Alison Kraigsley and Paul D. Ronney
Department of Aerospace and Mechanical Engineering
University of Southern California, Los Angeles, CA 90089-1453
Steven E. Finkel
Department of Biological Sciences
University of Southern California, Los Angeles, CA 90089-1340
Not proficient in English?
Biofilm formation is a major factor in the growth and transport of both desirable and undesirable bacteria as well as fouling and corrosion. While much is known about self-propagating reaction-diffusion fronts that occur in many chemically reacting systems such as flames, polymerization processes and some aqueous reactions, this vast knowledge base has not previously been systematically applied to biological systems such as motile bacteria or the spread and growth of biofilms. We have initiated a systematic of the study the influences of hydrodynamics on biofilm formation and growth, using a simple flow tube apparatus using Escherichia coli. Biofilm formation was monitored using a modified Gram-stain protocol and quantitative spectrophotometric assays. Initial experiments do indeed show behavior analogous to reaction-diffusion systems.
Biofilms are complex communities of surface-attached microorganisms, comprised either of a single or multiple species (Costerton, 1995; Davey & O’Toole, 2000). Over the past few decades, there has been a growing realization that bacteria in most environments are not found in a unicellular, planktonic (free-living) form such as those typically studied in the laboratory, but exist predominantly in multi-cellular surface attached communities called biofilms (Costerton et al., 1995). This realization has spurred much research into the physical and chemical properties of biofilms, the characterization of their morphology, and the mechanisms of their development.
Biofilms are found ubiquitously in virtually all natural, medical, and industrial settings where bacteria exist (Costerton, 1995; Costerton et al., 1995; Davey and O’Toole, 2000). Biofilms can form in almost any hydrated environment that has the proper nutrient conditions, and can develop on a wide variety of abiotic hydrophobic and hydrophilic surfaces, including glass, metals, and plastics (Miller & Ahearn, 1987; Marshall, 1992; Fletcher,1998; O’Toole & Kolter, 1998ab). Biofilms also readily form on biotic surfaces including human skin and epithelial cells. Generally surface material does not strongly affect biofilm growth. Examples of bacterial biofilms are chronic P. aeruginosa infections in the lungs of cystic fibrosis patients, oral microbes on teeth, the "slime" layer on the surface of submerged objects in aquatic environments, biofouling of water supply, sewage, and oil pipelines, and bacterial colonization of plant surfaces. The transition from the planktonic, free-swimming, mode of existence to a biofilm is a regulated developmental process that leads to a complex surface-attached bacterial community (O’Toole et al., 2000). This biofilm community has a number of distinct characteristics including the production of exopolysaccharides, the formation of chemical and pH gradients, a marked degree of structural heterogeneity, and the development of high level resistance to a wide variety of biocides (Hoyle et al, 1992). Formation of biofilms can have profound negative and positive impact in these environments, and, as a consequence, can have high costs in terms of both economics and human health.
A bacterial biofilm begins to form when individual cells initially attach to a surface (Costerton, 1995; O’Toole & Kolter, 1998b). The ability of a cell to perform this “initial attachment event” is controlled by both environmental factors, including nutrient levels, temperature, and pH, and genetic factors, including the presence of genes encoding motility functions, environmental sensors, adhesins, etc. (Costerton, 1995; O’Toole et al., 2000). The combination of factors influencing biofilm development are frequently species-specific, however, there are many features common to most bacteria studied to date. After initial attachment, the cells begin to grow and spread as a monolayer on the surface to form microcolonies. During microcolony formation, cells undergo developmental changes which give rise to the complex architecture of the mature biofilm. Paramount among these changes are the production of the exopolysaccharide (EPS) matrix, one of the hallmarks of a mature biofilm (Costerton, 1995; Danese et al., 2000). As the biofilm continues to grow several things can happen; the biofilm may spread into uninfected areas as environmental conditions allow and, occasionally, cells will detach from the biofilm and re-enter a planktonic mode. These planktonic cells can then repeat the cycle, infecting new surfaces.
