arXiv subjects

Kunihiko Kaneko

Publications and source records attributed to Kunihiko Kaneko.

At least 55 records · Page 3Linked to original sources

arXiv2021

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.

nlin.AO↗

arXiv2021

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.

q-bio.PE↗

arXiv2020

A Linear Reciprocal Relationship Between Robustness and Plasticity in Homeostatic Biological Networks

In physics of living systems, a search for relationships of a few macroscopic variables that emerge from many microscopic elements is a central issue. We evolved gene regulatory networks so that the expression of target genes (partial system) is insensitive to environmental changes. Then, we found the expression levels of the remaining genes autonomously increase as a plastic response. Negative proportionality was observed between the average changes in target and remnant genes, reflecting reciprocity between the macroscopic robustness of homeostatic genes and plasticity of regulator genes. This reciprocity follows the lever principle, which was satisfied throughout the evolutionary course, imposing an evolutionary constraint.

physics.bio-ph↗

arXiv2020

Entangled gene regulatory networks with cooperative expression endow robust adaptive responses to unforeseen environmental changes

Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also be robust to environmental or intracellular noise and mutations. Furthermore, cells must also respond to unforeseen environmental changes that have not previously been experienced, to avoid extinction prior to the evolutionary rewiring of their networks, which takes numerous generations. We have investigated gene regulatory networks that mutually activate or inhibit, and have demonstrated that complex entangled networks can make appropriate input-output relationships that satisfy the robust and adaptive responses required for unforeseen challenges. Such entangled networks function for sloppy and unreliable responses with low Hill coefficient reactions for the expression of each gene. To compensate for such sloppiness, several detours in the regulatory network exist. By taking advantage of the averaging over such detours, the network shows a higher robustness to environmental and intracellular noise as well as to mutations in the network, when compared to simple unidirectional circuits. Furthermore, the appropriate response to unforeseen challenges, allowing for functional outputs, is achieved as many genes exhibit similar dynamic expression responses, irrespective of inputs, as confirmed by applying dynamic time warping and dynamic mode decomposition. As complex entangled networks are common in gene regulatory networks and global gene expression responses are observed in microbial experiments, the present results provide a novel design principle for cellular networks.

q-bio.MN↗

arXiv2020

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.

physics.bio-ph↗

arXiv2019

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.

q-bio.MN↗

arXiv2019

Statistical Evolutionary Laws in Music Styles

If a cultural feature is transmitted over generations and exposed to stochastic selection when spreading in a population, its evolution may be governed by statistical laws and be partly predictable, as in the case of genetic evolution. Music exhibits steady changes of styles over time, with new characteristics developing from traditions. Recent studies have found trends in the evolution of music styles, but little is known about their relations to the evolution theory. Here we analyze Western classical music data and find statistical evolutionary laws. For example, distributions of the frequencies of some rare musical events (e.g. dissonant intervals) exhibit steady increase in the mean and standard deviation as well as constancy of their ratio. We then study an evolutionary model where creators learn their data-generation models from past data and generate new data that will be socially selected by evaluators according to the content dissimilarity (novelty) and style conformity (typicality) with respect to the past data. The model reproduces the observed statistical laws and can make non-trivial predictions for the evolution of independent musical features. In addition, the same model with different parameterization can predict the evolution of Japanese enka music, which is developed in a different society and has a qualitatively different tendency of evolution. Our results suggest that the evolution of musical styles can partly be explained and predicted by the evolutionary model incorporating statistical learning, which can be important for other cultures and future music technologies.

physics.soc-ph↗

arXiv2019

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.

q-bio.PE↗

arXiv2019

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.

nlin.CD↗

arXiv2019

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.

nlin.AO↗

arXiv2019

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.

physics.bio-ph↗

arXiv2019

Emergence of Exploitation as Symmetry Breaking in Iterated Prisoner's Dilemma

In society, mutual cooperation, defection, and asymmetric exploitative relationships are common. Whereas cooperation and defection are studied extensively in the literature on game theory, asymmetric exploitative relationships between players are little explored. In a recent study, Press and Dyson demonstrate that if only one player can learn about the other, asymmetric exploitation is achieved in the prisoner's dilemma game. In contrast, however, it is unknown whether such one-way exploitation is stably established when both players learn about each other symmetrically and try to optimize their payoffs. Here, we first formulate a dynamical system that describes the change in a player's probabilistic strategy with reinforcement learning to obtain greater payoffs, based on the recognition of the other player. By applying this formulation to the standard prisoner's dilemma game, we numerically and analytically demonstrate that an exploitative relationship can be achieved despite symmetric strategy dynamics and symmetric rule of games. This exploitative relationship is stable, even though the exploited player, who receives a lower payoff than the exploiting player, has optimized the own strategy. Whether the final equilibrium state is mutual cooperation, defection, or exploitation, crucially depends on the initial conditions: Punishment against a defector oscillates between the players, and thus a complicated basin structure to the final equilibrium appears. In other words, slight differences in the initial state may lead to drastic changes in the final state. Considering the generality of the result, this study provides a new perspective on the origin of exploitation in society.

