Persister cells in a biofilm treated with a biocide

This study investigated the physiology and behaviour following treatment with ortho-phthalaldehyde (OPA), of Pseudomonas fluorescens in both the planktonic and sessile states. Steady-state biofilms and planktonic cells were collected from a bioreactor and their extracellular polymeric substances (EPS) were extracted using a method that did not destroy the cells. Cell structure and physiology after EPS extraction were compared in terms of respiratory activity, morphology, cell protein and polysaccharide content, and expression of the outer membrane proteins (OMP). Significant differences were found between the physiological parameters analysed. Planktonic cells were more metabolically active, and contained greater amounts of proteins and polysaccharides than biofilm cells. Moreover, biofilm formation promoted the expression of distinct OMP. Additional experiments were performed with cells after EPS extraction in order to compare the susceptibility of planktonic and biofilm cells to OPA. Cells were completely inactivated after exposure to the biocide (minimum bactericidal concentration, MBC = 0.55 ± 0.20 mM for planktonic cells; MBC = 1.7 ± 0.30 mM for biofilm cells). After treatment, the potential of inactivated cells to recover from antimicrobial exposure was evaluated over time. Planktonic cells remained inactive over 48 h while cells from biofilms recovered 24 h after exposure to OPA, and the number of viable and culturable cells increased over time. The MBC of the recovered biofilm cells after a second exposure to OPA was 0.58 ± 0.40 mM, a concentration similar to the MBC of planktonic cells. This study demonstrates that persister cells may survive in biocide-treated biofilms, even in the absence of EPS.     

Persister cells in a biofilm treated with a biocide

This study investigated the physiology and behaviour following treatment with ortho-phthalaldehyde (OPA), of Pseudomonas fluorescens in both the planktonic and sessile states. Steady-state biofilms and planktonic cells were collected from a bioreactor and their extracellular polymeric substances (EPS) were extracted using a method that did not destroy the cells. Cell structure and physiology after EPS extraction were compared in terms of respiratory activity, morphology, cell protein and polysaccharide content, and expression of the outer membrane proteins (OMP). Significant differences were found between the physiological parameters analysed. Planktonic cells were more metabolically active, and contained greater amounts of proteins and polysaccharides than biofilm cells. Moreover, biofilm formation promoted the expression of distinct OMP. Additional experiments were performed with cells after EPS extraction in order to compare the susceptibility of planktonic and biofilm cells to OPA. Cells were completely inactivated after exposure to the biocide (minimum bactericidal concentration, MBC = 0.55 ± 0.20 mM for planktonic cells; MBC = 1.7 ± 0.30 mM for biofilm cells). After treatment, the potential of inactivated cells to recover from antimicrobial exposure was evaluated over time. Planktonic cells remained inactive over 48 h while cells from biofilms recovered 24 h after exposure to OPA, and the number of viable and culturable cells increased over time. The MBC of the recovered biofilm cells after a second exposure to OPA was 0.58 ± 0.40 mM, a concentration similar to the MBC of planktonic cells. This study demonstrates that persister cells may survive in biocide-treated biofilms, even in the absence of EPS.     

Differences in carbohydrate profiles in batch culture grown planktonic and biofilm cells of Amphora rostrata Wm. Sm

Diatoms are abundant in biofilms developed on surfaces immersed in sunlit waters. In both the planktonic and the biofilm mode of growth, diatoms produce carbohydrate polymers which perform several functions including motility, protection, production of macro-aggregates and detoxification. However, little is known about the differences, if any, in the production and characterization at the molecular level of carbohydrates in planktonic and biofilm cells. In order to identify the differences in these two modes of growth, the concentration of total carbohydrates, carbohydrate fractions, neutral carbohydrates, uronic acids and amino sugars in planktonic and biofilm cells of Amphora rostrata were measured. The results showed that the distribution of carbohydrate fractions, uronic acids and amino sugars was different in biofilm and planktonic cells. Cell normalized concentrations of these components were two to five times greater in planktonic cells compared with biofilm cells. The concentrations of glucose and glucosamine decreased, whereas fucose increased in planktonic cells over the period of cultivation. Conversely, the concentrations of glucose and glucosamine increased while that of fucose decreased in attached cells. The study suggests that marked differences exist between the carbohydrates of the planktonic and the biofilm cells of A. rostrata.     