Figure 1. Schematic diagram of biofilm formation and growth (after O’Toole et al., 2000)
As stated, bacteria will form biofilms on many biotic surfaces and virtually all abiotic surfaces. The ability to attach to a wide variety of plastics, glass, and metals is mediated by specific surface proteins and appendages (O’Toole & Kolter, 1998a; Pratt & Kolter, 1998). Also important for initial attachment is the ability of bacteria to “swim” using flagella for propulsion, referred to as flagellar-mediated motility. Non-swimming bacteria have reduced biofilm forming ability. For most Gram-negative motile bacteria, approximately 1% of the genome is devoted to flagellar function. Another form of bacterial motility, referred to as “twitching” motility, is not mediated by the rotation of flagella, but is due to the extension and retraction of another appendage called pili (O’Toole & Kolter, 1998a). Unlike flagellar-mediated swimming, twitching motility occurs only when cells are attached to a surface and the bacteria slide themselves across that surface. Twitching is important for both the formation of microcolonies and spreading of biofilm communities.
Bacterial biofilms cause “biofouling” in a wide variety of industrial settings. Biofilms grow inside pipelines transporting a myriad of substances, including potable water, oil, chemicals and fire extinguishing agents (Fig. 2). Costs associated with biofilm contamination are due to both constriction of pipeline diameter, reducing transmission rates, and due to contamination. In marine settings, biofilms reduce the hydrodynamic efficiency of ships and propellers. Fire protection systems represent a particularly complex challenge for biological fouling prevention and control (Mittelman, 2001). Fluid flow is nearly always stagnant, and the piping conduits are not designed to facilitate routine cleaning operations. Pitting corrosion occurring under deposits in fire protection systems can be initiated or propagated by these microbial activities. In pipeline applications, through-wall penetration of carbon steel and copper has been reported within months after a new line has been brought into service. This can cause occlusion of pipelines, sometimes completely blocking flow in six-inch diameter pipelines. The costs of disinfection, cleaning and replacement of biofilm-contaminated material run into the hundreds of billions of dollars per year worldwide.
It has been shown that biofilm grown cells can become 10-1000X more resistant to the effects of antimicrobial agents than their planktonic counterparts (Brown et al., 1988; Hoyle and Costerton, 1991; Ashby et al., 1994; Costerton et al., 1995; Koenig et al, 1995; Stewart, 1996; Lewis, 2001; Mah & O’Toole, 2001). Biofilms show resistance to a wide range of antibiotics (including ampicillins, strepotomycin, tetracyclines, gentamicin, and many others) and biocide oxidants such as ozone, chlorine and iodine. This characteristic of biofilms makes them extremely difficult to control in both medical and industrial settings. Traditional antibiotic therapy can eliminate sensitive planktonic bacteria, but these same organisms when growing in a biofilm can survive treatment. For example, when biofilms grow on the surfaces of medical implants requiring antibiotic treatment, the therapeutic levels of antibiotic required to eliminate biofilm bacteria often cannot be achieved in the patient or are toxic (Barie et al., 1990). Therefore, biofilm-based infections can become chronic with the only recourse being removal of the contaminated implant. Biofilm-associated infections extend hospital stays an average of about three days and it is estimated that up to 65% of nosocomial infections are biofilm-based with an associated treatment cost in excess of $1 billion per year. Biofilms formed on indwelling medical devices (Fig. 3) serve as a reservoir of bacteria that can be shed into the body, leading to a chronic systemic infection. Indeed, up to 82% of nosocomial bacteremias are the result of bacterial contamination of intravascular catheterizations (Archibald & Gaynes, 1997). Other examples of medically significant biofilms include oral microbes on teeth, chronic Pseudomonas aeruginosa infections in the lungs of cystic fibrosis patients and bacterial contaminants on medical devices such as pacemakers and catheters.
Figure 2. Left: Tubercle formation in a carbon steel fire protection pipe. Iron oxidizing bacteria were found in association with the tubercles. Right: Bacterial biofilm associated with stainless steel tube. Scanning electron micrograph magnification at 5,000X (Mittelman, 2001).
Figure 3. Electron micrograph of interior surface of a vascular catheter removed from a patient showing growth of a bacterial biofilm of P. aeruginosa. (Yassien et al., 1995). Biofilm bacteria leaving the catheter can cause sepsis.
