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Chromatin fibers composed of DNA and proteins fold into consecutive loops to form rod-shaped chromosome in mitosis. Although the loop growth dynamics is investigated in several studies, its detailed processes are unclear. Here, we describe the time evolution of the loop length for thermal-driven loop growth processes as an iterative map by calculating physical quantities involved in the processes. We quantify the energy during the chromatin loop formation by calculating the free energies of unlooped and looped chromatins using the Domb-Joyce model of a lattice polymer chain incorporating the bending elasticity for thermal-driven loop growth processes. The excluded volume interaction among loops is integrated by employing the mean-field theory. We compare the loop formation energy with the thermal energy and evaluate the growth of loop length via thermal fluctuation. By assuming the dependence of the excluded volume parameter on the loop length, we construct an iterative map for the loop growth dynamics. The map demonstrates that the growth length of the loop for a single reaction cycle decreases with time to reach the condensin size, where the loop growth dynamics can be less stochastic and be regarded as direct power stroke of condensin as a kind of motor proteins., Comment: 24 pages, 15 figures

Autophagy is an intracellular degradation process that is mediated by de novo formation of autophagosomes. Autophagosome formation involves dynamic morphological changes; a disk-shaped membrane cisterna grows, bends to become a cup-shaped structure, and finally develops into a spherical autophagosome. We have constructed a theoretical model that integrates the membrane morphological change and entropic partitioning of putative curvature generators, which we have used to investigate the autophagosome formation process quantitatively. We show that the membrane curvature and the distribution of the curvature generators stabilize disk- and cup-shaped intermediate structures during autophagosome formation, which is quantitatively consistent with in vivo observations. These results suggest that various autophagy proteins with membrane curvature-sensing properties control morphological change by stabilizing these intermediate structures. Our model provides a framework for understanding autophagosome formation., Comment: 33 pages, 8 figures

A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth, against the geometrically equivalent, circular stripe pattern. The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role in the realization of the wild-type pattern., Comment: REVTeX, 12 pages, 7 figures, published in Phys.Rev.E (v2)

A mathematical model to describe period-memorizing behavior in Physarum plasmodium are reported. In constructing the model, we first examine the basic characteristics required for the class of models, then create a minimal linear model to fulfill these requirements. We also propose two modifications of the minimal model, nonlinearization and noise addition, which improve the reproducibility of experimental evidences. Differences in the mechanisms and in the reproducibility of experiments between our models and the previous models are discussed., Comment: 13 pages, 4 figures

Frequency modulation by perturbation is the essential trait that differentiates limit cycle oscillators from phase oscillators. We studied networks of identical limit cycle oscillators whose frequencies are modulated sensitively by the change of their amplitudes, and demonstrated that the frequencies sustainably take distributed values. We observed two complex phenomena in the networks: stationarily distributed frequencies at a regular interval, and continuous irregular modulation of frequencies. In the analysis we reveal the mechanisms by which the frequencies are distributed, and show how the sensitive modulation of frequencies produces these complex phenomena. We also illustrate the topology of networks regulating the behaviors of the systems., Comment: 4 pages, 2 figures

The impact of environmental fluctuation on species diversity is studied with a model of the evolutionary ecology of microorganisms. We show that environmental fluctuation induces evolutionary branching and assures the consequential coexistence of multiple species. Pairwise invasibility analysis is applied to illustrate the speciation process. We also discuss how fluctuation affects species diversity., Comment: 4 pages, 4 figures. Submitted to Physical Review Letters

A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the coexistence and the plasticity of time scales in complex systems. It is found that initial conditions close to a one cluster states self-organize into multiple clusters with different angular velocities. Namely, hierarchization of the time scales emerges through the multi-clustering process in phases. Analyses for the clusters solution, the stability of the solution and the mechanism determining the time scales are reported., Comment: 4 pages, 4 figures, submitted to PRL

A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle attractors in the ambient phase space (i.e. not chaotic) and many limit cycles exist dividing the phase space as their basins. The patterns are constructed with a local law of difference of phases between the oscillators. The number of patterns grows exponentially with increasing of the number of oscillators., Comment: 10 pages, 6 figures