Workshop 2: Pattern Formation and Development in Colonial Organisms

(October 13,2008 - October 17,2008 )

Organizers


Philip Maini
Centre for Mathematical Biology, University of Oxford
Hans Othmer
School of Mathematics, University of Minnesota

E. coli and Dictyostelium are two of the most widely studied organisms in this area, so this workshop will focus in the main on these, but it is important that it is not restricted to these two examples. Research in this area falls naturally into the two broad categories of (1) single cell, and (2) population level dynamics. We consider each in more detail below:

  1. At the single cell level, there are a number of phenomena that have been studied to various degrees of depth but for which explanations remain elusive. For example, a full understanding of signal transduction, namely, how do bacteria convert external stimuli into internal dynamics in a robust, yet incredibly sensitive manner (responding to a change in a few molecules over a background range of several orders of magnitude of molecules)? Within this, the goal is to understand gain and amplification. One possible explanation is receptor clustering but recent research suggests that this is not sufficient in itself. There are several alternative models for many of these processes but none are consistent with all the key known experimental behaviours.

    Once the signal is internalised, the next question is to elucidate the cascade of reactions that determines response. For example, in E Coli, this triggers the flagellar motor to respond. One then has to understand the mechanism of motor operation and behaviour.
  2. At the cell population level it is known that within the laboratory bacteria can produce complex spatiotemporal patterns. Although this may be viewed as an interesting curiosity, it is felt that it will give important insights into the formation of biofilms which do have significant implications.

Other population level activity includes quorum sensing, differentiation etc. Complex patterns arise in myxobacteria, while in Dictyostelium discoideum (Dd) a range of morphogenetic behaviour is observed that is most likely conserved across species yielding important information for higher organisms. Dd is a powerful modelling paradigm for signal transduction, cell-cell signalling, cell differentiation, cell movement.

The implications of the above behaviours are widespread. For example, bacterial oral infections can lead to vascular disease, while biofilm formation is a major concern for the welfare of patients with surgical implants.

The mathematical disciplines used in the analysis of the models to be discussed in the workshop includes ordinary and partial differential equations, and stochastic equations.

Accepted Speakers

Mark Alber
Department of Mathematics, University of Notre Dame
David Chopp
Engineering Sciences and Applied Mathematics, J. L. Kellogg Graduate School of Management
John Dallon
Department of Mathematics, Brigham Young University
Jack Dockery
Department of Mathematical Sciences, Montana State University
Radek Erban
Mathematical Institute, University of Oxford
Richard Firtel
Section of Cell and Developmental Biology, University of California, San Diego
Roseanne Ford
Department of Chemical Engineering, University of Virginia
Thomas Hillen
Mathematical and Statistical Sciences, University of Alberta
John King
School of Mathematical Sciences, University of Nottingham
Isaac Klapper
Department of Mathematical Sciences, Montana State University
Timothy Newman
Department of Physics, Arizona State University
Hans Othmer
School of Mathematics, University of Minnesota
Tony Romeo
Microbiology and Cell Biology, University of Florida
James Shapiro
Biochemistry and Molecular Biology, University of Chicago
Angela Stevens
Applied Mathematics and Bioquant, Ruprecht-Karls-Universit""at Heidelberg
Harry Swinney
Physics Department and Center for Nonlinear Dynamics, University of Texas
Peter Thomas
Mathematics, Biology & Cognitive Science, Case Western Reserve University
Yuhai Tu
Physical Sciences & Computational Biology Center, IBM Thomas J. Watson Research Center
Xiangrong (Benny) Xin
Biomedical Engineering and Mathematics, University of Minnesota
Monday, October 13, 2008
Time Session
08:30 AM
09:00 AM
James Shapiro - What do colony patterns mean?

Colony patterns contain important information about the behavior and responses of the component cells in a particular experimental environment. Two critical questions are: (1) How do we extract mechanistic information from the observed patterns, and (2) What is the biological relevance of the behaviors revealed by the patterns? I will discuss patterns in E. coli, B. subtilis and Proteus mirabilis colonies and use these examples to describe how genetic and environmental manipulations can be used to draw meaningful conclusions about mechanism from pattern analysis. I will also discuss how we can interpret the biological relevance of patterns which do not themselves have adaptive utility.

10:30 AM
11:30 AM
Yuhai Tu - A biological signal processor: How E. coli responds to time-varying signals

In this talk, I will present our recent work in trying to understand bacterial chemotaxis (bacteria's ability to sense and track chemical gradient) by using a quantitative modeling approach. Based on molecular level knowledge of the E. coli chemotaxis pathway, we propose a simple model for bacterial chemotaxis and use it to understand signal processing in E. coli. In particular, we will address: 1) How E. coli respond to various time-varying stimuli, such as ramps, oscillatory signals and impulse signals. 2) How the cell uses its memory and computation capability to sense and respond to a minute chemical gradient among a wide range of background.



  • "Modeling the chemotactic response of E. coli to time-varying stimuli", Yuhai Tu, T. Shimizu and H. Berg, PNAS, 09/2008.

  • "Effects of adaptation in maintaining high sensitivity over a wide range of backgrounds for E. coli chemotaxis", B. Mello and Yuhai Tu, Biophysical Journal, 92, 2329-2337 (2007).

