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Source author record

Kunihiko Kaneko

Kunihiko Kaneko appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Biological PhysicsMolecular Networksnlin.AOPopulations and EvolutionCell Behaviornlin.CDcond-mat.stat-mechcond-mat.dis-nnadap-orgchao-dynSubcellular ProcessesBiomoleculesnlin.PSpatt-solphysics.soc-phq-bioQuantitative Methodscond-matcond-mat.otherGenomicsNeural and Evolutionary ComputingNeurons and Cognitionphysics.chem-ph

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Published work

53 published item(s)

preprint2026arXiv

Delayed control driven oscillations in plant roots

Arabidopsis roots show oscillatory growth patterns on homogeneous agar surfaces, whereas other plants, such as maize, do not. Although several explanations have been proposed, a simple and general model that makes testable predictions across species has been lacking. Roots sense gravity and correct their growth direction towards the vertical. Motivated by recent evidence for a time delay in this gravitropic correction, we develop a minimal nonlinear model based on the delay hypothesis that predicts whether a root oscillates or grows vertically downwards. The model identifies a fourfold relation between the delay and time period, robust across different response functions. Analysing images of Arabidopsis, we find that the mode of the oscillatory arc length is not significantly different between inclined and vertical growth conditions. The quantitative agreement between the experimentally measured oscillatory arc length and the arc length estimated from estimated root growth speed and response delay supports this fourfold delay-period rule for delay-driven root oscillations. The simplicity of our model allows for a direct comparison with data from diverse plant species.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Error Catastrophe Can Be Avoided by Proofreading Innate to Template-Directed Polymerization

An important issue for the origins of life is ensuring the accurate maintenance of information in replicating polymers in the face of inevitable errors. Here, we investigated how this maintenance depends on reaction kinetics by incorporating the elementary steps of polymerization into the population dynamics of polymers. We found that template-directed polymerization entails an inherent error-correction mechanism akin to kinetic proofreading, generating long polymers that are more tolerant to an error catastrophe. Because this mechanism does not require enzymes, it is likely to operate under broad prebiotic conditions.

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preprint2022arXiv

Transition of Social Organisations Driven by Gift Relationship

Anthropologists have observed gift relationships that establish social relations as well as the transference of goods in many human societies. The totality of such social relations constitutes the network. Social scientists have analysed different types of social organisations with their characteristic networks. However, the factors and mechanisms that cause the transition between these types have hardly been explained. Here, we focus on the gift as the driving force for such changes. We build the model by idealising gift interactions and simulating the consequent social change due to long-term massive interactions. We demonstrate the emergence of disparities and various social organisations depending on the frequency of the gift, consistent with the empirical data. The constructive simulation study, as presented here, explains how people's interactions shape various social structures in response to environmental conditions. Combined with empirical studies, this could contribute to the formulation of a general theory in the social sciences.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Direction and Constraint in Phenotypic Evolution: Dimension Reduction and Global Proportionality in Phenotype Fluctuation and Responses

A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations. Adaptive changes in high-dimensional phenotypes were shown to be restricted within a low-dimensional slow manifold, from which a macroscopic law for cellular states was derived, which was confirmed by adaptation experiments on bacteria under stress. Next, the theory was extended to phenotypic evolution, leading to proportionality between phenotypic responses against genetic evolution and environmental adaptation. The link between robustness to noise and mutation, as a result of robustness in developmental dynamics to perturbations, showed proportionality between phenotypic plasticity by genetic changes and by environmental noise. Accordingly, directionality and constraint in phenotypic evolution was quantitatively formulated in terms of phenotypic fluctuation and the response against environmental change. The evolutionary relevance of slow modes in controlling high-dimensional phenotypes is discussed.

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preprint2021arXiv

Multiple-timescale Neural Networks: Generation of Context-dependent Sequences and Inference through Autonomous Bifurcations

Sequential transitions between metastable states are ubiquitously observed in the neural system and underlie various cognitive functions. Although a number of studies with asymmetric Hebbian connectivity have investigated how such sequences are generated, the focused sequences are simple Markov ones. On the other hand, supervised machine learning methods can generate complex non-Markov sequences, but these sequences are vulnerable against perturbations. Further, concatenation of newly learned sequence to the already learned one is difficult due to catastrophe forgetting, although concatenation is essential for cognitive functions such as inference. How stable complex sequences are generated still remains unclear. We have developed a neural network with fast and slow dynamics, which are inspired by the experiments. The slow dynamics store history of inputs and outputs and affect the fast dynamics depending on the stored history. We show the learning rule that requires only local information can form the network generating the complex and robust sequences in the fast dynamics. The slow dynamics work as bifurcation parameters for the fast one, wherein they stabilize the next pattern of the sequence before the current pattern is destabilized. This co-existence period leads to the stable transition between the current and the next pattern in the sequence. We further find that timescale balance is critical to this period. Our study provides a novel mechanism generating the robust complex sequences with multiple timescales in neural dynamics. Considering the multiple timescales are widely observed, the mechanism advances our understanding of temporal processing in the neural system.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Dimensional reduction in evolving spin-glass model: correlation of phenotypic responses to environmental and mutational changes

The evolution of high-dimensional phenotypes is investigated using a statistical physics model consists of interacting spins, in which genotypes, phenotypes, and environments are represented by spin configurations, interaction matrices, and external fields, respectively. We found that phenotypic changes upon diverse environmental change and genetic variation are highly correlated across all spins, consistent with recent experimental observations of biological systems. The dimension reduction in phenotypic changes is shown to be a result of the evolution of the robustness to thermal noise, achieved at the replica symmetric phase.

