scholarly journals Untethering and Degradation of the Polysaccharide Matrix Are Essential Steps in the Dispersion Response of Pseudomonas aeruginosa Biofilms

2019 ◽  
Vol 202 (3) ◽  
Author(s):  
Kathryn E. Cherny ◽  
Karin Sauer
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Matrix Protein ◽  
Single Cells ◽  
Glycoside Hydrolases ◽  
Content Type ◽  
Endogenous Expression ◽  
Multicellular Aggregates ◽  
Insertional Inactivation ◽  
The Matrix ◽  
Biofilm Matrix

ABSTRACT Biofilms are multicellular aggregates of bacteria that are encased in an extracellular matrix. The biofilm matrix of Pseudomonas aeruginosa PAO1 is composed of eDNA, proteins, and the polysaccharides Pel and Psl. This matrix is thought to be degraded during dispersion to liberate cells from the biofilms, with dispersion being apparent not only by single cells escaping from the biofilm but also leaving behind eroded or hollowed-out biofilm. However, little is known of the factors involved in matrix degradation. Here, we focused on the glycoside hydrolases PelA and PslG. We demonstrate that induction of pelA but not pslG expression resulted in dispersion. As Psl is tethered to the matrix adhesin CdrA, we furthermore explored the role of CdrA in dispersion. cdrA mutant biofilms were hyperdispersive, while lapG mutant biofilms were impaired in dispersion in response to glutamate and nitric oxide, indicating the presence of the surface-associated matrix protein CdrA impedes the dispersion response. In turn, insertional inactivation of cdrA enabled pslG-induced dispersion. Lowering of the intracellular c-di-GMP level via induction of PA2133 encoding a phosphodiesterase was not sufficient to induce dispersion by wild-type strains and strains overexpressing pslG, indicating that pslG-induced dispersion is independent of c-di-GMP modulation and, likely, LapG. IMPORTANCE Pseudomonas aeruginosa forms multicellular aggregates or biofilms encased in a matrix. We show for the first time here that dispersion by P. aeruginosa requires the endogenous expression of pelA and pslG, leading to the degradation of both Pel and Psl polysaccharides, with PslG-induced dispersion being CdrA dependent. The findings suggested that endogenously induced Psl degradation is a sequential process, initiated by untethering of CdrA-bound Psl or CdrA-dependent cell interactions to enable Psl degradation and ultimately, dispersion. Untethering likely involves CdrA release in a manner independent of c-di-GMP modulation and thus LapG. Our findings not only provide insight into matrix degrading factors contributing to dispersion but also identify key steps in the degradation of structural components of the P. aeruginosa biofilm matrix.

scholarly journals CdrA Interactions within thePseudomonas aeruginosaBiofilm Matrix Safeguard It from Proteolysis and Promote Cellular Packing

mBio ◽  
2018 ◽  
Vol 9 (5) ◽  
Author(s):  
Courtney Reichhardt ◽  
Cynthis Wong ◽  
Daniel Passos da Silva ◽  
Daniel J. Wozniak ◽  
Matthew R. Parsek
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Matrix Protein ◽  
Bacterial Species ◽  
Model Organism ◽  
Biofilm Growth ◽  
Content Type ◽  
Multicellular Aggregates ◽  
The Matrix ◽  
Matrix Stability ◽  
First Time

ABSTRACTBiofilms are robust multicellular aggregates of bacteria that are encased in an extracellular matrix. Different bacterial species have been shown to use a range of biopolymers to build their matrices.Pseudomonas aeruginosais a model organism for the laboratory study of biofilms, and past work has suggested that exopolysaccharides are a required matrix component. However, we found that expression of the matrix protein CdrA, in the absence of biofilm exopolysaccharides, allowed biofilm formation through the production of a CdrA-rich proteinaceous matrix. This represents a novel function for CdrA. Similar observations have been made for other species such asEscherichia coliandStaphylococcus aureus, which can utilize protein-dominant biofilm matrices. However, we found that these CdrA-containing matrices were susceptible to both exogenous and self-produced proteases. We previously reported that CdrA directly binds the biofilm matrix exopolysaccharide Psl. Now we have found that when CdrA bound to Psl, it was protected from proteolysis. Together, these results support the idea of the importance of multibiomolecular components in matrix stability and led us to propose a model in which CdrA-CdrA interactions can enhance cell-cell packing in an aggregate that is resistant to physical shear, while Psl-CdrA interactions enhance aggregate integrity in the presence of self-produced and exogenous proteases.IMPORTANCEPseudomonas aeruginosaforms multicellular aggregates or biofilms using both exopolysaccharides and the CdrA matrix adhesin. We showed for the first time thatP. aeruginosacan use CdrA to build biofilms that do not require known matrix exopolysaccharides. It is appreciated that biofilm growth is protective against environmental assaults. However, little is known about how the interactions between individual matrix components aid in this protection. We found that interactions between CdrA and the exopolysaccharide Psl fortify the matrix by preventing CdrA proteolysis. When both components—CdrA and Psl—are part of the matrix, robust aggregates form that are tightly packed and protease resistant. These findings provide insight into how biofilms persist in protease-rich host environments.

