Quantitative studies of bacterial chemotaxis and microbial population dynamics

Although there is a long history of conjecture regarding the role and significance of bacterial chemotaxis in microbial ecology, only recently has a significant body of work appeared attempting to address this issue. The purpose of this paper is to provide a concise overview of this work, which combined mathematical modeling of bacterial population migration and experimental measurement of the model parameters with modeling of competitive microbial population dynamics in a nonmixed environment. Predictions from the population dynamics models, based on experimental estimates of the various motility and growth parameter values, are related to the small number of experimental observations available to date dealing with the effects of bacterial motility on competition in a nonmixed environment. Current results indicate that cell motility and chemotaxis properties can be as important to population dynamics as cell growth kinetic properties, so that greater attention to this aspect of microbial behavior is warranted in future studies of microbial ecology.     

Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.     

Colony Expansion of Socially Motile Myxococcus xanthus Cells Is Driven by Growth,Motility, and Exopolysaccharide Production

Myxococcus xanthus, a model organism for studies of multicellular behavior in bacteria, moves exclusively on solid surfaces using two distinct but coordinated motility mechanisms. One of these, social (S) motility is powered by the extension and retraction of type IV pili and requires the presence of exopolysaccharides (EPS) produced by neighboring cells. As a result, S motility requires close cell-to-cell proximity and isolated cells do not translocate. Previous studies measuring S motility by observing the colony expansion of cells deposited on agar have shown that the expansion rate increases with initial cell density, but the biophysical mechanisms involved remain largely unknown. To understand the dynamics of S motility-driven colony expansion, we developed a reaction-diffusion model describing the effects of cell density, EPS deposition and nutrient exposure on the expansion rate. Our results show that at steady state the population expands as a traveling wave with a speed determined by the interplay of cell motility and growth, a well-known characteristic of Fisher’s equation. The model explains the density-dependence of the colony expansion by demonstrating the presence of a lag phase–a transient period of very slow expansion with a duration dependent on the initial cell density. We propose that at a low initial density, more time is required for the cells to accumulate enough EPS to activate S-motility resulting in a longer lag period. Furthermore, our model makes the novel prediction that following the lag phase the population expands at a constant rate independent of the cell density. These predictions were confirmed by S motility experiments capturing long-term expansion dynamics.     

Sliding on the surface: bacterial spreading without an active motor

Bacteria are able to translocate over surfaces using different types of active and passive motility mechanisms. Sliding is one of the passive types of movement since it is powered by the pushing force of dividing cells and additional factors facilitating the expansion over surfaces. In this review, we describe the sliding proficient bacteria that were previously investigated in details highlighting the sliding facilitating compounds and the regulation of sliding motility. Besides surfactants that reduce the friction between cells and substratum, other compounds including exopolysaccharides, hydrophobic proteins, or glycopeptidolipids where discovered to promote sliding. Therefore, we present the sliding bacteria in three groups depending on the additional compound required for sliding. Despite recent accomplishments in sliding research there are still many open questions about the mechanisms underlying sliding motility and its regulation in diverse bacterial species.     

A random graph model of density thresholds in swarming cells

Swarming behaviour is a type of bacterial motility that has been found to be dependent on reaching a local density threshold of cells. With this in mind, the process through which cell‐to‐cell interactions develop and how an assembly of cells reaches collective motility becomes increasingly important to understand. Additionally, populations of cells and organisms have been modelled through graphs to draw insightful conclusions about population dynamics on a spatial level. In the present study, we make use of analogous random graph structures to model the formation of large chain subgraphs, representing interactions between multiple cells, as a random graph Markov process. Using numerical simulations and analytical results on how quickly paths of certain lengths are reached in a random graph process, metrics for intercellular interaction dynamics at the swarm layer that may be experimentally evaluated are proposed.     

Effect of short-range forces on the length distribution of fibrous cytoskeletal proteins

The length distribution of cytoskeletal filaments is an important physical parameter, which can modulate physiological cell functions. In both eukaryotic and prokaryotic cells various biological cytoskeletal polymers form supramolecular structures due to short-range forces induced mainly by molecular crowding or cross linking proteins, but their in vivo length distribution remains difficult to measure. In general, based on experimental evidence and mathematical modeling of actin filaments in aqueous solutions, the steady state length distribution of fibrous proteins is believed to be exponential. We performed in vitro TIRF- and electron-microscopy to demonstrate that in the presence of short-range forces, which are an integral part of any living cell, the steady state length distributions of the eukaryotic cytoskeletal biopolymer actin, its prokaryotic homolog ParM and microtubule homolog FtsZ deviate from the classical exponential and are either double-exponential or Gaussian, as recent theoretical modeling predicts. Double exponential or Gaussian distributions opposed to exponential can change for example the visco-elastic properties of actin networks within the cell, influence cell motility by decreasing the amount of free ends at the leading edge of the cell or effect the assembly of FtsZ into the bacterial Z-ring thus modulating membrane constriction.     

