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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)