scholarly journals The Versatile Pseudomonas aeruginosa Biofilm Matrix Protein CdrA Promotes Aggregation through Different Extracellular Exopolysaccharide Interactions

2020 ◽  
Vol 202 (19) ◽  
Author(s):  
Courtney Reichhardt ◽  
Holly M. Jacobs ◽  
Michael Matwichuk ◽  
Cynthis Wong ◽  
Daniel J. Wozniak ◽  
...  
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Biofilm Formation ◽  
Matrix Protein ◽  
Specific Interaction ◽  
Aggregate Stability ◽  
Laboratory Strain ◽  
Chronic Infections ◽  
Content Type ◽  
Chemical Structures ◽  
Biofilm Matrix

ABSTRACT Pseudomonas aeruginosa is an important pathogen that causes chronic infections that involve multicellular aggregates called biofilms. Within biofilms, bacteria are surrounded in a protective extracellular matrix of proteins, exopolysaccharides (EPS), and DNA. A key P. aeruginosa matrix protein is an extracellular adhesin called CdrA, which promotes aggregation by binding to the EPS Psl and via CdrA-CdrA interactions. We hypothesized that because of its ability to bind Psl, CdrA would be important only for strains that use Psl as the primary EPS (e.g., the laboratory strain PAO1). Thus, we predicted that cdrA might be dispensable for biofilm formation by strains that do not utilize Psl (e.g., the laboratory strain PA14). Instead, we observed that cdrA deletion strains exhibited biofilm defects, regardless of their EPS dependencies. We screened a panel of clinical and environmental P. aeruginosa isolates for the presence of the cdrA allele and production of CdrA protein. All isolates that we tested contained the cdrA allele, and these alleles had minimal sequence variation compared to the reference PAO1 cdrA gene. Additionally, all isolates except one produced detectable CdrA protein. We investigated the possible mechanisms of CdrA-promoted biofilm formation in these strains where Psl is not dominant, and we discovered that CdrA binds to Pel. Although Psl and Pel chemical structures are distinct, this appears to be a specific interaction, since previous work has shown that CdrA binds discriminately to other EPS. Our findings provide new understanding of biofilm formation across P. aeruginosa isolates and emphasize the versatility of CdrA. IMPORTANCE Depending upon the strain, Pseudomonas aeruginosa can use different exopolysaccharides (e.g., Psl, Pel, and alginate) to build its biofilm matrix. Previously, we demonstrated that the biofilm matrix protein CdrA binds to Psl, promoting biofilm formation and aggregate stability. As such, it was thought that CdrA might be important for biofilm assembly only in strains that rely upon Psl. However, past studies indicated that CdrA can interact with monosaccharides not present in Psl, including N-acetylglucosamine, a constituent of another EPS called Pel. We discovered that CdrA also binds to Pel and promotes biofilm formation by strains in which Psl is not dominant. Thus, our findings suggest that CdrA plays a common role as a biofilm matrix cross-linker across P. aeruginosa isolates with different EPS.

scholarly journals Role of Matrix β-1,3 Glucan in Antifungal Resistance of Non-albicans Candida Biofilms