math.OC↗

arXiv2019

Molecular Diversity and Network Complexity in Growing Protocells

A great variety of molecular components is encapsulated in cells. Each of these components is replicated for cell reproduction. To address an essential role of the huge diversity of cellular components, we study a model of protocells that convert resources into catalysts with the aid of a catalytic reaction network. As the resources are limited, it is shown that diversity in intracellular components is increased to allow the use of diverse resources for cellular growth. Scaling relation is demonstrated between resource abundances and molecular diversity. We then study how the molecule species diversify and complex catalytic reaction networks develop through the evolutionary course. It is shown that molecule species first appear, at some generations, as parasitic ones that do not contribute to replication of other molecules. Later, the species turn to be host species that support the replication of other species. With this successive increase of host species, a complex joint network evolves. The present study sheds new light on the origin of molecular diversity and complex reaction network at the primitive stage of a cell.

q-bio.CB↗

arXiv2019

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.

q-bio.PE↗

arXiv2019

Horizontal transfer between loose compartments stabilizes replication of fragmented ribozymes

The emergence of replicases that can replicate themselves is a central issue in the origin of life. Recent experiments suggest that such replicases can be realized if an RNA polymerase ribozyme is divided into fragments short enough to be replicable by the ribozyme and if these fragments self-assemble into a functional ribozyme. However, the continued self-replication of such replicases requires that the production of every essential fragment be balanced and sustained. Here, we use mathematical modeling to investigate whether and under what conditions fragmented replicases achieve continued self-replication. We first show that under a simple batch condition, the replicases fail to display continued self-replication owing to positive feedback inherent in these replicases. This positive feedback inevitably biases replication toward a subset of fragments, so that the replicases eventually fail to sustain the production of all essential fragments. We then show that this inherent instability can be resolved by small rates of random content exchange between loose compartments (i.e., horizontal transfer). In this case, the balanced production of all fragments is achieved through negative frequency-dependent selection operating in the population dynamics of compartments. This selection mechanism arises from an interaction mediated by horizontal transfer between intracellular and intercellular symmetry breaking. The horizontal transfer also ensures the presence of all essential fragments in each compartment, sustaining self-replication. Taken together, our results underline compartmentalization and horizontal transfer in the origin of the first self-replicating replicases.

q-bio.CB↗

arXiv2019

Epigenetic Ratchet: Spontaneous Adaptation via Stochastic Gene Expression

Adaptation mechanism of cells on the basis of stochastic gene expression and epigenetic modification is proposed. From marginally stable states generated by epigenetic modification, a gene expression pattern that achieves greater cell growth is selected, as confirmed by simulations and analysis of several models. The mechanism does not require any design of gene regulation networks and is shown to be generic in a stochastic system with marginal stability. General relevance of the mechanism to cell biology is also discussed.

q-bio.MN↗

arXiv2018

Functional Dynamics by Intention Recognition in Iterated Games

Intention recognition is an important characteristic of intelligent agents. In their interactions with others, they try to read others' intentions and make an image of others to choose their actions accordingly. While the way in which players choose their actions depending on such intentions has been investigated in game theory, how dynamic changes in intentions by mutually reading others' intentions are incorporated into game theory has not been explored. We present a novel formulation of game theory in which players read others' intentions and change their own through an iterated game. Here, intention is given as a function of the other's action and the own action to be taken accordingly as the dependent variable, while the mutual recognition of intention is represented as the functional dynamics. It is shown that a player suffers no disadvantage when he/she recognizes the other's intention, whereas the functional dynamics reach equilibria in which both players' intentions are optimized. These cover a classical Nash and Stackelberg equilibria but we extend them in this study: Novel equilibria exist depending on the degree of mutual recognition. Moreover, the degree to which each player recognizes the other can also differ. This formulation is applied to resource competition, duopoly, and prisoner's dilemma games. For example, in the resource competition game with player-dependent capacity on gaining the resource, the superior player's recognition leads to the exploitation of the other, while the inferior player's recognition leads to cooperation through which both players' payoffs increase.

math.OC↗

arXiv2018

Optimal size for emergence of self-replicating polymer system

A biological system consists of a variety of polymers that are synthesized from monomers, by catalysis that exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization. We analyze here the stochastic polymerization reaction dynamics, to investigate the transition time from a state with almost no catalysts to a state with sufficient catalysts. We found an optimal volume that minimizes this transition time, which agrees with the inverse of the catalyst concentration at the unstable fixed point that separates the two states, as is theoretically explained. Relevance to the origin of life is also discussed.

physics.chem-ph↗