It is known that motile bacteria form biofilms more readily than cells that cannot perform flagellar-mediated swimming, but the reasons for this requirement are not fully understood (Fletcher, 1988; O’Toole & Kolter, 1998a; Pratt & Kolter, 1998). Cells that do not exhibit twitching motility, because they lack the pili genes, still form biofilms, but they do not achieve the characteristic biofilm architecture of wild-type cells. Hyperpiliated mutants, which also do not twitch, adhere to surfaces even better than wild-type cells, but also show altered morphologies (Gibbs & O’Toole, manuscript in preparation). The study of the formation of biofilms in terms of cell motility have generally focused on the ability of the cell to locomote; less attention has been focused on characterizing the effects of the flow of the liquid environment on biofilm formation. There is increasing interest in these questions and many investigators are now using various forms of flow cell technology to characterize biofilm formation. However, many of these studies have been focusing either on the kinetics of early attachment events or characterizing the morphologies of biofilms grown under differing flow regimes. What is lacking is a systematic study of the effects of hydrodynamics (e.g. flow rates and shear forces) on the formation, spread, and persistence of biofilms. Studies characterizing hydrodynamics effects on biofilm formation can address many fundamental questions. For example, cells adhere to water on a surface, how do they gain a foothold? In a deep layer of water, motile cells adhere to the surface, but non-motile cells do not. In order for cells to colonize a surface and form a biofilm, they need to reach the surface. Is motility required for biofilm spread as opposed to growth and maturation at a fixed location?
While a number of investigations of the flow characteristics on biofilm formation (e.g. Heydorn et al., 2000) have been performed, these studies only report the volumetric flow rate (or sometimes mean flow velocity (um), i.e. the velocity averaged over the cross-section of the flow channel). The flow environments are not well characterized in terms of flow velocity profiles at the biofilm growth location. Key questions have not been addressed, e.g. is mean flow velocity (um) sufficient or relevant to characterize biofilm growth? Due to the hydrodynamic no-slip condition, the flow velocity at the surface where the biofilm is growing is always zero – does this mean that the biofilm can attach and grow no matter how strong the flow? This seems unlikely. In order to predict momentum, heat and mass transfer, it is well known in the fluid mechanics literature that the gradient of velocity, temperature and composition at the surface, not the mean value of velocity, temperature or composition itself is the key factor affecting transport since all of these are gradient-transport properties (i.e. if the velocity, temperature or composition are uniform there is no flux of momentum, heat or mass, respectively).
As an example of these effects, consider motile planktonic Escherichia coli attempting to colonize a surface and form a biofilm. E. coli swim at typically 20 Ķm/s (Berg, 2000) and are about 1 Ķm in diameter, and thus can produce a fluid velocity gradient of about 20 Ķm/s / 1 Ķm = 20/s. If the local velocity gradient at the surface (in particular the shear rate ∂u/∂y, i.e. the gradient of velocity (u) in the direction (y) perpendicular to the velocity) is significantly smaller than this value, the E. coli can swim to the surface (where u = 0) and remain within a distance from the surface equal to their size without being dispersed. For laminar flow inside a cylindrical tube, the velocity gradient ∂u/∂r (i.e. the radial gradient of axial velocity) at the wall is 8um/d, where d is the inside diameter of the tube. For a flow rate of 1 ml/min in a tube of 1/8” inside diameter, this corresponds to um = 0.21 cm/s and ∂u/∂r = 5.3/s, which should be well within the swimming capability of the bacterium. If the flow rate were increased to 3.8 ml/min, ∂u/∂r would be 20/s and the E. coli might have much more difficulty colonizing the surface because the side of their body away from the wall would experience a fluid velocity equal to its swimming speed capability, and so would wind up tumbling along the wall rather than adhering to it – despite the fact that the fluid velocity at the wall is zero.
One reason for the lack of characterization and quantitative prediction of fluid flow and motility effects on biofilm formation and growth is the absence of an appropriate modeling foundation. The number of organisms in a macroscopic biofilm is far too large to track each individual. It is standard in many fields (e.g. chemistry, nuclear physics, macroeconomics) to use thermodynamically-based models in which the behavior of ensemble averages rather than individuals (e.g. molecules, sub-atomic particles, consumers) is analyzed to predict system performance. A natural choice for a thermodynamic approach to studying biofilm formation is the reaction-diffusion system because the biofilm grows and/or spreads in response to the transport (via diffusion and convection) of “reactants” (nutrients) to the “products” (individual bacterium) that then generate more products and cause the population of products to spread. (The term “reaction-diffusion” is generally understood to encompass convective as well as diffusive transport where appropriate). While much is known about reaction-diffusion systems that produce self-propagating fronts in many chemically reacting systems such as flames, polymerization processes and some aqueous reactions, this vast knowledge base has not previously been systematically applied to microbiological systems such as motile bacteria or spreading biofilms. For the use of reaction-diffusion models to be valid it is necessary to demonstrate, at least in concept, that reaction-diffusion behavior is exhibited in biofilms. This led us to perform the feasibility tests described below. The results do show that these hypotheses are in fact valid in principle.