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preprint2019arXiv

Chaos on a High-Dimensional Torus

Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed while they become exponentially rare with $N$. Besides, chaos exists even when the map is invertible, and such chaos has more null Lyapunov exponents as $N$ increases. This unusual form of "chaos on a torus," termed toric chaos, exhibits delocalization and slow dynamics of the first Lyapunov vector. Fractalization of tori at the transition to chaos is also suggested. The relevance of toric chaos to neural dynamics and turbulence is discussed in relation to chaotic itinerancy.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Evolutionary dimension reduction in phenotypic space

In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in response to environmental changes are effectively restricted to a low-dimensional subspace. Thus, uncovering the origin and nature of such a drastic dimension reduction is crucial to understanding the general characteristics of biological adaptation and evolution. Herein, we first formulated the dimension reduction in terms of dynamical systems theory: considering the steady growth state of cells, the reduction is represented by the separation of a few large singular values of the inverse Jacobian matrix around a fixed point. We then examined this dimension reduction by numerical evolution of cells consisting of thousands of chemicals whose concentrations determine phenotype. As a result of the evolution, phenotypic changes due to mutations and external perturbations were found to be mainly restricted to a one-dimensional subspace. One singular value of the inverse Jacobian matrix at a fixed point of concentrations was significantly larger than the others. The major phenotypic changes due to mutations and external perturbations occur along the corresponding left-singular vector, which leads to phenotypic constraint, and fitness dominantly changes in the same direction. Once such phenotypic constraint is acquired, phenotypic evolution to a novel environment takes advantage of this restricted phenotypic direction. This results in the convergence of phenotypic pathways across genetically different strains, as is experimentally observed, while accelerating further evolution.

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preprint2019arXiv

Homeorhesis in Waddington's Landscape by Epigenetic Feedback Regulation

In multicellular organisms, cells differentiate into several distinct types during early development. Determination of each cellular state, along with the ratio of each cell type, as well as the developmental course during cell differentiation are highly regulated processes that are robust to noise and environmental perturbations throughout development. Waddington metaphorically depicted this robustness as the epigenetic landscape in which the robustness of each cellular state is represented by each valley in the landscape. This robustness is now conceptualized as an approach toward an attractor in a gene-expression dynamical system. However, there is still an incomplete understanding of the origin of landscape change, which is accompanied by branching of valleys that corresponds to the differentiation process. Recent progress in developmental biology has unveiled the molecular processes involved in epigenetic modification, which will be a key to understanding the nature of slow landscape change. Nevertheless, the contribution of the interplay between gene expression and epigenetic modification to robust landscape changes, known as homeorhesis, remains elusive. Here, we introduce a theoretical model that combines epigenetic modification with gene expression dynamics driven by a regulatory network. In this model, epigenetic modification changes the feasibility of expression, i.e., the threshold for expression dynamics, and a slow positive-feedback process from expression to the threshold level is introduced. Under such epigenetic feedback, several fixed-point attractors with distinct expression patterns are generated hierarchically shaping the epigenetic landscape with successive branching of valleys. This theory provides a quantitative framework for explaining homeorhesis in development as postulated by Waddington, based on dynamical-system theory with slow feedback reinforcement.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Repeated sequential learning increases memory capacity via effective decorrelation in a recurrent neural network

Memories in neural system are shaped through the interplay of neural and learning dynamics under external inputs. By introducing a simple local learning rule to a neural network, we found that the memory capacity is drastically increased by sequentially repeating the learning steps of input-output mappings. The origin of this enhancement is attributed to the generation of a Psuedo-inverse correlation in the connectivity. This is associated with the emergence of spontaneous activity that intermittently exhibits neural patterns corresponding to embedded memories. Stablization of memories is achieved by a distinct bifurcation from the spontaneous activity under the application of each input.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

The advantage of leakage of essential metabolites and resultant symbiosis of diverse species

Microbial communities display extreme diversity. A variety of strains or species coexist even when limited by a single resource. It has been argued that metabolite secretion creates new niches and facilitates such diversity. Nonetheless, it is still a controversial topic why cells secrete even essential metabolites so often; in fact, even under isolation conditions, microbial cells secrete various metabolites, including those essential for their growth. First, we demonstrate that leaking essential metabolites can be advantageous. If the intracellular chemical reactions include multibody reactions like catalytic reactions, this advantageous leakage of essential metabolites is possible and indeed typical for most metabolic networks via "flux control" and "growth-dilution" mechanisms; the later is a result of the balance between synthesis and growth-induced dilution with autocatalytic reactions. Counterintuitively, the mechanisms can work even when the supplied resource is scarce. Next, when such cells are crowded, the presence of another cell type, which consumes the leaked chemicals is beneficial for both cell types, so that their coexistence enhances the growth of both. The latter part of the paper is devoted to the analysis of such unusual form of symbiosis: "consumer" cell types benefit from the uptake of metabolites secreted by "leaker" cell types, and such consumption reduces the concentration of metabolites accumulated in the environment; this environmental change enables further secretion from the leaker cell types. This situation leads to frequency-dependent coexistence of several cell types, as supported by extensive simulations. A new look at the diversity in a microbial ecosystem is thus presented.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Transition in relaxation paths in allosteric molecules: enzymatic kinetically constrained model

A hierarchy of timescales is ubiquitous in biological systems, where enzymatic reactions play an important role because they can hasten the relaxation to equilibrium. We introduced a statistical physics model of interacting spins that also incorporates enzymatic reactions to extend the classic model for allosteric regulation. Through Monte Carlo simulations, we found that the relaxation dynamics are much slower than the elementary reactions and are logarithmic in time with several plateaus, as is commonly observed for glasses. This is because of the kinetic constraints from the cooperativity via the competition for an enzyme, which has different affinity for molecules with different structures. Our model showed symmetry breaking in the relaxation trajectories that led to inherently kinetic transitions without any correspondence to the equilibrium state. In this paper, we discuss the relevance of these results for diverse responses in biology.

