentration the spatial distribution of adsorbing CFU becomes uniform indicating a formation of a repulsing area around adsorbed cells. I INTRODUCTION Microbial cells attach f irmly to almost any surface submerged in aquatic environments. The immobilized cells grow, reproduce, and produce extracellular polymers which extend from the cell forming a matrix of molecular fibers which provide structure to the assemblage termed a biofilm. Biofilms are sometimes distributed relatively evenly over the wetted surface . and other times are quite "patchy" in appearance. Biofilms can consist of a monolayer of cells covering only a fraction of the substratum or can be 300- 400 mm thick as observed in algal mats. Biofilms are generally heterogenous, frequently containing more than one distinct microbial environment. For example, biofilms with aerobic as well as anaerobic environments are frequently observed. Consequently, the term biofilm does not necessarily reflect a surface accumulation which is uniform in time and/or space. Relevance of Biofilms Biofilms serve beneficial purposes in the natural environment as well as in some modulated or engineered biological systems. Biofilms are responsible for removal of 2 contaminants from natural streams and in wastewater treatment plants. Biofilms in natural waters frequently control water quality by influencing dissolved oxygen levels and serve as a sink for many toxic and/or hazardous materials. Blofilm reactors are used in some common fermentation processes (e.g. "guick" vinegar process) and are being considered more frequently for biotechnological applications. On the negative side biofilms result in fouling. Fouling is the accumulation of a deposit on equipment surfaces which result in decreased performance and/or reduced equipment lifetime. Biofilms have been observed to increase fluid, frictional resistance in water conduits and on ship hull surfaces. Microbial (as opposed to macrobial) films can significantly increase drag of a ship. Biofilm accumulation in pipes has been observed to reduce the flow rate by as much as 50% even when the film thickness was 0.1% of the pipe diameter (Characklis, 1973). Biofouling deposits decrease heat transfer in power plant condensers on shipboard as well as in land based power plants (Turakhia and Characklis, 1984). As a result, the power plant consumes more fuel to produce the same amount of power. The accumulation of biofilms has also been linked with accelerated corrosion of metallic surfaces, deterioration of 3 wooden structures, and degradation of concrete structures. Reduced performance may be observed in many other ways. For a better understanding of biofilma it is essential not only to study fully developed biofilms but also the mechanisms of the buildup, i.e. the early colonization of surfaces.by bacteria, the separation between adsorption and desorption, and between other, growth related processes. Previous Research Much of the emphasis on adsorption of microbial cells has concentrated on biological and chemical aspects of mechanisms with little emphasis on physical factors in the environment or concern about the rate of adsorption. Nor has much consideration been given to the influence of the initial events on the extent of subsequent biofilm accumulation or the biofilm composition. In most, if not all reported research on microbial cell adsorption, net cell accumulation at the substratum is observed (Figure I). Most of the microbial adsorption research has been conducted in quiescent (i.e., fluid velocity equals zero), closed (i.e., no input or output flows) systems. Such systems create a significant number of 4 2500 2 000 Time (min) Figure I. Experimental data from Powell and Slater (1983) for adsorption of Bacillus cereus to the surface of clean glass at a shear stress of 0.075 N m--1 and temperature of 53* C. The straight line represents the theoretical adsorption rate for non-motile cells calculated from Bowen et aI. (1979). experimental artifacts leading to rate data which are irrelevant to environmental and/or technical applications. Thus, open, continuous flow experimental systems will be described. The initial events in the accumulation of cells at the substratum consist of the following steps, each occurring with a characteristic rate: I- Transport of the cell from the liquid phase to the substratum. 5 2. Cell adsorption to the substratum, a direct substratum-partide interaction. 3. Desorption of some of the adsorbed cells and ,their reentrainment in the liquid phase. 4. In some cases, microbial reproduction may contribute to the initial events. These processes occur either in parallel or in series and, thus, the overall rate of cell accumulation at the substratum will be determined by the combination of the different rates. Variables such as fluid shear stress. liquid phase cell density. and nutrient concentration influence each individual process rate to a different extent and, therefore, influence net cell accumulation. Consequently, the process for cell accumulation in a tube enclosing turbulent flow will be very different from the one for a glass slide immersed in quiescent water, even though the net rate of accumulation may appear to be equal in both cases. Therefore, a closer look at each process is essential to develop a useful, predictive model for cell adsorption. Goal of Research The goal of the research is to determine the influence of different independent parameters, such as fluid dynamics. 6 biomass concentration in the bulk flow, surface characteristics (interface free energy), and cell physiology on early colonization of surfaces. Objectives of Research The specific objectives of the research related to early colonization of substrata are as follows: 1. Develop a method to directly measure the rate of different processes contributing to colonization. 2. Develop a method to observe individual “behavioral" •L characteristics of the organisms at the substratum for elucidating mechanisms contributing to early colonization of surfaces. 3. Derive a mathematical model describing the accumulation of biomass during the early stage of biofilms accumulation. ± "Behavioral" characteristics include all the characteristics which can be observed but are not part of the kinetic system, such as shape, orientation, gliding at, the substratum, and more. 7 BACKGROUND Process Analysis During the early events of fouling, biomass can be expressed as colony forming units (CFU), or, cells. This distinction is essential since cells can adsorb in groups or as single cells. Moreover, not all the cells accumulate at the surface through transport alone. Cells can be produced at the substratum (growth), the number of cells per colony can change with time, or cells may glide away from their colony of origin to form a new colony. The following four processes must be distinguished (Figure 2) in terms of CFU: Transport: This process is responsible for carrying the CFU to a point adjacent to the substratum. This step does not include the adsorption process. Adsorption: This process is defined as the linking of the CFU with the substratum. The cell is adsorbed to the substratum only if it has a linkage to it and, hence, becomes immobilized for a finite time. Desorption: Desorption is the breaking of the linkage of the CFU and its complete removal from the substratum. Desorption is the reverse of adsorption. CFU - Separation: A CFU with more than one cell can split into two independent CFU. This process forms a new CFU at the substratum and, hence, contributes to the accumulation of CFU at the substratum. CFU-separation is a growth related process. 8 T R A N S P O R T A D S O R P T I O NXp M U L T I P L I C A T I O N E R O S I O N C P U - S E P A R A T I O N D E S O R P T I O N /m,S Figure 2. Definition of processes during early colonization of a substratum. 