Role of planktonic and sessile extracellular metabolic byproducts on <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis> and <Emphasis Type="Italic">Escherichia coli</Emphasis> intra and interspecies relationships

Bacterial species are found primarily as residents of complex surface-associated communities, known as biofilms. Although these structures prevail in nature, bacteria still exist in planktonic lifestyle and differ from those in morphology, physiology, and metabolism. This study aimed to investigate the influence of physiological states of Pseudomonas aeruginosa and Escherichia coli in cell-to-cell interactions. Filtered supernatants obtained under planktonic and biofilm cultures of each single species were supplemented with tryptic soy broth (TSB) and used as the growth media (conditioned media) to planktonic and sessile growth of both single- and two-species cultures. Planktonic bacterial growth was examined through OD₆₄₀ measurement. One-day-old biofilms were evaluated in terms of biofilm biomass (CV), respiratory activity (XTT), and CFU number. Conditioned media obtained either in biofilm or in planktonic mode of life triggered a synergistic effect on planktonic growth, mainly for E. coli single cultures growing in P. aeruginosa supernatants. Biofilms grown in the presence of P. aeruginosa biofilms-derived metabolites presented less mass and activity. These events highlight that, when developed in biofilm, P. aeruginosa release signals or metabolites able to prejudice single and binary biofilm growth of others species and of their own species. However, products released by their planktonic counterparts did not impair biofilm growth or activity. E. coli, living as planktonic or sessile cultures, released signals and metabolites or removed un-beneficial compounds which promoted the growth and activity of all the species. Our findings revealed that inter and intraspecies behaviors depend on the involved bacteria and their adopted mode of life.     

Biofilm formation by <Emphasis Type="Italic">Candida albicans</Emphasis> isolated from intrauterine devices

Our survey revealed that infected intrauterine devices (IUDs) recovered from patients suffering from reproductive tract infections (RTIs) were tainted with Candida biofilm composed of a single or multiple species. Scanning electron microscopy (SEM) analysis of C. albicans biofilm topography showed that it consists of a dense network of mono- or multilayer of cells embedded within the matrix of extracellular polymeric substances (EPS). Confocal scanning laser microscopy (CSLM) and atomic force microscopy (AFM) images depicted that C. albicans biofilms have a highly heterogeneous architecture composed of cellular and noncellular elements with EPS distributed in the cell-surface periphery or at cell-cell interface. Biochemical analysis showed that EPS produced by C. albicans biofilm contained significantly reduced total carbohydrate (40%), protein (5%) and enhanced amount of hexosamine (4%) in contrast to its planktonic counterparts. The in vitro activity of antifungal agents amphotericin B, nystatin, fluconazole and chlorhexidine against pre-formed C. albicans biofilm, assessed using XTT (2,3-bis[2-methoxy-4-nitro-5-sulfophenyl]-2H-tetrazolium-5-carboxanilide) reduction assay revealed increased resistance of these infectious biofilm (50% reduction in metabolic activity at a concentration of 8, 16, 64, 128 μg/ml respectively) in comparison to its planktonic form.     

Characterization of extracellular polymeric substances from denitrifying organism Comamonas denitrificans

Extracellular polymeric substances (EPS) play an important role in the formation and activity of biofilms in wastewater treatment (WWT). The EPS of the denitrifying biomarker Comamonas denitrificans strain 110, produced in different culture media and growth modes, were characterized. The EPS mainly contained protein (3–37%), nucleic acids (9–50%), and carbohydrates (3–21%). The extracellular DNA was found to be important for initial biofilm formation since biofilm, but not planktonic growth, was inhibited in the presence of DNase. The polysaccharide fraction appeared to consist of at least two distinct polymers, one branched fraction (A) made up of glucose and mannose with a molecular weight around 100 kDa. The other fraction (B) was larger and consisted of ribose, mannose, glucose, rhamnose, arabinose, galactose, and N-acetylglucosamine. Fraction B polysaccharides were mainly found in capsular EPS which was the dominant type in biofilms and agar-grown colonies. Fraction A was abundant in the released EPS, the dominant type in planktonic cultures. Biofilm and agar-grown EPS displayed similar overall properties while planktonic EPS showed clear compositional disparity. This study presents results on the physiology of a key WWT organism, which may be useful in the future development of improved biofilm techniques for WWT purposes.     

