Mechanism for collective cell alignment in Myxococcus xanthus bacteria

Myxococcus xanthus cells self-organize into aligned groups, clusters, at various stages of their lifecycle. Formation of these clusters is crucial for the complex dynamic multi-cellular behavior of these bacteria. However, the mechanism underlying the cell alignment and clustering is not fully understood. Motivated by studies of clustering in self-propelled rods, we hypothesized that M. xanthus cells can align and form clusters through pure mechanical interactions among cells and between cells and substrate. We test this hypothesis using an agent-based simulation framework in which each agent is based on the biophysical model of an individual M. xanthus cell. We show that model agents, under realistic cell flexibility values, can align and form cell clusters but only when periodic reversals of cell directions are suppressed. However, by extending our model to introduce the observed ability of cells to deposit and follow slime trails, we show that effective trail-following leads to clusters in reversing cells. Furthermore, we conclude that mechanical cell alignment combined with slime-trail-following is sufficient to explain the distinct clustering behaviors observed for wild-type and non-reversing M. xanthus mutants in recent experiments. Our results are robust to variation in model parameters, match the experimentally observed trends and can be applied to understand surface motility patterns of other bacterial species.Comment: Added paragraph on high cell density simulations (new Supp. Figure S6) in Discussion section; Moved cell model and simulation procedure from Supplementary methods to Methods section in Main Tex

Myxococcus xanthus gliding motors are elastically coupled to the substrate as predicted by the focal adhesion model of gliding motility

Myxococcus xanthus is a model organism for studying bacterial social behaviors due to its ability to form complex multi-cellular structures. Knowledge of M. xanthus surface gliding motility and the mechanisms that coordinate it are critically important to our understanding of collective cell behaviors. Although the mechanism of gliding motility is still under investigation, recent experiments suggest that there are two possible mechanisms underlying force production for cell motility: the focal adhesion mechanism and the helical rotor mechanism which differ in the biophysics of the cell-substrate interactions. Whereas the focal adhesion model predicts an elastic coupling, the helical rotor model predicts a viscous coupling. Using a combination of computational modeling, imaging, and force microscopy, we find evidence for elastic coupling in support of the focal adhesion model. Using a biophysical model of the M. xanthus cell, we investigated how the mechanical interactions between cells are affected by interactions with the substrate. Comparison of modeling results with experimental data for cell-cell collision events pointed to a strong, elastic attachment between the cell and substrate. These results are robust to variations in the mechanical and geometrical parameters of the model. We then directly measured the motor-substrate coupling by monitoring the motion of optically trapped beads and find that motor velocity decreases exponentially with opposing load. At high loads, motor velocity approaches zero velocity asymptotically and motors remain bound to beads indicating a strong, elastic attachment

Interplay of gene expression noise and ultrasensitive dynamics affects bacterial operon organization

This is the publisher's version, also available electronically from "http://journals.plos.org".Bacterial chromosomes are organized into polycistronic cotranscribed operons, but the evolutionary pressures maintaining them are unclear. We hypothesized that operons alter gene expression noise characteristics, resulting in selection for or against maintaining operons depending on network architecture. Mathematical models for 6 functional classes of network modules showed that three classes exhibited decreased noise and 3 exhibited increased noise with same-operon cotranscription of interacting proteins. Noise reduction was often associated with a decreased chance of reaching an ultrasensitive threshold. Stochastic simulations of the lac operon demonstrated that the predicted effects of transcriptional coupling hold for a complex network module. We employed bioinformatic analysis to find overrepresentation of noise-minimizing operon organization compared with randomized controls. Among constitutively expressed physically interacting protein pairs, higher coupling frequencies appeared at lower expression levels, where noise effects are expected to be dominant. Our results thereby suggest an important role for gene expression noise, in many cases interacting with an ultrasensitive switch, in maintaining or selecting for operons in bacterial chromosomes

A mean-field model for nematic alignment of self-propelled rods

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.Comment: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.03461

Interplay of Gene Expression Noise and Ultrasensitive Dynamics Affects Bacterial Operon Organization

Bacterial chromosomes are organized into polycistronic cotranscribed operons, but the evolutionary pressures maintaining them are unclear. We hypothesized that operons alter gene expression noise characteristics, resulting in selection for or against maintaining operons depending on network architecture. Mathematical models for 6 functional classes of network modules showed that three classes exhibited decreased noise and 3 exhibited increased noise with same-operon cotranscription of interacting proteins. Noise reduction was often associated with a decreased chance of reaching an ultrasensitive threshold. Stochastic simulations of the lac operon demonstrated that the predicted effects of transcriptional coupling hold for a complex network module. We employed bioinformatic analysis to find overrepresentation of noiseminimizing operon organization compared with randomized controls. Among constitutively expressed physically interacting protein pairs, higher coupling frequencies appeared at lower expression levels, where noise effects are expected to be dominant. Our results thereby suggest an important role for gene expression noise, in many cases interacting with an ultrasensitive switch, in maintaining or selecting for operons in bacterial chromosomes

Modeling mechanical interactions in growing populations of rod-shaped bacteria

Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular fluid flow lead to complex, changing arrangements of cells within the population. To rationally engineer and control the behavior of cell collectives we need theoretical and computational tools to understand their emergent spatiotemporal dynamics. Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions. Crucially, our model couples the dynamics of cell growth to the cell's environment: Mechanical constraints can affect cellular growth rate and a cell may alter its behavior in response to these constraints. This coupling links the mechanical forces that influence cell growth and emergent behaviors in cell assemblies. We illustrate our approach by showing how mechanical interactions can impact the dynamics of bacterial collectives growing in microfluidic traps