9 These four processes can be expressed in terms of cells by using the number of cells in each individual CFU. However, CFU - separation does not contribute to the accumulation in terms of cells. Two additional processes can be defined (after transport, adsorption, and desorption) when cell accumulation is considered: Multiplication: Multiplication is related to cellular growth,, but only refers to those daughter cells which remain within the same CFU. Cells within a CFU multiply and increase the number of cells within this CFU. This does not change the accumulated number of CFU but does change the accumulated number of cells. CFU - Erosion: Cells within a CFU can "detach" and, hence, reduce the cell number of the CFU. This process is the reverse of multiplication. Therefore, processes of early colonization can be separated into sorption- and growth-related which then can be expressed as rates. With these rates, mass balances for accumulation both in terms of CFU and cells can be accomplished: d CFU dt + Kjads Kj +des K 2.1sep Accumulation CFU Adsorption CFU Desorption CFU Separation CFU 10 d cell Kj +desdt T tx .ads m̂ul Kero Accumu­ lation cells Adsorption cells Desorption cells Multipli­ cation cells Erosion cells Equatiorts 2.1 and 2.2 demonstrate the importance of measuring the different process rates for a better understanding of surface colonization mechanisms, since they reveal whether growth- or sorption-related processes dominate the accumulation. Transport For a better understanding of adsorption processes and comparison between adsorbed and suspended biomass, the transport process must be understood very well, both in terms of transport of biomass to the substratum and the transport of nutrients to the adsorbed biomass. Currently, most of the information about kinetics of cellular adsorption and desorption has been derived from stagnant systems with no shear stress. The absence of flow or shear forces in natural and engineered systems is not common and, therefore, not of great practical interest. To define transport in quiescent systems is not an easy task. 11 since it depends on parameters , i.e. diffusiyity, which can not be measured directly. Additionally, adsorption kinetics in stagnant systems are subject to artifacts produced by the combination of sedimentation and active adsorption rates. Some studies in flow systems have been published, focusing on net accumulation rates at the substratum. From the literature, it appears that it is essential to measure both adsorption and desorption rates independently. Figure I (Powell and Slater, 1983) illustrates the difficulty in determining adsorption rates from the accumulation alone. The data fit the theoretical calculated rates poorly. Measuring accumulation rates instead of adsorption can lead to artifacts since accumulation can include other processes,. such as cellular multiplication at the substratum, which are not related to adsorption itself but which can be a major contribution to an increased accumulation. Transport and Adsorption to the Substratum Piffusivity: Under laminar flow conditions, particles are transported to the substratum by diffusion perpendicular to the flow. Microorganisms with a size of I to 4 pm3 have a very small Brownian motion and, hence, a small Brownian diffusiyity. Therefore, motility is of considerable importance during the processes of transport but has often 12 been neglected in adsorption studies. Jang and Yen C1985) calculated the non-Brownian diffusivity (motility) for different microorganisms to be in the range of 0.4"IO-3 to 5.6“ 10'”3 mm2 s”1, compared to the Brownian diffusivity of 50HlO"® mm * t—1. They used the following equation to calculate non-Brownian diffusion: v » d Dc = --- £--- — --- 2.3 3 • ( I - a ) Dc. : diffusivity [ L1 t-1] Vv- : velocity of motility CL t-1] dr : free length of random run [L3 a : main cosine of angle of turn [-] Under condition of no chemotaxis, a can be assumed to be zero. If motility is not considered as a contributing factor in the process of transport to the substratum, the transport rate might be underestimated 20 to 50 times. The non-Brownian diffusivity can be calculated from the velocity and the meah free path length. Vaituzi and Doetsch (1969) measured speeds up to 55.8 pm s~1 for Pseudomonas aeruginosa with "track photography". Their results suggest a mean free path length of random run in the range of 50 to 85 pm. These values yield a non-Brownian diffusivity (Equation 2.3) of 10 3 mm"'" s— for P aeruginosa. 13 Transport Rate to the Substratum: available for the transport and particles to different substrata. proposed an analysis with a approximation for the surface-particle Good information is adsorption of inert Bowen et al. (1976) first-order-reaction capture rate, which leads to an expanded Graetz solution. This solution converges well for relatively large Peclet numbers and proved to be accurate for inert particles adsorbing to charged surfaces. The resulting equation has the following form: C0-Dc CFU 2.4 Kcfu I Adsorption rate of CFU to the substratum [# L-2 t-1] C0 2 CFU concentration in bulk liquid [.# L“3] D0 : Diffusivity of CFU CL”2 t"1] h : Half-thickness of channel CL! Ki : Dimensionless distance from channel inlet [-] € : Surface-particle capture factor [-] F 2 Gamma function [ F (4Z3) = 0.89338 ] In the special case where the surface-particle capture rate € approaches infinity (€=m ),.Equation 2.4 becomes: 14 NCFU •Dc h 2 9Ki 1/3 r 4 3 \ 2.5 Ncr-Lj I Flux of CFU to Substratum [# L-1 t- ^ 3 The strength of this solution is that one can estimate the flux of particles to the substratum (€=«,, Eq. 2.5) and obtain a discrete value for the surface-particle capture factor, independent of concentration and motility, for different substrata. In addition, a "sticking efficiency" can be calculated with Equations 2.4 and 2.5 by dividing adsorption rate by the CFU flux to the substratum. Assay for Substratum Properties: The use of Equations 2.4 and 2.5 to describe transport and adsorption processes, especially the dimensionless factor €, is a good analysis for studying the effects of different degrees of hydrophobicity of substrata Cindependent of concentration and diffusivity). Fletcher and Marshall (1982) show an increase of accumulation with an increased hydrophobicity. They use the double-layer theory (DLVO) of the colloidal chemistry to explain these mechanisms, based on the calculated charge of the substratum measured with the bubble contact angle method 15 and the overall charge of the organisms. Van Pelt et al. (1985) showed that there is statistically seen a very poor correlation between the free surface energy and extent of accumulation. They propose as possible reasons for this poor correlation that accumulation as the measured value is not the most appropriate parameter to describe adsorption, that the free surface energy during the experiment is not the same as that previously measured, or that the mechanisms of adsorption are different depending on the free surface energy. Van Pelt's first proposition is that the change in accumulation or the net adsorption is the result of adsorption minus desorption and, therefore, measurements of accumulation does not reflect the primary occurring process. The second proposition is in accordance with the observation of the "conditioning film". This change of well defined surfaces due to exposure to water containing organic macro molecules has been described by Loeb and Neihof (1975), Baler and Weiss (1975), Abbott et al. (1983), and Little and Zsolnay (1986). They summarize the effect of a conditioning film that a solid surface in contact with liquids containing diverse organic macromolecules alter due to the formation of a monolayer of adsorbed macromolecules; This results in the following: hydrophobic surfaces become 16 hydrophilic, positively- and negatively-charged surfaces acquire a net negative charge and Zeta potentials, contact potentials, and critical surface tensions are increased. The third proposition is that depending on the free surface energy cells use a different mechanism for adsorption. Fletcher and Marshall (1982) indicated the importance of proteins in the processes of adsorption. By adding Pronase they reduced the increase of accumulation. Paul and Jeffrey (1985) showed that for hydrophobic substrata, such as polystyrene, the protein linking is essential, whereas for hydrophilic substrata other adsorptive mechanisms dominate. Their result indicates that, indeed, different mechanisms of adsorption dominate depending on the free energy of the substratum. Growth-Related Processes Very little work has been done in regard to growth-" related processes during early colonization of surfaces. Only two groups of studies are available: 1. The early phase of biofilm accumulation (Trulear, 1983; Turakhia, 1986). 2. Growth measurements with Image Analysis (Caldwell and Lawrence, 1986,). 