Myxococcus Experiments

Abstract

Surface motility of many organisms is described as swarming where movement is coordinated for spreading of groups. Here we investigate the coordination of swarming events for two model bacteria, Myxococcus xanthus and Pseudomonas aeruginosa. Our investigation will utilize an integrated approach that combines multiscale model predictive simulations to direct laboratory experiments to discern the actions and regulation of single bacteria that act within a group.

We present an off lattice stochastic model which incorporates the different motility engines and the reversing capability to examine the swarming of M. xanthus. The model also accounts for the interactions of individual cells with the slime on the surface left by other cells. Simulations involving the variation of cell density, aspect ratio, and reversing period were made and we present some of the results including the optimization of M. xanthus reversing period at 8 minutes which was observed experimentally.

We propose to develop a thin liquid film submodel to be coupled with the cell-based discrete submodel to create a three-dimensional multiscale modeling environment for P. aeruginosa that describes population-dependent surface swarming of bacteria that incorporates genetic, chemical, and hydrodynamic phenomena as well as motility of individual bacteria. Submodel from M. xanthus will be extended to describe motion of individual bacteria. (P. aeruginosa also uses type IV pili.)

Multiscale Models of Bacterial Swarming Huijing Du1,3, Cameron Harvey1,4, Yilin Wu2, Mark Alber1,3, Zhilian Xu1,3, and Dale Kaiser5.

1 Interdisciplinary Center for the Study of Biocomplexity, 2 Harvard University, 3 Notre Dame Dept. of Mathematics ,4 Notre Dame Dept. of Physics,5 Stanford University University of Notre Dame, Notre Dame, IN 46556, USA.

Background

Many bacteria utilize self-generated motility to populate their desired niche; on surfaces these bacteria move, or swarm, with complexity and organization that is only partly understood. Specifically, it is not clear how groups of bacteria interpret environmental cues and coordinate their swarming. Understanding these microbial actions will be useful for describing cellular responses to chemical and physical perturbations, interactions between cells, and coordination of these events over time.

Psuedomonas aeruginosa

P. aeruginosa is a ubiquitous, environmental organism that is opportunistic human pathogen infecting susceptible individuals including burn victims, contact lens wearers, and immunocompromised individuals. P. aeruginosa utilizes acyl-homoserine lactone quorum sensing molecules to regulate the synthesis of rhamnolipid, a surfactant that lowers the surface tension and increases surface spreading based on flagellar rotation; quorum sensing has been linked with swarming for P. aeruginosa in this way. On semi-solid agar surfaces swarming of flagellated bacteria such as P. aeruginosa, and others is controlled by thin layer of fluid (up to 40 microns depending on the softness of agar), which bacteria extract from the agar.

Motility

Swarm motility of P. aeruginosa transpires as cells use their single polar flagellum as a rear propulsion engine. P. aeruginosa swarming has also been shown to be greatly influenced via the production of rhamnolipid; this bio-surfactant acts to lower the local surface tension of the liquid layer and ease spreading over surfaces. Rhamnolipid synthesis is only initiated in the presence of a threshold, or quorum, of cells. Such population-dependent regulation of genes is generally described as quorum sensing. Cell-cell contact is not required for initiation of quorum sensing processes. Thus, P. aeruginosa will be utilized as a model species that does use long-range communication to coordinate motility. The rhlI and rhlR quorum sensing system regulates transcription of the gene rhlA and subsequently, production of P. aeruginosa rhamnolipid. However, it has been observed that the mere presence of a threshold quorum sensing population does not ensure increased swarming. The influence of quorum sensing upon swarming has been shown to be conditional; changes to the growth medium (e.g. chemical composition) can significantly impact both P. aeruginosa surface motility and the importance of cell-cell signaling as bacteria attach to surfaces [3]. Surface motility of P. aeruginosa is also complex because in addition to swarming, P. aeruginosa displays at least two additional surface motility phenotypes described as twitching and sliding. Several genes specific to swarming, twitching, and sliding have been identified, but the conditions that lead to use of one or multiple motility modes are not well understood.

Myxococcus xanthus

Myxobacteria is comm soil bacteria that has been rigourously investigated throughout the 20 th century. A wide variety of behaviors have been observed and investigated including active growth on nutrient rich surfaces, the predation of other bacterial cells (hence myxo are the 'wolf pack' of the bacterial world), and formation of ripples and fruiting bodies when nutrient starved.