2013 ◽  
Vol 57 (4) ◽  
pp. 1918-1920 ◽  
Author(s):  
K. F. Mitchell ◽  
H. T. Taff ◽  
M. A. Cuevas ◽  
E. L. Reinicke ◽  
H. Sanchez ◽  
...  
Keyword(s):  
Health Care ◽  
Drug Resistance ◽  
Candida Albicans ◽  
Care Setting ◽  
Antifungal Susceptibility ◽  
Antifungal Drug ◽  
Content Type ◽  
The Matrix ◽  
Biofilm Matrix

ABSTRACTCandidabiofilm infections pose an increasing threat in the health care setting due to the drug resistance associated with this lifestyle. Several mechanisms underlie the resistance phenomenon. InCandida albicans, one mechanism involves drug impedance by the biofilm matrix linked to β-1,3 glucan. Here, we show this is important for otherCandidaspp. We identified β-1,3 glucan in the matrix, found that the matrix sequesters antifungal drug, and enhanced antifungal susceptibility with matrix β-1,3 glucan hydrolysis.

scholarly journals Pseudomonas aeruginosa Requires the DNA-Specific Endonuclease EndA To Degrade Extracellular Genomic DNA To Disperse from the Biofilm

2019 ◽  
Vol 201 (18) ◽  
Author(s):  
Kathryn E. Cherny ◽  
Karin Sauer
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Biofilm Formation ◽  
Genomic Dna ◽  
Early Stage ◽  
Content Type ◽  
Biofilm Dispersion ◽  
Biofilm Structure ◽  
First Time ◽  
Biofilm Matrix ◽  
Dispersed Cells

ABSTRACT The dispersion of biofilms is an active process resulting in the release of planktonic cells from the biofilm structure. While much is known about the process of dispersion cue perception and the subsequent modulation of the c-di-GMP pool, little is known about subsequent events resulting in the release of cells from the biofilm. Given that dispersion coincides with void formation and an overall erosion of the biofilm structure, we asked whether dispersion involves degradation of the biofilm matrix. Here, we focused on extracellular genomic DNA (eDNA) due to its almost universal presence in the matrix of biofilm-forming species. We identified two probable nucleases, endA and eddB, and eddA encoding a phosphatase that were significantly increased in transcript abundance in dispersed cells. However, only inactivation of endA but not eddA or eddB impaired dispersion by Pseudomonas aeruginosa biofilms in response to glutamate and nitric oxide (NO). Heterologously produced EndA was found to be secreted and active in degrading genomic DNA. While endA inactivation had little effect on biofilm formation and the presence of eDNA in biofilms, eDNA degradation upon induction of dispersion was impaired. In contrast, induction of endA expression coincided with eDNA degradation and resulted in biofilm dispersion. Thus, released cells demonstrated a hyperattaching phenotype but remained as resistant to tobramycin as biofilm cells from which they egress, indicating EndA-dispersed cells adopted some but not all of the phenotypes associated with dispersed cells. Our findings indicate for the first time a role of DNase EndA in dispersion and suggest weakening of the biofilm matrix is a requisite for biofilm dispersion. IMPORTANCE The finding that exposure to DNase I impairs biofilm formation or leads to the dispersal of early stage biofilms has led to the realization of extracellular genomic DNA (eDNA) as a structural component of the biofilm matrix. However, little is known about the contribution of intrinsic DNases to the weakening of the biofilm matrix and dispersion of established biofilms. Here, we demonstrate for the first time that nucleases are induced in dispersed Pseudomonas aeruginosa cells and are essential to the dispersion response and that degradation of matrix eDNA by endogenously produced/secreted EndA is required for P. aeruginosa biofilm dispersion. Our findings suggest that dispersing cells mediate their active release from the biofilm matrix via the induction of nucleases.

scholarly journals Pushing beyond the Envelope: the Potential Roles of OprF inPseudomonas aeruginosaBiofilm Formation and Pathogenicity

2019 ◽  
Vol 201 (18) ◽  
Author(s):  
Erin K. Cassin ◽  
Boo Shan Tseng
Keyword(s):  
Extracellular Matrix ◽  
Outer Membrane ◽  
Biofilm Formation ◽  
Matrix Protein ◽  
Cell Envelope ◽  
Outer Membrane Vesicles ◽  
Extracellular Dna ◽  
Future Research ◽  
Content Type ◽  
Biofilm Matrix