11:30 AM
12:30 PM
Roseanne Ford - Interactions of swimming bacteria with surfaces

The onset of biofilm formation requires the attachment of individual bacteria to surfaces. Our long-standing interest in swimming bacteria prompted the question, how does bacterial motility affect this initial attachment event? As bacteria swim toward a surface will they collide with the surface or alter their trajectory and move along the surface? Do bacterial flagella increase the likelihood of attachment or provide a mechanism to release adsorbed bacteria from a surface? How is the individual swimming behavior of bacteria near a surface manifested collectively in a population of bacteria that encounter a saturated porous medium? To address these questions we developed a series of experimental approaches that include: tracking swimming cells near a surface; measuring sorption rates of motile bacteria in a parallel plate flow chamber; and Monte Carlo simulations of bacteriall populations at interfaces between porous media and bulk solution.

02:00 PM
03:00 PM
Xiangrong (Benny) Xin - A systematic model of bacterial chemotaxis: from signal transduction to cell motility in Escherichia coli

The movement of bacteria in response to environmental changes of specific metabolites and signaling molecules is called bacterial chemotaxis. Chemotaxis in Escherichia coli (E. coli) is a best studied system. The authors will present a systematic model of E. coli chemotaxis that can capture many features of the system and reproduce a full range of experimental observations from signaling (excitation, perfect adaptation, robustness, high sensitivity, wide dynamic range, etc.) to motor behavior and cellular motility. A remarkable feature of the signaling pathway is its high sensitivity to small relative changes in concentrations of chemical stimuli over a broad range of ambient concentrations. To account for it, the signaling part of the model is based on the structural and functional unit of receptor clusters, 'trimer of chemoreceptor dimers', which has been solidly experimentally established but not well quantitatively modeled, so the theoretical work includes more molecular mechanism in modeling and provides a more mechanistically based description of the origin of high sensitivity.


Work done in collaboration with David J. Odde and Hans G. Othmer.


Key References



  1. Sourjik V, Berg HC. (2002). Receptor sensitivity in bacterial chemotaxis. Proc. Natl. Acad. Sci. U.S.A. 99: 123-127.

  2. Sourjik V. (2004). Receptor clustering and signal processing in E. coli chemotaxis. Trends Microbiol. 12: 569-576.

Tuesday, October 14, 2008
Time Session
09:00 AM
10:00 AM
Mark Alber - Role of reversals in Myxobacterial Swarming

Many bacteria are able to spread rapidly over the surface using a strategy called swarming. When the cells cover a surface at high density and compete with each other for nutrients, swarming permits them to maintain rapid growth at the swarm edge. Swarming with flagella has been investigated for many years, and much has been learned about its regulation. Nevertheless, its choreography, which is somewhat related to the counterflow of pedestrians on a city sidewalk, has remained elusive. It is the bacterial equivalent of dancing toward the exit in a crowd of moving bodies that usually are in close contact. Myxococcus xanthus expands its swarms at 1.6 lm/min, about a third the speed of individual cells gliding over the same surface. Each cell has pilus engines at its front end and slime secretion engines at its rear. Using the known mechanics of these engines and the ways they are coordinated, we have developed a cell-based model to study the role of social interactions in bacterial swarming. The model is able to quantify the contributions of individual motility engines to swarming. It also shows that microscopic social interactions and cell reversals help to form the ordered collective motion observed in swarms.

10:30 AM
11:30 AM
Isaac Klapper - Physical Influences on Biofilm Structure

The familiar view of microbes in their free (planktonic) state is not the norm; rather it is believed that much of the microbial biomass, perhaps 95-99%, is located in close-knit communities, designated biofilms and microbial mats, consisting of large numbers of organisms living within self-secreted matrices constructed of polymers and other molecules. (Microbes in collective behave very differently from their planktonic state; even genetic expression patterns change.) These matrices serve the purposes of anchoring and protecting their communities in favorable locations while providing a framework in which structured populations can differentiate and self-organize.


Viewed as materials, biofilms are quite interesting: they are living, growing fluids with surprising ability to respond to and defend against their environments. This talk wlll present a general overview of efforts to characterize and model biofilms on a continuum macroscale, and present an application related to bacterial-induced mineralization.

02:00 PM
03:00 PM
Harry Swinney - Deadly competition between sibling bacterial colonies

Bacteria can secrete a wide array of antibacterial compounds when competing with other bacteria for the same resources. Some of these compounds, such as bacteriocins, can affect bacteria of similar or closely related strains. In some cases these secretions have been found to kill sibling cells that belong to the same colony. Here we present experimental observations of competition between two sibling colonies of Paenibacillus dendritiformis grown on a low nutrient agar gel. We find that neighboring colonies (growing from inoculation droplets) mutually inhibit growth through secretions that become lethal if the level exceeds a well-defined threshold. In contrast, within a single colony developing from a droplet inoculation, no growth inhibition is observed. However, growth inhibition and cell death are observed outside a growing single colony if material extracted from the agar between two growing colonies is introduced. To interpret the observations we devised a simple mathematical model for the secretion of an antibacterial compound. Simulations of this model illustrate how secretions from neighboring colonies can be deadly while secretions from a single colony growing from a droplet are not suicidal.