17 Trulear and Turakhia determined growth rates in biofilms grown under constant shear stress and turbulent flow. During the first or second day after exposure of acrylic plastic surfaces to P. aeruginosa. the adsorbed biomass had a growth rate (jaiO.65 h"3-) exceeding the maximum . growth rate in suspension h”1). After this initial time, the measured overall growth rates were reduced to levels below the maximum rate in suspension. Their results do not indicate whether this increased initial activity is due to prior physiologic or genetic phenomena or due to analytical variations after adsorption. Data suggest that the process of adsorption is very selective for the "more active" organisms (cells with a high motility have a greater diffusivity). Caldwell and Lawrence (1986) measured "behavior" of adsorbed P. fluorescens under laminar flow conditions. They observed different patterns of adsorption and subsequent growth at the substratum. Unfortunately, they do not state the shear stress of the liquid on the wall but only an average velocity. From the publication, shear stress cannot be calculated since the geometry is unknown. The growth rates measured do not answer all questions since the substrate concentration used were unusually high (I g glucose I-1 and 100 mg glucose I-1). The cells were grown in batch cultures and washed twice before being used in the IS adsorption study. The measured specific growth rates are in the range of 0.42 h-1. Spatial Distribution The spatial distribution of the CFU during adsorption can be of great value since it can determine whether the process is controlled by the adsorbing cells alone or a cell - substratum interaction (including the existing colonization). If the process is due to cells only, without any influence by the substratum's present state of colonization, a random distribution would be expected. If conditioning and occupation of the surface positively influences adsorption, then an aggregated distribution can be anticipated. A uniform distribution, conversely, results when the area around an existing CFU is blocked for adsorption indicating a negative influence. Classic Nearest Neighborhood Analysis cannot be used for this analysis since only distance to the single nearest neighbor is used ignoring the other adsorbed cells. An analysis is needed which accounts for the overall population density. An extensive description of a unique solution for spatial distribution analysis is presented in Appendix A. 19 Fluid Dynamics Defined fluid dynamics is essential for adsorption studies under constant shear stress. Hydrodynamics control both transport and adsorption: Transport is a function of the loading rate and adsorption.depends on shear stress. Due to this relationship, it. is difficult to compare experimental results obtained under different hydrodynamic conditions without their precise definition. Two different flow patterns must be considered: 1. Turbulent flow 2. Laminar flow Turbulent Flow The nature of turbulent flow does not allow an easy determination of the velocity gradients near the wall. Depending on the Reynolds number of the flow and the roughness of the wall, a wide variety of velocity gradients and, thus, shear stresses are possible. Using the theory of the "viscous sublayer", within its limitations, i.e. smooth surface, it is possible to estimate the shear forces. 20 According to Prandtl, this viscous sublayer can be explained and estimated in the following way: Due to the viscosity of the liquid, the velocity at the wall is zero and the resulting shear forces in the liquid adjacent result in reduction of the velocity. This generates a layer with a viscous flow which extends into,the flow with an increasing velocity up to the point where the flow starts to become fully turbulent. The transition from the boundary layer to the turbulent bulk flow is asymptotical.. Therefore, the thickness of this layer cannot be determined unequivocally. Generally, the thickness of the layer is defined as the point where the theoretical flow velocity reaches 99% of the outer bulk velocity. In reality, this problem is complicated by the possible existence of three forms in the viscous sublayer: a laminar boundary layer, a transition region, and a turbulent boundary layer with a laminar sublayer. In addition, any disturbance of the substratum changes the development of the boundary layer. According to Dracos (1973), the shear stress at the wall can be estimated if the friction factor is known (flat plate): Laminar boundary layer: Cf = 0.66 - 1/2 2.6 C friction factor 1-3 V „ , X H 21 mean bulk velocity CL t™13 length of layer development CL] viscosity CL1 f"-1] Turbulent boundary layer: v • x -1/5 0.059 - CO C'f 2.7 with the c-r values of Equations 2.6 or 2.7 the shear force at the wall can be calculated: According to Equations 2.6 - 2.8, a turbulent flow with mean bulk velocity of 0.5 m s”3- will produce a shear stress of 0.34 N m""1 along a flat plate after a length of 10 m. This calculation for flat plates can, with caution, be used for larger diameters of pipes, especially if one assumes frequent irregularities and, hence, uses Equation 2.6 for the calculation of the friction factor. Laminar Flow 2 CO • 2.8 To d shear stress at wall CF L~23 density of liquid CF t2 L"A3 Laminar flow is analytically much simpler than 22 turbulent flow. The velocity profile ia parabolic and shear stress can be calculated according Newton's law: 'T =xy dv X y « length axis of system ‘ height The boundary conditions for this system are fairly simple: both the wall velocity and the shear stress at the symmetry point are zero. There are no undefined boundary layers troublesome asymptotic approaches as in turbulent flow. or 23 CONCEPTUAL MODEL OF SURFACE COLONIZATION The analysis of adsorption, desorption and growth related processes during the early colonization of" a substratum cannot be considered in traditional terms of continuum mass balances. Rather, population balances, where the single observed particles are individual members of the total population must be used. For population balances, the probability of an event, in terms of the total population, is the key factor. Population Balance in Terms of CFU The population balance will be made in terms of Colony Forming Units (CFU), an individual observable particle which consists of one to many cells. Each CFU can be observed and treated individually with the image analyzing system. Transport Particles or cells are transported by momentum transport in the laminar flow parallel to the substratum. There is no momentum transport perpendicular to the 24 substratum. However, the particles or cells are transported to the surface by a diffusive random movement. Assuming that chemotaxis is absent, this diffusive transport is either a Brownian motion or the random motility of the cell itself. Hence, a Brownian and a "non-Brownian" diffusion is responsible for the transport to the substratum. The non- Brownian diffusion, which can be calculated with the average free path length and velocity of the random movement, can exceed the Brownian motion by orders of magnitude. "Transport" does not define the physicochemical interaction of the particles with the substratum, but only the transport to the substratum. Particles might "hit" the substratum due to transport and come to a brief stop. But as long as they do not interact with the substratum, even if they are visible to the observer, they are not considered adsorbed. Transport depends on the total concentration of particles through the system and the particle diffusivity Dc,. The rate of transport is the number of particles transported to the substratum per unit area and per time. ^ — — L 25 Adsorption Adsorption refers to a direct particle-substratum interaction. It does not include the transport to the substratum but only the direct interaction of a. particle, which has been transported to the substratum, with the substratum. The probability of adsorption for a CFU transported to the substratum can be defined as "sticking efficiency". This probability may depend on surface characteristics of the particles and the substratum as well as the fluid shear ,stress at the surface. Last, but not least, the physiological state of organisms can influence adsorption. The rate of adsorption, therefore, is a function of the rate of transport and the probability of adsorption and has units of particles per unit area per time. Reversible versus Irreversible Adsorption When CFU adsorb to a substratum, their linkage can be relatively weak, but strong enough to resist- shear stress of the liquid for some time. Due to the poor connection, they have a probability to desorb after a short time. By 26 improving their linkage to the substratum with time, their probability of desorption decreases. Hence, as soon as their probability to desorb reaches zero, they are irreversibly adsorbed. During the period where their probability to desorb is greater than zero, they are "reversibly adsorbed". The time interval between adsorption and the time at which CFUzS are either sheared off or irreversibly adsorbed, is the offset time of desorption for reversibly adsorbed CFU. This concept of reversibly adsorbed CFU and ■offset time is not the same as used in other experiments (Fletcher and Marshall, 1982), where the term "irreversibly adsorbed CFU" indicates the amount of CFU washed off after termination of an experiment. In this text, it is used to describe a mechanism during the process of adsorption; Therefore, the offset time is a specific time interval during the process of adsorption dependent on the physiology of the adsorbing CFU, shear stress, and substratum. This concept can be used to describe kinetically the findings by Brash and Samak, 1978. They found that there is a dynamic equilibrium (turnover) between proteins in the bulk flow and adsorbed to the substratum. As soon the bulk concentration was reduced to zero, the surface concentration remained constant in a static equilibrium (no turnover). 