The swarming behavior of bacteria is an important phenomena which raises numerous questions. For Myxobacteria, the absense of long-range signal detection, like that of chemotaxis, leads one to wonder what governs their swarming behavior. It is reasonable to suspect three features common to swarming bacteria which include 1) cell elongation, 2) social interactions, and 3) directional reversals.[1]

Motility

Myxobacteria are flexible rod-shaped baceria which move bi-directional along the long-axis of the cell body. Like other species within Myxobacteria, M. xanthus cells do not have flagella as a mechanism for propolusion. Instead, cells use two seperate coordinated motility engines. The first type of motility uses the secretion of slime to propell the cell forward and is known as Adventurous motility or A-motility. Unlike the second motility, A-motility does not depend on social interactions which allows cells to explore areas of a surface outside of the swarm. The social interaction of the second motility, S-motility, involves cells extending type IV pili and attaching to clusters of neighboring cells before retracting the pili to pull cells forward. Together, the two motilities allow myxobacteria cells to glide across surfaces. Intuitively, one might think cells would only glide forward in one direction to explore their envrionment more effectively. However, is has been observed that every few minutes, the polarity of the two motility types is reversed causing the cell to move in opposite direction. The combination of the two motility types directly effects the swarming behavior as seen when viewing mutant strains which lack one or the other motiltiy capability.

Modeling Bacteria Cells

Psuedomonas model

Modeling production of thin liquid film: P. aeruginosa swarming is characterized by the production of the extracellular wetting agent-rhamnolipid. We observed that the spreading process of P. aeruginosa is accompanied by a liquid instability that manifests itself via the formation of fractal patterns (in the shape of fingers). We will implement the following thin viscous fluid flow submodel by a lubrication approximation of the Navier-Stokes equations:

Here h is the fluid height, U the fluid velocity, γm the minimal surface

tension at maximum packing. Here γ is the surface tension depending on the rhamnolipid concentration and µ is the apparent dynamic viscosity altered by the concentration of cells. ρ is the fluid density and g the gravitational acceleration. Γ describes extraction of fluid by the bacteria and Π a disjoining pressure by liquid, which accounts for the van der Waals force-driven instability. The second rhs term of (2) accounts for Marangoni stresses arise due to non-uniformities in surface tension at the interface bounding the gaseous and aqueous phases that are in turn, induced by local differences in interfacial surfactant concentration. These stresses drive flow from areas of high surfactant concentration to less contaminated regions. Modeling quorum sensing (QS) and nutrient uptake: Cellular nutrient uptake, production of QS acyl-homoserine lactone signals (produced by LasI and RhlI) and rhamnolipid will be modeled using equations describing dynamics of various field concentrations:

Ci

represents either nutrient, rhamnolipid or one QS molecule

concentration. The first rhs term describes field diffusion. The second represents nutrient uptake by cells, or secretion of QS signal or rhamnolipid molecules by cells. Notice that the second term couples the off-lattice submodel and continuum submodels. The third term represents decay of the molecules concentration.

Myxo Model

The movement of a cell's head node during one time step is determined by

with V0 a constant and the direction, s, given by the sum of four contributing

factors; A-motility (Ak), S-motility(S

k), slime-cell interactions (L

k), and cell-cell

collisions(Ck).

where α, β, γ, and ε are key parameters and ηk is a random fluctuation term.

A-motility is parallel to the vector pointing from the middle to the head node.S-motility uses a search algorithm to find orientation angles of neighboring cells in search box Area I (see below left ) to calculate the direction of the S-motility.L

k is determined by a slime vector field which is updated every step. The grid

'below' a cell is assigned the direction of the cell's orientation. The slime-cell interaction uses an additional search algorithm to determine the average value of the slime vector field in Area II (see below right).

Finally, collisions between cells are resolved by a volume exclusion potential. A colliding cell attempts to align with the cell its is colliding with. If bending is rejected based on energy considerations, then the cell stalls.

Model ExtensionNew model implementations are being developed to model A-S+ mutants. The interaction of pili with fibrils will be examined as well as cell-cell pushing which is hypothesized to be the cause of the swarm edge advancement in A- mutants.

