Role of streams in myxobacteria aggregate formation

Mean-field model for nematic alignment of self-propelled rods

Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.

Complete genome sequence and identification of polyunsaturated fatty acid biosynthesis genes of the myxobacterium Minicystis rosea DSM 24000T

Background

Myxobacteria harbor numerous biosynthetic gene clusters that can produce a diverse range of secondary metabolites. Minicystis rosea DSM 24000^T is a soil-dwelling myxobacterium belonging to the suborderSorangiineae and family Polyangiaceae and is known to produce various secondary metabolites as well as polyunsaturated fatty acids (PUFAs). Here, we use whole-genome sequencing to explore the diversity of biosynthetic gene clusters in M. rosea.

Results

Using PacBio sequencing technology, we assembled the 16.04 Mbp complete genome of M. rosea DSM 24000^T, the largest bacterial genome sequenced to date. About 44% of its coding potential represents paralogous genes predominantly associated with signal transduction, transcriptional regulation, and protein folding. These genes are involved in various essential functions such as cellular organization, diverse niche adaptation, and bacterial cooperation, and enable social behavior like gliding motility, sporulation, and predation, typical of myxobacteria. A profusion of eukaryotic-like kinases (353) and an elevated ratio of phosphatases (8.2/1) in M. rosea as compared to other myxobacteria suggest gene duplication as one of the primary modes of genome expansion. About 7.7% of the genes are involved in the biosynthesis of a diverse array of secondary metabolites such as polyketides, terpenes, and bacteriocins. Phylogeny of the genes involved in PUFA biosynthesis (pfa) together with the conserved synteny of the complete pfa gene cluster suggests acquisition via horizontal gene transfer from Actinobacteria.

Conclusion

Overall, this study describes the complete genome sequence of M. rosea, comparative genomic analysis to explore the putative reasons for its large genome size, and explores the secondary metabolite potential, including the biosynthesis of polyunsaturated fatty acids.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12864-021-07955-x.

Matrix adhesion and remodeling diversifies modes of cancer invasion across spatial scales

The metastasis of malignant epithelial tumors begins with the egress of transformed cells from the confines of their basement membrane (BM) to their surrounding collagen-rich stroma. Invasion can be morphologically diverse: when breast cancer cells are separately cultured within BM-like matrix, collagen I (Coll I), or a combination of both, they exhibit collective-, dispersed mesenchymal-, and a mixed collective-dispersed (multimodal)- invasion, respectively. In this paper, we asked how distinct these invasive modes are with respect to the cellular and microenvironmental cues that drive them. A rigorous computational exploration of invasion was performed within an experimentally motivated Cellular Potts-based modeling environment. The model comprised of adhesive interactions between cancer cells, BM- and Coll I-like extracellular matrix (ECM), and reaction-diffusion-based remodeling of ECM. The model outputs were parameters cognate to dispersed- and collective- invasion. A clustering analysis of the output distribution curated through a careful examination of subsumed phenotypes suggested at least four distinct invasive states: dispersed, papillary-collective, bulk-collective, and multimodal, in addition to an indolent/non-invasive state. Mapping input values to specific output clusters suggested that each of these invasive states are specified by distinct input signatures of proliferation, adhesion and ECM remodeling. In addition, specific input perturbations allowed transitions between the clusters and revealed the variation in the robustness between the invasive states. Our systems-level approach proffers quantitative insights into how the diversity in ECM microenvironments may steer invasion into diverse phenotypic modes during early dissemination of breast cancer and contributes to tumor heterogeneity.