*Work done in collaboration with Avraham Be'er, Hepeng Zhang, E.-L. Florin, and Shelley M. Payne (University of Texas) and Eshel Ben-Jacob (Tel Aviv University)

03:00 PM
04:00 PM
Angela Stevens - Self-organization and local interaction

N/A

Wednesday, October 15, 2008
Time Session
09:00 AM
10:00 AM
Wouter Rappel - At the interface of modeling and experiments in eukaryotic chemotaxis

Chemotactic eukaryotic cells are able to detect chemoattractant gradients that are both shallow and have a low background concentration. We will present our modeling efforts to understand this directional sensing process, including calculations on the effect of noise in the number of bound receptors. Furthermore, we will present preliminary data from our experimental efforts, aimed at addressing the predictions generated by our theoretical work.

10:30 AM
11:30 AM
Richard Firtel - Ras control of chemotaxis

Cells' ability to detect and orient themselves in chemoattractant gradients has been the subject of numerous studies, but the underlying molecular mechanisms remain largely unknown. Ras activation is the earliest polarized response to chemoattractant gradients downstream from heterotrimeric G proteins in Dictyostelium and inhibition of Ras signaling induces directional migration defects. Activated Ras is enriched at the leading edge, promoting the localized activation of key chemotactic effectors, such as PI3K and TORC2. In Dictyostelium, Ras controls cell motility, chemotaxis and signal relay, acting, in part, through the regulation of PI3K and TORC2, downstream from GPCR and heterotrimeric G proteins. To understand this process, we have investigated the mechanism by which Ras is spatially and temporally controls and the pathways that are regulated by Ras and by which Ras is regulated.


To investigate the role of Ras in directional sensing, we studied the effect of its mis-regulation using cells with disrupted RasGAP activity. We identified an orthologue of mammalian NF1, DdNF1, as a major regulator of Ras activity in Dictyostelium. We show that disruption of nfaA leads to spatially and temporally unregulated Ras activity, causing cytokinesis and chemotaxis defects. Furthermore, we find that RasGAP activity also affects the rate of Ras activation, in addition to promoting Ras deactivation. Using unpolarized, latrunculin-treated cells, we show that tight regulation of Ras is essential for gradient sensing and indicates a role for Ras as a component of the cell's compass.


The Aimless RasGEF (gefA) was suggested to be an upstream regulator of these Ras functions. To get insight into the mechanisms regulating Ras signaling, we undertook a sequential affinity purification and mass spectrometry approach to identify proteins interacting with Aimless. We found that Aimless is part of a stable protein complex that includes another RasGEF, RasGEFH, PP2A, and a previously uncharacterized Armadillo-like repeat-containing protein of 175 kDa. Co-immunoprecipitation studies indicate that the latter acts as a scaffold, which we named Sca1, bringing together an Aimless-RasGEFH heterodimer and PP2A. Whereas disruption of gefH alone produced minor effects, cells that lack only Aimless, both RasGEFs, or Sca1 display reduced Ras and PKB activity as well as F-actin polymerization, and exhibit cell motility as well as chemotaxis defects. We identified RasC, an orthologue of mammalian H-Ras, as the major Ras protein regulated by the RasGEF/Sca1/ PP2A complex. Our data suggest that the Sca1-scaffolded signaling complex regulates PKB activity by controlling the Ras-dependent activation of TORC2, but not that of PI3K, which are both Ras effectors regulating PKB. Furthermore, phospho-proteomics coupled to biochemical studies revealed that Sca1 undergoes dynamic phosphorylation, which includes transient and chemoattractant-induced PKB-promoted phosphorylation as a potential desensitization mechanism. Together, our data suggest that the RasGEF/Sca1/PP2A signaling complex selectively regulates the activation of a Ras-TORC2-PKB pathway, and undergoes PKB-promoted negative feedback regulation. Studies aiming at understanding the role of PP2A in the regulation of this Ras signaling pathway are underway.

11:30 AM
12:30 PM
Peter Thomas - Stochastic phenomena in chemotaxis

Chemical reaction networks by which individual cells gather and process information about their chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradient sensing in eukaryotic cells such as the social amoeba {it Dictyostelium discoideum} and human polymorphonuclear leukocytes (neutrophils) comprise a well characterized class of signal transduction systems underlying the process of chemotaxis (or directed cell motion guided by chemical gradients). During gradient sensing, a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. The local directional signal results from a combination of diffusion of signaling molecules from nearby cells and interactions between these molecules and receptor proteins on the cellular surface. Eukaryotic cells show exquisite ability to navigate even in shallow gradients and low concentrations of signaling molecules. Under these conditions significant stochastic effects arise both due to the diffusive motions of the signaling molecules and the stochastic nature of the ligand-receptor binding interaction. This talk will explore several aspects of the problem, including (1) estimates of the optimal gradient detection accuracy within a maximum likelihood framework, (2) exploration of the information capacity of purely diffusion-mediated singaling processes, and (3) explicit Monte Carlo methods for constructing ensembles of trajectories in a fully 3D geometry for quantitative analysis of receptor-ligand interaction. To interpret such ensembles we adapt a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko). This dimension reduction method allows us to estimate lower bounds on the mutual information between the transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Our long range goal is to provide a quantitative framework for addressing the question: how much could.