细菌群集运动特性的研究进展

群集运动(swarming motility)是细菌以群体方式协调性地依靠鞭毛和Ⅳ型菌毛(type Ⅳ pili,TFP)在半固体表面共同运动,是一种典型的协同运动。群集运动因其与生物被膜、子实体的形成、病原体的侵入和微生物的扩散及共生等过程都有着密切的关系而备受人们的关注,是当前微生物领域的一个研究热点。人们对细菌群集运动开展了大量的研究,包括群集运动中关键蛋白表达的变化、细胞间化学交流的变化以及机械性变化等。鞭毛蛋白的表达以及胞内环二鸟苷酸(cyclic diguanosine monophosphate,c-di-GMP)的水平等会对群集运动产生一定的影响,在菌落中复杂地调控着细菌集体行为;群集运动细胞独特的物理性质表现有益于菌落整体的扩张;细菌周围生长环境中的营养和水分含量等因素也在不同程度上影响细菌群集运动的能力。未来,在解析群集运动分子机制的基础上,如何构建一个统一的群集运动模型成为该领域研究面临的一个挑战。     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Molecular dynamics simulations of the interaction of phospholipid bilayers with polycaprolactone

The molecular interaction between common polymer chains and the cell membrane is unknown. Molecular dynamics simulations offer an emerging tool to characterise the nature of the interaction between common degradable polymer chains used in biomedical applications, such as polycaprolactone, and model cell membranes. Herein we characterise with all-atomistic and coarse-grained molecular dynamics simulations the interaction between single polycaprolactone chains of varying chain lengths with a phospholipid membrane. We find that the length of the polymer chain greatly affects the nature of interaction with the membrane, as well as the membrane properties. Furthermore, we next utilise advanced sampling techniques in molecular dynamics to characterise the two-dimensional free energy surface for the interaction of varying polymer chain lengths (short, intermediate, and long) with model cell membranes. We find that the free energy minimum shifts from the membrane-water interface to the hydrophobic core of the phospholipid membrane as a function of chain length. Finally, we perform coarse-grained molecular dynamics simulations of slightly larger membranes with polymers of the same length and characterise the results as compared with all-atomistic molecular dynamics simulations. These results can be used to design polymer chain lengths and chemistries to optimise their interaction with cell membranes at the molecular level.     

Correlating single cell motility with population growth dynamics for flagellated bacteria

Many bacteria used for biotechnological applications are naturally motile. Their "bio-nanopropeller" driven movement allows searching for better environments in a process called chemotaxis. Since bacteria are extremely small in size compared to the bulk fluid volumes in bioreactors, single cell motility is not considered to influence bioreactor operations. However, with increasing interest in localized fluid flow inside reactors, it is important to ask whether individual motility characteristics of bacteria are important in bioreactor operations. The first step in this direction is to try to correlate single cell measurements with population data of motile bacteria in a bioreactor. Thus, we observed the motility behavior of individual bacterial cells, using video microscopy with 33 ms time resolution, as a function of population growth dynamics of batch cultures in shake flasks. While observing the motility behavior of the most intensively studied bacteria, Escherichia coli, we find that overall bacterial motility decreases with progression of the growth curve. Remarkably, this is due to a decrease in a specific motility behavior called "running". Our results not only have direct implications on biofilm formations, but also provide a new direction in bioprocess design research highlighting the role of individual bacterial cell motility as an important parameter.     

An Experimental and Computational Study of the Effect of ActA Polarity on the Speed of Listeria monocytogenes Actin-based Motility

Listeria monocytogenes is a pathogenic bacterium that moves within infected cells and spreads directly between cells by harnessing the cell's dendritic actin machinery. This motility is dependent on expression of a single bacterial surface protein, ActA, a constitutively active Arp2,3 activator, and has been widely studied as a biochemical and biophysical model system for actin-based motility. Dendritic actin network dynamics are important for cell processes including eukaryotic cell motility, cytokinesis, and endocytosis. Here we experimentally altered the degree of ActA polarity on a population of bacteria and made use of an ActA-RFP fusion to determine the relationship between ActA distribution and speed of bacterial motion. We found a positive linear relationship for both ActA intensity and polarity with speed. We explored the underlying mechanisms of this dependence with two distinctly different quantitative models: a detailed agent-based model in which each actin filament and branched network is explicitly simulated, and a three-state continuum model that describes a simplified relationship between bacterial speed and barbed-end actin populations. In silico bacterial motility required a cooperative restraining mechanism to reconstitute our observed speed-polarity relationship, suggesting that kinetic friction between actin filaments and the bacterial surface, a restraining force previously neglected in motility models, is important in determining the effect of ActA polarity on bacterial motility. The continuum model was less restrictive, requiring only a filament number-dependent restraining mechanism to reproduce our experimental observations. However, seemingly rational assumptions in the continuum model, e.g. an average propulsive force per filament, were invalidated by further analysis with the agent-based model. We found that the average contribution to motility from side-interacting filaments was actually a function of the ActA distribution. This ActA-dependence would be difficult to intuit but emerges naturally from the nanoscale interactions in the agent-based representation.     