ABSTRACTThe ability ofPseudomonas aeruginosato form biofilms, which are communities of cells encased in a self-produced extracellular matrix, protects the cells from antibiotics and the host immune response. While some biofilm matrix components, such as exopolysaccharides and extracellular DNA, are relatively well characterized, the extracellular matrix proteins remain understudied. Multiple proteomic analyses of theP. aeruginosasoluble biofilm matrix and outer membrane vesicles, which are a component of the matrix, have identified OprF as an abundant matrix protein. To date, the few reports on the effects ofoprFmutations on biofilm formation are conflicting, and little is known about the potential role of OprF in the biofilm matrix. The majority of OprF studies focus on the protein as a cell-associated porin. As a component of the outer membrane, OprF assumes dual conformations and is involved in solute transport, as well as cell envelope integrity. Here, we review the current literature on OprF inP. aeruginosa, discussing how the structure and function of the cell-associated and matrix-associated protein may affect biofilm formation and pathogenesis in order to inform future research on this understudied matrix protein.

scholarly journals Galactose Metabolism Plays a Crucial Role in Biofilm Formation by Bacillus subtilis

mBio ◽  
2012 ◽  
Vol 3 (4) ◽  
Author(s):  
Yunrong Chai ◽  
Pascale B. Beauregard ◽  
Hera Vlamakis ◽  
Richard Losick ◽  
Roberto Kolter
Keyword(s):  
Bacillus Subtilis ◽  
Biofilm Formation ◽  
Carbon Sources ◽  
Galactose Metabolism ◽  
Content Type ◽  
Leloir Pathway ◽  
The Matrix ◽  
Living Organisms ◽  
Galactose Metabolites ◽  
Biofilm Matrix

ABSTRACTGalactose is a common monosaccharide that can be utilized by all living organisms via the activities of three main enzymes that make up the Leloir pathway: GalK, GalT, and GalE. InBacillus subtilis, the absence of GalE causes sensitivity to exogenous galactose, leading to rapid cell lysis. This effect can be attributed to the accumulation of toxic galactose metabolites, since thegalEmutant is blocked in the final step of galactose catabolism. In a screen for suppressor mutants restoring viability to agalEnull mutant in the presence of galactose, we identified mutations insinR, which is the major biofilm repressor gene. These mutations caused an increase in the production of the exopolysaccharide (EPS) component of the biofilm matrix. We propose that UDP-galactose is the toxic galactose metabolite and that it is used in the synthesis of EPS. Thus, EPS production can function as a shunt mechanism for this toxic molecule. Additionally, we demonstrated that galactose metabolism genes play an essential role inB. subtilisbiofilm formation and that the expressions of both thegalandepsgenes are interrelated. Finally, we propose thatB. subtilisand other members of theBacillusgenus may have evolved to utilize naturally occurring polymers of galactose, such as galactan, as carbon sources.IMPORTANCEBacteria switch from unicellular to multicellular states by producing extracellular matrices that contain exopolysaccharides. In such aggregates, known as biofilms, bacteria are more resistant to antibiotics. This makes biofilms a serious problem in clinical settings. The resilience of biofilms makes them very useful in industrial settings. Thus, understanding the production of biofilm matrices is an important problem in microbiology. In studying the synthesis of the biofilm matrix ofBacillus subtilis, we provide further understanding of a long-standing microbiological observation that certain mutants defective in the utilization of galactose became sensitive to it. In this work, we show that the toxicity observed before was because cells were grown under conditions that were not propitious to produce the exopolysaccharide component of the matrix. When cells are grown under conditions that favor matrix production, the toxicity of galactose is relieved. This allowed us to demonstrate that galactose metabolism is essential for the synthesis of the extracellular matrix.

scholarly journals Molecular Determinants of the Thickened Matrix in a Dual-Species Pseudomonas aeruginosa and Enterococcus faecalis Biofilm

2017 ◽  
Vol 83 (21) ◽  
Author(s):  
Keehoon Lee ◽  
Kang-Mu Lee ◽  
Donggeun Kim ◽  
Sang Sun Yoon
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Enterococcus Faecalis ◽  
Synergistic Effects ◽  
Bacterial Species ◽  
Extracellular Dna ◽  
Infection Model ◽  
Surgical Removal ◽  
Chronic Infections ◽  
Content Type ◽  
Biofilm Matrix

