arXiv subjects

Tetsuya J. Kobayashi

Publications and source records attributed to Tetsuya J. Kobayashi.

At least 19 recordsLinked to original sources

arXiv2026

Optimal Control of Chemical Reaction Networks with Thermodynamic Cost

Thermodynamic control seeks to realize desired functions at minimal thermodynamic cost, yet existing frameworks remain largely confined to slow driving regimes or state-to-state transport. Here we establish a thermodynamic optimal-control theory for Markov jump processes (MJPs) and chemical reaction networks (CRNs) that accommodates objectives over both states and reaction fluxes beyond slow-driving limit. By deriving the thermodynamic Hamilton--Jacobi--Bellman equation, we demonstrate that the optimal dynamics take the form of a perturbed generalized-gradient flow driven by the value function. A convex representation of the entropy-production rate via generalized means identifies its Legendre--Fenchel dual as the dissipation function. The resulting dynamics shares the thermodynamic structure of CRNs and admits an information-geometric characterization. We further derive a thermodynamic Pontryagin equation by recasting the control problem in terms of thermodynamic forces, providing a complementary description of optimal trajectories and clarifying connections to thermodynamic optimal transport. Our results establish a thermodynamic and geometric foundation for controlling MJPs and CRNs beyond mere transport, opening avenues for optimizing biological processes and finite-time thermodynamic operations in far-from-equilibrium regimes.

physics.chem-ph↗

arXiv2026

Convex Analysis of Relaxation Dynamics in Chemical Reaction Networks and Generalized Gradient Flows

We obtain bounds on the Kullback--Leibler divergence to equilibrium for mass-action chemical reaction networks (CRNs) with equilibrium. The associated trajectory-dependent bounds are characterized in terms of the singular values of the stoichiometric matrix, convexity parameters, and time-integrated activities via deformed-exponential-type functions. We further extend these bounds within a generalized gradient flow framework. We highlight the biological relevance of this framework: the resulting bounds apply to quasi-steady-state regimes, where long transients and plateau-like behavior are common and functionally important. We illustrate the framework using a catalytic CRN exhibiting plateaus, where the bounds provide an a posteriori characterization of slow relaxation induced by local convexity and provide a bound-based approach to quantifying relaxation in CRNs.

q-bio.MN↗

arXiv2026

Accelerating Evolutionary Strategy via Rao-Blackwellizing Realization of Uncertain Input

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

math.OC↗

arXiv2026

Local stabilizability implies global controllability in catalytic reaction systems

Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the stoichiometric coefficient match: the local stabilizability of a given state implies global controllability within its stoichiometric compatibility class. In other words, if a target state can be maintained against small perturbations, the system can be controlled from any initial condition to that state. This result highlights a tight link between the local and global dynamics of nonlinear chemical reaction systems, providing a mathematical criterion for global reachability that is often elusive in high-dimensional systems. The finding illuminate the robustness of biochemical systems and offers a way to control catalytic reaction systems in a generic framework.

physics.bio-ph↗

arXiv2025

Theoretical Analysis of Resource-Induced Phase Transitions in Estimation Strategies

Organisms adapt to volatile environments by integrating sensory information with internal memory, yet their information processing is constrained by resource limitations. Such limitations can fundamentally alter optimal estimation strategies in biological systems. For example, recent experiments suggest that organisms exhibit nonmonotonic phase transitions between memoryless and memory-based estimation strategies depending on sensory reliability. However, an analytical understanding of these resource-induced phase transitions is still missing. This Letter presents an analytical characterization of resource-induced phase transitions in optimal estimation strategies. Our result identifies the conditions under which resource limitations alter estimation strategies and analytically reveals the mechanism underlying the emergence of discontinuous, nonmonotonic, and scaling behaviors. These results provide a theoretical foundation for understanding how limited resources shape information processing in biological systems.

physics.bio-ph↗

arXiv2025

Optimal control of stochastic reaction networks with entropic control cost and emergence of mode-switching strategies

Controlling the stochastic dynamics of biological populations is a challenge that arises across various biological contexts. However, these dynamics are inherently nonlinear and involve a discrete state space, i.e., the number of molecules, cells, or organisms. Additionally, the possibility of extinction has a significant impact on both dynamics and control strategies, particularly when the population size is small. These factors hamper the direct application of conventional control theories to biological systems. To address these challenges, we formulate the optimal control problem for stochastic population dynamics by utilizing control cost functions based on the f-divergence, which naturally accounts for population-specific factors. If Kullback-Leibler (KL) divergence is adopted for the cost function, the complex nonlinear Hamilton-Jacobi-Bellman equation is simplified into a linear form, facilitating efficient computation of optimal solutions. We demonstrate the effectiveness of our approach by applying it to the control of interacting random walkers, Moran processes, and SIR models, and observe the mode-switching phenomena in the control strategies. Our approach provides new opportunities for applying control theory to a wide range of biological problems.