A mechanochemical model of actin filaments

In eukaryotic cells, actin filaments are involved in important processes such as motility, division, cell shape regulation, contractility, and mechanosensation. Actin filaments are polymerized chains of monomers, which themselves undergo a range of chemical events such as ATP hydrolysis, polymerization, and depolymerization. When forces are applied to F-actin, in addition to filament mechanical deformations, the applied force must also influence chemical events in the filament. We develop an intermediate-scale model of actin filaments that combines actin chemistry with filament-level deformations. The model is able to compute mechanical responses of F-actin during bending and stretching. The model also describes the interplay between ATP hydrolysis and filament deformations, including possible force-induced chemical state changes of actin monomers in the filament. The model can also be used to model the action of several actin-associated proteins, and for large-scale simulation of F-actin networks. All together, our model shows that mechanics and chemistry must be considered together to understand cytoskeletal dynamics in living cells.     

Probing Cellular Mechanoadaptation Using Cell-Substrate De-Adhesion Dynamics: Experiments and Model

Physical properties of the extracellular matrix (ECM) are known to regulate cellular processes ranging from spreading to differentiation, with alterations in cell phenotype closely associated with changes in physical properties of cells themselves. When plated on substrates of varying stiffness, fibroblasts have been shown to exhibit stiffness matching property, wherein cell cortical stiffness increases in proportion to substrate stiffness up to 5 kPa, and subsequently saturates. Similar mechanoadaptation responses have also been observed in other cell types. Trypsin de-adhesion represents a simple experimental framework for probing the contractile mechanics of adherent cells, with de-adhesion timescales shown to scale inversely with cortical stiffness values. In this study, we combine experiments and computation in deciphering the influence of substrate properties in regulating de-adhesion dynamics of adherent cells. We first show that NIH 3T3 fibroblasts cultured on collagen-coated polyacrylamide hydrogels de-adhere faster on stiffer substrates. Using a simple computational model, we qualitatively show how substrate stiffness and cell-substrate bond breakage rate collectively influence de-adhesion timescales, and also obtain analytical expressions of de-adhesion timescales in certain regimes of the parameter space. Finally, by comparing stiffness-dependent experimental and computational de-adhesion responses, we show that faster de-adhesion on stiffer substrates arises due to force-dependent breakage of cell-matrix adhesions. In addition to illustrating the utility of employing trypsin de-adhesion as a biophysical tool for probing mechanoadaptation, our computational results highlight the collective interplay of substrate properties and bond breakage rate in setting de-adhesion timescales.     

Acylation of Glucagon-Like Peptide-2: Interaction with Lipid Membranes and In Vitro Intestinal Permeability

Background

Acylation of peptide drugs with fatty acid chains has proven beneficial for prolonging systemic circulation as well as increasing enzymatic stability without disrupting biological potency. Acylation has furthermore been shown to increase interactions with the lipid membranes of mammalian cells. The extent to which such interactions hinder or benefit delivery of acylated peptide drugs across cellular barriers such as the intestinal epithelia is currently unknown. The present study investigates the effect of acylating peptide drugs from a drug delivery perspective.

Purpose

We hypothesize that the membrane interaction is an important parameter for intestinal translocation, which may be used to optimize the acylation chain length for intestinal permeation. This work aims to characterize acylated analogues of the intestinotrophic Glucagon-like peptide-2 by systematically increasing acyl chain length, in order to elucidate its influence on membrane interaction and intestinal cell translocation in vitro.

Results

Peptide self-association and binding to both model lipid and cell membranes was found to increase gradually with acyl chain length, whereas translocation across Caco-2 cells depended non-linearly on chain length. Short and medium acyl chains increased translocation compared to the native peptide, but long chain acylation displayed no improvement in translocation. Co-administration of a paracellular absorption enhancer was found to increase translocation irrespective of acyl chain length, whereas a transcellular enhancer displayed increased synergy with the long chain acylation.