Structural organization and dynamics of exopolysaccharide matrix and microcolonies formation by Streptococcus mutans in biofilms

Aims: To investigate the structural organization and dynamics of exopolysaccharides (EPS) matrix and microcolonies formation by Streptococcus mutans during the biofilm development process. Methods and Results: Biofilms of Strep. mutans were formed on saliva‐coated hydroxyapatite (sHA) discs in the presence of glucose or sucrose (alone or mixed with starch). At specific time points, biofilms were subjected to confocal fluorescence imaging and computational analysis. EPS matrix was steadily formed on sHA surface in the presence of sucrose during the first 8 h followed by a threefold biomass increase between 8 and 30 h of biofilm development. The initial formation and further development of three‐dimensional microcolony structure occurred concomitantly with EPS matrix synthesis. Tridimensional renderings showed EPS closely associated with microcolonies throughout the biofilm development process forming four distinct domains (i) between sHA surface and microcolonies, (ii) within, (iii) covering and (iv) filling the spaces between microcolonies. The combination of starch and sucrose resulted in rapid formation of elevated amounts of EPS matrix and faster assembly of microcolonies by Strep. mutans, which altered their structural organization and susceptibility of the biofilm to acid killing (vs sucrose‐grown biofilms; P < 0·05). Conclusions: Our data indicate that EPS modulate the development, sequence of assembly and spatial distribution of microcolonies by Strep. mutans. Significance and Impact of the Study: Simultaneous visualization and analysis of EPS matrix and microcolonies provide a more precise examination of the structural organization of biofilms than labelling bacteria alone, which could be a useful approach to elucidate the exact mechanisms by which Strep. mutans influences oral biofilm formation and possibly identify novel targets for effective antibiofilm therapies.     

Antifungal effects of the flavonoids kaempferol and quercetin: a possible alternative for the control of fungal biofilms

This study aimed to determine the minimum inhibitory concentration (MIC) of kaempferol and quercetin against planktonic and biofilm forms of the Candida parapsilosis complex. Initially, nine C. parapsilosis sensu stricto, nine C. orthopsilosis and nine C. metapsilosis strains were used. Planktonic susceptibility to kaempferol and quercetin was assessed. Growing and mature biofilms were then exposed to the flavonoids at MIC or 10xMIC, respectively, and theywere also analyzed by confocal laser scanning microscopy. The MIC ranges were 32-128 µg ml^?1 for kaempferol and 0.5-16 µg ml^?1 for quercetin. Kaempferol and quercetin decreased (P?<?0.05) the metabolic activity and biomass of growing biofilms of the C. parapsilosis complex. As for mature biofilms, the metabolic effects of the flavonoids varied, according to the cryptic species, but kaempferol caused an overall reduction in biofilm biomass. Microscopic analyses showed restructuring of biofilms after flavonoid exposure. These results highlight the potential use of these compounds as sustainable resources for the control of fungal biofilms.     

Biofilm characteristics and evaluation of the sanitation procedures of thermophilic Aeribacillus pallidus E334 biofilms

The ability of Aeribacillus pallidus E334 to produce pellicle and form a biofilm was studied. Optimal biofilm formation occurred at 60 °C, pH 7.5 and 1.5% NaCl. Extra polymeric substances (EPS) were composed of proteins and eDNA (21.4 kb). E334 formed biofilm on many surfaces, but mostly preferred polypropylene and glass. Using CLSM analysis, the network-like structure of the EPS was observed. The A. pallidus biofilm had a novel eDNA content. DNaseI susceptibility (86.8% removal) of eDNA revealed its importance in mature biofilms, but the purified eDNA was resistant to DNaseI, probably due to its extended folding outside the matrix. Among 15 cleaning agents, biofilms could be removed with alkaline protease and sodium dodecyl sulphate (SDS). The removal of cells from polypropylene and biomass on glass was achieved with combined SDS/alkaline protease treatment. Strong A. pallidus biofilms could cause risks for industrial processes and abiotic surfaces must be taken into consideration in terms of sanitation procedures.     