ABSTRACT Biofilms are microbial communities that inhabit various surfaces and are surrounded by extracellular matrices (ECMs). Clinical microbiologists have shown that the majority of chronic infections are caused by biofilms, following the introduction of the first biofilm infection model by J. W. Costerton and colleagues (J. Lam, R. Chan, K. Lam, and J. W. Costerton, Infect Immun 28:546–556, 1980). However, treatments for chronic biofilm infections are still limited to surgical removal of the infected sites. Pseudomonas aeruginosa and Enterococcus faecalis are two frequently identified bacterial species in biofilm infections; nevertheless, the interactions between these two species, especially during biofilm growth, are not clearly understood. In this study, we observed phenotypic changes in a dual-species biofilm of P. aeruginosa and E. faecalis, including a dramatic increase in biofilm matrix thickness. For clear elucidation of the spatial distribution of the dual-species biofilm, P. aeruginosa and E. faecalis were labeled with red and green fluorescence, respectively. E. faecalis was located at the lower part of the dual-species biofilm, while P. aeruginosa developed a structured biofilm on the upper part. Mutants with altered exopolysaccharide (EPS) productions were constructed in order to determine the molecular basis for the synergistic effect of the dual-species biofilm. Increased biofilm matrix thickness was associated with EPSs, not extracellular DNA. In particular, Pel and Psl contributed to interspecies and intraspecies interactions, respectively, in the dual-species P. aeruginosa and E. faecalis biofilm. Accordingly, targeting Pel and Psl might be an effective part of eradicating P. aeruginosa polymicrobial biofilms. IMPORTANCE Chronic infection is a serious problem in the medical field. Scientists have observed that chronic infections are closely associated with biofilms, and the vast majority of infection-causing biofilms are polymicrobial. Many studies have reported that microbes in polymicrobial biofilms interact with each other and that the bacterial interactions result in elevated virulence, in terms of factors, such as infectivity and antibiotic resistance. Pseudomonas aeruginosa and Enterococcus faecalis are frequently isolated pathogens in chronic biofilm infections. Nevertheless, while both bacteria are known to be agents of numerous nosocomial infections and can cause serious diseases, interactions between the bacteria in biofilms have rarely been examined. In this investigation, we aimed to characterize P. aeruginosa and E. faecalis dual-species biofilms and to determine the molecular factors that cause synergistic effects, especially on the matrix thickening of the biofilm. We suspect that our findings will contribute to the development of more efficient methods for eradicating polymicrobial biofilm infections.

scholarly journals A Biofilm Matrix-Associated Protease Inhibitor ProtectsPseudomonas aeruginosafrom Proteolytic Attack

mBio ◽  
2018 ◽  
Vol 9 (2) ◽  
Author(s):  
Boo Shan Tseng ◽  
Courtney Reichhardt ◽  
Gennifer E. Merrihew ◽  
Sophia A. Araujo-Hernandez ◽  
Joe J. Harrison ◽  
...  
Keyword(s):  
Immune Response ◽  
Immune System ◽  
Protease Inhibitor ◽  
Neutrophil Elastase ◽  
Matrix Protein ◽  
Lipid Vesicles ◽  
Matrix Proteins ◽  
Host Immune System ◽  
Content Type ◽  
Biofilm Matrix

ABSTRACTPseudomonas aeruginosaproduces an extracellular biofilm matrix that consists of nucleic acids, exopolysaccharides, lipid vesicles, and proteins. In general, the protein component of the biofilm matrix is poorly defined and understudied relative to the other major matrix constituents. While matrix proteins have been suggested to provide many functions to the biofilm, only proteins that play a structural role have been characterized thus far. Here we identify proteins enriched in the matrix ofP. aeruginosabiofilms. We then focused on a candidate matrix protein, the serine protease inhibitor ecotin (PA2755). This protein is able to inhibit neutrophil elastase, a bactericidal enzyme produced by the host immune system duringP. aeruginosabiofilm infections. We show that ecotin binds to the key biofilm matrix exopolysaccharide Psl and that it can inhibit neutrophil elastase when associated with Psl. Finally, we show that ecotin protects both planktonic and biofilmP. aeruginosacells from neutrophil elastase-mediated killing. This may represent a novel mechanism of protection for biofilms to increase their tolerance against the innate immune response.IMPORTANCEProteins associated with the extracellular matrix of bacterial aggregates called biofilms have long been suggested to provide many important functions to the community. To date, however, only proteins that provide structural roles have been described, and few matrix-associated proteins have been identified. We developed a method to identify matrix proteins and characterized one. We show that this protein, when associated with the biofilm matrix, can inhibit a bactericidal enzyme produced by the immune system during infection and protect biofilm cells from death induced by the enzyme. This may represent a novel mechanism of protection for biofilms, further increasing their tolerance against the immune response. Together, our results are the first to show a nonstructural function for a confirmed matrix-interacting protein.

