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We comprehensively studied the morphology of the self-organized effective network structures that form in simple coupled maps with interelement synchronization-dependent connection changes. Based on the parameter values, the spontaneous formation of four types of directional hierarchical networks, named pair-driven networks, loop-driven networks, hidden trio-driven networks, and hidden community-driven networks, was observed. This study provides novel insights into the self-organized complex networks that form in neural networks, various other biological networks, and social networks.

Along with recent progress in structural biology and genome biology, structural dynamics of molecular systems including nucleic acids has attracted attention in the context of gene regulation. Structure-function relationship is an important topic, where physicochemical properties of nucleotides are important as well as those of amino acids in proteins. Simulation is a useful tool for the analysis of molecular dynamics in detail, complementary to experiments. However, molecular simulation of nucleic acids has less developed than that of proteins yet, partly due to the physical nature of nucleic acids. In this review, we briefly describe the current situation and future directions of the field, hopefully as a guide to collaboration between experiment and computation., Comment: 15 pages, review article

In this study, we performed comprehensive morphological investigations of the spontaneous formations of effective network structures among elements in coupled logistic maps, specifically with a delayed connection change. Our proposed model showed ten states with different structural and dynamic features of the network topologies. Based on the parameter values, various stable networks, such as hierarchal networks with pacemakers or multiple layers, and a loop-shaped network were found. We also found various dynamic networks with temporal changes in the connections, which involved hidden network structures. Furthermore, we found that the shapes of the formed network structures were highly correlated to the dynamic features of the constituent elements. The present results provide diverse insights into the dynamics of neural networks and various other biological and social networks.

A mathematical model of garden ants (Laius japonicus) is introduced herein to investigate the relationship between the distribution of the degree of stochasticity in following pheromone trails and the group foraging efficiency. Numerical simulations of the model indicate that depending on the systematic change of the feeding environment, the optimal distribution of stochasticity shifts from a mixture of almost deterministic and mildly stochastic ants to a contrasted mixture of almost deterministic ants and highly stochastic ants. In addition, the interaction between the stochasticity and the pheromone path regulates the dynamics of the foraging efficiency optimization. Stochasticity could strengthen the collective efficiency when stochasticity to the sensitivity of pheromone for ants is introduced in the model., Comment: 21 pages, 7 figures

To investigate the structural dynamics of the homology pairing of polymers, we mod- eled the scenario of homologous chromosome pairings during meiosis in Schizosaccharomyces pombe, one of the simplest model organisms of eukaryotes. We consider a simple model consist- ing of pairs of homologous polymers with the same structures that are confined in a cylindrical container, which represents the local parts of chromosomes contained in an elongated nucleus of S. pombe. Brownian dynamics simulations of this model showed that the excluded volume effects among non-homological chromosomes and the transitional dynamics of nuclear shape serve to enhance the pairing of homologous chromosomes.

A theoretical model was developed to investigate the rod phototransduction process in the mouse. In particular, we explored the biochemical reactions of several chemical components that contribute to the signaling process into/around the membranous disks in the outer segments of the rod cells. We constructed a rate equation model incorporating the molecular crowding effects of rhodopsin according to experimental results, which may hinder the diffusion of molecules on the disk mem- brane. The present model could effectively reproduce and explain the mechanisms of the following phenomena observed in experiments. First, the activations and relaxation of the wild-type mouse rod cell progressed more slowly than those of mutant cells containing half the amount of rhodopsin on the disk membrane. Second, the strong photoactivated state of the cell was sustained for a longer period when the light stimuli were strong. Finally, the lifetime of photoactivation exhibited a logarithmic increase with increasing light strength given exposure to strong light stimuli.

Gene expression levels exhibit stochastic variations among genetically identical organisms under the same environmental conditions (called gene expression "noise" or phenotype "fluctuation"). In yeast and Escherichia coli, positive correlations have been found between such gene expression noise and "plasticity" with environmental variations. To determine the universality of such correlations in both unicellular and multicellular organisms, we focused on the relationships between gene expression "noise" and "plasticity" in Arabidopsis thaliana, a multicellular model organism. In recent studies on yeast and E. coli, only some gene groups with specific properties of promoter architecture, average expression levels, and functions exhibited strong noise-plasticity correlations. However, we found strong noise-plasticity correlations for most gene groups in Arabidopsis; additionally, promoter architecture, functional essentiality of genes, and circadian rhythm appeared to have only a weak influence on the correlation strength. The differences in the characteristics of noise-plasticity correlations may result from three-dimensional chromosomal structures and/or circadian rhythm.

Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately $\sim 150$ bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.