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preprint2016arXiv

Chaotic Griffiths Phase with Anomalous Lyapunov Spectra in Coupled Map Networks

Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent clusters. The distribution of the cluster size follows a power law with the exponent $α$, which changes with the parameter values. The number of positive Lyapunov exponents and their spectra are scaled anomalously with the power of the system size with the exponent $β$, which also changes with the parameters. The scaling relation $α\sim 2(β+1)$ is uncovered, which seems to be universal independent of parameters and networks.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Discreteness-induced transitions in multi-body reaction systems

A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a 1- and 3-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior.

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preprint2016arXiv

Hierarchical Prisoner's Dilemma in Hierarchical Public-Goods Game

The dilemma in cooperation is one of the major concerns in game theory. In a public-goods game, each individual pays a cost for cooperation, or to prevent defection, and receives a reward from the collected cost in a group. Thus, defection is beneficial for each individual, while cooperation is beneficial for the group. Now, groups (say, countries) consisting of individual players also play games. To study such a multi-level game, we introduce a hierarchical public-goods (HPG) game in which two groups compete for finite resources by utilizing costs collected from individuals in each group. Analyzing this HPG game, we found a hierarchical prisoner's dilemma, in which groups choose the defection policy (say, armaments) as a Nash strategy to optimize each group's benefit, while cooperation optimizes the total benefit. On the other hand, for each individual within a group, refusing to pay the cost (say, tax) is a Nash strategy, which turns to be a cooperation policy for the group, thus leading to a hierarchical dilemma. Here, the reward received by one group increases with the population, as does the collected cost. In spite of this, we find that there exists an optimal group size that maximizes its payoff. Furthermore, when the population asymmetry between two groups is large, a smaller group will choose a cooperation policy (say, disarmament) to avoid excessive response from the larger group, which leads to the resolution of the prisoner's dilemma between the groups. The relevance of the HPG game to policy selection in society and the optimal size in human or animal groups are discussed accordingly.

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preprint2016arXiv

Motif Analysis for Small-Number Effects in Chemical Reaction Dynamics

The number of molecules involved in a cell or subcellular structure is sometimes rather small. In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and statistics compared to those observed under a macroscopic system (i.e., with a large number of molecules). In order to understand how salient changes emerge from fluctuations in molecular number, we here quantitatively define small-number effect by focusing on a `mesoscopic' level, in which the concentration distribution is distinguishable both from micro- and macroscopic ones, and propose a criterion for determining whether or not such an effect can emerge in a given chemical reaction network. Using the proposed criterion, we systematically derive a list of motifs of chemical reaction networks that can show small-number effects, which includes motifs showing emergence of the power law and the bimodal distribution observable in a mesoscopic regime with respect to molecule number. The list of motifs provided herein is helpful in the search for candidates of biochemical reactions with a small-number effect for possible biological functions, as well as for designing a reaction system whose behavior can change drastically depending on molecule number, rather than concentration.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Enzyme oscillation can enhance the thermodynamic efficiency of cellular metabolism: Consequence of anti-phase coupling between reaction flux and affinity

Cells generally convert nutrient resources to useful products via energy transduction. Accordingly, the thermodynamic efficiency of this conversion process is one of the most essential characteristics of living organisms. However, although these processes occur under conditions of dynamic metabolism, most studies of cellular thermodynamic efficiency have been restricted to examining steady states; thus, the relevance of dynamics to this efficiency has not yet been elucidated. Here, we develop a simple model of metabolic reactions with anabolism-catabolism coupling catalysed by enzymes. Through application of external oscillation in the enzyme abundances, the thermodynamic efficiency of metabolism was found to be improved. This result is in strong contrast with that observed in the oscillatory input, in which the efficiency always decreased with oscillation. This improvement was effectively achieved by separating the anabolic and catabolic reactions, which tend to disequilibrate each other, and taking advantage of the temporal oscillations so that each of the antagonistic reactions could progress near equilibrium. In this case, anti-phase oscillation between the reaction flux and chemical affinity through oscillation of enzyme abundances is essential. This improvement was also confirmed in a model capable of generating autonomous oscillations in enzyme abundances. Finally, the possible relevance of the improvement in thermodynamic efficiency is discussed with respect to the potential for manipulation of metabolic oscillations in microorganisms.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Evolution-Development Congruence in Pattern Formation Dynamics: Bifurcations in Gene Expressions and Regulation of Networks Structures

Search for possible relationships between phylogeny and ontogeny is one of the most important issues in the field of evolutionary developmental biology. By representing developmental dynamics of spatially located cells with gene expression dynamics with cell-to-cell interaction under external morphogen gradient, evolved are gene regulation networks under mutation and selection with the fitness to approach a prescribed spatial pattern of expressed genes. For most of thousands of numerical evolution experiments, evolution of pattern over generations and development of pattern by an evolved network exhibit remarkable congruence. Here, both the pattern dynamics consist of several epochs to form successive stripe formations between quasi-stationary regimes. In evolution, the regimes are generations needed to hit relevant mutations, while in development, they are due to the emergence of slowly varying expression that controls the pattern change. Successive pattern changes are thus generated, which are regulated by successive combinations of feedback or feedforward regulations under the upstream feedforward network that reads the morphogen gradient. By using a pattern generated by the upstream feedforward network as a boundary condition, downstream networks form later stripe patterns. These epochal changes in development and evolution are represented as same bifurcations in dynamical-systems theory, and this agreement of bifurcations lead to the evolution-development congruences. Violation of the evolution-development congruence, observed exceptionally, is shown to be originated in alteration of the boundary due to mutation at the upstream feedforward network. Our results provide a new look on developmental stages, punctuated equilibrium, developmental bottlenecks, and evolutionary acquisition of novelty in morphogenesis.