Characterisation of conditioning layers formed by exopolymeric substances of Pseudomonas NCIMB 2021 on surfaces of AISI 316 stainless steel

This investigation aimed to characterise conditioning layers formed on AISI 316 stainless steel by different types of extracellular polymeric substances (EPS), i.e. biofilm, planktonic and capsular exopolymers, isolated from continuous cultures of marine Pseudomonas received from the National Collection of Industrial and Marine Bacteria (strain NCIMB 2021). Colorimetric assays and gas chromatography‐mass spectrometry analysis confirmed previously obtained results based on a FTIR and SDS‐PAGE study of Pseudomonas NCIMB 2021 EPS demonstrating the presence of protein, neutral and amino sugars and uronic acids. The content and the ratio of these macromolecules differed depending on the type of EPS. X‐ray photoelectron spectroscopy revealed that conditioning layers formed upon exposure of steel to EPS solutions were chemically dissimilar. It is proposed that the observed difference in the chemistry of conditioning layers is the likely reason for reported differences in attachment of Pseudomonas cells to EPS‐conditioned steel surfaces.     

Biofilm form and function: carbon availability affects biofilm architecture, metabolic activity and planktonic cell yield

Aims: To investigate carbon transformation by biofilms and changes in biofilm architecture, metabolic activity and planktonic cell yield in response to fluctuating carbon availability. Methods and Results: Pseudomonas sp. biofilms were cultured under alternating carbon‐replete and carbon‐limited conditions. A shift to medium without added carbon led to a 90% decrease in biofilm respiration rate and a 40% reduction in planktonic cell yield within 1 h. Attached cell division and progeny release were shown to contribute to planktonic cell numbers during carbon limitation. Development of a significantly enlarged biofilm surface area during carbon limitation facilitated a rapid increase in whole‐biofilm metabolic activity, cell yield and biomass upon the re‐introduction of carbon after 8 days of limitation. The cumulative number of planktonic cells (>10¹⁰ CFU) released from the biofilm during the cultivation period contained only 1·0% of the total carbon available to the biofilm, with 6·5% of the carbon retained in the biofilm and 54% mineralized to CO₂. Conclusions: Biofilm‐derived planktonic cell yield is a proliferation mechanism. The rapid response of biofilms to environmental perturbations facilitates the optimal utilization of resources to promote both proliferation and survival. Biofilms function as efficient catalysts for environmental carbon transformation and mineralization. Significance and Impact of the study: A greater understanding of the relationship between biofilm form and function can inform strategies intended to control and/or promote biofilm formation.     

Characterization and anti-biofilm activity of extracellular polymeric substances produced by the marine biofilm-forming bacterium Pseudoalteromonas ulvae strain TC14

This study investigated soluble (Sol-EPS), loosely bound (LB-EPS), and tightly bound extracellular polymeric substances (TB-EPS) harvested from biofilm and planktonic cultures of the marine bacterium Pseudoalteromonas ulvae TC14. The aim of the characterization (colorimetric methods, FTIR, GC-MS, NMR, HPGPC, and AFM analyses) was to identify new anti-biofilm compounds; activity was assessed using the BioFilm Ring Test®. A step-wise separation of EPS was designed, based on differences in water-solubility and acidity. An acidic fraction was isolated from TB-EPS, which strongly inhibited biofilm formation by marine bacterial strains in a concentration-dependent manner. The main constituents of this fraction were characterized as two glucan-like polysaccharides. An active poly(glutamyl-glutamate) fraction was also recovered from TB-EPS. The distribution of these key EPS components in Sol-EPS, LB-EPS, and TB-EPS was distinct and differed quantitatively in biofilm vs planktonic cultures. The anti-biofilm potential of the fractions emphasizes the putative antifouling role of EPS in the environment.     

Mechanisms of Bacillus cereus biofilm formation: an investigation of the physicochemical characteristics of cell surfaces and extracellular proteins

Microbial biofilms contribute to biofouling in a wide range of processes from medical implants to processed food. The extracellular polymeric substances (EPS) are implicated in imparting biofilms with structural stability and resistance to cleaning products. Still, very little is known about the structural role of the EPS in Gram-positive systems. Here, we have compared the cell surface and EPS of surface-attached (biofilm) and free-floating (planktonic) cells of Bacillus cereus, an organism routinely isolated from within biofilms on different surfaces. Our results indicate that the surface properties of cells change during biofilm formation and that the EPS proteins function as non-specific adhesions during biofilm formation. The physicochemical traits of the cell surface and the EPS proteins give us an insight into the forces that drive biofilm formation and maintenance in B. cereus.     