Agent-Based Modeling Reveals Possible Mechanisms for Observed Aggregation Cell Behaviors

Myxococcus xanthus is a soil bacterium that serves as a model system for biological self-organization. Cells form distinct, dynamic patterns depending on environmental conditions. An agent-based model was used to understand how M. xanthus cells aggregate into multicellular mounds in response to starvation. In this model, each cell is modeled as an agent represented by a point particle and characterized by its position and moving direction. At low agent density, the model recapitulates the dynamic patterns observed by experiments and a previous biophysical model. To study aggregation at high cell density, we extended the model based on the recent experimental observation that cells exhibit biased movement toward aggregates. We tested two possible mechanisms for this biased movement and demonstrate that a chemotaxis model with adaptation can reproduce the observed experimental results leading to the formation of stable aggregates. Furthermore, our model reproduces the experimentally observed patterns of cell alignment around aggregates.

Short-range guiding can result in the formation of circular aggregates in myxobacteria populations

Myxobacteria are social bacteria that upon starvation form multicellular fruiting bodies whose shape in different species can range from simple mounds to elaborate tree-like structures. The formation of fruiting bodies is a result of collective cell movement on a solid surface. In the course of development, groups of flexible rod-shaped cells form streams and move in circular or spiral patterns to form aggregation centers that can become sites of fruiting body formation. The mechanisms of such cell movement patterns are not well understood. It has been suggested that myxobacterial development depends on short-range contact-mediated interactions between individual cells, i.e. cell aggregation does not require long-range signaling in the population. In this study, by means of a computational mass-spring model, we investigate what types of short-range interactions between cells can result in the formation of streams and circular aggregates during myxobacterial development. We consider short-range head-to-tail guiding between individual cells, whereby movement direction of the head of one cell is affected by the nearby presence of the tail of another cell. We demonstrate that stable streams and circular aggregates can arise only when the trailing cell, in addition to being steered by the tail of the leading cell, is able to speed up to catch up with it. It is suggested that necessary head-to-tail interactions between cells can arise from physical adhesion, response to a diffusible substance or slime extruded by cells, or pulling by motility engine pili. Finally, we consider a case of long-range guiding between cells and show that circular aggregates are able to form without cells increasing speed. These findings present a possibility to discriminate between short-range and long-range guiding mechanisms in myxobacteria by experimentally measuring distribution of cell speeds in circular aggregates.

Myxobacteria are social bacteria that upon starvation form multicellular fruiting bodies whose shape in different species can range from simple mounds to elaborate tree-like structures. The formation of fruiting bodies is a result of collective cell movement on a solid surface. Since collective cell motility during biological morphogenesis is also common in higher organisms, myxobacteria serve as a relatively simple model organism to study multicellular movement, organization and development. In the course of myxobacterial development, groups of flexible rod-shaped cells form streams and move in circular or spiral patterns to form aggregation centers that can become sites of fruiting body formation. The mechanisms of such cell movement patterns are not well understood. In this study, by means of a computational mass-spring model, we demonstrate that the formation of streams and circular aggregates during myxobacterial development can be explained by short-range head-to-tail guiding between individual cells, whereby movement direction of the head of one cell is affected by the nearby presence of the tail of another cell. We suggest that such interactions between cells can result from physical adhesion, response to a diffusible substance or slime extruded by cells, or the action of cell motility engine.

Macroscopic model of self-propelled bacteria swarming with regular reversals

Periodic reversals in the direction of motion in systems of self-propelled rod-shaped bacteria enable them to effectively resolve traffic jams formed during swarming and maximize the swarming rate of the colony. In this paper, a connection is established between a microscopic one-dimensional cell-based stochastic model of reversing nonoverlapping bacteria and a macroscopic nonlinear diffusion equation describing the dynamics of cellular density. Boltzmann-Matano analysis is used to determine the nonlinear diffusion equation corresponding to the specific reversal frequency. Stochastic dynamics averaged over an ensemble is shown to be in very good agreement with the numerical solutions of this nonlinear diffusion equation. Critical density p(0) is obtained such that nonlinear diffusion is dominated by the collisions between cells for the densities p>p(0). An analytical approximation of the pairwise collision time and semianalytical fit for the total jam time per reversal period are also obtained. It is shown that cell populations with high reversal frequencies are able to spread out effectively at high densities. If the cells rarely reverse, then they are able to spread out at lower densities but are less efficient at spreading out at higher densities.