27 indicating that the molecules went through the state from reversibly to irreversibly adsorbed. Desorption Desorption refers to an entire CFU detaching from the substratum and reentering the bulk liquid. The probability of desorption is more related to probability of adsorption than to the total number of CFU at the substratum, indicating that the chances for a CFU remaining at the substratum increases as its residence time increases (see reversible adsorption versus irreversible adsorption). Thus, the probability of desorption is not equal for all adsorbed CFU since a CFU improves its bonding to the substratum with time. The rate of desorption can be defined as the product of the probability of desorption (3) with the rate of adsorption. This probability is a function of shear stress, physiological state of CFU, and characteristics of the substratum. Desorption offset time, t,..., defines the time interval between the start of adsorption Ct=O) and the first desorption event (t = t,.) in an experimental run. 28 CFU-Separation CFU-separation is the separation of a CFU into two independent CFU's and is a process related to growth at the substratum. CFU-separation increases the number of CFU at the substratum but not the number of cells so it is important to the CFU population balance. Since all irreversibly adsorbed CFU have the same probability per time to separate, this probability is defined as a first order kinetic rate coefficient. The total rate expression of CFU- separation has the units of number of CFU per area and per time. The probability (not the rate) of CFU-separation depends on shear stress, substratum characteristics, and physiology of the CFU, but . is independent of the CFU concentration at the substratum. Other Processes at the Substratum Adsorption, desorption, and CFU-separation are the only processes, relevant to the description of the colonization processes in terms of CFU. However, the experimental system only permits observation of a limited substratum area and CFU can enter or exit the field of observation. Therefore, for experimental purposes, two additional processes have to 29 be considered: I.) CFU entering and 2.) CFU exiting the field. Population Balance in Terms of Cells The number of cells per CFU can be calculated (area measurement and division by standard cell size) to obtain a population balance in terms of cells. All processes described in terms of CFU can be translated into terms of cells. As indicated before, CFU-separation does not contribute to ■ the cell accumulation. However, other growth related processes contribute to the population balance in terms of cells. Multiplication and Erosion Multiplication is a growth related process at the substratum. Whenever a cell within a discrete CFU is growing and the newly formed daughter cell remains within the same CFU, the process of multiplication is observed. If the newly formed cell is lost immediately due to shear forces, no multiplication will be observed since this process describes only the formation of new cells which remain within the same CFU. In case an established cell 30 ® CFU (with more than one cell) detaches and reenters the bulk flow, the CFU is eroding. If a CFU erodes, it loses cells to the bulk flow without being removed itself. The ;probabilities of multiplication and erosion are ;defined in the same way as CFU-separation. All the irreversibly adsorbed cells have the same probability for multiplication and subsequent erosion. The probability terms for both are defined as a probability per time (analog to first order kinetics). The rates for multiplication and erosion are expressed as number of cells per area per time. Kinetic Expressions in Terms of CFU The rate expressions of the model, conceptually described above, will be used in this section more explicitly to derive the kinetic equations of the population balance. According to the previously described processes the "stoichiometry" of the CFU population balance can be written in the following way: 31 ™("bulk < -- > ECFU3 -> ECFU3rev irrev suspended reversible irreversiblebiomass adsorbed biomass 3.1 a ECFU]tot [CPU] +rev [CPU]Irrev Total adsorbed CPU total reversibly t total irreversibly adsorbed CPU adsorbed CPU 3.1 b Using these stoichiometric equations (3.1 a and 3.1 b), the kinetics and surface concentrations can be determined with the equations that follow. Transport from Bulk Flow to Substratum Deposition rate of colloidal particles from a laminar flow to the walls of a parallel plate, as described by Bowen et al. (1976) will be used for CFU. The local transport rate to the substratum is given by: 3.2 K c f u : Adsorption rate of CPU to the substratum [# CPU L~J t-1] C0 : CPU concentration in bulk liquid [# CPU L“3] . D0 : Diffusivity of CPU EL2 t“l3 h : half-thickness of channel EU Ki : dimensionless distance from channel inlet E-] 6 : surface-particle capture factor E-3 F : Gamma function E F(4Z3) = 0.89338 3 32 Equation 3.2 accounts for the CFU transport to the region ultimately adjacent to the substratum and also for the particle-substratum interaction (adsorption). K x , the dimensionless length, is calculated with the following equation: ( " ( 8x 3h ) h : Half-thickness o£ channel x : Length from inlet CL]Pe ' : Peclet number C-J 3.3 Peclet number describes the ratio of bulk velocity to convective velocity and is defined: 4 » v • h Pe . ----*---- C Vm : Average velocity in channel Dm : Diffusivity CL1 t”1] 3.4 CL t-i] The non-Brownian diffusivity of bacteria (motility) (Equation 2.3) can be calculated with the free path length and the rate of motion in the random movement of bacteria (Jang and Yen, 1985): Dc v » d r r 3 ( 1 - « ) 3.5 vv, dv. a "linear swimming speed" CL t-*] mean' traveling length of random run CL] mean cosine of angle in random turn 33 If a non chemotactic movement is assumedf CCFU] V-ToV = O and t SL t,- ---> Kfiae,.,, Ko1s m m = 0 Ct=O : first observation of adsorption). This boundary condition leads to a discontinuous function with respect to t: CCFU]rev : Offset time of reversible adsorption Ct"11 The rates Kocleam and Kotl̂ mv., (for t i tva) can be expressed by the probability term Ci0 for desorption: CCFU]rev = kCFU " [ 11 " tBc + ( 1 " fcr 1 3 3.11 If O0 is independent of time, then the population balance of reversible adsorbed CFU in Equation 3.11 can (for t i t0> be reduced to: = K * t rev CFU r t i tv CFU ckCFU ' ^ ‘ (Kcdes+ Kctran 3 * Ct ™ 3.10 t I tv CCFU] 3.12 I 36 Equation 3.12 states that the number of reversibly, adsorbed CFU per area is independent of time. The population balance for the irreversible CFU (Eq. 3.8 ) can be integrated with the boundary conditions: t = tv. > CCFUl !Ivivimv = O . This boundary condition stands for the assumption that, for any time smaller than tvl no transformation from CFUvimv to CFUivivimv will occur. This assumption leads to a discontinuous function for CCFUli^vlmv with the break point t=tv,: CCFU].irrev 0 K . ""I. ctran k ■ ̂ ̂too p - IL seP _ — —I t i t r 3.13 t i t r In Equation 3.13 the term for Ktrffcvî vi can be replaced with the probability term: K = Kctran CFU ( 1 - 6 ) c 3.14 which puts irreversible accumulation into a direct relationship to the adsorption rather than the transformation rate. According to Equation 3.1 b, Equations 3.12 and 3.13 can be combined for total CFU, using the assumption of Equation 3.14: I 37 ECFUJ kCFU * t t i t t + r I-Bc . kgaoB C t 3.15 t 2 t This equation describes the kinetics in terms of total CFU. Kinetic Expressions in Terms of Cells Since the cell number for each individual CFU can be measured, all the events in term of CFU can be translated into terms of cells. Additionally, a change in cells per individual CFU can be observed. Hence, the processes of cell multiplication and erosion can also be defined. CFU- separation, a process which does not contribute to the change of total cells adsorbed, is omitted. 