q-bio.PE↗

arXiv2025

Quantification of Information Flow by Dual Reporter System and Its Application to Bacterial Chemotaxis

Mutual information is a theoretically grounded metric for quantifying cellular signaling pathways. However, its measurement demands characterization of both input and output distributions, limiting practical applications. Here, we present alternative method that alleviates this requirement using dual reporter systems. By extending extrinsic-intrinsic noise analysis, we derive a mutual information estimator that eliminates the need to measure input distribution. We demonstrate our method by analyzing the bacterial chemotactic pathway, regarding multiple flagellar motors as natural dual reporters. We show the biological relevance of the measured information flow by comparing it with theoretical bounds on sensory information. This framework opens new possibilities for quantifying information flow in cellular signaling pathways.

q-bio.QM↗

arXiv2025

Statistical mechanics of fluids with hidden degrees of freedom

Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom that such fluids inherently possess. In this study, we propose a model that incorporates distinct microscopic degrees of freedom and their interactions, without directly relying on conventional coarse-grained descriptions. By introducing two key assumptions, we show that the system can exhibit equilibrium states characterized by heterogeneous density profiles with finite length scales, resembling those typically associated with non-equilibrium phenomena. These findings highlight the importance of distinguishing between equilibrium states and non-equilibrium steady states in highly complex systems.

cond-mat.soft↗

arXiv2025

Information geometry of chemical reaction networks: Cramer-Rao bound and absolute sensitivity revisited

Information geometry is based on classical Legendre duality but allows to incorporate additional structure such as algebraic constraints and Bregman divergence functions. It is naturally suited, and has been successfully used, to describe the thermodynamics of chemical reaction networks (CRNs) based on the Legendre duality between concentration and potential spaces, where algebraic constraints are enforced by the stoichiometry. In this article, the Riemannian geometrical aspects of the theory are explored. It is shown that duality between concentration and potential spaces and the natural parametrizations of equilibrium subspace are isometries, which leads to a multivariate Cramer-Rao bound through the comparison of two Riemannian metric tensors. In the subsequent part, the theory is applied to the recently introduced concept of absolute sensitivity. Using the Riemannian geometric tools, it is proven that the absolute sensitivity is a projection operator onto the tangent bundle of the equilibrium manifold. A linear algebraic characterization and explicit results on first order corrections to the thermodynamics of ideal solutions are provided. Finally, the theory is applied to the IDHKP-IDH glyoxylate bypass regulation system. The novelty of the theory is that it is applicable to CRNs with non-ideal thermodynamical behavior, which are prevalent in highly crowded cellular environments due to various interactions between the chemicals. Indeed, the analyzed example shows remarkable behavior ranging from hypersensitivity to negative-self regulations. These are effects which usually require strongly nonlinear reaction kinetics. However, here, they are obtained by tuning thermodynamical interactions providing a complementary, and physically well-founded, viewpoint on such phenomena.

q-bio.MN↗

arXiv2025

Cramer-Rao bound and absolute sensitivity in chemical reaction networks

Chemical reaction networks (CRN) comprise an important class of models to understand biological functions such as cellular information processing, the robustness and control of metabolic pathways, circadian rhythms, and many more. However, any CRN describing a certain function does not act in isolation but is a part of a much larger network and as such is constantly subject to external changes. In [Shinar, Alon, and Feinberg. "Sensitivity and robustness in chemical reaction networks." SIAM J App Math (2009): 977-998.], the responses of CRN to changes in the linear conserved quantities, called sensitivities, were studied in and the question of how to construct absolute, i.e., basis-independent, sensitivities was raised. In this article, by applying information geometric methods, such a construction is provided. The idea is to track how concentration changes in a particular chemical propagate to changes of all concentrations within a steady state. This is encoded in the matrix of absolute sensitivities. As the main technical tool, a multivariate Cramer-Rao bound for CRN is proven, which is based on the the analogy between quasi-thermostatic steady states and the exponential family of probability distributions. This leads to a linear algebraic characterization of the matrix of absolute sensitivities for quasi-thermostatic CRN. As an example, the core module of the IDHKP-IDH glyoxylate bypass regulation system is analyzed analytically and numerically by extensive random sampling of the concentration space. The experimentally known findings for the robustness of the IDH enzyme are confirmed and a hidden symmetry at the level of distributions is revealed, providing a blueprint for the analysis of the robustness properties of CRNs.