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preprint2015arXiv

Global Relationships in Fluctuation and Response in Adaptive Evolution

Cells generally change their internal state to adapt to an environmental change, and accordingly evolve in response to the new conditions. This process involves phenotypic changes that occur over several different time scales, ranging from faster environmental adaptation without a corresponding change in the genomic sequence to slower evolutionary dynamics involving genetic mutations and subsequent selection. In this regard, a question arises as to whether there are any relationships between such phenotypic changes over the different time scales at which adaptive evolution occurs. In this study, we analyzed simulated adaptive evolution in a simple cell model, and found that proportionality between concentration changes in adaptation and evolution over all components, and the proportion coefficients were closely linked to the change in the growth rate of a cell. Furthermore, we demonstrated that the phenotypic variances in component concentrations due to (non-genetic) noise and genomic alternations are proportional across all components. These global relationships in cellular states were also supported by phenomenological theory and transcriptome analysis of laboratory evolution in {\it Escherichia coli}. These findings provide a basis for the development of a quantitative theory of plasticity and robustness, and to determine the general restriction of phenotypic changes imposed by evolution.

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preprint2015arXiv

Inverse Relationship Between Molecular Diversity And Resource Abundances

Cell reproduction involves replication of diverse molecule species, in contrast to simple replication system with fewer components. Here, we address why such diversity is sustained despite the efficiency of simple replication systems, using a cell model with catalytic reaction dynamics that grew by uptake of environmental resources. Limited resources led to increased diversity of components within the system, and the number of coexisting species increased with a negative power of the resource abundances. The diversity was explained from the optimum growth speed of the cell, determined by a tradeoff between the utility of diverse resources and the concentration onto fewer components to increase the reaction rate.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Pluripotency, differentiation, and reprogramming: A gene expression dynamics model with epigenetic feedback regulation

Characterization of pluripotent states, in which cells can both self-renew and differentiate, and the irreversible loss of pluripotency are important research areas in developmental biology. In particular, an understanding of these processes is essential to the reprogramming of cells for biomedical applications, i.e., the experimental recovery of pluripotency in differentiated cells. Based on recent advances in dynamical-systems theory for gene expression, we propose a gene-regulatory-network model consisting of several pluripotent and differentiation genes. Our results show that cellular-state transition to differentiated cell types occurs as the number of cells increases, beginning with the pluripotent state and oscillatory expression of pluripotent genes. Cell-cell signaling mediates the differentiation process with robustness to noise, while epigenetic modifications affecting gene expression dynamics fix the cellular state. These modifications ensure the cellular state to be protected against external perturbation, but they also work as an epigenetic barrier to recovery of pluripotency. We show that overexpression of several genes leads to the reprogramming of cells, consistent with the methods for establishing induced pluripotent stem cells. Our model, which involves the inter-relationship between gene expression dynamics and epigenetic modifications, improves our basic understanding of cell differentiation and reprogramming.

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preprint2015arXiv

Reciprocity Between Robustness of Period and Plasticity of Phase in Biological Clocks

Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating distinct models of circadian clocks, we demonstrate reci- procity between robustness and plasticity: higher robustness in the period implies higher plasticity in the phase, where changes in period and in phase follow a linear relationship with a negative coef- ficient. The robustness of period is achieved by the adaptation on the limit cycle via a concentration change of a buffer molecule, whose temporal change leads to a phase shift following a shift of the limit-cycle orbit in phase space. Generality of reciprocity in clocks with the adaptation mechanism is confirmed with theoretical analysis of simple models, while biological significance is discussed.

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preprint2015arXiv

Requirements for efficient cell-type proportioning: regulatory timescales, stochasticity and lateral inhibition

The proper functioning of multicellular organisms requires the robust establishment of precise proportions between distinct cell-types. This developmental differentiation process typically involves intracellular regulatory and stochastic mechanisms to generate cell-fate diversity as well as intercellular mechanisms to coordinate cell-fate decisions at tissue level. We thus surmise that key insights about the developmental regulation of cell-type proportion can be captured by the modeling study of clustering dynamics in population of inhibitory-coupled noisy bistable systems. This general class of dynamical system is shown to exhibit a very stable two-cluster state, but also frustrated relaxation, collective oscillations or steady-state hopping which prevents from timely and reliably reaching a robust and well-proportioned clustered state. To circumvent these obstacles or to avoid fine-tuning, we highlight a general strategy based on dual-time positive feedback loops, such as mediated through transcriptional versus epigenetic mechanisms, which improves proportion regulation by coordinating early and flexible lineage priming with late and firm commitment. This result sheds new light on the respective and cooperative roles of multiple regulatory feedback, stochasticity and lateral inhibition in developmental dynamics.