Model Results

Reference1. Wu, Y.L., A.D. Kaiser, Y. Jiang, and M.S. Alber. Periodic reversal of direction allows Myxobacteria to swarm. Proc. Natl. Acad. Sci. USA. 106(4):1222-1227 (2009).2. Wu, Y., Y. Jiang, D. Kaiser, and M. Alber. Social interactions in Myxobacterial swarming. PLoS Comput. Biol. 3(12):e253 (2007).3. Shrout, J.D., D.L. Chopp, C.L. Just, M. Hentzer, M. Givskov, and M.R. Parsek. The impact of quorum sensing and swarming motility on Pseudomonas aeruginosa biofilm formation is nutritionally conditional. Mol. Microbiol. 62(5):1264-1277 (2006).4. Kaiser, D. Crosby C Cell movement and its coordination in swarms of Myxococcus xanthus. Cell Motility 3:227-245 (1983).5. Kaiser, D. Coupling Cell Movement to Multicellular Development in Myxobacteria. Nat Rev Microbiol 1:45-54 (2003).6. Xu, Z., J. Lioi, J. Mu, M.M. Kamocka, X. Liu, D.Z. Chen, E.D. Eosen, and M. Alber. A Multiscale model of Venous Thrombus Formation with Surface-Mediated Control of Blood Coagulation Cascade. Biophys. J. 98(9) (2010).7. Craster, R.V. and O.K. Matar. Numerical simulations of fingering instabilities in surfactant-driven thin films. Phys. Fluids. 18(3): 032103-12 (2006).8. Bustamante, V.H., I. Martinez-Flores, H.C. Vlamakis, and D.R. Zusman 2004 Analysis of the Frz signal transduction system of Myxococcus xanthus shows the importance of the conserved C-terminal region of the cytoplasmic chemoreceptor FrzCD in sensing signals. Mol. Microbiol. 53(5): 1501-13.

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In myxo simulations, the cell number flux dN/dt across the initial swarming domain edge (or rate of cell increase outside initial area) is correlated with swarm expansion rate dr/dt. Swarm rate is a key measurement when comparing simulations.

We propose to develop a 3D detailed cell-based discrete stochastic submodel to account for type IV pili interactions among cells. Individual cells will be represented by N nodes connected by (N-1) segments moving in a 3D space in which pili, extending forward from the head node, sweep out an interaction area for contact with fibrils on other cells. Each cell will be led forward by the motion of its head node determined by the stochastic local rules based on biological details of motility engines, cell-cell and cell-environment interactions [1, 2].

Tracking of individual cells within a P.aeruginosa swarm colony. GFP-labeled cells were mixed 1/10,000 with non-fluorescent cells and tracked over time. The top frames show only the green fluorescent channel compared to the entire swarm (DIC+GFP) below. The arrow points to one cell specifically tracked over 7 minutes with the apparent track indicated by the dashed line.

Priliminary simulation of fingering development by P. aeruginosa swarming. Top: (left) cell distribution; (right) the profile of the liquid film. Bottom: Simulation with similar initial conditions but with lower threshold for thickness of liquid layer which switches cell motility and lower probability of cell alignment. Simulation time: 1hr; total 80,000 cells are used.

The model has been also used for predicting the relative swarming efficiencies of Frz mutants [1] where frizzy gene mutants have been observed experimentally to change the average reversal period significantly [8]. Accordingly, the swarming model could be challenged with predicting the quantitative effect of changing the average reversal period on the flux, inasmuch as the reversal period of the frizzilator is an adjustable parameter of the model. For this purpose, two deletion mutants with short periods have been investigated in [1], one in FrzG and another in FrzCD, and three with long periods, comparing them all with wild type. Three experimental points provided a perfect match with model predictions in the domain of model applicability (see above).

Psuedomonas Experiments

Previous investigations of A-S+ swarming have revealed striking strucutres that resemble arrowheads when the density of cells is sufficiently low. At higher densties, swarming patterns in A-S+ resemble finger-like structures. Current investigations are attempted to better understand the behavior of individual cells within these structures. To that end, introduction of GFP-labeled cells into a swarm of non-fluorescent cells will allow us to track cells in the structure (see Psuedomonas Image above). Quantifying these structures will include cell population, cell ordering, as well as the size of the gaps which form behind arrowheads (see Red arrowin fig). Additionally, techniques to detect fibrils with Calcafluor white binding fluorescence will be used to explore the relationship between fibril density and cell motility at the swarming edge. Experiments will seek to verify predictions made by the model.

Preliminary investigation into P. aeruginosa swarming suggests that the influence of quorum sensing upon swarming is greatly affected by surface conditions. Variation to the agar concentration used in laboratory assay swarm plates results in a significant difference in swarm motility of P. aeruginosa.

The heterogeneity of the environment such as surface roughness and liquid velocity will be taken into account as well. M. xanthus cells will also reverse direction of motion at intervals chosen in accordance with certain probability distribution function.

At each simulation step, the head node

will make a tentative movement attempt in 3D space, which will be accepted or rejected according to Metropolis algorithm. Then other nodes will adjust their positions in a way to minimize the energy Hamiltonian (below) consisting of stretching and bending terms to preserve the cell shape.

Images from Kaiser Lab

Images from Shrout Lab