38 Transport from Bulk to Substratum Transport can be defined in the same way as for CFU (Eq. 3.2): 3.16 Adsorption rate of cells [# cell L-1 t-1] cell concentration in bulk liquid [# cell L-=] Diffusivity of CFU CL2 t"1] half-thickness of channel CL] dimensionless distance from channel inlet [-] surface-particle capture factor [-] The main difference between Equation 3.2 and Equation 3.16 is the difference of concentration. As is the case for Equation 3.2, Equation 3.16 represents the rate of adsorption. The dimensionless distance Ki is the same for both equations, since the initial measurement is made in terms of CFU and then translated into cells. Hence, Equation 3.3 - 3.5 are unchanged. The rate of transport (not adsorption) can be defined in analogy to Equation 3.6: Ck Dc h Ki € .2 S K 1 1/ 3 3.17Nx C X -D C h r 4 3 flux of cells to substratum E# cell .L"2 t"13 Population Balance at Substratum Cells at the substratum undergo a transformation from reversibly to irreversibly adsorbed cells. The population balances for cells are similar to those for CFU Cxlvirov=O and t * ty.---> Kxclefro=O, Kxt^mn=O. This boundary condition leads to a . discontinuous function in respect of t: [x]rev K X ' t t I tv (K ■ t) X xdes + Kxtran r t i tv 3.20 If the probability Bh of desorption is independent of time then Equation 3.20 can for the case of t Z tv, simplified (analogous to Eq.ll and 12) to: Cxl = K « t rev x r 3.21 With that simplification, Cxl^rov becomes independent of time. For the irreversible adsorbed cells Equation ‘ 3.13 can be adapted after combining and krov.oro in Equation 3.18: 41 k = kxnet mult keros Then Equation 3.13 becomes: — :0 Ex] . = —irrev “ K . ~xtran . x̂net 3.22 kxnto-b Ct — ti t i t t i t 3.23 Using an analogous step to Equation 3.14 and combining Equations 3.20 - 3.23, the Equation for the total cell concentration at the substratum can be written as it has been done in Equation 3.15 for CFU: t i t tr + I-Gx , x̂net kxnot * ̂t 1 ) e -I 3.24 t i t Thus, with Equation 3.15 and 3.24 it is possible to estimate the accumulation of both CFU and cells at the substratum with time. 42 Sticking Efficiency Sticking efficiency is a parameter frequently used to describe the ratio of adsorption rates to the flux to the substratum. Thus, it is an overall probability of adsorption. The sticking efficiency is not identical to the Surface-Particle Capture Factor €, but rather a function of it. In terms of CFU, the sticking efficiency can be described by the ratio of Equations 3.2 to 3.7, and in terms of cells by the ratio of Equations 3.1(5 to 3.17: 3.25 B : Sticking efficiency [-] € : Surface-particle capture factor [-] • Dimensionless distance from channel inlet [-] r : Gamma function [ T(aZ3) = 0.89338 ] Thus, the sticking efficiency I has a range of zero to one. Sticking efficiency, 3, is the probability that a CFU being transported to the substratum will adsorb. The surface- particle capture factor € is part of the extended Graetz solution for a mass balance of the bulk liquid and the substratum in terms of adsorption. 43 Summary of the Conceptual Model The model describes the population balance for both CFU and cells at the substratum. The parameters used in this model can vary with cell concentration in the bulk liquid and shear stress at the substratum. All relevant parameters in this model, with the exception of the non-Brownian diffusivity, can be measured experimentally or calculated with the method described in "kinetic Results". Non- Brownian diffusivity can be estimated with literature values and direct observations. 44 EXPERIMENTAL SYSTEM AND METHODS Experimental System The experimental system consists of" a chemostat system, a rectangular capillary tube, and an image analyzer similar to the system described by Powell and Slater (1983): Microbial cells grown in continuous culture (chemostat) provide continuous inoculum for the experimental system with minimal variation in cell physiological state and cell concentration throughout an experiment. Prior to beginning the experiment, cell concentration in the chemostat is measured by direct count. The cell size distribution is also determined for calculating cell numbers per CFU. The desired cell concentration at the capillary entrance is obtained by dilution in the mixing chamber. The effluent from the mixing chamber is pumped through the rectangular capillary (Wale Apparatus) at a constant rate using a non-pulsing gear pump. The inside surface of the rectangular capillary is the substratum in these experiments and the processes occurring at this surface are monitored continuously by a video camera mounted on the microscope. 45 ImageGrowth AnalyzeMedium DilutionMedium Camera MeterPumpMixing h a m b e rCFSTR ___Capillary 0.2 m m f Figure 3. Schematic of the system. The video signal is transmitted to the image analyzer which then converts the grey image into a binary image. The image analyzer accumulates this image into a "tracking" image which is similar to a multiple exposure and displays all of the images simultaneously in different colors on the screen. 46 A single binary image of" the specimen is stored on disk at constant time intervals % : - Z fM m v ^ V - Z-T-.--V. -- .--ft'*': — " - -. z_"-r i . * >;2-r u?- -■ - ~ Jc :-;V-'. ■ : ~ r * - - - ----- ’ ------- -^s£: -ZZZi--IV-; -e$s • - ... -EL: _ - -\s. / Z « z , ► W- ---- ■ «3*. v; -I" - -■ ̂ s.--“_Z -. r - I j i - g t e W - -V . - - - - - - - - - - : : V " W *. - ". - --T». „ -^= . -- = - - --VJ=:-V ... - --V. :,- ; »_V = : ,T - - - - -: V- -U-S--.-.:. -- - - -’-• # - - - _ — ^ Z- _- ^IiSiMiS:-; ‘ ■ - .v- -rtE--' Figure 4. Tracking Image. 1.0 N m-2, 10G cells/ml. Flow direction from left to right. The grayish areas are the tracks of the colonies and the dark areas within the tracks the colony forming units (CFU). The streaks are markings of "hits" by CFU transported to the substratum without adsorbing. Size of observed image: 150 ■ 150 pm 50 Fixpoint Calculation After completion of the real time experiment and prior to the analysis of the single timages, the movement of the fixpoint has to be calculated. This step requires that the fixpoint be isolated from all the other CFU within the image. The easiest way to achieve this task is by manually editing the image of the total tracks for the track of the -fixpoint alone. Then, with a logical exclusion, the feature 0-f the fixpoint for each image can be separated and measured individually. The measurements include the true midpoint coordinates which are stored in a data file. This routine can be done either before or within the analysis routine. Image Analysis Once the coordinates of the fixpoint have been calculated, it is then possible to analyze the images for the CFU. For each CFU detected, the following measurements are done: X- and Y- coordinates of each detected CFU (feature count point). 51 Minimum and maximum X- and Y- values of the CFU to calculate the true midpoint corrected for the drift of the specimen holder. Area, Length, Width, ' Orientation of the length axis. Shape (roundness). At the same time, the cell number per CFU is calculated to obtain a cell number per CFU distribution for the analyzed field. In this routine, the results will be corrected for the possible drift of the specimen holder during the experimental run using the fixpoint coordinates. All the data obtained are stored on disk in form of random access files for further analysis. Up to this point, the evaluation of the data is done in a two dimensional way with the coordinates as the two dimensions. Data Assembly In this routine, data will sorted and assembled for each CFU with time as the third dimension. This can either be done with the image analyzer or with an IBM compatible system. In the image analyzer, the tracking image provides a criterion for the continuation of a CFU with time. As 52 long as the routine finds a data point in the next image, within the same track, it will use it as the continuing point of the same CFU. If it finds two possible points for continuation, it selects the closer of the two to the last analyzed point, and labels the other as a potential daughter CFU (CFU-separation). Withip the image analyzer, this routine is relatively .slow since it requires frequent interactions with the image analyzer unit and multiple image handling. The routine within an IBM-compatible computer uses a less rigid criterion for the evaluation of the continuation. Instead of using the tracks, it uses a range <4 by 6 pm) within which a continuation is allowed. If it finds two possibilities to continue, it selects the closer one and labels the other a possible daughter-CFU (CFU-separation). Since this system can use a hard disk setup and a machine language version of the programs, this routine is much faster in an IBM-compatible system than in the Image Analyzer. Both systems reevaluate possible CFU-separations during the assembly process. If the mother-CFU does not decrease in size during a possible division, the separation will be rejected. 