q-bio.MN↗

arXiv2025

Optimality theory of stigmergic collective information processing by chemotactic cells

Collective information processing is fundamental in various biological systems, where the cooperation of multiple cells results in complex functions beyond individual capabilities. A distinctive example is collective exploration where chemotactic cells not only sense the gradient of guiding exogeneous cues originating from targets but also generate and modulate endogenous cues to coordinate their collective behaviors. While the optimality of gradient sensing has been studied extensively in the context of single-cell information processing, the optimality of collective information processing that includes both gradient sensing and gradient generation remains underexplored. In this study, we formulate the collective exploration problem as a reinforcement learning (RL) by a population. Based on RL theory, we derive the optimal exploration dynamics of agents and identify their structural correspondence with the Keller-Segel model, the established phenomenological model of collective cellular dynamics. Our theory identifies an optimal coupling relation between gradient sensing and gradient generation and demonstrates that the optimal way to generate a gradient qualitatively differs depending on whether the gradient sensing is logarithmic or linear. The underlying RL structure is leveraged to compare the derived collective dynamics with single-agent searching dynamics, showing that distributed information processing by population enables a fraction of agents to reach the target robustly. Our formulation provides a foundation for understanding the collective information processing mediated by dynamic sensing and modulation of cues.

q-bio.CB↗

arXiv2024

Integrating GNN and Neural ODEs for Estimating Non-Reciprocal Two-Body Interactions in Mixed-Species Collective Motion

Analyzing the motion of multiple biological agents, be it cells or individual animals, is pivotal for the understanding of complex collective behaviors. With the advent of advanced microscopy, detailed images of complex tissue formations involving multiple cell types have become more accessible in recent years. However, deciphering the underlying rules that govern cell movements is far from trivial. Here, we present a novel deep learning framework for estimating the underlying equations of motion from observed trajectories, a pivotal step in decoding such complex dynamics. Our framework integrates graph neural networks with neural differential equations, enabling effective prediction of two-body interactions based on the states of the interacting entities. We demonstrate the efficacy of our approach through two numerical experiments. First, we used simulated data from a toy model to tune the hyperparameters. Based on the obtained hyperparameters, we then applied this approach to a more complex model with non-reciprocal forces that mimic the collective dynamics of the cells of slime molds. Our results show that the proposed method can accurately estimate the functional forms of two-body interactions -- even when they are nonreciprocal -- thereby precisely replicating both individual and collective behaviors within these systems.

physics.bio-ph↗

arXiv2024

A theoretical basis for cell deaths

Understanding deaths and life-death boundaries of cells is a fundamental challenge in biological sciences. In this study, we present a theoretical framework for investigating cell death. We conceptualize cell death as a controllability problem within dynamical systems, and compute the life-death boundary through the development of "stoichiometric rays". This method utilizes enzyme activity as control parameters, exploiting the inherent property of enzymes to enhance reaction rates without shifting equilibrium states. This approach facilitates the efficient evaluation of the global controllability of models. We demonstrate the utility of our framework using its application to a toy metabolic model, where we delineate the life-death boundary. The formulation of cell death through mathematical principles provides a foundation for the theoretical study of cellular mortality.

physics.bio-ph↗

arXiv2024

Theory for Optimal Estimation and Control under Resource Limitations and Its Applications to Biological Information Processing and Decision-Making

Despite being optimized, the information processing of biological organisms exhibits significant variability in its complexity and capability. One potential source of this diversity is the limitation of resources required for information processing. However, we lack a theoretical framework that comprehends the relationship between biological information processing and resource limitations and integrates it with decision-making conduced downstream of the information processing. In this paper, we propose a novel optimal estimation and control theory that accounts for the resource limitations inherent in biological systems. This theory explicitly formulates the memory that organisms can store and operate and obtains optimal memory dynamics using optimal control theory. This approach takes account of various resource limitations, such as memory capacity, intrinsic noise, and energy cost, and unifies state estimation and control. We apply this theory to minimal models of biological information processing and decision-making under resource limitations and find that such limitations induce discontinuous and non-monotonic phase transitions between memory-less and memory-based strategies. Therefore, this theory establishes a comprehensive framework for addressing biological information processing and decision-making under resource limitations, revealing the rich and complex behaviors that arise from resource limitations.