02:00 PM
03:00 PM
John Dallon - Modeling Cell-Cell Interactions and Motion with Discrete Visoelastic Ellipsoids

Cell motion is crucial to many diverse processes including morphogenesis, embryonic development, wound healing, angiogenesis and cancer. In all these processes it is not only cell motion that is critical but the local interactions of moving cells with one another. In this talk I will present a model for aggregate cell motion which focuses on the local cell-cell interactions. The cells are treated as viscoelastic ellipsoids and force equations are used to determine their motion. Results of the model applied to collective cell motion in Dd and wound healing will be discussed.

Thursday, October 16, 2008
Time Session
09:00 AM
10:00 AM
Radek Erban - Connecting single cell level and population level descriptions of colonial organisms

Chemotaxis is widely studied from both the microscopic (cell) and macroscopic (population) points of view. In this talk, we connect these different levels of description by deriving the macroscopic description for chemotaxis from several individual-based models. We start with the derivation of the classical macroscopic chemotaxis equations from an individual-based description of the tactic response of cells that use a run-and-tumble strategy in response to environmental cues. Then we derive macroscopic equations for the more complex type of behavioural response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behaviour accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally-measured statistics can be obtained from the transport equation formalism. If time permits, we will also derive connections between reaction-diffusion models with a different level of detail.

10:30 AM
11:30 AM
Tony Romeo - Identification and regulation of an adhesin that influences cell organization during Escherichia coli biofilm formation

Surface-associated communities known as biofilms represent the major pattern of microbial growth in the environment and affect diverse processes throughout the biosphere. Biofilms of various bacteria exhibit complex architectures that provide a sheltered environment for cells and at the same time permit exchange of nutrients, waste products and signaling molecules. In Escherichia coli K-12, the CsrA gene (carbon storage regulator A) represents an important regulator (repressor) of biofilm development. This effect is mediated in part by its direct interaction with the transcript of the pgaABCD operon, which is needed for the synthesis and secretion of the biofilm adhesin, poly-beta-1,6-N-acetyl-D-glucosame (PGA). Biofilm formation occurs rapidly and extensively in a CsrA mutant, and is blocked by disruption of any of the four pga genes. Both csrA mutant and wild type E. coli cells attach to surfaces and form biofilm microstructure in nonrandom or periodic cell distribution patterns. This involves an initial reversible interaction with an abiotic surface via a cell pole, conversion of the temporary attachment to "permanent" attachment, and continued growth of the biofilm via cell-surface and cell-cell interactions. Two kinds of mutants fail to form periodic patterns of attachment: LPS mutants, which exhibit clumpy growth patterns, and pga mutants, which attach, without clumping, and form quasi-random patterns. The mechanistic basis of the periodic cell distribution patterns and the role of PGA in this process remain to be determined.


Related Papers:



  1. Agladze, K., Jackson, D., and Romeo, T. 2003. Periodicity of Cell Attachment Patterns During Escherichia coli Biofilm Development. J. Bacteriol. 185, 5632-5638.

  2. Wang, X., Dubey, A.K., Suzuki, K., Baker, C.S., Babitzke, P., and Romeo, T. 2005. CsrA Post-transcriptionally Represses pgaABCD, Responsible for Synthesis of a Biofilm Polysaccharide Adhesin of Escherichia coli. Mol. Microbiol. 56, 1648- 1663.

  3. Agladze, K., Wang, X., and Romeo, T. 2005. Spatial Periodicity of Escherichia coli K-12 Biofilm Microstructure Initiates During a Polar-Attachment Phase of Development and Requires the Polysaccharide Adhesin PGA. J. Bacteriol. 187, 8237-8246.

  4. Itoh, Y., Rice, J.D., Goller, C., Taylor, J., Meisner, J., Beveridge, T.J., Preston, J.F., III, and Romeo, T. 2008. Roles of the pgaABCD genes in Synthesis, Modification, and Export of the Biofilm Adhesin, Poly-b-1,6-N-acetyl-D-glucosamine (PGA). J. Bacteriol. 190:3670-3680.

11:30 AM
12:30 PM
John King - Thin-film modelling of growth and quorum sensing within a bacterial biofilm

Asymptotic methods are applied to investigate growth and upregulation (due to cell-cell signalling) in a simple macroscopic model that encompasses biofilm deformation. While a number of the physical assumptions are of limited applicability, the approach perhaps provides the most tractable setting in which to investigate genuinely multidimensional effects, and in addition leads to evolution equations that are of mathematical interest in their own right.

02:00 PM
03:00 PM
David Chopp - Modeling and simulation of bacterial biofilms

Bacterial biofilms are the most ubiquitous form of life on the planet. Biofilms impact our lives in many ways, both positive and negative. In this talk, we will give an overview of our modeling efforts including studies on cell-to-cell communication, mechanical stresses due to fluid pressure and shear, and so-called "fuzzy layering" of some multi-species biofilms.

03:00 PM
04:00 PM
Thomas Hillen - Merging and emerging patterns in chemotaxis

The study of pattern formation for chemotaxis PDEs (partial differential equations) started with the identification of blow-up solutions. If, however, the model is adapted to allow for global existence of solutions, then another interesting pattern formation process arises. Local maxima form and they show an interaction of merging (two local maxima coagulate) or emerging (a new maximum is formed). This dynamics can lead to steady states, periodic solutions or to (what we think is) chaotic behavior. I will show that this pattern interaction is very typical for a wide variety of chemotaxis models and I will discuss possible ideas on how to understand this complicated pattern interaction.