53 Other than the above differences, the sorting routiiie performs the same functions in the two systems. In addition to the three dimensional analysis this routine calculates the neighbor analysis, the dimensionless nearest neighbor distance, the influence number (not dimensionless), and the dimensionless influence number. Additionally, this routine calculates the movements and directions of the CFU at the surface and monitors changes in cell numbers per CFU. The latter will be used to determine the number of events of cell multiplications with time at the surface as well as erosion of CFU. The organization of these data files is listed in Appendix B. Since accumulation of both CFU and cells can be influenced by colonies moving into and out of the field, the program identifies those new appearances close to the image frame. The calculation by this routine can be summarized in the following way: 1. Calculation of the values for each CFU, including first and last observations. 2. Determination whether each CFU adsorbed, separated, or migrated into the field, and whether they desorbed, or migrated out of the field. 3. Calculation of movement and direction for each CFU. 4. Conversion of the area of each CFU into cells per CFU and calculation of the events of adsorption, desorption, multiplication and erosion in terms of cells at the surface. 5 5. Calculation of the neighborhood analysis during the first observation of each CFU. 54 Subsequently, the sorting routine builds, several data files with a summary of data obtained. These files are in form of ASCII - files which can be translated into a format for Super Calc spread sheets and other statistical software. Method of Analysis and Chemostat Operation Direct Cell Count Cell concentration in the bulk flow of the capillary tube was one of the main parameters of the experimental series. Therefore, it was necessary to use a fast and accurate method to determine, the cell concentration of the chemostat effluent. The method of Hobble et al. (1976) was adapted to use the Image Analyzer for counting. The filters used were evenly hydrophilic, so that surfactant treatment could be omitted. Thus, the filters retained the irgalan black much better under the high energy illumination than surfactant-treated filters. Counting the cells with the Image Analyzer facilitated and significantly improved the analysis. 10 fields on each filter were counted and the average of these counts used to determine the cell concentration. Standard errors of the counts per filter were in the range of 7 to 12%, significantly lower than the error by the manual method. Replicates of several filters with the same sample, (count of three filters per sample) 55 yielded for the average values per filter a standard error of less than 10%. Chemostat effluent samples were sonicated prior to the count to break up aggregation of the cells. A sub-sample (75 pi) was suspended in three ml 0.01% acridine orange (AO) for at least 5 min. It appears to be noteworthy to mention that cells from chempstat cultures appear mainly orange, whereas bacteria from natural environments (very low growth rate) are often green. Since orange cells are much better detected by the Image Analyzer than green ones (in contrast to direct count by eye) it can be necessary to heat the sample before staining to change green fluorescens to orange (denaturalizing of protein). Cell Size Distribution Cell size for single cells and the total population of the chemostat effluent were measured with the image analyzer prior to the experimental series to determine the cell number per adsorbed CFU in the capillary analysis. For this analysis white light phase contrast was used with a microscope magnification of 40*I.5. Single cells for the size distribution were selected manually, whereas all cells were accepted for the size distribution of the total population. 56 Mounting of Capillary Tube Capillary tubes (Wale Apparatus) were precleaned by combustion (SOO0C) for several hours (over night) to remove all organic contamination in e the inside. They were connected to iZza inch diameter high pressure nylon tubing (6 cm) with heat-shrink PVC tubing (2 cm, diameter nominally iZa inches). The connections were sealed and secured with silicon glue dispensed out of a tuberculin syringe (I ml), and then heat fitted with hot air. This procedure to connected the flat capillary tubes tightly to the round tubing (no leaks on the microscope stage). Chemostat Operation A New Brunswick Bioflow C30 with a volume of 330 ml and a flow rate of 1.0 ml min™1 was used as chemostat. Thus, the dilution rate and growth rate was 0.18 h™1. Temperature was maintained at ,25° ± C. Growth was carbon-limited with glucose as sole carbon source (44.4 mg l™*- as TOC) . C to N ratio was 10 and C to P ratio 15. Phosphorus was used to buffer the system at pH 6.8. Calcium concentration was 50 mg l™i as CaCO3 (added sterile after heat sterilization to prevent precipitation in form of calcium phosphate). 57 Magnesium chloride1 concentration was 7.5 mg I"1. Micronutrients were added according to Trulear (1983). The dilution liquid had the identical composition as the growth medium except that ̂. . rio organic, carbon was present. The chemostat could be operated continuously for up to five days without heavy wall growth. Effluent glucose was measured colorimetricalIy with a specific enzyme reaction (Trulear, 1983). 58 RESULTS Progression of Experiments. The results are based on 15 experiments, 9 at 0.5 N m"1 ,and two each at 0.75, I.O1, and 1.25 N m~2 . CFU concentration in the bulk flow of the capillary tube ranged from 1.1"IOs to 11.2-10= CFU ml”*. Each experiment lasted 300 min for colonization, and images were taken at 5 min intervals. The extent of surface colonization by CFU under ^ ^ 1Sat conditions and the total surface coverage by tracks is displayed in Figures 5, 6, and 7 (not ' real tracks but artificial display of tracks; see "Image Collection"). The small dark areas are the colonies and the grayish, larger fields are the "tracks". The figures of the tracks were generated over a period of 300 minutes, and the colonies are the ones observed .at 300 minutes after beginning of the experiment. Figures 5 and 6 are from experiments at 0.5 N m~* with I.1-10= and 10-10= CFU ml-1 respectively. Shear stress during colonization in Figure 7 was 1.25 N m-2 and CFU concentration 12.2-10= CFU ml-1. 59 Figure 5. Tracking Image: 0.5 N m™1, I.I-IOs CFU ml”1, flow from left to right. The grayish areas are the tracks of the colonies and the dark within the tracks are the colonies (after 300 min). Size of observed area:150•150 pm. Area coverage by CFU: 0.35%, by tracks: 3.325% 60 % f ^ * w 4 $> ^ # % k l> * + '^t- # S a f IP*lv ^ 6 - W s C " . / A - ' ** st ‘ ^ * * * j? <* 4» * ®*> * * 4%'* # “» ;» " *** T «g» * *' " S Jtiili, Wf «» 5 usaiCTw - *% **% -?<, *p - « * ^ v v - » - # » H * S •** % t *.0» * , ' O % . - V ^ *»y »* < » * - S • . 1̂ U A <• - * \ •„ .- i ' - S ^ v » . . X f - - > v f » * * »-. % r **'.. -. # ' ^ . A *» *! m *m>4 » > T ■ypj < *= * » * • ' - 4 » + . V * m * * + , ' / - . C * # - * 4 * * 1» .J y -~* .- -i 4. - # * * ♦ e , « r.* » V - , ' ^ ■ * \ *'- v * : & 5 j * JjTtS « /- & tr m^ — % - * V. V- *,- ** Figure 7. Tracking Image: 1.25 N m-', 12.2-IOg CFU mI™1, flow from left to right. The grayish areas are the tracks of the colonies and the dark within the tracks are the colonies (after 300 min). Size of observed area:150-150 pm. Area coverage by CFU: 1.9%, by tracks: 8.46% 62 The results can be grouped in three classes: 1. Kinetic measurements 2. Behavioral distributions 3. Spatial distributions Kinetic measurements describe the events at the substratum, i.e. events of adsorption, desorption, and growth related processes during the observation time interval (5 min) and their rates. The results describe the kinetics of substratum colonization. “Behavioral" characteristics of each CFU observed, include size during first and last observation, age during last observation, movement,' orientation, net growth, and , so on. These results are not useful for kinetic analysis but help to elucidate the processes involved. during the early colonization of a substratum. The third group, spatial distribution, determines the degree of interaction of each CFU during its first observation with other CFU already established. This analysis is uncommon but very powerful in establishing mechanisms of adsorption in terms of spatial distribution. 