A structured-population model of Proteus mirabilis swarm-colony development

Adjustment in the Composition and Organization of Proteus mirabilis Lipids during the Swarming Process

Proteus mirabilis, an opportunistic pathogen of the urinary tract, is known for its dimorphism and mobility. A connection of lipid alterations, induced by the rods elongation process, with enhanced pathogenicity of long-form morphotype for the development of urinary tract infections, seems highly probable. Therefore, research on the adjustment in the composition and organization of P. mirabilis lipids forming elongated rods was undertaken. The analyses performed using the ultra-high performance liquid chromatography with tandem mass spectrometry showed that drastic modifications in the morphology of P. mirabilis rods that occur during the swarming process are directly related to deprivation of the long-form cells of PE 33:1 and PG 31:2 and their enrichment with PE 32:1, PE 34:1, PE 34:2, PG 30:2, PG 32:1, and PG 34:1. The analyses conducted by the gas chromatography-mass spectrometry showed negligible effects of the swarming process on fatty acids synthesis. However, the constant proportions between unsaturated and saturated fatty acids confirmed that phenotypic modifications in the P. mirabilis rods induced by motility were independent of the saturation of the phospholipid tails. The method of the Förster resonance energy transfer revealed the influence of the swarming process on the melting of ordered lipid rafts present in the short-form rods, corresponding to the homogeneity of lipid bilayers in the long-form rods of P. mirabilis. Confocal microscope photographs visualized strong Rhod-PE fluorescence of the whole area of swarmer cells, in contrast to weak membrane fluorescence of non-swarmer cells. It suggested an increased permeability of the P. mirabilis bilayers in long-form rods morphologically adapted to the swarming process. These studies clearly demonstrate that swarming motility regulates the lipid composition and organization in P. mirabilis rods.

Considerations for Modeling Proteus mirabilis Swarming

In this chapter we provide some initial guidance to experimentalists on how they might go about creating mathematical representations of their systems under study. Because the interests and goals of different researchers can differ, we try to provide broad instruction on the creation and use of mathematical models. We provide a brief overview of some modeling that has been done with Proteus mirabilis colonies, and discuss the goals of modeling. We suggest ways that collaborative teams may communicate with one another more effectively, and how they can build more confidence in their model results.

Structured models of cell migration incorporating molecular binding processes

The dynamic interplay between collective cell movement and the various molecules involved in the accompanying cell signalling mechanisms plays a crucial role in many biological processes including normal tissue development and pathological scenarios such as wound healing and cancer. Information about the various structures embedded within these processes allows a detailed exploration of the binding of molecular species to cell-surface receptors within the evolving cell population. In this paper we establish a general spatio-temporal-structural framework that enables the description of molecular binding to cell membranes coupled with the cell population dynamics. We first provide a general theoretical description for this approach and then illustrate it with three examples arising from cancer invasion.

Mathematics as a conduit for translational research in post-traumatic osteoarthritis

Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017.

Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model

Post-traumatic osteoarthritis affects almost 20% of the adult US population. An injurious impact applies a significant amount of physical stress on articular cartilage and can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. In our effort to understand the underlying biochemical mechanisms of this debilitating disease, we have constructed a multiscale mathematical model of the process with three components: cellular, chemical, and mechanical. The cellular component describes the different chondrocyte states according to the chemicals these cells release. The chemical component models the change in concentrations of those chemicals. The mechanical component contains a simulation of a blunt impact applied onto a cartilage explant and the resulting strains that initiate the biochemical processes. The scales are modeled through a system of partial-differential equations and solved numerically. The results of the model qualitatively capture the results of laboratory experiments of drop-tower impacts on cartilage explants. The model creates a framework for incorporating explicit mechanics, simulated by finite element analysis, into a theoretical biology framework. The effort is a step toward a complete virtual platform for modeling the development of post-traumatic osteoarthritis, which will be used to inform biomedical researchers on possible non-invasive strategies for mitigating the disease.

