Reproduction of bacterial chemotaxis by a non-living self-propelled object.

Taxic behavior as a response to an external stimulus is a fundamental function of living organisms. Some bacteria successfully implement chemotaxis without directly controlling the direction of movement. They periodically alternate between run and tumble, i.e., straight movement and change in direction, respectively. They tune their running period depending on the concentration gradient of attractants around them. Consequently, they respond to a gentle concentration gradient stochastically, which is called "bacterial chemotaxis." In this study, such a stochastic response was reproduced by a non-living self-propelled object. We used a phenanthroline disk floating on an aqueous solution of Fe[Formula: see text]. The disk spontaneously alternated between rapid motion and rest, similar to the run-and-tumble motion of bacteria. The movement direction of the disk was isotropic independent of the concentration gradient. However, the existing probability of the self-propelled object was higher at the low-concentration region, where the run length was longer. To explain the mechanism underlying this phenomenon, we proposed a simple mathematical model that considers random walkers whose run length depends on the local concentration and direction of movement against the gradient. Our model adopts deterministic functions to reproduce the both effects, which is instead of stochastic tuning the period of operation used in the previous reports. This allows us to analyze the proposed model mathematically, which indicated that our model reproduces both positive and negative chemotaxis depending on the competition between the local concentration effect and it's gradient effect. Owing to the newly introduced directional bias, the experimental observations were reproduced numerically and analytically. The results indicate that the directional bias response to the concentration gradient is an essential parameter for determining bacterial chemotaxis. This rule might be universal for the stochastic response of self-propelled particles in living and non-living systems.

Mathematical model for promotion of wound closure with ATP release.

To computationally investigate the recent experimental finding such that extracellular ATP release caused by exogeneous mechanical forces promote wound closure, we introduce a mathematical model, the Cellular Potts Model (CPM), which is a popular discretized model on a lattice, where the movement of a "cell" is determined by a Monte Carlo procedure. In the experiment, it was observed that there is mechanosensitive ATP release from the leading cells facing the wound gap and the subsequent extracellular Ca2+ influx. To model these phenomena, the Reaction-Diffusion equations for extracellular ATP and intracellular Ca2+ concentrations are adopted and combined with CPM, where we also add a polarity term because the cell migration is enhanced in the case of ATP release. From the numerical simulations using this hybrid model, we discuss effects of the collective cell migration due to the ATP release and the Ca2+ influx caused by the mechanical forces and the consequent promotion of wound closure.

Coil-globule transition of a polymer involved in excluded-volume interactions with macromolecules.

Polymers adopt extended coil and compact globule states according to the balance between entropy and interaction energies. The transition of a polymer between an extended coil state and compact globule state can be induced by changing thermodynamic force such as temperature to alter the energy/entropy balance. Previously, this transition was theoretically studied by taking into account the excluded-volume interaction between monomers of a polymer chain using the partition function. For binary mixtures of a long polymer and short polymers, the coil-globule transition can be induced by changing the concentration of the shorter polymers. Here, we investigate the transition caused by short polymers by generalizing the partition function of the long polymer to include the excluded-volume effect of short polymers. The coil-globule transition is studied as a function of the concentration of mixed polymers by systematically varying Flory's χ-parameters. We show that the transition is caused by the interplay between the excluded-volume interaction and the dispersion state of short polymers in the solvent. We also reveal that the same results can be obtained by combining the mixing entropy and elastic energy if the volume of a long polymer is properly defined.

Traveling excitable waves successively generated in a nonlinear proliferation system.

We study the dynamics of spatiotemporal pattern formation in a nonlinear proliferation system (e.g., cell division supported on a field of nutrition), in which the mechanism of activation and its self-suppression is simultaneously implemented. This dynamical model has been numerically realized with coupled cellular automata (CA), and various long-standing spatiotemporal patterns have been observed. Among others, a successive generation of traveling waves by implanting a spot of cells onto the field consisting of nutrition and activator is particularly interesting. This takes place despite the fact that the present reaction network has a stable fixed point and therefore autonomous temporal oscillatory does not exist in the mean field. Indeed, the reaction-diffusion equation method (RD) applied to this network reproduces only a single excitable wave and soon falls into a steady state (a fixed point) without the following propagating waves. This system, having a stable fixed point, is an excitable system of different kind from the FitzHugh-Nagumo model in that it can generate a pulse propagating outwards by adding only a single cell onto it from outside the system. The present excitation upon dropping a cell is amplified to macroscopic level by a hidden dynamics of oscillation between the activation and its self-suppression. A pulse thus generated is propagated in space time with the help of diffusion. Through a precise comparison between CA and RD, it is found that a very small amount of residue of the cells and activators, which are left unburned in the stochastic treatment of reactions by the CA, becomes a seed to excite the system and generate the next pulse wave. This newly born wave can leave another seed of reaction in the field after its propagation. Based on this analysis, we account for the appearance of other patterns observed. A possible control of these patterns by varying the spatial distribution of initial concentration of the relevant agents such as the activator is also discussed.

Threshold effect with stochastic fluctuation in bacteria-colony-like proliferation dynamics as analyzed through a comparative study of reaction-diffusion equations and cellular automata.

We report a comparative study on pattern formation between the methods of cellular automata (CA) and reaction-diffusion equations (RD) applying to a morphology of bacterial colony formation. To do so, we began the study with setting an extremely simple model, which was designed to realize autocatalytic proliferation of bacteria (denoted as X ) fed with nutrition (N) and their inactive state (prespore state) P1 due to starvation: X+N-->2X and X-->P1, respectively. It was found numerically that while the CA could successfully generate rich patterns ranging from the circular fat structure to the viscous-finger-like complicated one, the naive RD reproduced only the circular pattern but failed to give a finger structure. Augmenting the RD equations by adding two physical factors, (i) a threshold effect in the dynamics of X+N-->2X (breaking the continuity limit of RD) and (ii) internal noise with onset threshold (breaking the inherent symmetry of RD), we have found that the viscous-finger-like realistic patterns are indeed recovered by thus modified RD. This highlights the important difference between CA and RD, and at the same time, clarifies the necessary factors for the complicated patterns to emerge in such a surprisingly simple model system.