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preprint2015arXiv

Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics

Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable states are analytically calculated in agreement with numerical simulations. In addition, a novel transition involving the reversal of the chemical reaction flow is found in the model under an external flow, and also in a three-component model. The generality of this transition and its correspondence to biological phenomena are also discussed.

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preprint2014arXiv

Entropy production of a steady-growth cell with catalytic reactions

Cells generally convert external nutrient resources to support metabolismand growth. Understanding the thermodynamic efficiency of this conversion is essential to determine the general characteristics of cellular growth. Using a simple protocell model with catalytic reaction dynamics to synthesize the necessary enzyme and membrane components from nutrients, the entropy production per unit cell-volume growth is calculated analytically and numerically based on the rate equation for chemical kinetics and linear non-equilibrium thermodynamics. The minimal entropy production per unit cell growth is found to be achieved at a non-zero nutrient uptake rate, rather than at a quasi-static limit as in the standard Carnot engine. This difference appears because the equilibration mediated by the enzyme exists only within cells that grow through enzyme and membrane synthesis. Optimal nutrient uptake is also confirmed by protocell models with many chemical components synthesized through a catalytic reaction network. The possible relevance of the identified optimal uptake to optimal yield for cellular growth is also discussed.

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preprint2014arXiv

Transition to diversification by competition for resources in catalytic reaction networks

All life, including cells and artificial protocells, must integrate diverse molecules into a single unit in order to reproduce. Despite expected pressure to evolve a simple system with the fastest replication speed, the mechanism by which the use of the great variety of components, and the coexistence of diverse cell-types with different compositions are achieved is as yet unknown. Here we show that coexistence of such diverse compositions and cell-types is the result of competitions for a variety of limited resources. We find that a transition to diversity occurs both in chemical compositions and in protocell types, as the resource supply is decreased, when the maximum inflow and consumption of resources are balanced.

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preprint2014arXiv

Universal relationship in gene-expression changes for cells in steady-growth state

Cells adapt to different conditions by altering a vast number of components, which is measurable using transcriptome analysis. Given that a cell undergoing steady growth is constrained to sustain each of its internal components, the abundance of all the components in the cell has to be roughly doubled during each cell division event. From this steady-growth constraint, expression of all genes is shown to change along a one-parameter curve in the state space in response to the environmental stress. This leads to a global relationship that governs the cellular state: By considering a relatively moderate change around a steady state, logarithmic changes in expression are shown to be proportional across all genes, upon alteration of stress strength, with the proportionality coefficient given by the change in the growth rate of the cell. This theory is confirmed by transcriptome analysis of Escherichia Coli in response to several stresses.

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preprint2013arXiv

Evolution of Genetic Redundancy : The Relevance of Complexity in Genotype-Phenotype Mapping

Genetic redundancy is ubiquitous and can be found in any organism. However, it has been argued that genetic redundancy reduces total population fitness, and therefore, redundancy is unlikely to evolve. In this letter, we study an evolutionary model with high-dimensional genotype-phenotype mapping (GPM) to investigate the relevance of complexity in GPM to the evolution of genetic redundancy. By applying the replica method to deal with quenched randomness, the redundancy dependence of the fitness is analytically obtained, which demonstrates that genetic redundancy can indeed evolve, provided that the GPM is complex. Our result provides a novel insight into how genetic redundancy evolves.

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preprint2013arXiv

Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in terms of Phenotypic Variances

The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic variances of epigenetic and genetic origins is confirmed. The former is given by the variance of the phenotypic fluctuation due to noise in the developmental process; and the latter, by the variance of the phenotypic fluctuation due to genetic mutation. The relationship suggests a link between robustness to noise and to mutation, since robustness can be defined by the sharpness of the distribution of the phenotype. Next, the proportionality between the variances is demonstrated to also hold over expressions of different genes (phenotypic traits) when the system acquires robustness through the evolution. Then, evolution under environmental variation is numerically investigated and it is found that both the adaptability to a novel environment and the robustness are made compatible when a certain degree of phenotypic fluctuations exists due to noise. The highest adaptability is achieved at a certain noise level at which the gene expression dynamics are near the critical state to lose the robustness. Based on our results, we revisit Waddington's canalization and genetic assimilation with regard to the two types of phenotypic fluctuations.

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preprint2013arXiv

Minimal Model for Stem-Cell Differentiation

To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein expression networks consisting of two genes under cell--cell interactions mediated by the diffusion of a protein. Networks that show cell differentiation are extracted and two forms of symmetric differentiation based on Turing's mechanism and asymmetric differentiation are identified. In the latter network, the intracellular protein levels show oscillatory dynamics at a single-cell level, while cell-to-cell synchronicity of the oscillation is lost with an increase in the number of cells. Differentiation to a fixed-point type behavior follows with a further increase in the number of cells. The cell type with oscillatory dynamics corresponds to a stem cell that can both proliferate and differentiate, while the latter fixed-point type only proliferates. This differentiation is analyzed as a saddle-node bifurcation on an invariant circle, while the number ratio of each cell type is shown to be robust against perturbations due to self-consistent determination of the effective bifurcation parameter as a result of the cell--cell interaction. Complex cell differentiation is designed by combing these simple two-gene networks. The generality of the present differentiation mechanism, as well as its biological relevance, is discussed.