Proteus mirabilis and Urinary Tract Infections

Proteus mirabilis is a Gram-negative bacterium and is well known for its ability to robustly swarm across surfaces in a striking bulls'-eye pattern. Clinically, this organism is most frequently a pathogen of the urinary tract, particularly in patients undergoing long-term catheterization. This review covers P. mirabilis with a focus on urinary tract infections (UTI), including disease models, vaccine development efforts, and clinical perspectives. Flagella-mediated motility, both swimming and swarming, is a central facet of this organism. The regulation of this complex process and its contribution to virulence is discussed, along with the type VI-secretion system-dependent intra-strain competition, which occurs during swarming. P. mirabilis uses a diverse set of virulence factors to access and colonize the host urinary tract, including urease and stone formation, fimbriae and other adhesins, iron and zinc acquisition, proteases and toxins, biofilm formation, and regulation of pathogenesis. While significant advances in this field have been made, challenges remain to combatting complicated UTI and deciphering P. mirabilis pathogenesis.

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.

A validated model of the pro- and anti-inflammatory cytokine balancing act in articular cartilage lesion formation

Traumatic injuries of articular cartilage result in the formation of a cartilage lesion and contribute to cartilage degeneration and the risk of osteoarthritis (OA). A better understanding of the framework for the formation of a cartilage lesion formation would be helpful in therapy development. Toward this end, we present an age and space-structured model of articular cartilage lesion formation after a single blunt impact. This model modifies the reaction-diffusion-delay models in Graham et al. (2012) (single impact) and Wang et al. (2014) (cyclic loading), focusing on the "balancing act" between pro- and anti-inflammatory cytokines. Age structure is introduced to replace the delay terms for cell transitions used in these earlier models; we find age structured models to be more flexible in representing the underlying biological system and more tractable computationally. Numerical results show a successful capture of chondrocyte behavior and chemical activities associated with the cartilage lesion after the initial injury; experimental validation of our computational results is presented. We anticipate that our in silico model of cartilage damage from a single blunt impact can be used to provide information that may not be easily obtained through in in vivo or in vitro studies.

Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation

We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al., 2012 for the spread of a lesion formed though a single traumatic event. Our model represents 'implicitly' the effects of loading, meaning through a cyclic sink term in the equations for live cells. Our model forms the basis for in silico studies of cartilage damage relevant to questions in osteoarthritis, for example, that may not be easily answered through in vivo or in vitro studies. Computational results are presented that indicate the impact of differing levels of erythropoietin on articular cartilage lesion abatement.

Modeling the role of water in Bacillus subtilis colonies

We propose a simple cellular automaton model for the description of the evolution of a colony of Bacillus subtilis. The originality of our model lies in the fact that the bacteria can move in a pool of liquid. We assume that each migrating bacterium is surrounded by an individual pool, and the overlap of the latter gives rise to a collective pool with a higher water level. The bacteria migrate collectively when the level of water is high enough. When the bacteria are far enough from each other, the level of water becomes locally too low to allow migration, and the bacteria switch to a proliferating state. The proliferation-to-migration switch is triggered by high levels of a substance produced by proliferating bacteria. We show that it is possible to reproduce in a fairly satisfactory way the various forms that make up the experimentally observed morphological diagram of B. subtilis. We propose a phenomenological relation between the size of the water pool used in our model and the agar concentration of the substrate on which the bacteria migrate. We also compare experimental results from cutting the central part of the colony with the results of our simulations.

