Workshop 2: Pattern Formation and Development in Colonial Organisms : Abstracts and Lecture Materials
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.
Colonial microorganisms provide spectacular examples of self-organizing populations. In Dictyostelium, large scale aggregation patterns emerge from motile cells emitting and responding to diffusible signals. While much understanding has been gained from the analysis of population-level models, such as the Keller-Segel equations, these models cannot yield information on fluctuations and statistical correlations within the population. It turns out to be non-trivial to describe fluctuations due to the strong feedback between motile agents and their fluctuating environment. In order to probe fluctuations and correlation we have used a many-body theory approach, borrowing tools from theoretical physics that have been tremendously successful in describing emergent properties in condensed matter physics. In this lecture I will discuss the many-body theory approach in some detail, in the context of a minimal model of cell aggregation via chemotaxis. In particular I will describe a perturbation expansion in the strength of chemotaxis, and the utility of Feynman diagrams. I will show that within perturbation theory, at low cell densities new dominant interactions arise from statistical correlations that are absent in population-level models.
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.
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:
- Agladze, K., Jackson, D., and Romeo, T. 2003. Periodicity of Cell Attachment Patterns During Escherichia coli Biofilm Development. J. Bacteriol. 185, 5632-5638.
- 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.
- 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.
- 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.
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.
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)
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.
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).
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
- Sourjik V, Berg HC. (2002). Receptor sensitivity in bacterial chemotaxis. Proc. Natl. Acad. Sci. U.S.A. 99: 123-127.
- Sourjik V. (2004). Receptor clustering and signal processing in E. coli chemotaxis. Trends Microbiol. 12: 569-576.
The bacterium Proteus mirabilis is known for its ability to swarm over hard surfaces and form spectacular concentric ring patterns. During pattern formation, the colony front is observed to move outward from the inoculation site either continuously or periodically, due to collective movement of elongated, hyper-flagellated swarmer cells at the leading edge. The formation of the rings was thought to arise from periodic colony expansion. However, recent experimental results show that swimmer cells stream inward toward the inoculation site, and form a number of complex patterns, including radial and spiral streams, rings and traveling trains. To understand the underlying mechanism of these complicated patterns, we developed a hybrid cell-based model which incorporates a simplified single cell signal transduction model with both the adaptation and excitation components. By assuming that swimmer cells respond to a chemoattractant that they produce, we are able to predict the formation of radial streams as a result of the modulation of the local attractant concentration by the cells. We further predict the spiral streams by incorporating a swimming bias of the cells near the surface of the medium. The hybrid cell-based model becomes computationally expensive because of the large number of cells due to cell division, therefore a higer level description is needed. We also present a moment-closure method for deriving macroscopic evolution equations from the hybrid cell-based model using perturbation analysis, and compare the solutions of the cell-based model and the derived continuum model.
Joint work with Hans Othmer and Elena Budrene-Kac.