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preprint2013arXiv

Slow Stochastic Switching by Collective Chaos of Fast Elements

Coupled dynamical systems with one slow element and many fast elements are analyzed. By averaging over the dynamics of the fast variables, the adiabatic kinetic branch is introduced for the dynamics of the slow variable in the adiabatic limit. The dynamics without the limit are found to be represented by stochastic switching over these branches mediated by the collective chaos of the fast elements, while the switching frequency shows a complicated dependence on the ratio of the two timescales with some resonance structure. The ubiquity of the phenomena in the slow--fast dynamics is also discussed.

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preprint2013arXiv

The Baldwin effect under multi-peaked fitness landscapes: Phenotypic fluctuation accelerates evolutionary rate

Phenotypic fluctuations and plasticity can generally affect the course of evolution, a process known as the Baldwin effect. Several studies have recast this effect and claimed that phenotypic plasticity acceler- ates evolutionary rate (the Baldwin expediting effect); however, the validity of this claim is still controversial. In this study, we investi- gate the evolutionary population dynamics of a quantitative genetic model under a multi-peaked fitness landscape, in order to evaluate the validity of the effect. We provide analytical expressions for the evolutionary rate and average population fitness. Our results indicate that under a multi-peaked fitness landscape, phenotypic fluctuation always accelerates evolutionary rate, but it decreases the average fit- ness. As an extreme case of the trade-off between the rate of evolution and average fitness, phenotypic fluctuation is shown to accelerate the error catastrophe, in which a population fails to sustain a high-fitness peak. In the context of our findings, we discuss the role of phenotypic plasticity in adaptive evolution.

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preprint2012arXiv

Identifying dynamical systems with bifurcations from noisy partial observation

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically integrate information in noisy time-series data from partial observations. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations, and the learned systems are shown to robustly inherit the bifurcation structure.

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preprint2011arXiv

Generic temperature compensation of biological clocks by autonomous regulation of catalyst concentration

Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellular organisms, often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite the expected Arrhenius form for the reaction coefficient. Observations have shown that the amplitude of the oscillation depends on the temperature but the period does not---this suggests that although not every reaction step is temperature independent, the total system comprising several reactions still exhibits compensation. We present a general mechanism for such temperature compensation. Consider a system with multiple activation energy barriers for reactions, with a common enzyme shared across several reaction steps with a higher activation energy. These reaction steps rate-limit the cycle if the temperature is not high. If the total abundance of the enzyme is limited, the amount of free enzyme available to catalyze a specific reaction decreases as more substrates bind to common enzyme. We show that this change in free enzyme abundance compensate for the Arrhenius-type temperature dependence of the reaction coefficient. Taking the example of circadian clocks with cyanobacterial proteins KaiABC consisting of several phosphorylation sites, we show that this temperature compensation mechanisms is indeed valid. Specifically, if the activation energy for phosphorylation is larger than that for dephosphorylation, competition for KaiA shared among the phosphorylation reactions leads to temperature compensation. Moreover, taking a simpler model, we demonstrate the generality of the proposed compensation mechanism, suggesting relevance not only to circadian clocks but to other (bio)chemical oscillators as well.

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preprint2011arXiv

Growth states of catalytic reaction networks exhibiting energy metabolism

All cells derive nutrition by absorbing some chemical and energy resources from the environment; these resources are used by the cells to reproduce the chemicals within them, which in turn leads to an increase in their volume. In this study, we introduce a protocell model exhibiting catalytic reaction dynamics, energy metabolism, and cell growth. Results of extensive simulations of this model show the existence of four phases with regard to the rates of both the influx of resources and the cell growth. These phases include an active phase with high influx and high growth rates, an inefficient phase with high influx but low growth rates, a quasi-static phase with low influx and low growth rates, and a death phase with negative growth rate. A mean field model well explains the transition among these phases as bifurcations. The statistical distribution of the active phase is characterized by a power law and that of the inefficient phase is characterized by a nearly equilibrium distribution. We also discuss the relevance of the results of this study to distinct states in the existing cells.

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preprint2011arXiv

Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.

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preprint2011arXiv

Weber's Law in Autocatalytic Reaction Networks

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows such response when a chemical is slowly synthesized by the reaction from a faster influx process. We also show that an autocatalytic reaction process occurring in series or in parallel can obey Weber's law with an oscillatory adaptive response. Considering the simplicity and ubiquity of the autocatalytic process, our proposed mechanism is thought to be commonly observed in biological reactions.

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preprint2010arXiv

Discreteness-Induced Slow Relaxation in Reversible Catalytic Reaction Networks

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 $h = N \exp(-βV)$, and it becomes prominent as $N$ becomes less than a critical value $h \sim 1$, where $β$ is the inverse temperature and $V$ is the energy gap between a product and a resource.

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preprint2010arXiv

Reproduction of a Protocell by Replication of Minority Molecule in Catalytic Reaction Network

For understanding the origin of life, it is essential to explain the development of a compartmentalized structure, which undergoes growth and division, from a set of chemical reactions. In this study, a hypercycle with two chemicals that mutually catalyze each other is considered in order to show that the reproduction of a protocell with a growth-division process naturally occurs when the replication speed of one chemical is considerably slower than that of the other chemical. It is observed that the protocell divides after a minority molecule is replicated at a slow synthesis rate, and thus, a synchrony between the reproduction of a cell and molecule replication is achieved. The robustness of such protocells against the invasion of parasitic molecules is also demonstrated.

