Synechocystis sp., a common unicellular freshwater cyanobacterium, has been used as a model organism to study phototaxis, an ability to move in the direction of a light source. This microorganism displays a number of additional characteristics such as delayed motion, surface dependence, and a quasi-random motion, where cells move in a seemingly disordered fashion instead of in the direction of the light source, a global force on the system. These unexplained motions are thought to be modulated by local interactions between cells such as intercellular communication. In this paper, we consider only local interactions of these phototactic cells in order to mathematically model this quasi-random motion. We analyze an experimental data set to illustrate the presence of quasi-random motion and then derive a stochastic dynamic particle system modeling interacting phototactic cells. The simulations of our model are consistent with experimentally observed phototactic motion.
[Show abstract][Hide abstract] ABSTRACT: The emergent behaviors of communities of genotypically identical cells cannot be easily predicted from the behaviors of individual cells. In many cases, it is thought that direct cell-cell communication plays a critical role in the transition from individual to community behaviors. In the unicellular photosynthetic cyanobacterium Synechocystis sp. PCC 6803, individual cells exhibit light-directed motility ("phototaxis") over surfaces, resulting in the emergence of dynamic spatial organization of multicellular communities. To probe this striking community behavior, we carried out time-lapse video microscopy coupled with quantitative analysis of single-cell dynamics under varying light conditions. These analyses suggest that cells secrete an extracellular substance that modifies the physical properties of the substrate, leading to enhanced motility and the ability for groups of cells to passively guide one another. We developed a biophysical model that demonstrates that this form of indirect, surface-based communication is sufficient to create distinct motile groups whose shape, velocity, and dynamics qualitatively match our experimental observations, even in the absence of direct cellular interactions or changes in single-cell behavior. Our computational analysis of the predicted community behavior, across a matrix of cellular concentrations and light biases, demonstrates that spatial patterning follows robust scaling laws and provides a useful resource for the generation of testable hypotheses regarding phototactic behavior. In addition, we predict that degradation of the surface modification may account for the secondary patterns occasionally observed after the initial formation of a community structure. Taken together, our modeling and experiments provide a framework to show that the emergent spatial organization of phototactic communities requires modification of the substrate, and this form of surface-based communication could provide insight into the behavior of a wide array of biological communities.
[Show abstract][Hide abstract] ABSTRACT: Recently we developed a stochastic particle system describing local interactions between cyanobacteria. We focused on the common freshwater cyanobacteria Synechocystis sp., which are coccoidal bacteria that utilize group dynamics to move toward a light source, a motion referred to as phototaxis. We were particularly interested in the local interactions between cells that were located in low to medium density areas away from the front. The simulations of our stochastic particle system in 2D replicated many experimentally observed phenomena, such as the formation of aggregations and the quasi-random motion of cells. In this paper, we seek to develop a better understanding of group dynamics produced by this model. To facilitate this study, we replace the stochastic model with a system of ordinary differential equations describing the evolution of particles in 1D. Unlike many other models, our emphasis is on particles that selectively choose one of their neighbors as the preferred direction of motion. Furthermore, we incorporate memory by allowing persistence in the motion. We conduct numerical simulations which allow us to efficiently explore the space of parameters, in order to study the stability, size, and merging of aggregations.
[Show abstract][Hide abstract] ABSTRACT: The editorial section of Physica D addresses emergent behavior in multi-particle systems with non-local interactions. The special issue contains new research contributions from a broad spectrum of researchers on topics contributions from a broad spectrum of researchers on topics related to emergent behavior. The goal is to present the current research in a single volume to showcase the diversity and vitality of this area and to serve as a useful resource for future reference. The emergence of very complex behavior is a consequence of individuals following very simple rules without any external coordination. Many models of group behavior have been proposed that involve nonlocal interactions between the species. Related models also arise in many physical systems such as granular media, self-assembly of nanoparticles, vortex dynamics in Bose-Einstein Condensates, and other media.
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