Laminar flow in a cylindrical tube is a simple and well-characterized flow system, and so was chosen for our initial tests of flow effects on biofilm formation. Figure 4 shows the experimental apparatus and procedure we used. 10 cm long pieces of transparent Tygon PVC tubing of 1/8” inside diameter were placed for 12 hr at 37ŻC in a medium of Luria-Bertani (LB) nutrient broth + E. coli with half of the tube immersed in the medium and half exposed to air. This incubation period results in the formation of a dense biofilm near the air-medium interface due to the abundant supply of oxygen there. As seen in Fig. 5 (upper left, “control” case), a biofilm of much lower density forms in the submerged region and of course no growth occurs far above the interface. These samples were then placed in the flow system composed of an LB reservoir, peristaltic pump, pluming connections for the test samples, and a waste tank for LB after it passes through the sample tube. Both flow rate and test duration were varied.
Figure 4. Schematic diagram of apparatus and procedure for testing of flow effects on biofilm formation
Following O’Toole (1999), quantification of attachment of biofilm bacteria was accomplished by staining cells with the dye Crystal Violet (CV). CV will specifically stain bacteria (minimal staining of tubing material has been observed.) After staining and extensive washing, CV is solubilized by treatment with methanol and quantitated by determining the absorbance at 550 nm (A550) in a spectrophotometer. Experiments (O’Toole, 1999) have shown a quantitative relationship between the A550 measured and the number of colony forming units (CFU) of biofilm bacteria.
Figure 5 shows typical images of CV-stained biofilms resulting from these tests. It can be seen that for a fixed flow rate (left side, lower 3 images), the density of the film increases over time as expected. It is interesting to note that the biofilm can spread upstream of the location of the initial biofilm with a speed (for times < 12 hr) on the order of 0.5 mm/hr. This upstream spread is analogous to a flame spreading over a solid fuel bed (e.g. wood, paper, plastic) in the upwind direction. This phenomenon has been widely studied (e.g. de Ris (1969), Fernandez-Pello et al. (1980), Honda and Ronney (1998)) in the fire safety community and it is well known that under many circumstances the upwind spread is increases as the wind speed increases due to the increased rate of oxygen transport to the flame. It is also interesting to note that the spread seems to show a marked change between 12 and 24 hr, where a low-density film appears in the upstream region. Figure 5 (right column) shows the effect of flow rate for a fixed test time (3.5 hr). It can be seen that there is an optimal flow rate on the order of a few ml/min that maximizes both the upstream (of the initial dense region) progress of the biofilm and the density of the downstream growth. This is consistent with the suggestion that a flow velocity exceeding 3.8 ml/min (for a 1/8” I.D. tube), which corresponds to a shear rate ∂u/∂r at the wall of 20/s, is the maximum shear that the E. coli can readily withstand without dispersing. It is also worth nothing that at high shear rates (Fig. 5, lower right), the biofilm growth becomes very non-uniform and forms patches rather than coating the surface contiguously. This behavior is often found in reaction-diffusion systems, i.e. that at small shear rates, an increase in shear rate increases the flux of “reactants” (LB nutrients in this case) to the “reaction zone’ (the biofilm surface), thus increasing the rate of reaction, whereas too high a shear rate discourages reaction (because of insufficient residence time which results in loss of “heat” (bacterium in this case) from the reaction zone.) Moreover, at high shear rates the fire spreading process becomes unstable and leads to non-uniform spread (e.g. Wichman, 1999, Wichman and Olsen, 1999).
It should be noted that even for the highest flow studied (16 ml/min), the Reynolds number (Re) = umd/n, where n is the kinematic viscosity, is only 107, which is well below that required for transition to turbulent flow (Re Ň 2000), so turbulence effects cannot explain the patchy nature of the biofilms at the high flow rates.
Additional tests (not shown) in which the medium flowing through the sample tubes included planktonic E. coli as well as LB, generally showed less biofilm formation for the same flow rate and test duration, presumably because the planktonic bacteria were competing with the biofilm for nutrients. It might have been expected that the presence of planktonic bacteria might increase biofilm growth due to “recruitment” of planktonic bacteria by the biofilm, but there was no evidence to support this suggestion. Thus, we conclude that generally the biofilms we observed grew by spreading along the surface rather than by recruitment from the flowing media – recruitment is neither necessary nor desirable. This again supports the notion of modeling biofilms as reaction-diffusion systems.