A multiscale model of thrombus development

A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.

A three-dimensional model of myxobacterial fruiting-body formation

Myxobacterial cells are social; they swarm by gliding on surfaces as they feed cooperatively. When they sense starvation, tens of thousands of cells change their movement pattern from outward spreading to inward concentration and form aggregates that become fruiting bodies. Cells inside fruiting bodies differentiate into round, nonmotile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis, a long-range cell interaction that shares many features of chemical reaction-diffusion dynamics. The biological evidence, however, suggests that Myxococcus xanthus aggregation is the consequence of direct cell-contact interactions that are different from chemotaxis. To test whether local interactions suffice to explain the formation of fruiting bodies and the differentiation of spores within them, we have simulated the process. In this article, we present a unified 3D model that reproduces in one continuous simulation all the stages of fruiting-body formation that have been experimentally observed: nonsymmetric initial aggregates (traffic jams), streams, formation of toroidal aggregates, hemispherical 3D mounds, and finally sporulation within the fruiting body.

Aggregation during fruiting body formation in Myxococcus xanthus is driven by reducing cell movement

When starved, Myxococcus xanthus cells assemble themselves into aggregates of about 10(5) cells that grow into complex structures called fruiting bodies, where they later sporulate. Here we present new observations on the velocities of the cells, their orientations, and reversal rates during the early stages of fruiting body formation. Most strikingly, we find that during aggregation, cell velocities slow dramatically and cells orient themselves in parallel inside the aggregates, while later cell orientations are circumferential to the periphery. The slowing of cell velocity, rather than changes in reversal frequency, can account for the accumulation of cells into aggregates. These observations are mimicked by a continuous agent-based computational model that reproduces the early stages of fruiting body formation. We also show, both experimentally and computationally, how changes in reversal frequency controlled by the Frz system mutants affect the shape of these early fruiting bodies.

A framework for three-dimensional simulation of morphogenesis

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility to allow an almost unlimited variety of simulations. We have verified COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http:// compucell.sourceforge.net.

Reversing cell polarity: evidence and hypothesis

The long, rod-shaped cells of myxobacteria are polarized by their gliding engines. At the rear, A-engines push while pili pull the front end forward. An hypothesis is developed whereby both engines are partially dis-assembled, then re-assembled at the opposite pole when cells reverse their movement direction. Reversals are induced by an Mgl G-protein switch that controls engine polarity. The switch is driven by an oscillatory circuit of Frizzy proteins. In growing cells, the circuit gives rise to an occasional reversal that makes swarming possible. Then, as myxobacteria begin fruiting body development, a rising level of C-signal input drives the oscillator and changes the reversal pattern. Cells reverse regularly every eight minutes in traveling waves, the reversal period is then prolonged enabling cells to form streams that enlarge tiny random aggregates into fruiting bodies.

A three-dimensional model of myxobacterial aggregation by contact-mediated interactions

Myxobacteria provide one of the simplest models of cell-cell interaction and organized cell movement leading to cellular differentiation. When starved, tens of thousands of cells change their movement pattern from outward spreading to inward concentration; they form aggregates that become fruiting bodies. Cells inside fruiting bodies differentiate into round, nonmotile, environmentally resistant spores. Traditionally, cell aggregation has been considered to imply chemotaxis; a long-range cell interaction. However, myxobacterial aggregation is the consequence of direct cell-contact interactions, not chemotaxis. We present here a 3D stochastic lattice-gas cellular automata model of cell aggregation based on local cell-cell contact, and no chemotaxis. We demonstrate that a 3D discrete stochastic model can simulate two stages of cell aggregation. First, a "traffic jam" forms embedded in a field of motile cells. The jam then becomes an aggregation center that accumulates more cells. We show that, at high cell density, cells stream around the traffic jam, generating a 3D hemispherical mound. Later, when the nuclear traffic jam dissolves, the aggregation center becomes a 3D ring of streaming cells.