Conclusions

These results show that membrane interactions play a prominent role during intestinal translocation of an acylated peptide. Acylation benefits permeation for shorter and medium chains due to increased membrane interactions, however, for longer chains insertion in the membrane becomes dominant and hinders translocation, i.e. the peptides get ‘stuck’ in the cell membrane. Applying a transcellular absorption enhancer increases the dynamics of membrane insertion and detachment by fluidizing the membrane, thus facilitating its effects primarily on membrane associated peptides.     

Mechanisms for maintaining cell shape in rod-shaped Gram-negative bacteria

For the rod-shaped Gram-negative bacterium Escherichia coli, changes in cell shape have critical consequences for motility, immune system evasion, proliferation and adhesion. For most bacteria, the peptidoglycan cell wall is both necessary and sufficient to determine cell shape. However, how the synthesis machinery assembles a peptidoglycan network with a robustly maintained micron-scale shape has remained elusive. To explore shape maintenance, we have quantified the robustness of cell shape in three Gram-negative bacteria in different genetic backgrounds and in the presence of an antibiotic that inhibits division. Building on previous modelling suggesting a prominent role for mechanical forces in shape regulation, we introduce a biophysical model for the growth dynamics of rod-shaped cells to investigate the roles of spatial regulation of peptidoglycan synthesis, glycan-strand biochemistry and mechanical stretching during insertion. Our studies reveal that rod-shape maintenance requires insertion to be insensitive to fluctuations in cell-wall density and stress, and even a simple helical pattern of insertion is sufficient for over sixfold elongation without significant loss in shape. In addition, we demonstrate that both the length and pre-stretching of newly inserted strands regulate cell width. In sum, we show that simple physical rules can allow bacteria to achieve robust, shape-preserving cell-wall growth.     

Cell flexibility affects the alignment of model myxobacteria

Myxobacteria are social bacteria that exhibit a complex life cycle culminating in the development of multicellular fruiting bodies. The alignment of rod-shaped myxobacteria cells within populations is crucial for development to proceed. It has been suggested that myxobacteria align due to mechanical interactions between gliding cells and that cell flexibility facilitates reorientation of cells upon mechanical contact. However, these suggestions have not been based on experimental or theoretical evidence. Here we created a computational mass-spring model of a flexible rod-shaped cell that glides on a substratum periodically reversing direction. The model was formulated in terms of experimentally measurable mechanical parameters, such as engine force, bending stiffness, and drag coefficient. We investigated how cell flexibility and motility engine type affected the pattern of cell gliding and the alignment of a population of 500 mechanically interacting cells. It was found that a flexible cell powered by engine force at the rear of the cell, as suggested by the slime extrusion hypothesis for myxobacteria motility engine, would not be able to glide in the direction of its long axis. A population of rigid reversing cells could indeed align due to mechanical interactions between cells, but cell flexibility impaired the alignment.     

Physical Model of the Dynamic Instability in an Expanding Cell Culture

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.     

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.     

Human disease mortality kinetics are explored through a chain model embodying principles of extreme value theory and competing risks.

The distributions for human disease-specific mortality exhibit two striking characteristics: survivorship curves that intersect near the longevity limit; and, the clustering of best-fitting Weibull shape parameter values into groups centered on integers. Correspondingly, we have hypothesized that the distribution intersections result from either competitive processes or population partitioning and the integral clustering in the shape parameter results from the occurrence of a small number of rare, rate-limiting events in disease progression. In this report we initiate a theoretical examination of these questions by exploring serial chain model dynamics and parameteric competing risks theory. The links in our chain models are composed of more than one bond, where the number of bonds in a link are denoted the link size and are the number of events necessary to break the link and, hence, the chain. We explored chains with all links of the same size or with segments of the chain composed of different size links (competition). Simulations showed that chain breakage dynamics depended on the weakest-link principle and followed kinetics of extreme-values which were very similar to human mortality kinetics. In particular, failure distributions for simple chains were Weibull-type extreme-value distributions with shape parameter values that were identifiable with the integral link size in the limit of infinite chain length. Furthermore, for chains composed of several segments of differing link size, the survival distributions for the various segments converged at a point in the S(t) tails indistinguishable from human data. This was also predicted by parameteric competing risks theory using Weibull underlying distributions. In both the competitive chain simulations and the parametric competing risks theory, however, the shape values for the intersecting distributions deviated from the integer values typical of human data. We conclude that rare events can be the source of integral shapes in human mortality, that convergence is a salient feature of multiple endpoints, but that pure competition may not be the best explanation for the exact type of convergence observable in human mortality. Finally, while the chain models were not motivated by any specific biological structures, interesting biological correlates to them may be useful in gerontological research.