Secretion of extracellular polymeric substances (EPSs) by growing bacteria is an integral part of forming biofilm-like structures. In such dense systems, mechanical interactions among the structural components can be expected to significantly contribute to morphological properties. Here, we use a particle-based modeling approach to study the self-organization of nonmotile rod-shaped bacterial cells growing on a solid substrate in the presence of selfproduced EPSs. In our simulation, all of the components interact mechanically via repulsive forces, occurring as the bacterial cells grow and divide (via consuming diffusing nutrient) and produce EPSs. Based on our simulation, we show that mechanical interactions control the collective behavior of the system. In particular, we find that the presence of nonadsorbing EPSs can lead to spontaneous aggregation of bacterial cells by a depletion attraction and thereby generates phase separated patterns in the nonequilibrium growing colony. Both repulsive interactions between cell and EPSs and the overall concentration of EPSs are important factors in the self-organization in a nonequilibrium growing colony. Furthermore, we investigate the interplay of mechanics with the nutrient diffusion and consumption by bacterial cells and observe that suppression of branch formation occurs due to EPSs compared with the case where no EPS is produced.A common underlying theme of biophysics of living matter is the quest to understand how local interactions of individual components lead to collective behavior and formation of highly self-organized systems (1-6). In this regard, bacterial systems are an especially interesting example. Bacteria are known to selforganize into multicellular communities, commonly known as biofilms, in which microbial cells live in close association with a solid surface or liquid-air interface and are embedded in a self-produced extracellular matrix. Extracellular polymeric substances (EPSs) play an important role in determining the structural and mechanical architecture of a biofilm (7-12). Generally, the collective dynamics of bacterial colony involves a complex interplay of various physical, chemical, and biological mechanisms, such as growth and differentiation of cells, production of EPSs, the collective movement of cells determined by interacting physical forces and chemical cues, e.g., chemotaxis, motility, cellcell signaling, adhesion, and gene regulation (13)(14)(15)(16)(17)(18)(19). At low density, communication among cells occurs mainly through chemical signals (20). However, at a higher density, as bacteria aggregate and form dense communities, direct mechanical interaction becomes increasingly relevant in the self-organization (21-23). In this regard, microfluidics-based experiments coupled with continuum modeling of cellular dynamics by Volfson et al.(24) was a pioneering study emphasizing the role of cell-cell mechanical interaction in the growth of a highly organized bacterial colony. As a significant extension, Farrell and coworkers (25, 26) hav...

Time delay in the kinetic terms of reaction-diffusion systems has been investigated. It has been shown that short delay beyond a critical threshold may induce spatiotemporal instabilities. For unequal diffusivities and appropriate parameter space delay may induce Turing instability resulting in stationary patterns and also interesting Turing-Hopf transition with the formation of spirals. The theoretical scheme has been numerically explored in two different prototypical reaction-diffusion systems.

Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.

We study spreading of a non-motile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility and the inherent demographic noise. Population fluctuations are inherent in an agent based model whereas, for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with non-linear diffusivity lead to a transition from Diffusion Limited Aggregation (DLA) type morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

Self-organization by bacterial cells often leads to the formation of a highly complex spatially-structured biofilm. In such a bacterial biofilm, cells adhere to each other and are embedded in a self-produced extracellular matrix (ECM). Bacillus substilis bacteria utilize localized cell-death patterns which focuses mechanical forces to form wrinkled sheet-like structures in three dimensions. A most intriguing feature underlying this biofilm formation is that vertical buckling and ridge location is biased to occur in region of high cell-death. Here we present a spatially extended model to investigate the role of the bacterial secreted ECM during the biofilm formation and the self-organization of cell-death. Using this reaction-diffusion model we show that the interaction between the cell's motion and the ECM concentration gives rise to a self-trapping instability, leading to variety of cell-death patterns. The resultant spot patterns generated by our model are shown to be in semi-quantitative agreement with recent experimental observation.

Application of time-delayed feedback is a practical method of controlling bifurcations in reaction-diffusion systems. It has been shown that for a suitable feedback strength, time delay beyond a threshold may induce spatiotemporal instabilities. For an appropriate parameter space with differential diffusivities of the activator-inhibitor species, delayed feedback may generate Turing instability via a Hopf-Turing transition, resulting in stationary patterns. This is explored by a theoretical scheme in a photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system where the delayed feedback is externally tuned by photoillumination intensity. Our analytical results corroborate with direct numerical simulations.

Bacterial cells can often self-organize into multicellular structures with complex spatiotemporal morphology. In this work, we study the spatiotemporal dynamics of a growing microbial colony in the presence of cell death. We present an individual-based model of nonmotile bacterial cells which grow and proliferate by consuming diffusing nutrients on a semisolid two-dimensional surface. The colony spreads by growth forces and sliding motility of cells and undergoes cell death followed by subsequent disintegration of the dead cells in the medium. We model cell death by considering two possible situations: In one of the cases, cell death occurs in response to the limitation of local nutrients, while the other case corresponds to an active death process, known as apoptotic or programmed cell death. We demonstrate how the colony morphology is influenced by the presence of cell death. Our results show that cell death facilitates transitions from roughly circular to highly branched structures at the periphery of an expanding colony. Interestingly, our results also reveal that for the colonies which are growing in higher initial nutrient concentrations, cell death occurs much earlier compared to the colonies which are growing in lower initial nutrient concentrations. This work provides new insights into the branched patterning of growing bacterial colonies as a consequence of complex interplay among the biochemical and mechanical effects.

Bacteria, while developing a multicellular colony or biofilm, can undergo pattern formation by diverse intricate mechanisms. One such route is directional movement or chemotaxis toward or away from self-secreted or externally employed chemicals. In some bacteria, the self-produced signaling chemicals or autoinducers themselves act as chemoattractants or chemorepellents and thereby regulate the directional movements of the cells in the colony. In addition, bacteria follow a certain growth kinetics which is integrated in the process of colony development. Here, we study the interplay of bacterial growth dynamics, cell motility, and autochemotactic motion with respect to the self-secreted diffusive signaling chemicals in spatial pattern formation. Using a continuum model of motile bacteria, we show growth can act as a crucial tuning parameter in determining the spatiotemporal dynamics of a colony. In action of growth dynamics, while chemoattraction toward autoinducers creates arrested phase separation, pattern transitions and suppression can occur for a fixed chemorepulsive strength.