63 Kinetic Results The events o£ colonization on a glass substratum during the first 300 min can be presented in terms of CFU (Figure 8a), and areal coverage (Figure Sb). Adsorption kinetics can also be demonstrated in terms of cells (Figure Sc). Growth related processes are displayed in Figure Sc. Accumulation of biomass and areal coverage are presented as measured, but adsorption, desorption, and growth related processes are shown cumulative, i.e. the number of observed events were added to the number of the previous events. The slope of data displayed in this manner is equal to the rate. Thus, an increase of the slope indicates an increase of the rate. Directly Measured Results All results are presented in the Tables 9 to 23 (Appendix C). Each table represents an entire experimental series, whereas Figures 41 to 55 (Appendix D) represent the same results in graphic form. The summarized results are displayed in Tables I to 3. The nomenclature is in accordance to ones used in the conceptual model. Adsorption rate is a function of CFU concentration in the bulk flow AR EA C OV ER AG E BY C FU I N % CF U (N um be r/s qm m ) 64 ABI, 0.5 N/sqm, 5.0 • 10*6 cells/ml ADSORPTION, DESORPTION AND ACCUMULATION OF CFU ------------------------ ----------------------------------------------------------- D ADSORPT. CUUUL X DESORPT. CUUUL v CFU SEP. CUUUL ■ ACCUUULAHON CFU 20000 10000- SOOO- TIME (min) AREA COVERAGE BY CFU IN % TIME (min) % AREA COVERAGE Figure 8. Typical progression of colonization in CFU (8a> and area coverage (8b) during 300 min. of glass substratum. Shear stress: 0.5 N m™2 terms of a smooth 65 ABI, 0.5 N/sqm, 5.0 . 10*6 cells/ml ___ADSORPTION, DESORPTION AND ACCUMULATION OF CELLS 4 0 0 0 0 ---- ----------------------------------------------------------------------------- * ADSORPT. CUUUL » DESORPT. CUUUL ♦ ACCUUULAT10N CELLS 200 300 TIME (min) MULTIPLICATION, EROSION AND ACCUMULATION OF CELLS ----------------------------- ------------------------- --------------------------- * UULT1PL. CUUUL A EROSION CUUUL ♦ ACCUUULAT10N CELLS 40000 *->30000 ■ g 20000 ■ O 10000- TIME (min) Figure 8. Typical progression of colonization in terms of cells. Adsorption related processes (8c) and growth related Processes (8d) 66 (Figure 9a and 9b). The linear regressions in these figures is calculated in Table I and presented as “Slope" and intercept . Thus, the assumption of a direct proportionality between adsorption rate and bulk CFU concentration as stated in Equations 3.2 and 3.16 is valid. Figure IOa displays the desorption rates at the same shear stress for CFU and Figure IOb for cells. Data from these figures suggest that all regressions of the rates with cell concentration have their origin through the zero points of the coordinate system. Growth related processes, such as CFU-separation, cell multiplication, and erosion for a shear stress of 0.5 N m~2 are displayed in Figure 11, 12a and 12b respectively. These first order rates do not show a correlation with cell concentration in the bulk flow, which is in accordance with Equations 3.8 and 3.18. 67 Shear Stress: 0.5 N nr2 ZERO ORDER KINETICS, Rate I# min-1 ram--2] Series # CFU/ral Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AAl LleS 8.18 i 2.46 7.54 + 4.17 14.38 + 2.46 11.37 ± 5.81 AB3 I.IeS 5.99 + 2.38 2.34 ± .90 10.43 + 4.28 3.73 + 1.47 AA4 1.92e6 13.52 + 4.53 10.07 ± 4.82 ' 16.20 + 5.5 10.92 ± 4.97 AB2. 2.45e6 19.34 ± 3.48 10.24 ± 4.63 ' 30.18 ± 3.62 15.26 + 6.80 AA3 2.75e6 20.50 + 6.28 11.11 ± 5.29 34.33 + 10.29 16.70 + 7.89 AC2 3. S4eS 27.29 t 3.75 11.11 ± 8.24 47.61 + 3.2 15.12 + 8.83 ACl 4.7e6 35.34 + 13.44 27.11 ± 23.95 46.29 + 16.75 27.11 + 23.95 ABl 5e6 43.45 i 5.51 36.81 ± 15.04 57.51 + 6.61 50.80 + 29.15 AA2 le7 71.68 + 26.40 57.20 + 31.75 135.66 + 47.48 107.03 + 58.56 Slope 7.39e-6 + 8.26e-7 5. ISe-S ± 1.54e-6 1.36e-5 + 1.86e-6 1.12e-5 i 2.BOe-S Intercept .423 i 2.16 -3.146 ± 4.03 -5.779 + 4.87 -12.122 + 7.33 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ral CFU-Separation Multipl. (Cells) Erosion (Cells) AAl . I. IeS .239 ± .225 .712 + .431 .474 + .386 AB3 I.IeS .015 ± .045 .306 + .204 .212 + .262 AA4 1.92e6 .074 + .107 .638 + .337 .482 + .397 AB2 2.45e6 .067 ± .061 .581 i .243 .394 + .129 AA3 2.75eS .055 i .071 .556 + .336 .290 + .130 AC2 3.64e6 .048 + .044 .392 + .084 .254 + .068 ACl 4.7e6 .039 ± .043 .433 + .238 .286 + .130 ABl ■ 5e6 .180 + .084 .550 + .208 .294 + .106 AA2 le7 .193 + .107 .593 + .191 .360 + .209 Average .099 + .076 .559 + .124 .391 + .104 T a b l e I. S u m m a r y o f d i r e c t l y m e a s u r e d r a t e s a t ID . 5 KI m " i s h e a r s t r e s s . S l o p e a n d i n t e r c e p t a r e t h e l i n e a r r e g r e s s i o n s u s e d i n F i g u r e s 9 a n d I O t o s h o w t h e p r o p o r t i o n a l i t y o f t h e r a t e s w i t h b u l k C F U c o n c e n t r a t i o n . 68 Shear Stress : 0.75 N ur* ZERO ORDER KINETICS, Rate [# mitr1 Series # CFU/ml Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AB4 AC3 2.65e6 6.3e6 18.82 + 6.99 42.61 + 15.93 10.21 i 4. 87 21.50 + 10.18 27.33 + 9.47 . 74.17 + 27.2 13.44 + 6.32 27.86 + 10.87 Slope Intercept 6.52e-6 1.548 3.09e-6 2.013 1.28e-5 -6.677 3.95e-6 2.971 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ml CFU-Separatioh Multipl. (Cells) Erosion (Cells) AB4 AC3 2.65e6 6.3e6 .065 + .061 .012 ± .030 .457 + .191 .431 + .097 .210 + .114 .321 + .081 Average .039 .444 .266 Shear Stress : 1.0 N rir* ZERO ORDER KINETICS, Rate [# ruin"1 mm-;] Series # CFU/ml Adsorption CFU Desorption CFU Adsorption Cell Desorption Cell AB5 6.75e6 31.75 + 4.01 - 22.17 ± 12.33 56.01 + 8.81 36.99 ± 21.22 AC4 B.71e6 41.33 + 16.86 26.78 ± 15.21 73.86 + 33.82 39.92 ± 20.38 Slope 4.89e-6 2.35e-6 9.lle-6 1.49e-6 Intercept - -1.242 6.294 -5.463 26.899 FIRST ORDER KINETIC COEFFICIENT Ch-1] in respect to surface concentration Series # CFU/ml CFU-Separation Multipl. (Cells) Erosion (Cells) AB5 6.75e6 .126 ± .098 .455 ± .199 .229 ± .132 AC4 8.7e6 ' .055 + .062 .433 + .132 .301 ± .099 Average .091 .444 .265 Table 2. Summary of directly measured rates at 0.75 and 1.0 N m"2. Slope and intercept describe the proportionality between the rates and the bulk CFU concentration. 69 Shear Stress : 1.25 N nr2 ZERO ORDER KINETICS, Rate I# mirr1 mnr2] Series # CFU/ral Adsorption CFU Desorption CFU Adsorption Cell. Desorption Cell AB6 AC5 6. SeB 1.2£e7 19.69 ± 2.71 51.76 ± 22.57 11.76 ± 3.56 17.36 + 10.76 30.42 ± 3.74 180.40 ± 30.38 15.69 ± 4.75 28.85 + 12.35 Slope Intercept 6.OSe-B -22.062 I.06e-6 4.469 9.43e-6 -34.648 2.48e-6 -1.443 FIRST ORDER KINETIC COEFFICIENT U r 1I in respect to surface concentration Series # CFU/ml CFU-Separation Multipl. (Cells) Erosion (Cells) ABB AC5 6.9e6 1.2067' .057 + .059 .034 ± .044 .563 + .234 .572 ± .247 .345 + .149 .370 + .183 Average - .046 .568 .358 Table 3. Summary of directly measured rates at 1.25 N m~2. Slope and intercept describe the proportionality between the rates and the bulk CFU concentration. 7 0 Adsorption CFU1 0.5 N/sqm 5.6 7.5.6 CFU-Concentration 1.25.7 A deorpU on CFU Adsorption Cell, 0.5 N/sqm iso- CFU-Concentration AdMtpUon Cell Figure 9. Adsorption rates plotted against cell concentration in the bulk flow for CFU (9a) and for cells (9b). Shear stress: 0.5 N m- 2 . The slope and intercept of the regressions are presented in Table I. Ce ll [# /m in s qm m ] CF U [# /m in a qm m ] 7 1 Desorption CPU, 0.5 N/eqm 1.25.75.6 7.5.6 CFU-Concentration D w o rp U o n CFU Desorption Cell, 0.5 N/sqm 150 100 7.5.6 CFU-Concentration D w o rp U o n C d l Figure 10. Desorption rates plotted against cell concentration in the bulk flow for CFU (10a) and for cells (10b). Shear stress: 0.5 N m~2. The slope and intercept of the regressions are presented in Table I. 7 2 CRJ-Separatlon, 0.5 N/sqm OZ .2- 2.5.6 5.6 7.5.6 CFU—Concentration C F U -S e p a ra tio n Figure 11. CFU-separation as a first order rate plotted against cell concentration in the bulk flow. Shear stress: 0.5 N m”i. Average rate coefficient is 0.099 ± 0.076 h"1. 7 3 Call Multiplication, 0.5 N/sqm K .2- 5*8 7.5*6 CFU-Concentratlon 1.25*7 Multlpl. (CU.) Erosion Cells, 0.5 N/sqm 5*6 7.5*6 CFU-Concentration Ero.len (CM.) Figure 12. First order rate coefficient for cell multiplication (12a) and cell erosion (12b) plotted against cell concentration in the bulk flow. Shear Stress: 0.5 N m~"2 . 