These qualitative findings are supported by the quantitative data based on CV-A550 measurements (Fig. 6). In Fig. 6 (upper), the effect of time spent in the flow cell on the increase in biofilm density, as well as the formation of the biofilm far upstream of the initial biofilm inoculation region, is clearly seen. It can also be seen that (at least for a flow rate of 0.6 ml/min) in the downstream region the growth “saturates” after about 3.5 hr and after that time the growth is primarily spreading upstream. There is no evidence of “attrition” from the biofilm in that the biofilm density does not decrease at later times, at least up to 24 hr. In Fig. 6 (lower), it can be seen that the effect of flow rate is non-monotonic, namely that the densest growth occurs at an intermediate flow rate, and that for higher or lower flow rates the growth rate decreases substantially. In particular, between 7.8 ml/min (∂u/∂r at the wall = 42/s) and 16 ml/min (∂u/∂r = 85/s) the growth downstream of the inoculation point drops by a factor of at least 2. This range of ∂u/∂r is comparable to the predicted transition value of 20/s expected for E. coli. Also, the patchy nature of the growth at high flow rates can be seen in the fluctuations in absorbance as a function of distance. Finally, it can be see that as the flow rate increases, the steepness of the biofilm front (i.e. the slope of the plot of biofilm density vs. distance) increases also. This is consistent with the notion of a convection-diffusion zone at the upstream edge of the biofilm whose thickness scales as (D/(∂u/∂r))1/2 (Williams, 1985), i.e. the steepness increases as the flow rate (and thus stretch rate) increases.
Figure 6. Quantitative measurements of effect of flow and test duration on biofilm growth. Upper: fixed flow rate (0.6 ml/min), varying test duration; lower: fixed test duration (3.5 hr), varying flow rate. Negative distances refer to regions upstream of the inoculation point (i.e. the location of the medium-air interface where the dense biofilm was pre-formed (see Fig. 4).
Archibald, L. K., and R. P. Gaynes. 1997. Hospital acquired infections in the United States: the importance of interhospital comparisons. Nosocomial Inf. 11(2):245-255.
Ashby, M. J., J. E. Neale, S. J. Knott, and I. A. Critchley. 1994. Effect of antibiotics on non-growing planktonic cells and biofilms of Escherichia coli. J Antimicrob Chemother. 33(3):443-52.
Ausubel, F. A., R. Brent, R. E. Kingston, D. D. Moore, J. G. Seidman, J. A. Smith, and K. Struhl. 1990. Current Protocols in Molecular Biology. Wiley Interscience, New York.
Barie, P. S., N. V. Christou, E. P. Dellinger, W. R. Rout, H. H. Stone, and J. P. Waymack. 1990. Pathogenicity of the enterococcus in surgical infections. Ann. Surg. 212(2):155-158.
Berg, H. C., "Motile Behavior of Bacteria" Phys. Today 53, 24 (2000).
Bloemberg, G. V., G. A. O'Toole, B. J. J. Lugtenberg, and R. Kolter. 1997. Green fluorescent protein as a marker for Pseudomonas spp. Appl. Environ. Microbiol. 63(11):4543-4551.
Brooun, A., S. Liu, and K. Lewis. 2000. A dose-response study of antibiotic resistance in Pseudomonas aeruginosa biofilms. Antimicrob Agents Chemother. 44(3):640-6.
Brown, M. R., D. G. Allison, and P. Gilbert. 1988. Resistance of bacterial biofilms to antibiotics: a growth-rate related effect? J Antimicrob Chemother. 22(6):777-80.
Budrene E.O., Berg H. C., "Complex patterns formed by motile cells of E. coli," Nature 349, 630 (1991).
Cochran, W. L., G. A. McFeters, and P. S. Stewart. 2000. Reduced susceptibility of thin Pseudomonas aeruginosa biofilms to hydrogen peroxide and monochloramine. J Appl Microbiol. 88(1):22-30.
Cormack, B. P., R. H. Valdivia, and S. Falkow. 1996. FACS-optimized mutants of the green fluorescent protein (GFP). Gene. 173:33-8.
Costerton, J. W. 1995. Overview of microbial biofilms. J. Indus. Microbiol. 15:137-140.