(joint work with K. Painter and Z. Wang)

Friday, October 17, 2008
Time Session
10:30 AM
11:30 AM
Jack Dockery - Senescence and Microbial Persistence

It has been known for many years that small fractions of persister cells resist killing in many bacterial colony-antimicrobial confrontations. These persisters are not mutants. Rather it has been hypothesized that they are phenotypic variants. Current models allow cells to switch in and out of the persister phenotype. We suggest a different explanation, namely senescence, for persister formation. Using several mathematical models including age structure, we show that senescence provides a natural explanation for persister-related phenomena including the observations that persister fraction depends on growth phase in batch culture and dilution rate in continuous culture. Along the way we have some new theoretical results for the Chemostat.

Name Affiliation
Alber, Mark malber@nd.edu; Department of Mathematics, University of Notre Dame
Ayati, Bruce ayati@math.uiowa.edu Department of Mathematics, University of Iowa
Chopp, David chopp@northwestern.edu Engineering Sciences and Applied Mathematics, J. L. Kellogg Graduate School of Management
Cogan, Nicholas cogan@math.fsu.edu Department of Mathematics, Florida State University
Dallon, John dallon@math.byu.edu Department of Mathematics, Brigham Young University
Dockery, Jack umsfjdoc@math.montana.edu; Department of Mathematical Sciences, Montana State University
Erban, Radek erban@maths.ox.ac.uk Mathematical Institute, University of Oxford
Firtel, Richard rafirtel@ucsd.edu Section of Cell and Developmental Biology, University of California, San Diego
Ford, Roseanne rmf3f@virginia.edu Department of Chemical Engineering, University of Virginia
Guan, Bo guan@math.ohio-state.edu Department of Mathematics, The Ohio State University
Hardway, Heather hardway@rice.edu Mathematics, Rice University
Hillen, Thomas thillen@math.ualberta.ca Mathematical and Statistical Sciences, University of Alberta
King, John john.king@nottingham.ac.uk; School of Mathematical Sciences, University of Nottingham
Klapper, Isaac klapper@math.montana.edu Department of Mathematical Sciences, Montana State University
Maini, Philip maini@maths.ox.ac.uk Centre for Mathematical Biology, University of Oxford
Newman, Timothy Timothy.Newman@asu.edu Department of Physics, Arizona State University
Othmer, Hans othmer@math.umn.edu School of Mathematics, University of Minnesota
Rappel, Wouter rappel@physics.ucsd.edu Department of Physics, University of California, San Diego
Romeo, Tony tromeo@ufl.edu Microbiology and Cell Biology, University of Florida
Shapiro, James jsha@uchicago.edu Biochemistry and Molecular Biology, University of Chicago
Stevens, Angela angela.stevens@uni-hd.de Applied Mathematics and Bioquant, Ruprecht-Karls-Universit""at Heidelberg
Swinney, Harry swinney@chaos.utexas.edu Physics Department and Center for Nonlinear Dynamics, University of Texas
Thomas, Peter pjthomas@cwru.edu Mathematics, Biology & Cognitive Science, Case Western Reserve University
Tu, Yuhai yuhai@us.ibm.com Physical Sciences & Computational Biology Center, IBM Thomas J. Watson Research Center
Wang, Haiyan wangh@asu.edu Division of Mathematical & Natural Sciences, Arizona State University
Wu, Yilin wyilin@gmail.com Department of Physics, University of Notre Dame
Xin, Xiangrong (Benny) xinx0016@umn.edu Biomedical Engineering and Mathematics, University of Minnesota
Role of reversals in Myxobacterial Swarming

Many bacteria are able to spread rapidly over the surface using a strategy called swarming. When the cells cover a surface at high density and compete with each other for nutrients, swarming permits them to maintain rapid growth at the swarm edge. Swarming with flagella has been investigated for many years, and much has been learned about its regulation. Nevertheless, its choreography, which is somewhat related to the counterflow of pedestrians on a city sidewalk, has remained elusive. It is the bacterial equivalent of dancing toward the exit in a crowd of moving bodies that usually are in close contact. Myxococcus xanthus expands its swarms at 1.6 lm/min, about a third the speed of individual cells gliding over the same surface. Each cell has pilus engines at its front end and slime secretion engines at its rear. Using the known mechanics of these engines and the ways they are coordinated, we have developed a cell-based model to study the role of social interactions in bacterial swarming. The model is able to quantify the contributions of individual motility engines to swarming. It also shows that microscopic social interactions and cell reversals help to form the ordered collective motion observed in swarms.

Modeling and simulation of bacterial biofilms

Bacterial biofilms are the most ubiquitous form of life on the planet. Biofilms impact our lives in many ways, both positive and negative. In this talk, we will give an overview of our modeling efforts including studies on cell-to-cell communication, mechanical stresses due to fluid pressure and shear, and so-called "fuzzy layering" of some multi-species biofilms.

Modeling Cell-Cell Interactions and Motion with Discrete Visoelastic Ellipsoids

Cell motion is crucial to many diverse processes including morphogenesis, embryonic development, wound healing, angiogenesis and cancer. In all these processes it is not only cell motion that is critical but the local interactions of moving cells with one another. In this talk I will present a model for aggregate cell motion which focuses on the local cell-cell interactions. The cells are treated as viscoelastic ellipsoids and force equations are used to determine their motion. Results of the model applied to collective cell motion in Dd and wound healing will be discussed.