Radial and spiral stream formation in Proteus mirabilis colonies

The enteric bacterium Proteus mirabilis, which is a pathogen that forms biofilms in vivo, can swarm over hard surfaces and form a variety of spatial patterns in colonies. Colony formation involves two distinct cell types: swarmer cells that dominate near the surface and the leading edge, and swimmer cells that prefer a less viscous medium, but the mechanisms underlying pattern formation are not understood. New experimental investigations reported here show that swimmer cells in the center of the colony stream inward toward the inoculation site and in the process form many complex patterns, including radial and spiral streams, in addition to previously-reported concentric rings. These new observations suggest that swimmers are motile and that indirect interactions between them are essential in the pattern formation. To explain these observations we develop a hybrid model comprising cell-based and continuum components that incorporates a chemotactic response of swimmers to a chemical they produce. The model predicts that formation of radial streams can be explained as the modulation of the local attractant concentration by the cells, and that the chirality of the spiral streams results from a swimming bias of the cells near the surface of the substrate. The spatial patterns generated from the model are in qualitative agreement with the experimental observations.

Bacteria frequently colonize surfaces and grow as biofilm communities embedded in a gel-like polysaccharide matrix, and when this occurs on catheters, heart valves and other medical implants, it can lead to serious, hard-to-treat infections. Proteus mirabilis is an enteric bacterium that forms biofilms on urinary catheters, but in laboratory experiments it can swarm over hard surfaces and form a variety of spatial patterns. Understanding these patterns is a first step toward understanding biofilm formation, and here we describe new experimental results and mathematical models of pattern formation in Proteus. The experiments show that swimmer cells in the center of the colony stream inward toward the inoculation site and in the process form many complex patterns, including radial and spiral streams, in addition to concentric rings. To explain these observations we develop a model that incorporates a chemotactic response of swimmers to a chemical they produce. The model predicts that formation of radial streams can be explained as the modulation of the local attractant concentration by the cells, and that the chirality of the spiral streams can be predicted by incorporating a swimming bias of the cells near the surface of the substrate.

Patterning of mutually interacting bacterial bodies: close contacts and airborne signals

Background

Bacterial bodies (colonies) can develop complex patterns of color and structure. These patterns may arise as a result of both colony-autonomous developmental and regulatory processes (self-patterning) and environmental influences, including those generated by neighbor bodies. We have studied the interplay of intra-colony signaling (self-patterning) and inter-colony influences in related clones of Serratia rubidaea grown on rich media.

Results

Colonies are shaped by both autonomous patterning and by signals generated by co-habitants of the morphogenetic space, mediating both internal shaping of the body, and communication between bodies sharing the same living space. The result of development is affected by the overall distribution of neighbors in the dish. The neighbors' presence is communicated via at least two putative signals, while additional signals may be involved in generating some unusual patterns observed upon encounters of different clones. A formal model accounting for some aspects of colony morphogenesis and inter-colony interactions is proposed.

Conclusions

The complex patterns of color and texture observed in Serratia rubidaea colonies may be based on at least two signals produced by cells, one of them diffusing through the substrate (agar) and the other carried by a volatile compound and absorbed into the substrate. Differences between clones with regard to the interpretation of signals may result from different sensitivity to signal threshold(s).

Bacterial Swarming: A Model System for Studying Dynamic Self-assembly

Bacterial swarming is an example of dynamic self-assembly in microbiology in which the collective interaction of a population of bacterial cells leads to emergent behavior. Swarming occurs when cells interact with surfaces, reprogram their physiology and behavior, and adapt to changes in their environment by coordinating their growth and motility with other cells in the colony. This review summarizes the salient biological and biophysical features of this system and describes our current understanding of swarming motility. We have organized this review into four sections: 1) The biophysics and mechanisms of bacterial motility in fluids and its relevance to swarming. 2) The role of cell/molecule, cell/surface, and cell/cell interactions during swarming. 3) The changes in physiology and behavior that accompany swarming motility. 4) A concluding discussion of several interesting, unanswered questions that is particularly relevant to soft matter scientists.

An explanatory model to validate the way water activity rules periodic terrace generation in Proteus mirabilis swarm

This paper explains the biophysical principles which, according to us, govern the Proteus mirabilis swarm phenomenon. Then, this explanation is translated into a mathematical model, essentially based on partial differential equations. This model is then implemented using numerical methods of the finite volume type in order to make simulations. The simulations show most of the characteristics which are observed in situ and in particular the terrace generation.