Biophysics at the coffee shop: lessons learned working with George Oster

Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists.Comment: 22 pages, 3 figures, accepted in Molecular Biology of the Cel

Breakdown of Boltzmann-type Models for Nematic Alignment of Self-propelled Rods

Studies in active matter systems and in the collective motility of organisms utilize a range of analytical approaches to formulate continuous kinetic models of collective dynamics from the rules or equations describing agent interactions. However, the derivation of these models often relies on Boltzmann's hypothesis of "molecular chaos", often simply called statistical independence. While it is often the simplest way to derive tractable models it is not clear whether the statistical independence assumption is valid in practice. In this work, we develop a Boltzmann-type kinetic model for the nematic alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We identify relevant parameters and derive kinetic equations for the corresponding asymptotic regime. By comparing numerical solutions of the kinetic equations to an agent-based model that implements our microscopic alignment rules, we examine the accuracy of the continuous model. The results indicate that our kinetic model fails to replicate the underlying dynamics due to the formation of clusters that violate statistical independence. Additionally, we show that a mechanism limiting cluster formation helps to improve the agreement between the analytical model and agent simulations. These results highlight the need to improve modeling approaches for active matter systems

О значении теории алгоритмов для системы современного профессионального образования и методики ее преподавания

The article explores the role and relevance of the theory of algorithms in the fundamentalization of mathematical education of specialists in the fi of computer science and information technology, trained at vocational schools and higher institutions. In this case, the theory of algorithms appears in two fi the fi fi assumes theory of specifi algorithms (or intuitively-containing theory of algorithms) whereas the second one implies a formal-logical (abstract) theory of algorithms. In the fi case, the theory of algorithms explores algorithms as means for solving specifi problems, and the problem of developing this kind of algorithm is seen as the basic one. This algorithm should be implemented by a modern computer in real time. The second problem assumes comparing different specifi algorithms for solving the same problem in terms of their complexity, mainly in terms of the time required to solve the problem. Due to this fact, the classes of complexity of algorithms P and NP appear followed by the problem of relationships between these classes. These problems are not solved until now. In the second case, the theory of algorithms creates mathematical (abstract) concepts of the algorithm and explores the properties of these concepts. In the 30s and the fi postwar years of the XX century, several abstract concepts of the algorithm, or formalizations of the intuitive understanding of the algorithm, were developed. This is a Turing machine, recursive functions as functions computable by some algorithm, normal algorithms of A. A. Markov. The abstract theory of algorithms establishes the equivalence of these abstract con cepts. The problem of these algorithms existing is seen as the most important one. In particular, the abstract theory of algorithms establishes the absence of algorithms for solving a number of mass problems. This paper describes a methodological system of teaching algorithm theory, taking into ac­count its two intuitive and abstract fields.Статья посвящена выявлению роли и значения теории алгоритмов в фундаментализации математического образования специалистов в области компьютерных наук и информационных технологий, обучающихся в образовательных учреждениях СПО и ВО. При этом теория алгоритмов предстает в двух своих ипостасях: как теория конкретных алгоритмов (или интуитивно-содержательная теория алгоритмов) и как формально-логическая (абстрактная) теория алгоритмов. В первом случае теория алгоритмов занимается созданием и изучением алгоритмов решения конкретных задач, и главной проблемой здесь является проблема разработки такого конкретного алгоритма, который может быть реализован современным компьютером в реальное время, а также проблема сравнения различных конкретных алгоритмов решения одной и той же задачи по степени их сложности, в основном по времени, требуемом для решения задачи. В связи с этим возникают классы сложности алгоритмов P и NP, а вместе с ними и проблема взаимоотношений между этими классами, не решенная до конца до настоящего времени. Во втором случае теория алгоритмов создает строго математические (абстрактные) понятия алгоритма и изучает свойства таких понятий. В 1930-е годы и первые послевоенные годы было разработано несколько абстрактных понятий алгоритма или, как говорят, формализаций интуитивного понимания алгоритма. Это машины Тьюринга и вычислимые с их помощью функции, рекурсивные функции как функции вычислимые с помощью некоторого алгоритма, нормальные алгоритмы А. А. Маркова и вычислимые с их помощью функции. Абстрактная теория алгоритмов устанавливает эквивалентность этих абстрактных понятий. Важнейшей проблемой здесь является также проблема существования таких алгоритмов для решения той или иной массовой проблемы. В частности, абстрактная теория алгоритмов устанавливает отсутствие алгоритмов для решения ряда массовых проблем. В нашей работе характеризуется методическая система обучения теории алгоритмов, учитывающая эти две ее ипостаси: интуитивно-содержательную и абстрактную

Lattice gas cellular automata model for rippling and aggregation in myxobacteria

A lattice-gas cellular automaton (LGCA) model is used to simulate rippling and aggregation in myxobacteria. An efficient way of representing cells of different cell size, shape and orientation is presented that may be easily extended to model later stages of fruiting body formation. This LGCA model is designed to investigate whether a refractory period, a minimum response time, a maximum oscillation period and non-linear dependence of reversals of cells on C-factor are necessary assumptions for rippling. It is shown that a refractory period of 2-3 minutes, a minimum response time of up to 1 minute and no maximum oscillation period best reproduce rippling in the experiments of {\it Myxoccoccus xanthus}. Non-linear dependence of reversals on C-factor is critical at high cell density. Quantitative simulations demonstrate that the increase in wavelength of ripples when a culture is diluted with non-signaling cells can be explained entirely by the decreased density of C-signaling cells. This result further supports the hypothesis that levels of C-signaling quantitatively depend on and modulate cell density. Analysis of the interpenetrating high density waves shows the presence of a phase shift analogous to the phase shift of interpenetrating solitons. Finally, a model for swarming, aggregation and early fruiting body formation is presented