Senescence and Microbial Persistence

It has been known for many years that small fractions of persister cells resist killing in many bacterial colony-antimicrobial confrontations. These persisters are not mutants. Rather it has been hypothesized that they are phenotypic variants. Current models allow cells to switch in and out of the persister phenotype. We suggest a different explanation, namely senescence, for persister formation. Using several mathematical models including age structure, we show that senescence provides a natural explanation for persister-related phenomena including the observations that persister fraction depends on growth phase in batch culture and dilution rate in continuous culture. Along the way we have some new theoretical results for the Chemostat.

Connecting single cell level and population level descriptions of colonial organisms

Chemotaxis is widely studied from both the microscopic (cell) and macroscopic (population) points of view. In this talk, we connect these different levels of description by deriving the macroscopic description for chemotaxis from several individual-based models. We start with the derivation of the classical macroscopic chemotaxis equations from an individual-based description of the tactic response of cells that use a run-and-tumble strategy in response to environmental cues. Then we derive macroscopic equations for the more complex type of behavioural response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behaviour accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally-measured statistics can be obtained from the transport equation formalism. If time permits, we will also derive connections between reaction-diffusion models with a different level of detail.

Ras control of chemotaxis

Cells' ability to detect and orient themselves in chemoattractant gradients has been the subject of numerous studies, but the underlying molecular mechanisms remain largely unknown. Ras activation is the earliest polarized response to chemoattractant gradients downstream from heterotrimeric G proteins in Dictyostelium and inhibition of Ras signaling induces directional migration defects. Activated Ras is enriched at the leading edge, promoting the localized activation of key chemotactic effectors, such as PI3K and TORC2. In Dictyostelium, Ras controls cell motility, chemotaxis and signal relay, acting, in part, through the regulation of PI3K and TORC2, downstream from GPCR and heterotrimeric G proteins. To understand this process, we have investigated the mechanism by which Ras is spatially and temporally controls and the pathways that are regulated by Ras and by which Ras is regulated.


To investigate the role of Ras in directional sensing, we studied the effect of its mis-regulation using cells with disrupted RasGAP activity. We identified an orthologue of mammalian NF1, DdNF1, as a major regulator of Ras activity in Dictyostelium. We show that disruption of nfaA leads to spatially and temporally unregulated Ras activity, causing cytokinesis and chemotaxis defects. Furthermore, we find that RasGAP activity also affects the rate of Ras activation, in addition to promoting Ras deactivation. Using unpolarized, latrunculin-treated cells, we show that tight regulation of Ras is essential for gradient sensing and indicates a role for Ras as a component of the cell's compass.


The Aimless RasGEF (gefA) was suggested to be an upstream regulator of these Ras functions. To get insight into the mechanisms regulating Ras signaling, we undertook a sequential affinity purification and mass spectrometry approach to identify proteins interacting with Aimless. We found that Aimless is part of a stable protein complex that includes another RasGEF, RasGEFH, PP2A, and a previously uncharacterized Armadillo-like repeat-containing protein of 175 kDa. Co-immunoprecipitation studies indicate that the latter acts as a scaffold, which we named Sca1, bringing together an Aimless-RasGEFH heterodimer and PP2A. Whereas disruption of gefH alone produced minor effects, cells that lack only Aimless, both RasGEFs, or Sca1 display reduced Ras and PKB activity as well as F-actin polymerization, and exhibit cell motility as well as chemotaxis defects. We identified RasC, an orthologue of mammalian H-Ras, as the major Ras protein regulated by the RasGEF/Sca1/ PP2A complex. Our data suggest that the Sca1-scaffolded signaling complex regulates PKB activity by controlling the Ras-dependent activation of TORC2, but not that of PI3K, which are both Ras effectors regulating PKB. Furthermore, phospho-proteomics coupled to biochemical studies revealed that Sca1 undergoes dynamic phosphorylation, which includes transient and chemoattractant-induced PKB-promoted phosphorylation as a potential desensitization mechanism. Together, our data suggest that the RasGEF/Sca1/PP2A signaling complex selectively regulates the activation of a Ras-TORC2-PKB pathway, and undergoes PKB-promoted negative feedback regulation. Studies aiming at understanding the role of PP2A in the regulation of this Ras signaling pathway are underway.

Interactions of swimming bacteria with surfaces

The onset of biofilm formation requires the attachment of individual bacteria to surfaces. Our long-standing interest in swimming bacteria prompted the question, how does bacterial motility affect this initial attachment event? As bacteria swim toward a surface will they collide with the surface or alter their trajectory and move along the surface? Do bacterial flagella increase the likelihood of attachment or provide a mechanism to release adsorbed bacteria from a surface? How is the individual swimming behavior of bacteria near a surface manifested collectively in a population of bacteria that encounter a saturated porous medium? To address these questions we developed a series of experimental approaches that include: tracking swimming cells near a surface; measuring sorption rates of motile bacteria in a parallel plate flow chamber; and Monte Carlo simulations of bacteriall populations at interfaces between porous media and bulk solution.