The contributions of active deformation dynamics in cell nuclei to the intra-nuclear positioning of hetero- and euchromatin are investigated. We analyzed the behaviors of model chains containing two types of regions, one with high and the other with low mobility, confined in a pulsating container. Here, the regions with high and low mobility represent eu- and heterochromatic regions, respectively, and the pulsating container simulates a nucleus exhibiting dynamic deformations. The Brownian dynamics simulations of this model show that the positioning of low mobility regions transition from sites near the periphery to the central region of the container if the affinity between low mobility regions and the container periphery disappears. Here, the former and latter positioning are similar to the "conventional" and "inverted" chromatin positioning observed in nuclei of normal differentiated cells and cells lacking Lamin-related proteins like mouse rod photoreceptor cell.

We investigate the segregation pattern formations of strongly and weakly fluctuated Brownian particle mixtures, which are confined in spherical containers with finite volumes. We consider systems where the container restricts the motions of particles combining two familiar methods: spherically symmetric linear potential and the container edge wall. In such systems, the following two segregation patterns are observed. When the container radius is large enough, more weakly fluctuated particles accumulate around the center of the container than strongly fluctuated particles. On the other hand, inverted distributions of strongly and weakly fluctuated particles are observed when the container radius is small. We also found a similar segregation and phase inversion if such particle mixtures construct a chain (hetero-fluctuated polymer) and are confined in a container with no linear potential. We provide the qualitative mechanism and the relationships for the biopolymer behaviors of such phase inversions.

To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving force, repulsive force due to particle collision, and drag force as the particle-- interaction through the ambient fluid. Numerical simulations of this model are conducted in two different types of two-dimensional planes, i.e., the monolayer was treated. In the horizontal plane parallel to the slope, particles aggregate at the moving front of the granular flow; and subsequently, flow instability occurs as a wavy pattern. This flow pattern is caused by the interparticle interaction arising from the drag force. Additionally, a vortex convection of particles is formed inside the aggregations. Meanwhile, in the vertical plane on the slope, particle aggregation is also found at the moving front of the granular flow. The aggregation resembles a head--tail structure, where the frontal angle against the slope approaches 60 degree from a larger angle as time progresses. Comparing the numerical result by varying the particle size, the qualitative dynamics of the granular flow are independent of size. To elucidate this reason, we perform a nondimensionalization for this model. The result indicates that our model can be simplified to dimensionless equations with one dimensionless parameter that represents the ratio of the gravity term to the excluded volume effect., Comment: 10 pages, 10 figures

We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activated. If the target proteins bind frequently, the volume fraction of molecules on the membrane becomes so large that the excluded volume of the molecules for the reaction and diffusion dynamics cannot be negligible. We find that such excluded volume effects of the molecules induce non-trivial variations of the signal flow, defined as the activation frequency of target proteins, as follows. With an increase in the binding rate of target proteins, the signal flow varies by i) monotonically increasing; ii) increasing then decreasing in a bell-shaped curve; or iii) increasing, decreasing, then increasing in an S-shaped curve. We further demonstrate that the excluded volume of molecules influences the hierarchical molecular distributions throughout the reaction processes. In particular, when the system exhibits a large signal flow, the signaling proteins tend to surround the receptors to form receptor-signaling protein clusters, and the target proteins tend to become distributed around such clusters. To explain these phenomena, we analyze the stochastic model of the local motions of molecules around the receptor., Comment: 31 pages, 10 figures

Reorientation of the segregation pattern of a binary granular mixture on a two-dimensional hor- izontally oscillating tray is numerically realized. The mixture consists of large-and-heavy particles and small-and-light particles, the segregation pattern of which shows a transition between a striped pattern perpendicular to the oscillation and that parallel to the oscillating direction according to the change of area-fractions of two types of particles. The transition mechanism is discussed on the basis of a simplified 1-dimensional dynamics., Comment: 10 pages, 6 figures

When an ensemble of self-propelled camphor boats move in a one-dimensional channel, they exhibit a variety of collective behaviors. Under certain conditions, the boats tend to cluster together and move in a relatively tight formation. This type of behavior, referred to as clustering or swarming here, is one of three types recently observed in experiment. Similar clustering behavior is also reproduced in simulations based on a simple theoretical model. Here we examine this model to determine the clustering mechanism and the conditions under which clustering occurs. We also propose a method of quantifying the behavior that may be used in future experimental work., Comment: 4 pages, 5 figures

The motion of several self-propelled boats in a narrow channel displays spontaneous pattern formation and kinetic phase transitions. In contrast with previous studies on self-propelled particles, this model does not require stochastic fluctuations and it is experimentally accessible. By varying the viscosity in the system, it is possible to form either a stationary state, correlated or uncorrelated oscillations, or unidirectional flow. Here, we describe and analyze these self organized patterns and their transitions., Comment: 6 pages, 6 figures

A bifurcation analysis of dune shape transition is made. By use of a reduced model of dune morphodynamics, dune skeleton model, we elucidate the transition mechanism between different shapes of dunes under unidirectional wind. It was found that the decrease in the total amount of sand in the system and/or the lateral sand flow shifts the stable state from a straight transverse dune to wavy transverse dune through a pitchfork bifurcation. A further decrease causes wavy transverse dunes to shift into barchans through a Hopf bifurcation. These bifurcation structures reveal the transition mechanism of dune shapes under unidirectional wind.