EPS II-Dependent Autoaggregation of Sinorhizobium meliloti Planktonic Cells

Planktonic cells of Sinorhizobium meliloti, a Gram-negative symbiotic bacterium, display autoaggregation under static conditions. ExpR is a LuxR-type regulator that controls many functions in S. meliloti, including synthesis of two exopolysaccharides, EPS I (succinoglycan) and EPS II (galactoglucan). Since exopolysaccharides are important for bacterial attachment, we studied the involvement of EPS I and II in autoaggregation of S. meliloti. Presence of an intact copy of the expR locus was shown to be necessary for autoaggregation. A mutant incapable of producing EPS I displayed autoaggregation percentage similar to that of parental strain, whereas autoaggregation was significantly lower for a mutant defective in biosynthesis of EPS II. Our findings clearly indicate that EPS II is the essential component involved in autoaggregation of planktonic S. meliloti cells, and that EPS I plays no role in such aggregation.     

Planktonic or non‐planktonic food in young‐of‐the‐year European perch Perca fluviatilis in ponds

Higher biomass especially of some aquatic macrophyte species offered a higher density of phytophilous zoobenthos, but did not increase the proportion of non‐planktonic to planktonic prey in young‐of‐the‐year perch Perca fluviatilis. Both abundance and biomass of non‐planktonic prey dominated over planktonic prey in the pond with lower biomass of aquatic macrophytes and lower food. Survival of P. fluviatilis was lower (20%) in the pond with lower food than in the other pond (34%), however, specific growth rate (1·3% day^?1) and final Fulton's condition factor of P. fluviatilis were similar in both ponds.     

Extracellular DNA in Helicobacter pylori biofilm: a backstairs rumour

Aims: This study detected and characterized the extracellular DNA (eDNA) in the biofilm extracellular polymeric substance (EPS) matrix of Helicobacter pylori and investigated the role of such component in the biofilm development. Methods and Results: Extracellular DNA was purified and characterized in a 2‐day‐old mature biofilm developed by the reference strain H. pylori ATCC 43629, the clinical isolate H. pylori SDB60 and the environmental strain H. pylori MDC1. Subsequently, the role of eDNA in the H. pylori biofilm was evaluated by adding DNase I during biofilm formation and on mature biofilms. Extracellular DNA was detected in the 2‐day‐old EPS biofilm matrix of all analysed H. pylori strains. The DNA fingerprintings, performed by RAPD analysis, on eDNA and intracellular DNA (iDNA), showed some remarkable differences. The data obtained by microtitre biofilm assay as well as colony forming unit count and CLSM (confocal laser scanning microscopy) qualitative analysis did not show any significant differences between the DNase I‐treated biofilms and the corresponding not treated controls both in formation and on mature biofilms. Conclusions: In this study, we provide evidence that eDNA is a component of the EPS matrix of H. pylori biofilm. The different profiles of eDNA and iDNA indicate that lysed cells are not the primary source of eDNA release, suggesting that other active mechanisms might be involved in this process. Moreover, the biomass assay suggests that eDNA may not be the main component of biofilm matrix, suggesting that it could be primarily involved in other mechanisms such as recombination processes, via transformation, contributing to the wide genomic variability of this micro‐organism defined as a ‘quasi‐species’. Significance and Impact of the Study: The presence of eDNA in H. pylori biofilm can contribute to the active dynamic exchange of information aimed to reach the best condition for the bacterial survival in the host and in the environment.     

The use of biocides to control sulphate‐reducing bacteria in biofilms on mild steel surfaces

Three different types of biocides, viz. formaldehyde (FM), glutaraldehyde (GA) and isothiozolone (ITZ) were used to control planktonic and sessile populations of two marine isolates of sulphate‐reducing bacteria (SRB). The influence of these biocides on the initial attachment of cells to mild steel surfaces, on subsequent biofilm formation and on the activity of hydrogenase enzymes within developed biofilms was evaluated. In the presence of biocides the rate and degree of colonization of mild steel by SRB depended on incubation time, bacterial isolate and the type of biocide used. Although SRB differed in their susceptibility to biocides, for all isolates the biofilm population was more resistant to the treatment than the planktonic population. GA showed highest efficiency in controlling planktonic and sessile SRB compared with the other two biocides. The activity of the enzyme hydrogenase measured in SRB biofilms varied between isolates and with the biocide treatment. No correlation was found between the number of sessile cells and hydrogenase activity.     