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preprint2009arXiv

A statistical-mechanical study of evolution of robustness in noisy environment

In biological systems, expression dynamics that can provide fitted phenotype patterns with respect to a specific function have evolved through mutations. This has been observed in the evolution of proteins for realizing folding dynamics through which a target structure is shaped. We study this evolutionary process by introducing a statistical-mechanical model of interacting spins, where a configuration of spins and their interactions $\bm{J}$ represent a phenotype and genotype, respectively. The phenotype dynamics are given by a stochastic process with temperature $T_{S}$ under a Hamiltonian with $\bm{J}$. The evolution of $\bm{J}$ is also stochastic with temperature $T_{J}$ and follows mutations introduced into $\bm{J}$ and selection based on a fitness defined for a configuration of a given set of target spins. Below a certain temperature $T_{S}^{c2}$, the interactions $\bm{J}$ that achieve the target pattern evolve, whereas another phase transition is observed at $T_{S}^{c1}<T_{S}^{c2}$. At low temperatures $T_{S}<T_{S}^{c1}$, the Hamiltonian exhibits a spin-glass like phase, where the dynamics toward the target pattern require long time steps, and the fitness often decreases drastically as a result of a single mutation to $\bm{J}$. In the intermediate-temperature region, the dynamics to shape the target pattern proceed rapidly and are robust to mutations of $\bm{J}$. The interactions in this region have no frustration around the target pattern and results in funnel-type dynamics. We propose that the ubiquity of funnel-type dynamics, as observed in protein folding, is a consequence of evolution subjected to thermal noise beyond a certain level; this also leads to mutational robustness of the fitness.

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preprint2009arXiv

Dynamics of Coupled Adaptive Elements : Bursting and Intermittent Oscillations Generated by Frustration in Networks

Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of two variables that show such adaptation dynamics, we studied a coupled dynamical system containing such elements to examine the diverse dynamics in the system and classified the behaviors on the basis of the network structure that determined the interaction among elements. For a system with two elements, two types of behaviors, perfect adaptation and simple oscillation, were observed. For a system with three elements, in addition to these two types, novel types of dynamics, namely, rapid burst-type oscillation and a slow cycle, were discovered; depending on the initial conditions, these novel types of dynamics coexisted. These behaviors are a result of the characteristic dynamics of each element, i.e., fast response and slow adaptation processes. The behaviors depend on the network structure (in specific, a combination of positive or negative feedback among elements). Cooperativity among elements due to a positive feedback loop leads to simple oscillation, whereas frustration involving alternating positive and negative interactions among elements leads to the coexistence of rapid bursting oscillation and a slow cycle. These behaviors are classified on the basis of the frustration indices defined by the network structure. The period of the slow cycle is much longer than the original adaptation time scale, while the burst-type oscillation is a continued response that does not involve any adaptation. We briefly discuss the universal applicability of our results to a network of a larger number of elements and their possible relevance to biological systems.

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preprint2009arXiv

Robustness under functional constraint: The genetic network for temporal expression in Drosophila neurogenesis

Precise temporal coordination of gene expression is crucial for many developmental processes. One central question in developmental biology is how such coordinated expression patterns are robustly controlled. During embryonic development of the Drosophila central nervous system, neural stem cells called neuroblasts sequentially express a group of genes in a definite order, which generates the diversity of cell types. By producing all possible regulatory networks of these genes and examining their expression dynamics numerically, we identify requisite regulations and predict an unknown factor to reproduce known expression profiles caused by loss-of-function or overexpression of the genes in vivo, as well as in the wild type. We then evaluate the stability of the actual Drosophila network for sequential expression. This network shows the highest robustness against parameter variations and gene expression fluctuations among the possible networks that reproduce the expression profiles. We propose a regulatory module composed of three kinds of regulations which is responsible for precise sequential expression. The present study suggests an underlying principle on how biological systems are robustly designed under functional constraint.

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preprint2008arXiv

"Glassy" Relaxation in Catalytic Reaction Networks

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.

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preprint2007arXiv

A generic mechanism for adaptive growth rate regulation

How can a microorganism adapt to a variety of environmental conditions despite there exists a limited number of signal transduction machineries? We show that for any growing cells whose gene expression is under stochastic fluctuations, adaptive cellular state is inevitably selected by noise, even without specific signal transduction network for it. In general, changes in protein concentration in a cell are given by its synthesis minus dilution and degradation, both of which are proportional to the rate of cell growth. In an adaptive state with a higher growth speed, both terms are large and balanced. Under the presence of noise in gene expression, the adaptive state is less affected by stochasticity since both the synthesis and dilution terms are large, while for a non-adaptive state both the terms are smaller so that cells are easily kicked out of the original state by noise. Hence, escape time from a cellular state and the cellular growth rate are negatively correlated. This leads to a selection of adaptive states with higher growth rates, and model simulations confirm this selection to take place in general. The results suggest a general form of adaptation that has never been brought to light - a process that requires no specific machineries for sensory adaptation. The present scheme may help explain a wide range of cellular adaptive responses including the metabolic flux optimization for maximal cell growth.

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preprint2007arXiv

Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics

Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these robustness? Robustness can be defined by the sharpness of the distribution of phenotype; the variance of phenotype distribution due to genetic variation gives a measure of `genetic robustness' while that of isogenic individuals gives a measure of `developmental robustness'. Through simulations of a simple stochastic gene expression network that undergoes mutation and selection, we show that in order for the network to acquire both types of robustness, the phenotypic variance induced by mutations must be smaller than that observed in an isogenic population. As the latter originates from noise in gene expression, this signifies that the genetic robustness evolves only when the noise strength in gene expression is larger than some threshold. In such a case, the two variances decrease throughout the evolutionary time course, indicating increase in robustness. The results reveal how noise that cells encounter during growth and development shapes networks' robustness to stochasticity in gene expression, which in turn shapes networks' robustness to mutation. The condition for evolution of robustness as well as relationship between genetic and developmental robustness is derived through the variance of phenotypic fluctuations, which are measurable experimentally.