74 Derived Results Derived results cannot be measured . directly in the experiments, but are calculated from direct measurements, such as the probabilities for desorption and erosion, surface-particle capture factors, and offset time. The derived results are presented in Tables 24 to 38 in Appendix E, and rates are summarized in Tables 4 to 7: Shear Stress : 0.5 N n-i Series # CFU/ral Desorption Erosion Adsorption Transport CFU Offset Time S CFU 8 Cell 5 Cell € CFU E Cell Rate $ W (CFU) tv. (Cell) Afll I. IeS 92.81 79.04 76.68 .01125 .01991 964.06 .0085 48.99 53.52 AB3 I. IeS 39.02 35.73 75.69 .00822 .01438 964.06 .0062 48.58 51.11 AA4 1.92e6 74.50 67.61 63.50 .01065 .01278 1682.72 .0080 37.21 44.67 AB2 2.45e6 52.94 50.57 67.84 .01195 .01874 2147.22 .0090 69.93 78.66 AA3 2.75eS 54.22 48.65 58.32 .01128 .01900 2410.15 .0085 35.74 41.89 AC2 3.64eS 40.73 31.75 54.94 .01134 .01992 3190.16 .0086 50.21 65.38 ACl ■ 4.7eS 76.71 58.56 41.13 .01138 .01494 4119.16 .0086 42.41 55.50 ABl SeS 84.70 88.32 77.11 .01317 .01748 4382.09 .0099 35.81 44.83 AA2 1b7 79.35 78.90 74.21 .01087 .02067 8764.17 .0082 62.89 68.40 Average 66.11 59.90 65.49 .01112 .01754 .0084 47.97 56.00 Standard Error 8.90 6.38 3.74 .00004 .00079 .00004 31.42 11.28 Table 4. Summary of derived rates calculated for 0.5 N m" 75 Shear Stress : 0.75 N i t 2 Series # C F U M Desorption B CFU S Cell Erosion 5 Cell Adsorption E CFU € Cell Transport CFU Rate $ Offset Time tr (CFU) tr (Cell) AB4 2.65e6 54.25 49.71 61.30 .01073 .01563 2658.6 .0071 57.42 60.25 AC3 b. 3eb 50.54 37.56 47.71 .01021 .01787 6320.46 .0067 33.86 47.06 Average 52.40 43:64 54.51 .01047 .01675 .0069 45.64 53.66 Standard Error 1.32 4.29 4.83 .00018 ,00079 .00015 20.51 10.31 Table 5. Summary of derived rates calculated for 0.75 N m~2 Shear Stress : 1.0 N nr2 Series # CFU/ral Desorption S CFU B Cell Erosion 5 Cell Adsorption E CFU € Cell Transport CFU Rate I Offset Time tr (CFU) tr (Cell) AB5 6.75e6 70.82 66.05 74.81 .00699 .01254 7453.46 .0042 65.36 64.81 AC4 8.7e6 64.79 54.05 57.41 .00716 .01283 9606.68 .0043 52.12 62.66 Average Standard Error 67.81 2.15 60.05 4.24 66.11 6.17 .00708 .00006 .01269 .00010 .0043 .00005 58.74 25.54 63.74 7.82 Table 6. Summary of derived rates calculated for 1.0 N m~2. Shear Stress : 1.25 N nr2 Series # C F U M Desorption Erosion . Adsorption Transport CFU ' Offset Time S CFU B Cell 6 Cell € CFU € Cell Rate I V (CFU) tr (Cell) AB6 AC5 6.9e6 1.22e7 59.26 33.54 51.56 35.88 66.20 59.06 .00429 .00639 .00664 .00994 82707.4 14511 '.0024 .0036 34.03 55.05 32.56 66.43 Average Standard Error 46.40 9.10 43.72 5.54 62.63 2.60 .00534 .00074 .00829 .00117 .0030 .00043 44.54 11.02 49.50 12.39 m"2Table 7. Summary of derived rates calculated for 1.25 N 7 6 Probability of Desorption: --------- CFU: 0.661 ------— Cells: 0.599 * CFU Adsorption (0.5 N /sqm ) Figure 13. Correlation between desorption and adsorption at 0.5 N/m'. The slope of the regression is equal to the probability of desorption in terms of adsorption. Probability of Erosion: Cells Erosion: 0.655 0.0 0.2 0.4 0.6 0.8 Uultiplication Rate Coefficient (0.5 N/sqm) Figure 14. Correlation between erosion and multiplication at 0.5 N/m2. The slope of the regression is equal to the probability of erosion in terms of multiplication 7 7 The probabilities o£ desorption and erosion as derived terms are directly related to their positive counter parts, adsorption and multiplication. The relatively good fit (Figure 13 and 14) indicates that these rates are rather dependent their positive counter rate than the bulk flow concentration. Offset time is calculated from the slopes and intercepts of adsorption and desorption. It is defined as the time difference between the beginning of adsorption and the "offset" beginning of desorption. This time interval is a function of the conditioning of the substratum and the residence time distribution, but it appears to be independent of the bulk CFU concentration (Figure 15). Offset Time of Desorption, 0.5 N/sqm S«6 7.5e6 CFU-Concentration Figure 15. Correlation between offset time and bulk CFU concentration. 78 Behavioral Distribution Results in this section represent measurements obtained from individual ■CFU and are not necessary related to the kinetics of colonization of substrata, i.e. events per unit time and area. The "behavioral" characteristics, measured and presented in this section, describe activities of CFU at the substratum such as movement, orientation of CFU during adsorption, cells per CFU, net growth, and more. The data, presented in distribution histograms, represent a defined subset of the data base. The criteria for the subset, depend on the specific behavioral characteristics. Data of individual CFU have been combined from several experiments and organized depending on shear stress. This reduces the number of distributions and increases the number■ of samples per distribution. Distributions representing 0.5 N m~2 are presented in this section and a complete set in Appendix F. Eight distributions per shear stress have been calculated. 79 Residence Time Two different distributions for residence time have been calculated: I. Total residence time, and 2. finite residence time. The difference between the two is the criterion for rejecting a CFU. For the total residence time distribution all CFU have been incorporated where adsorption has been observed including those which exceeded the last image. Hence, the residence time for these CFU could have been longer since their desorption has not been observed prior to termination of the experiment (Figure 16 a). For the finite residence time distribution only those CFU have been included where adsorption and desorption has been observed. In contrast to the total residence time distribution, this distribution represents the residence time of the reversibly adsorbed CFU. since both adsorption and desorption of these CFU have been observed. The difference between reversibly adsorbed and total CFU is reflected in the level of acceptance: 371 of 884 CFU were characterized in the finite compared to 815 of 884 CFU in the total residence time distribution. The probability of remaining at the substratum decreases with time. For 8 0 Total CFU S e rie s AA 0 .5 N /s q m AVERAGE - 6 7 .2 6 3 8 STANDARD DEVIATION - 8 3 .9 0 2 8 4 o 23- TOTAL RESIDENCE TIME [min] ACCEPT. 813 OF 884 Total CFU Series AA 0.5 N /sqm AVERAGE - 13.9973 STANDARD DEVIATION - 27.11492 ^ ACCEPT. 371 OF 884 FINITE RESIDENCE TIME [min] Figure 16. Residence time distribution Series AA (0.5 N m—2). a: Total residence time distribution representing all CFU AA except the ones entering or exiting, b. Finite residence time of series AA. Only CFU were accepted where adsorption and desorption has directly been observed (no daughter-CFU, entering, exiting, or CFU exceeding last image of the experiments). This distribution represents for reversibly adsorbed CFU the probability in respect to time to remain at the substratum. / example, the probability of desorbing between zero and five minutes at 0.5 N m""1 is 48%, between five and ten minutes 'it reduces to 12% and so on. Orientation of CFU During Adsorption The distribution of CFU orientation at its first observation after adsorption is presented in ' Figure 17. Only CFU were included where adsorption was observed Cno entry and no daughter-CFU). This distribution shows two peaks, one at 0° degree and one at 90° (flow direction 90°). In some case CFU length orientation could not be measured unequivocally and the image analyzer reported their orientation as 0°. About 25 to 30% of the CFU with a 0° orientation were identified as being squared or round (no valid measurement of orientation). That leaves about 30 to 35% of the CFU with a true 0° orientation. Therefore, it can be concluded that CFU either adsorb perpendicular or parallel to the flow direction with a very small probability for any values in between (Figure 17). 81 8 2 Total CFU S e rie s AA 0 .5 N /s q m AVERAGE - 4 8 .3 3 9 7 1 STANDARD DEVIATION - 4 3 .2 5 2 8 3 2 2 3 43 6 7 3 80 1123 133 1373 ORIENTATION OF CFU IN I . FIELD Figure 17. Orientation of adsorbing CFU at substratum. Only adsorbing CFU have been accepted for this distribution. Direction of flow: 90* Motility at Substratum Motility at the substratum was measured for all CFU which were observed for at least 15 minutes (three images). Figure 18 a displays the rate of gliding on the substratum. Rates of gliding less that 0.1 pm min™1 do not necessarily express motility. They can represent a change of location of the center point due to growth or resolution of the image analyzer. Figure 18 b shows the distribution of direction of gliding. CFU which were stationary are represented with a direction of 0* (flow direction 90*). Moving CFU have a 83 aoccpt. are or a84 Total CFU S eries AA 0 .5 N /s q m >E - 2 .1 7 2 3 2 7 E —0 2 STANDARD DEVIATION - . 0 3 8 3 3 8 7 INTEGRATED RATE OF GUDING Cum/mlnl Total CFU Series AA 0.5 N /sqm AVERAGE - 103.4289 STANDARD DEVIATION - 102.7*22 ACCEPT. 870 or 884 as28|3|8ga35g=g INTEGRATED DIRECTION OF GUDING Figure 18. Integrated movement at substratum. a: Integrated rate of gliding of CFU in Series AA. Minimum residence time for this distribution is 15 min. b: Integrated direction of gliding of CFU at substratum. 0* degree direction is associated with no motion. Direction of flow: 90". 84 Total CFU S e rie s AA 0 .5