The corrosion behaviour of galvanized steel in cooling tower water containing a biocide and a corrosion inhibitor

The corrosion behaviour of galvanized steel in cooling tower water containing a biocide and a corrosion inhibitor was investigated over a 10-month period in a hotel. Planktonic and sessile numbers of sulphate reducing bacteria (SRB) and heterotrophic bacteria were monitored. The corrosion rate was determined by the weight loss method. The corrosion products were analyzed by energy dispersive X-ray spectroscopy and X-ray diffraction. A mineralized, heterogeneous biofilm was observed on the coupons. Although a biocide and a corrosion inhibitor were regularly added to the cooling water, the results showed that microorganisms, such as SRB in the mixed species biofilm, caused corrosion of galvanized steel. It was observed that Zn layers on the test coupons were completely depleted after 3?months. The Fe concentrations in the biofilm showed significant correlations with the weight loss and carbohydrate concentration (respectively, p?<?0.01 and p?<?0.01).     

Biofilm Formation by Escherichia coli O157:H7 on Stainless Steel: Effect of Exopolysaccharide and Curli Production on Its Resistance to Chlorine

The resistance of Escherichia coli O157:H7 strains ATCC 43895-, 43895-EPS (an exopolysaccharide [EPS]-overproducing mutant), and ATCC 43895+ (a curli-producing mutant) to chlorine, a sanitizer commonly used in the food industry, was studied. Planktonic cells of strains 43895-EPS and/or ATCC 43895+ grown under conditions supporting EPS and curli production, respectively, showed the highest resistance to chlorine, indicating that EPS and curli afford protection. Planktonic cells (ca. 9 log₁₀ CFU/ml) of all strains, however, were killed within 10 min by treatment with 50 μg of chlorine/ml. Significantly lower numbers of strain 43895-EPS, compared to those of strain ATCC 43895-, attached to stainless steel coupons, but the growth rate of strain 43895-EPS on coupons was not significantly different from that of strain ATCC 43895-, indicating that EPS production did not affect cell growth during biofilm formation. Curli production did not affect the initial attachment of cells to coupons but did enhance biofilm production. The resistance of E. coli O157:H7 to chlorine increased significantly as cells formed biofilm on coupons; strain ATCC 43895+ was the most resistant. Population sizes of strains ATCC 43895+ and ATCC 43895- in biofilm formed at 12°C were not significantly different, but cells of strain ATCC 43895+ showed significantly higher resistance than did cells of strain ATCC 43895-. These observations support the hypothesis that the production of EPS and curli increase the resistance of E. coli O157:H7 to chlorine.     

Toluene degradation kinetics for planktonic and biofilm-grown cells of Pseudomonas putida 54G

Toluene degradation kinetics by biofilm and planktonic cells of Pseudomonas putida 54G were compared in this study. Batch degradation of (14)C toluene was used to evaluate kinetic parameters for planktonic cells. The kinetic parameters determined for toluene degradation were: specific growth rate, mu(max) = 10.08 +/- 1.2/day; half-saturation constant, K(S) = 3.98 +/- 1.28 mg/L; substrate inhibition constant, K(I) = 42.78 +/- 3.87 mg/L. Biofilm cells, grown on ceramic rings in vapor phase bioreactors, were removed and suspended in batch cultures to calculate (14)C toluene degradation rates. Specific activities measured for planktonic and biofilm cells were similar based on toluene degrading cells and total biomass. Long-term toluene exposure reduced specific activities that were based on total biomass for both biofilm and planktonic cells. These results suggest that long-term toluene exposure caused a large portion of the biomass to become inactive, even though the biofilm was not substrate limited. Conversely, specific activities based on numbers of toluene-culturable cells were comparable for both biofilm and planktonically grown cultures. Planktonic cell kinetics are often used in bioreactor models to model substrate degradation and growth of bacteria in biofilms, a procedure we found to be appropriate for this organism. For superior bioreactor design, however, changes in cellular activity that occur during biofilm development should be investigated under conditions relevant to reactor operation before predictive models for bioreactor systems are developed. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 535-546, 1997.