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preprint2003arXiv

Autonomous Energy Transducer: Proposition, Example, Basic Characteristics

We propose a concept of autonomous energy transducer at a molecular scale, where output is produced with small input energy, of the same order of the thermal energy, without restriction of magnitude or timing of input, and without any control after the input. As an example that satisfies these requisites, a dynamical systems model with several degrees of freedom is proposed, which transduces input energy to output motion on the average. It is shown that this transduction is robust and the coupling between the input and output is generally loose. How this transducer works is analyzed in terms of dynamical systems theory, where chaotic dynamics of the internal degrees of freedom, as well as duration of active state which is self-organized with the energy flow, is essential. We also discuss possible relationships to enzyme dynamics or protein motors.

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preprint1998arXiv

Diversity, Stability, Recursivity, and Rule Generation in Biological System: Intra-inter Dynamics Approach

Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction among the units, and the dynamics to change the dynamics itself, for example by replication (and death) of units according to their internal states. Applying the dynamics to cell differentiation, isologous diversification theory is proposed. According to it, orbital instability leads to diversified cell behaviors first. At the next stage, several cell types are formed, first triggered by clustering of oscillations, and then as attracting states of internal dynamics stabilized by the cell-to-cell interaction. At the third stage, the differentiation is determined as a recursive state by cell division. At the last stage, hierarchical differentiation proceeds, with the emergence of stochastic rule for the differentiation to sub-groups, where regulation of the probability for the differentiation provides the diversity and stability of cell society. Relevance of the theory to cell biology is discussed.

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preprint1996arXiv

Coupled Map Modeling for Cloud Dynamics

A coupled map model for cloud dynamics is proposed, which consists of the successive operations of the physical processes; buoyancy, diffusion, viscosity, adiabatic expansion, fall of a droplet by gravity, descent flow dragged by the falling droplet, and advection. Through extensive simulations, the phases corresponding to stratus, cumulus, stratocumulus and cumulonimbus are found, with the change of the ground temperature and the moisture of the air. They are characterized by order parameters such as the cluster number, perimeter-to-area ratio of a cloud, and Kolmogorov-Sinai entropy.

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preprint1995arXiv

A Theory of Differentiation with Dynamic Clustering

A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled chemical networks and division process lead to the following scenario of the differentiation: Up to some numbers of cells, divisions bring about almost identical cells with synchronized metabolic oscillations. As the number is increased the oscillations lose the synchrony, leading to groups of cells with different phases of oscillations. At later stage this differentiation is fixed in time, and cells spilt into groups with different chemical constituents spontaneously, which are transmitted to daughter cells by cell divisions. Hierarchical differentiation, origin of stem cells, and anomalous differentiation by transplantations are also discussed with relevance to real biological experimental results. (Keywords: differentiation, metabolic network, cell division, clustering, open chaos)

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preprint1995arXiv

Evolution of Cooperation, Differentiation, Complexity, and Diversity in an Iterated Three-person Game

A non-zero-sum 3-person coalition game is presented, to study the evolution of complexity and diversity in cooperation, where the population dynamics of players with strategies is given according to their scores in the iterated game and mutations. Two types of differentiations emerge initially; biased one to classes and temporal one to change their roles for coalition. Rules to change the hands are self-organized in a society through evolution. The co-evolution of diversity and complexity of strategies and interactions (or communications) are found at later stages of the simulation. Relevance of our results to the biological society is briefly discussed.

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preprint1994arXiv

Pattern Dynamics of a Coupled Map Lattice for Open Flow

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic, quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map. Criteria are established for predicting the down-flow bifurcation behavior of the coupled map lattice, and for selecting attractors through modulation of the boundary. For smaller coupling strengths we find a novel regime in which chaotic defects form a periodic lattice that is shown to be the result of a boundary crisis.

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preprint1994arXiv

Rayleigh-Bénard Convection; Patterns, Chaos, Spatiotemporal Chaos and Turbulence

A coupled map lattice for convection is proposed, which consists of Eulerian and Lagrangian procedures. Simulations of the model not only reproduce a wide-range of phenomena in Rayleigh-Bénard convection experiments but also lead to several prediction of novel phenomena there: For small aspect ratios, the formation of convective rolls, their oscillation, many routes to chaos, and chaotic itinerancy are found, with the increase of the Rayleigh number. For large aspect ratios, the collective oscillation of convective rolls, travelling waves, coherent chaos, and spatiotemporal intermittency are observed. At high Rayleigh numbers, the transition from soft to hard turbulence is confirmed, as is characterized by the change of the temperature distribution from Gaussian to exponential. Roll formation in three-dimensional convection is also simulated, and found to reproduce experiments well.

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preprint1994arXiv

Remarks on the mean field dynamics of networks of chaotic elements

Fluctuations of the mean field of a globally coupled dynamical systems are discussed. The origin of hidden coherence is related with the instability of the fixed point solution of the self-consistent Perron-Frobenius equation. Collective dynamics in globally coupled tent maps are re-examined, both with the help of direct simulation and the Perron-Frobenius equation. Collective chaos in a single band state, and bifurcation against initial conditions in a two-band state are clarified with the return maps of the mean-field, Lyapunov spectra, and also the newly introduced Lyapunov exponent for the Perron-Frobenius equation. Future problems on the collective dynamics are discussed.

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