Multiplicity of Limit Cycle Attractors in Coupled Heteroclinic Cycles

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 figure

Modeling membrane morphological change during autophagosome formation

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 figure

Fluctuation induces evolutionary branching in a modeled microbial ecosystem

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 Letter

Evolutionary process with bi-periodic fluctuation.

<p>Evolutionary branching and the resulting three quasi-species coexistence induced by a bi-periodic fluctuation in environment. We choose resource supplying function <i>c</i>′(<i>t</i>) which is constructed by two different periodic function with periods 5.9 and 50, <i>c</i>′(<i>t</i>) = 0.03+0.4Σ<i>δ</i>(<i>t</i>−5.9<i>n</i>)+500Σ<i>δ</i>(<i>t</i>−50<i>n</i>). The fluctuation starts at <i>t</i> = 5000. After that and the system shows transient branching dynamics and reaches the three quasi-species coexistence state.</p