To analyze theoretically the stability of the shape and the migration process of transverse dunes and barchans, we propose a {\it skeleton model} of 3D dunes described with coupled dynamics of 2D cross-sections. First, 2D cross-sections of a 3D dune parallel to the wind direction are extracted as elements of a skeleton of the 3D dune, hence, the dynamics of each and interaction between them is considered. This model simply describes the essential dynamics of 3D dunes as a system of coupled ordinary differential equations. Using the model we study the stability of the shape of 3D transversal dunes and their deformation to barchans depending on the amount of available sand in the dune field, sand flow in parallel and perpendicular to wind direction., Comment: 6 pages, 6 figures, letter

Slowing down of the relaxation of the fluctuations around equilibrium is investigated both by stochastic simulations and by analysis of Master equation of reversible reaction networks consisting of resources and the corresponding products that work as catalysts. As the number of molecules $N$ is decreased, the relaxation time to equilibrium is prolonged due to the deficiency of catalysts, as demonstrated by the amplification compared to that by the continuum limit. This amplification ratio of the relaxation time is represented by a scaling function as $h = N \exp(-\beta V)$, and it becomes prominent as $N$ becomes less than a critical value $h \sim 1$, where $\beta$ is the inverse temperature and $V$ is the energy gap between a product and a resource.

The transition of a counter chemotactic particle flow from a free-flow state to a jammed state in a quasi-one-dimensional path is investigated. One of the characteristic features of such a flow is that the constituent particles spontaneously form a cluster that blocks the path, called a path-blocking cluster (PBC), and causes a jammed state when the particle density is greater than a threshold value. Near the threshold value, the PBC occasionally desolve itself to recover the free flow. In other words, the time evolution of the size of the PBC governs the flux of a counter chemotactic flow. In this paper, on the basis of numerical results of a stochastic cellular automata (SCA) model, we introduce a Langevin equation model for the size evolution of the PBC that reproduces the qualitative characteristics of the SCA model. The results suggest that the emergence of the jammed state in a quasi-one-dimensional counter flow is caused by a saddle-node bifurcation., Comment: 5pages, 8figures

Quasi-one-dimensional bidirectional particle flow including the effect of chemotaxis is investigated through a modification of the John-Schadschneider-Chowdhury-Nishinari model. Specifically, we permit multiple lanes to be shared by both directionally traveling particles. The relation between particle density and flux is studied for several evaporation rates of pheromone, and the following results are obtained: i) in the low-particle-density range, the flux is enlarged by pheromone if the pheromone evaporation rate is sufficiently low, ii) in the high particle-density range, the flux is largest at a reasonably high evaporation rate and, iii) if the evaporation rate is at the level intermediate between the above two cases, the flux is kept small in the entire range of particle densities. The mechanism of these behaviors is investigated by observing the spatial-temporal evolution of particles and the average cluster size in the system., Comment: 4 pages, 9 figures

Effective stochastic resonance (SR) is numerically and analytically studied using a model with coupled two particles exposed to heterogeneous, i.e., particles dependent, amplitude of noise. Compared to previous SR models of single particle and to those of coupled two particles exposed to equivalent amplitude of noise, the present model exhibits a more intensive resonance of, at least, one particle exposed to the non-larger amplitude of noise with the assistance of another particle. In a certain range of conditions, this effective resonance of one particle overwhelms the poor resonance of the other particle, meaning that heterogeneous amplitude of noise leads the system, not only locally but also in the average of the whole, to the effective SR., Comment: 9 pages, 6 figures, submitted to Physics Letters E

Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the system undergoes a transition from a stationary to an intermittent reaction phase when the flow rate is decreased. In the intermittent reaction phase, two temporal regimes with active and halted reactions alternate. The number frequency of reaction events at each active regime and its duration time are shown to obey a universal power laws with the exponents 4/3 and 3/2, respectively. These power laws are explained by a one-dimensional random walk representation of the number of catalytically active chemicals. Possible relevance of the result to intra-cellular reaction dynamics is also discussed.