Costerton, J. W., Z. Lewandowski, D. E. Caldwell, D. R. Korber, and H. M. Lappin-Scott. 1995. Microbial biofilms, p. 711-745. In L. N. Ornston, A. Balows, and E. P. Greenberg (ed.), Annu. Rev. Microbiol., vol. 49. Annual Reviews, Inc., Palo Alto, CA.
Danese, P. N., L. A. Pratt, and R. Kolter. 2000. Exopolysaccharide production is required for development of Escherichia coli K-12 biofilm architecture. J Bacteriol. 182(12):3593-6.
Datsenko K. A. and, B. L. Wanner. 2000. One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products. Proc Natl Acad Sci U S A. 97:6640-5.
Davey, M. E., and G. O. O'Toole. 2000. Microbial biofilms: from ecology to molecular genetics. Microbiol. Mol. Biol. Revs. 64(4):847-67.
De Kievit, T. R., M. D. Parkins, R. J. Gillis, R. Srikumar, H. Ceri, K. Poole, B. H. Iglewski, and D. G. Storey. 2001. Multidrug efflux pumps: Expression patterns and contribution to antibiotic resistance in Pseudomonas aeruginosa biofilms. Antimicrob Agents Chemother. 45(6):1761-70.
deRis, J. N. 1969. Spread of a laminar diffusion flame. Twelfth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1969, p. 241.
Epstein, I. R. Pojman, J. A. 1998. An introduction to nonlinear chemical dynamics, Oxford.
Fernandez-Pello, A. C., Ray, S.R., Glassman, I. 1981. Eighteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, p. 579.
Fletcher, M. 1988. Attachment of Pseudomonas fluorescens to glass and influence of electrolytes on bacterium-substratum separation distance. J. Bacteriol. 170(5):2027-2030.
Govan, J. R. W., and V. Deretic. 1996. Microbial pathogenesis in cystic fibrosis: mucoid Pseudomonas aeruginosa and Burkholderia cepacia. Microbiol. Rev. 60(3):539-574.
Heydorn, A., B. K. Ersboll, M. Hentzer, M. R. Parsek, M. Givskov, and S. Molin. 2000. Experimental reproducibility in flow-chamber biofilms. Microbiology. 146(Pt 10):2409-15.
Heydorn, A., A. T. Nielsen, M. Hentzer, C. Sternberg, M. Givskov, B. K. Ersboll, and S. Molin. 2000. Quantification of biofilm structures by the novel computer program COMSTAT. Microbiology. 146(Pt 10):2395-407.
Honda, L. K. and Ronney, P. D. 1998. "Effects of Ambient Atmosphere on Flame Spread at Microgravity,” Combustion Science and Technology 133:267-291.
Hoyle, B. D., and W. J. Costerton. 1991. Bacterial resistance to antibiotics: the role of biofilms. Progress in Drug Research. 37:91-105.
Koenig D.W., S. K. Mishra, and D. L. Pierson. 1995. Removal of Burkholderia cepacia biofilms with oxidants. Biofouling. 9:51-62.
Koenig, D.W., and D. L. Pierson. 1997. Microbiology of the Space Shuttle water system. Water Sci Technol. 35:59-64.
Kuchma, S. L., and G. A. O'Toole. 2000. Surface-induced and biofilm-induced changes in gene expression. Curr. Opin. Biotech. 11:429-433.
Lewis, K. 2001. Riddle of biofilm resistance. Antimicrob Agents Chemother. 45(4):999-1007.
Lewis, B., von Elbe, G., Combustion, Flames, and Explosions of Gases, 3rd ed., Academic Press, 1987.
Mah, T.-F., and G. A. O'Toole. 2001. Mechanisms of biofilm resistance to antimicrobial agents. TIMS. 9:34-39.
Marshall, K. C. 1992. Biofilms:an overview of bacterial adhesion, activity, and control at surfaces. ASM News. 58(4):202-207.
Maruta, K., Takeda, K., Ahn, J., Borer, K., Sitzki, L, Ronney, P. D., Deutchman, O. (2002). Extinction Limits of Catalytic Combustion in Microchannels, To appear in the Proceedings of the Combustion Institute, Vol. 29.
McLean, R.J.C., Cassanto, J.M., Barnes, M.B., Koo, J.H., 2001. Bacterial biofilm formation under microgravity conditions. FEMS Microbiology Letters 195, 115-119.