scholarly journals Effect of host-mimicking medium and biofilm growth on the ability of colistin to kill Pseudomonas aeruginosa

Microbiology ◽  
2020 ◽  
Vol 166 (12) ◽  
pp. 1171-1180 ◽  
Author(s):  
Esther Sweeney ◽  
Akshay Sabnis ◽  
Andrew M. Edwards ◽  
Freya Harrison
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Ex Vivo ◽  
Clinical Success ◽  
Biofilm Growth ◽  
Content Type ◽  
The Matrix ◽  
Model Versus ◽  
High Doses

In vivo biofilms cause recalcitrant infections with extensive and unpredictable antibiotic tolerance. Here, we demonstrate increased tolerance of colistin by Pseudomonas aeruginosa when grown in medium that mimics cystic fibrosis (CF) sputum versus standard medium in in vitro biofilm assays, and drastically increased tolerance when grown in an ex vivo CF model versus the in vitro assay. We used colistin conjugated to the fluorescent dye BODIPY to assess the penetration of the antibiotic into ex vivo biofilms and showed that poor penetration partly explains the high doses of drug necessary to kill bacteria in these biofilms. The ability of antibiotics to penetrate the biofilm matrix is key to their clinical success, but hard to measure. Our results demonstrate both the importance of reduced entry into the matrix in in vivo-like biofilm, and the tractability of using a fluorescent tag and benchtop fluorimeter to assess antibiotic entry into biofilms. This method could be a relatively quick, cheap and useful addition to diagnostic and drug development pipelines, allowing the assessment of drug entry into biofilms, in in vivo-like conditions, prior to more detailed tests of biofilm killing.

scholarly journals Single Cells Exhibit Differing Behavioral Phases during Early Stages of Pseudomonas aeruginosa Swarming

2019 ◽  
Vol 201 (19) ◽  
Author(s):  
Chinedu S. Madukoma ◽  
Peixian Liang ◽  
Aleksandar Dimkovikj ◽  
Jianxu Chen ◽  
Shaun W. Lee ◽  
...  
Keyword(s):  
Pseudomonas Aeruginosa ◽  
Cell Motility ◽  
Single Cell ◽  
High Cell Density ◽  
Single Cells ◽  
High Cell ◽  
Wild Type ◽  
Content Type ◽  
Type Iv ◽  
The Many

ABSTRACT Pseudomonas aeruginosa is among the many bacteria that swarm, where groups of cells coordinate to move over surfaces. It has been challenging to determine the behavior of single cells within these high-cell-density swarms. To track individual cells within P. aeruginosa swarms, we imaged a fluorescently labeled subset of the larger population. Single cells at the advancing swarm edge varied in their motility dynamics as a function of time. From these data, we delineated four phases of early swarming prior to the formation of the tendril fractals characteristic of P. aeruginosa swarming by collectively considering both micro- and macroscale data. We determined that the period of greatest single-cell motility does not coincide with the period of greatest collective swarm expansion. We also noted that flagellar, rhamnolipid, and type IV pilus motility mutants exhibit substantially less single-cell motility than the wild type. IMPORTANCE Numerous bacteria exhibit coordinated swarming motion over surfaces. It is often challenging to assess the behavior of single cells within swarming communities due to the limitations of identifying, tracking, and analyzing the traits of swarming cells over time. Here, we show that the behavior of Pseudomonas aeruginosa swarming cells can vary substantially in the earliest phases of swarming. This is important to establish that dynamic behaviors should not be assumed to be constant over long periods when predicting and simulating the actions of swarming bacteria.

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