Merging and emerging patterns in chemotaxis

The study of pattern formation for chemotaxis PDEs (partial differential equations) started with the identification of blow-up solutions. If, however, the model is adapted to allow for global existence of solutions, then another interesting pattern formation process arises. Local maxima form and they show an interaction of merging (two local maxima coagulate) or emerging (a new maximum is formed). This dynamics can lead to steady states, periodic solutions or to (what we think is) chaotic behavior. I will show that this pattern interaction is very typical for a wide variety of chemotaxis models and I will discuss possible ideas on how to understand this complicated pattern interaction.


(joint work with K. Painter and Z. Wang)

Thin-film modelling of growth and quorum sensing within a bacterial biofilm

Asymptotic methods are applied to investigate growth and upregulation (due to cell-cell signalling) in a simple macroscopic model that encompasses biofilm deformation. While a number of the physical assumptions are of limited applicability, the approach perhaps provides the most tractable setting in which to investigate genuinely multidimensional effects, and in addition leads to evolution equations that are of mathematical interest in their own right.

Physical Influences on Biofilm Structure

The familiar view of microbes in their free (planktonic) state is not the norm; rather it is believed that much of the microbial biomass, perhaps 95-99%, is located in close-knit communities, designated biofilms and microbial mats, consisting of large numbers of organisms living within self-secreted matrices constructed of polymers and other molecules. (Microbes in collective behave very differently from their planktonic state; even genetic expression patterns change.) These matrices serve the purposes of anchoring and protecting their communities in favorable locations while providing a framework in which structured populations can differentiate and self-organize.


Viewed as materials, biofilms are quite interesting: they are living, growing fluids with surprising ability to respond to and defend against their environments. This talk wlll present a general overview of efforts to characterize and model biofilms on a continuum macroscale, and present an application related to bacterial-induced mineralization.

At the interface of modeling and experiments in eukaryotic chemotaxis

Chemotactic eukaryotic cells are able to detect chemoattractant gradients that are both shallow and have a low background concentration. We will present our modeling efforts to understand this directional sensing process, including calculations on the effect of noise in the number of bound receptors. Furthermore, we will present preliminary data from our experimental efforts, aimed at addressing the predictions generated by our theoretical work.

Identification and regulation of an adhesin that influences cell organization during Escherichia coli biofilm formation

Surface-associated communities known as biofilms represent the major pattern of microbial growth in the environment and affect diverse processes throughout the biosphere. Biofilms of various bacteria exhibit complex architectures that provide a sheltered environment for cells and at the same time permit exchange of nutrients, waste products and signaling molecules. In Escherichia coli K-12, the CsrA gene (carbon storage regulator A) represents an important regulator (repressor) of biofilm development. This effect is mediated in part by its direct interaction with the transcript of the pgaABCD operon, which is needed for the synthesis and secretion of the biofilm adhesin, poly-beta-1,6-N-acetyl-D-glucosame (PGA). Biofilm formation occurs rapidly and extensively in a CsrA mutant, and is blocked by disruption of any of the four pga genes. Both csrA mutant and wild type E. coli cells attach to surfaces and form biofilm microstructure in nonrandom or periodic cell distribution patterns. This involves an initial reversible interaction with an abiotic surface via a cell pole, conversion of the temporary attachment to "permanent" attachment, and continued growth of the biofilm via cell-surface and cell-cell interactions. Two kinds of mutants fail to form periodic patterns of attachment: LPS mutants, which exhibit clumpy growth patterns, and pga mutants, which attach, without clumping, and form quasi-random patterns. The mechanistic basis of the periodic cell distribution patterns and the role of PGA in this process remain to be determined.


Related Papers:



  1. Agladze, K., Jackson, D., and Romeo, T. 2003. Periodicity of Cell Attachment Patterns During Escherichia coli Biofilm Development. J. Bacteriol. 185, 5632-5638.

  2. Wang, X., Dubey, A.K., Suzuki, K., Baker, C.S., Babitzke, P., and Romeo, T. 2005. CsrA Post-transcriptionally Represses pgaABCD, Responsible for Synthesis of a Biofilm Polysaccharide Adhesin of Escherichia coli. Mol. Microbiol. 56, 1648- 1663.

  3. Agladze, K., Wang, X., and Romeo, T. 2005. Spatial Periodicity of Escherichia coli K-12 Biofilm Microstructure Initiates During a Polar-Attachment Phase of Development and Requires the Polysaccharide Adhesin PGA. J. Bacteriol. 187, 8237-8246.

  4. Itoh, Y., Rice, J.D., Goller, C., Taylor, J., Meisner, J., Beveridge, T.J., Preston, J.F., III, and Romeo, T. 2008. Roles of the pgaABCD genes in Synthesis, Modification, and Export of the Biofilm Adhesin, Poly-b-1,6-N-acetyl-D-glucosamine (PGA). J. Bacteriol. 190:3670-3680.

What do colony patterns mean?

Colony patterns contain important information about the behavior and responses of the component cells in a particular experimental environment. Two critical questions are: (1) How do we extract mechanistic information from the observed patterns, and (2) What is the biological relevance of the behaviors revealed by the patterns? I will discuss patterns in E. coli, B. subtilis and Proteus mirabilis colonies and use these examples to describe how genetic and environmental manipulations can be used to draw meaningful conclusions about mechanism from pattern analysis. I will also discuss how we can interpret the biological relevance of patterns which do not themselves have adaptive utility.