Miller, J.H. 1992. A short course in bacterial genetics. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.
Miller, M. J., and D. G. Ahearn. 1987. Adherence of Pseudomonas aeruginosa to hydrophilic contact lenses and other substrata. J. Clin. Microbiol. 25(8):1392-1397.
Mittelman, M. W. (2001). “Microbially Influenced Corrosion of Sprinkler Piping,” http://www.pmengineer.com/CDA/ArticleInformation/features/BNP__Features__Item/0,2732,24897,00.html.
Murray, J.D., Mathematical Biology, Springer-Verlag, 1993.
O'Toole, G. A., H. Kaplan, and R. Kolter. 2000. Biofilm formation as microbial development. Annu. Rev. Microbiol. 54:49-79.
O'Toole, G. A., and R. Kolter. 1998. Flagellar and twitching motility are necessary for Pseudomonas aeruginosa biofilm development. Mol. Microbiol. 30(2):295-304.
O'Toole, G. A., and R. Kolter. 1998. The initiation of biofilm formation in Pseudomonas fluorescens WCS365 proceeds via multiple, convergent signaling pathways: a genetic analysis. Mol. Microbiol. 28:449-461.
O'Toole, G. A., L. A. Pratt, P. I. Watnick, D. K. Newman, V. B. Weaver, and R. Kolter. 1999. Genetic approaches to the study of biofilms, p. 91-109. In R. J. Doyle (ed.), Methods in Enzymology, vol. 310. Academic Press, San Diego, CA.
Pier, G. 1998. Pseudomonas aeruginosa: a key problem in cystic fibrosis. ASM News. 64(6):339-347.
Pojman, J. A., Hyashenko, V. M., Khan, A. M., "Free-radical frontal polymerization: self-propagating reaction waves." J. Chem. Soc., Faraday Trans. 92, 2825 (1996).
Pratt, L. A., and R. Kolter. 1999. Genetic analysis of bacterial biofilm formation. Curr. Opin. Microbiol. 2:598-603.
Pratt, L. A., and R. Kolter. 1998. Genetic analysis of Escherichia coli biofilm formation: roles of flagella, motility, chemotaxis and type I pili. Mol. Microbiol. 30(2):285-294.
Prigent-Combaret, C., O. Vidal, C. Dorel, and P. Lejune. 1999. Abiotic surface sensing and biofilm-dependent regulation of gene expression in Escherichia coli. J. Bacteriol. 181(19):5993-6002.
Sauer, K., and A. K. Camper. 2001. Characterization of phenotypic changes in Pseudomonas putida in response to surface-associated growth. J Bacteriol. 183(22):6579-89.
Stewart, P. S. 1998. A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms. Biotechnol Bioeng. 59(3):261-72.
Stewart, P. S. 1996. Theoretical aspects of antibiotic diffusion into microbial biofilms. Antimicrob Agents Chemother. 40(11):2517-22.
Stover, C. K., X. Q. Pham, A. L. Erwin, S. D. Mizoguchi, P. Warrener, M. J. Hickey, F. S. Brinkman, W. O. Hufnagle, D. J. Kowalik, M. Lagrou, R. L. Garber, L. Goltry, E. Tolentino, S. Westbrock-Wadman, Y. Yuan, L. L. Brody, S. N. Coulter, K. R. Folger, A. Kas, K. Larbig, R. Lim, K. Smith, D. Spencer, G. K. Wong, Z. Wu, and I. T. Paulsen. 2000. Complete genome sequence of Pseudomonas aeruginosa PA01, an opportunistic pathogen. Nature. 406(6799):959-64.
Wichman, I. S. 1999. On Diffusion Flame Attachment Near Cold Surfaces. Combustion and Flame 117:384-393.
Wichman, I. S., Olson, S. L. 1999. Investigation of Diffusion Flame Tip Thermodiffusive and Hydrodynamic Instability Under Microgravity Conditions, 5th International Microgravity Combustion Workshop, Cleveland, OH, May 1999.
Williams, F. A., Combustion Theory, 2nd Ed., Benjamin-Cummins, 1985
Winfree, A.T., The Geometry of Biological Time, Springer-Verlag, 1990.
Yassien M, Khardori N, Ahmedy A, Toama M. (1995). Modulation of biofilms of Pseudomonas aeruginosa by quinolones. Antimicrob Agents Chemother. 39:2262-8.