physics.bio-ph↗

arXiv2024

Resource Limitations induce Phase Transitions in Biological Information Processing

Biological information processing manifests a huge variety in its complexity and capability among different organisms, which presumably stems from the evolutionary optimization under limited computational resources. Starting from the simplest memory-less responsive behaviors, more complicated information processing using internal memory may have developed in the evolution as more resources become available. In this letter, we report that optimal information processing strategy can show discontinuous transitions along with the available resources, i.e., reliability of sensing and intrinsic dynamics, or the cost of memory control. In addition, we show that transition is not always progressive but can be regressed. Our result obtained under a minimal setup suggests that the capability and complexity of information processing would be an evolvable trait that can switch back and forth between different strategies and architectures in a punctuated manner.

physics.bio-ph↗

arXiv2024

Ancestral Reinforcement Learning: Unifying Zeroth-Order Optimization and Genetic Algorithms for Reinforcement Learning

Reinforcement Learning (RL) offers a fundamental framework for discovering optimal action strategies through interactions within unknown environments. Recent advancement have shown that the performance and applicability of RL can significantly be enhanced by exploiting a population of agents in various ways. Zeroth-Order Optimization (ZOO) leverages an agent population to estimate the gradient of the objective function, enabling robust policy refinement even in non-differentiable scenarios. As another application, Genetic Algorithms (GA) boosts the exploration of policy landscapes by mutational generation of policy diversity in an agent population and its refinement by selection. A natural question is whether we can have the best of two worlds that the agent population can have. In this work, we propose Ancestral Reinforcement Learning (ARL), which synergistically combines the robust gradient estimation of ZOO with the exploratory power of GA. The key idea in ARL is that each agent within a population infers gradient by exploiting the history of its ancestors, i.e., the ancestor population in the past, while maintaining the diversity of policies in the current population as in GA. We also theoretically reveal that the populational search in ARL implicitly induces the KL-regularization of the objective function, resulting in the enhanced exploration. Our results extend the applicability of populational algorithms for RL.

cs.LG↗

arXiv2024

Gradient sensing limit of a cell when controlling the elongating direction

Eukaryotic cells perform chemotaxis by determining the direction of chemical gradients based on stochastic sensing of concentrations at the cell surface. To examine the efficiency of this process, previous studies have investigated the limit of estimation accuracy for gradients. However, these studies assume that the cell shape and gradient are constant, and do not consider how adaptive regulation of cell shape affects the estimation limit. Dynamics of cell shape during gradient sensing is biologically ubiquitous and can influence the estimation by altering the way the concentration is measured, and cells may strategically regulate their shape to improve estimation accuracy. To address this gap, we investigate the estimation limits in dynamic situations where cells change shape adaptively depending on the sensed signal. We approach this problem by analyzing the stationary solution of the Bayesian nonlinear filtering equation. By applying diffusion approximation to the ligand-receptor binding process and the Laplace method for the posterior expectation under a high signal-to-noise ratio regime, we obtain an analytical expression for the estimation limit. This expression indicates that estimation accuracy can be improved by elongating perpendicular to the estimated direction, which is also confirmed by numerical simulations. Our analysis provides a basis for clarifying the interplay between estimation and control in gradient sensing and sheds light on how cells optimize their shape to enhance chemotactic efficiency.

q-bio.CB↗

arXiv2024

Thermodynamic and Stoichiometric Laws Ruling the Fates of Growing Systems

We delve into growing open chemical reaction systems (CRSs) characterized by autocatalytic reactions within a variable volume, which changes in response to these reactions. Understanding the thermodynamics of such systems is crucial for comprehending biological cells and constructing protocells, as it sheds light on the physical conditions necessary for their self-replication. Building on our recent work, where we developed a thermodynamic theory for growing CRSs featuring basic autocatalytic motifs with regular stoichiometric matrices, we now expand this theory to include scenarios where the stoichiometric matrix has a nontrivial left kernel space. This extension introduces conservation laws, which limit the variations in chemical species due to reactions, thereby confining the system's possible states to those compatible with its initial conditions. By considering both thermodynamic and stoichiometric constraints, we clarify the environmental and initial conditions that dictate the CRSs' fate-whether they grow, shrink, or reach equilibrium. We also find that the conserved quantities significantly influence the equilibrium state achieved by a growing CRS. These results are derived independently of specific thermodynamic potentials or reaction kinetics, therefore underscoring the fundamental impact of conservation laws on the growth of the system.

cond-mat.stat-mech↗