Relaxation dynamics in reversible catalytic reaction networks is studied, revealing two salient behaviors that are reminiscent of glassy behavior: slow relaxation with log(time) dependence of the correlation function, and emergence of a few plateaus in the relaxation. The former is explained by the eigenvalue distribution of a Jacobian matrix around the equilibrium state that follows the distribution of kinetic coefficients of reactions. The latter is associated with kinetic constraints, rather than metastable states, and is due to the deficiency of catalysts for chemicals in excess and negative correlation between the two chemical species. Examples are given, and generality is discussed.

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a novel state is observed with the decrease in the total molecule number N, characterized by: i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., $N \to \infty$. The origin of transition is explained by the deficiency of molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecules species M and that of reaction paths K, while total reaction rates, scaled properly, are shown to follow a universal form as a function of NK/M.

The transport phenomena of a nonequilibrium lattice gas system are investigated. We consider a simple system that consists of two particles interacting repulsively and the potential forces acting on these particles. Under an external driving field applied to only one particle, we found the following relation between the mean velocity of the driven particle and the coefficient of effective drag of this particle under certain conditions; With the increase in the mean velocity, the coefficient of effective drag varies in the form, increase $\to$ decrease $\to$ increase $\to$ decrease. Moreover, under other conditions, we found the following relations between these values which show changes similar to those between shear rate and shear viscosity observed in the shear-thickening polymer or colloidal suspensions; With the increase in the mean velocity, the coefficient of effective drag varies in the form, increase $\to$ decrease or decrease $\to$ increase $\to$ decrease. We explain the mechanisms of such phenomena by considering the transition diagrams.

Dynamical aspects of coupled deformable gears are investigated to clarify the differences of mechanical properties between the machines consist of hard materials and those of soft materials. In particular, the performances of two functions, the transmission and the conversion of the energy, are compared between the hard and soft gears systems. First, the responses of the coupled gears against a constant torque working on one of gears are focused for two types of couplings; P) a pair gears are coupled, and T) three gears are coupled with forming a regular triangle. In systems with the coupling P), we obtain trivial results that the rotational energy can be transmitted to other gear only if these gears are hard enough. On the other hand, in systems with the coupling T), the transmission of the rotational energy to one of the other gears appears only if these gears are soft enough. Second, we show the responses of this system in which one of gears have contact with a high temperature heat bath and the other gears have contact with a 0 temperature heat bath. With the coupling T), the directional rotations appear in two gears having contact with 0 temperature heat bath. Here, the direction of these rotations change depending on the noise strength.

Dissipative structures are generally observed when a system relaxes from a far from equilibrium state. To address the reverse question given by the title, we investigate the relaxation process in a closed chemical reaction-diffusion system which can potentially form Turing-like patterns during the transient. We find that when certain conditions are fulfilled the relaxation process is indeed drastically hindered, once the pattern is formed. This slowing-down is shown to be due to stepwise relaxation, where each plateau in the relaxation process corresponds to residence at a certain spatial pattern. Universality of the phenomena as well as their biological relevance is briefly discussed., Comment: 3 figures

The segregation and the phase inversion are investigated through a simple granular system which consists of only two inelastic hard spheres in a square box with an energy source. With the variation of the coefficient of restitution, the mass ratio between two spheres or the box size, we show that two types of segregated states and crossover between them are realized in such a small simple system., Comment: 7 pages, 3 figures

Phase transition of strongly excited granular materials in 2D pipe is investigated numerically. By changing the ratio between width of the pipe and the height of the granular bed, we observe the transition between the 1 dimensional like state and the actual 2 dimensional state. Moreover, it is found that the character of the transition changes when the magnitude of dissipation passes through a critical value., Comment: 9 pages, 7 figures, other comments

We study the statistical properties of two hard spheres in a two dimensional rectangular box. In this system, the relation like Van der Waals equation loop is obtained between the width of the box and the pressure working on side walls. The auto-correlation function of each particle's position is calculated numerically. By this calculation near the critical width, the time at which the correlation become zero gets longer according to the increase of the height of the box. Moreover, fast and slow relaxation processes like $\alpha$ and $\beta$ relaxations observed in supper cooled liquid are observed when the height of the box is sufficiently large. These relaxation processes are discussed with the probability distribution of relative position of two particles., Comment: 6 figures

Size segregation of granular mixtures which are almost completely packed in a rotating drum is discussed with an effective simulation and a brief analysis. Instead of a 3D drum, we simulate 2D rotating thin box which is almost completely packed with granular mixtures. The phase inversion of radially segregated pattern which was found in a 3D experiment are qualitatively reproduced with this simulation, and a brief analysis is followed. Moreover in our simulation, a global convection appears after radial segregation pattern is formed, and this convection induces axially segregated pattern., Comment: 9 pages, 5 figures, PACS number(s): 45.70.-n, 45.70.Mg