Self-organization and local interaction

N/A

Deadly competition between sibling bacterial colonies

Bacteria can secrete a wide array of antibacterial compounds when competing with other bacteria for the same resources. Some of these compounds, such as bacteriocins, can affect bacteria of similar or closely related strains. In some cases these secretions have been found to kill sibling cells that belong to the same colony. Here we present experimental observations of competition between two sibling colonies of Paenibacillus dendritiformis grown on a low nutrient agar gel. We find that neighboring colonies (growing from inoculation droplets) mutually inhibit growth through secretions that become lethal if the level exceeds a well-defined threshold. In contrast, within a single colony developing from a droplet inoculation, no growth inhibition is observed. However, growth inhibition and cell death are observed outside a growing single colony if material extracted from the agar between two growing colonies is introduced. To interpret the observations we devised a simple mathematical model for the secretion of an antibacterial compound. Simulations of this model illustrate how secretions from neighboring colonies can be deadly while secretions from a single colony growing from a droplet are not suicidal.


*Work done in collaboration with Avraham Be'er, Hepeng Zhang, E.-L. Florin, and Shelley M. Payne (University of Texas) and Eshel Ben-Jacob (Tel Aviv University)

Stochastic phenomena in chemotaxis

Chemical reaction networks by which individual cells gather and process information about their chemical environments have been dubbed "signal transduction" networks. Despite this suggestive terminology, there have been few attempts to analyze chemical signaling systems with the quantitative tools of information theory. Gradient sensing in eukaryotic cells such as the social amoeba {it Dictyostelium discoideum} and human polymorphonuclear leukocytes (neutrophils) comprise a well characterized class of signal transduction systems underlying the process of chemotaxis (or directed cell motion guided by chemical gradients). During gradient sensing, a cell estimates the direction of a source of diffusing chemoattractant molecules based on the spatiotemporal sequence of ligand-receptor binding events at the cell membrane. The local directional signal results from a combination of diffusion of signaling molecules from nearby cells and interactions between these molecules and receptor proteins on the cellular surface. Eukaryotic cells show exquisite ability to navigate even in shallow gradients and low concentrations of signaling molecules. Under these conditions significant stochastic effects arise both due to the diffusive motions of the signaling molecules and the stochastic nature of the ligand-receptor binding interaction. This talk will explore several aspects of the problem, including (1) estimates of the optimal gradient detection accuracy within a maximum likelihood framework, (2) exploration of the information capacity of purely diffusion-mediated singaling processes, and (3) explicit Monte Carlo methods for constructing ensembles of trajectories in a fully 3D geometry for quantitative analysis of receptor-ligand interaction. To interpret such ensembles we adapt a method for estimation of spike train entropies described by Victor (originally due to Kozachenko and Leonenko). This dimension reduction method allows us to estimate lower bounds on the mutual information between the transmitted signal (direction of ligand source) and the received signal (spatiotemporal pattern of receptor binding/unbinding events). Our long range goal is to provide a quantitative framework for addressing the question: how much could.

A biological signal processor: How E. coli responds to time-varying signals

In this talk, I will present our recent work in trying to understand bacterial chemotaxis (bacteria's ability to sense and track chemical gradient) by using a quantitative modeling approach. Based on molecular level knowledge of the E. coli chemotaxis pathway, we propose a simple model for bacterial chemotaxis and use it to understand signal processing in E. coli. In particular, we will address: 1) How E. coli respond to various time-varying stimuli, such as ramps, oscillatory signals and impulse signals. 2) How the cell uses its memory and computation capability to sense and respond to a minute chemical gradient among a wide range of background.



  • "Modeling the chemotactic response of E. coli to time-varying stimuli", Yuhai Tu, T. Shimizu and H. Berg, PNAS, 09/2008.

  • "Effects of adaptation in maintaining high sensitivity over a wide range of backgrounds for E. coli chemotaxis", B. Mello and Yuhai Tu, Biophysical Journal, 92, 2329-2337 (2007).

A systematic model of bacterial chemotaxis: from signal transduction to cell motility in Escherichia coli

The movement of bacteria in response to environmental changes of specific metabolites and signaling molecules is called bacterial chemotaxis. Chemotaxis in Escherichia coli (E. coli) is a best studied system. The authors will present a systematic model of E. coli chemotaxis that can capture many features of the system and reproduce a full range of experimental observations from signaling (excitation, perfect adaptation, robustness, high sensitivity, wide dynamic range, etc.) to motor behavior and cellular motility. A remarkable feature of the signaling pathway is its high sensitivity to small relative changes in concentrations of chemical stimuli over a broad range of ambient concentrations. To account for it, the signaling part of the model is based on the structural and functional unit of receptor clusters, 'trimer of chemoreceptor dimers', which has been solidly experimentally established but not well quantitatively modeled, so the theoretical work includes more molecular mechanism in modeling and provides a more mechanistically based description of the origin of high sensitivity.


Work done in collaboration with David J. Odde and Hans G. Othmer.


Key References



  1. Sourjik V, Berg HC. (2002). Receptor sensitivity in bacterial chemotaxis. Proc. Natl. Acad. Sci. U.S.A. 99: 123-127.

  2. Sourjik V. (2004). Receptor clustering and signal processing in E. coli chemotaxis. Trends Microbiol. 12: 569-576.