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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, most studies have treated a circular cell shape, and the few considering elongated shapes assume the elongated direction as fixed. This leaves the question of 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 elongated cells change their orientation 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 aligning the elongated direction 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.

The chemotactic network of Escherichia coli has been studied extensively both biophysically and information theoretically. Nevertheless, connection between these two aspects is still elusive. In this work, we report such a connection. We derive an optimal filtering dynamics under the assumption that E. coli's sensory system optimally infers the binary information whether it is swimming up or down along an exponential ligand gradient from noisy sensory signals. Then we show that a standard biochemical model of the chemotactic network is mathematically equivalent to this information-theoretically optimal dynamics. Moreover, we demonstrate that an experimentally observed nonlinear response relation can be reproduced from the optimal dynamics. These results suggest that the biochemical network of E. coli chemotaxis is designed to optimally extract the binary information along an exponential gradient in a noisy condition.

Intracellular reactions are intrinsically stochastic. Nonetheless, cells can reliably respond to the changing environment by sensing their target molecules sensitively and specifically, even with the existence of abundant structurally-similar non-target molecules. The mechanism of how the cells can balance and achieve such different characteristics is not yet fully understood. In this work, we demonstrate that these characteristics can be attained by a ligand-induced stochastic cluster formation of receptors via the noise-induced symmetry breaking, in which the intrinsic stochasticity works to enhance sensitivity and specificity. We also show that the noise-induced cluster formation enables cells to detect the target ligand reliably by compensating the abundant non-target ligands in the environment. The proposed mechanism may lead to a deeper understanding of a biological function of the receptor clustering and provide an alternative candidate for the reliable ligand detection to the kinetic proofreading.

Thymic crosstalk, a set of reciprocal regulations between thymocytes and the thymic environment, is relevant for orchestrating appropriate thymocyte development as well as thymic recovery from various exogenous insults. In this work, interactions shaping thymic crosstalk and the resultant dynamics of thymocytes and thymic epithelial cells are inferred based on quantitative analysis and modeling of the recovery dynamics induced by irradiation. The analysis identifies regulatory interactions consistent with known molecular evidence and reveals their dynamic roles in the recovery process. Moreover, the analysis also predicts, and a subsequent experiment verifies, a previously unrecognized regulation of CD4+CD8+ double positive thymocytes which temporarily increases their proliferation rate upon the decrease in their population size. Our model establishes a pivotal step towards the dynamic understanding of thymic crosstalk as a regulatory network system., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2019.)

We construct a pathwise formulation for a multitype age-structured population dynamics, which involves an age-dependent cell replication and transition of gene- or phenotypes. By employing the formulation, we derive a variational representation of the stationary population growth rate; the representation comprises a tradeoff relation between growth effects and a single-cell intrinsic dynamics described by a semi-Markov process. This variational representation leads to a response relation of the stationary population growth rate, in which statistics on a retrospective history work as the response coefficients. These results contribute to predicting and controlling growing populations based on experimentally observed cell-lineage information.

Adaptation in a fluctuating environment is a process of fueling environmental information to gain fitness. Living systems have gradually developed strategies for adaptation from random and passive diversification of the phenotype to more proactive decision making, in which environmental information is sensed and exploited more actively and effectively. Understanding the fundamental relation between fitness and information is therefore crucial to clarify the limits and universal properties of adaptation. In this work, we elucidate the underlying stochastic and information-thermodynamic structure in this process, by deriving causal fluctuation relations (FRs) of fitness and information. Combined with a duality between phenotypic and environmental dynamics, the FRs reveal the limit of fitness gain, the relation of time reversibility with the achievability of the limit, and the possibility and condition for gaining excess fitness due to environmental fluctuation. The loss of fitness due to causal constraints and the limited capacity of real organisms is shown to be the difference between time-forward and time-backward path probabilities of phenotypic and environmental dynamics. Furthermore, the FRs generalize the concept of the evolutionary stable state (ESS) for fluctuating environment by giving the probability that the optimal strategy on average can be invaded by a suboptimal one owing to rare environmental fluctuation. These results clarify the information-thermodynamic structures in adaptation and evolution.

In vivo reaction space is constrained by complex structures which are made of entwined cytoskeletons and organelles; this create the difference between in vivo and in vitro in respect of molecular mobility, and it may affect reaction processes. Our motivation is to reveal the background mechanisms of the properties of molecular behaviors in vivo by numerical approach. For this object, we reassembled a pseudo-intracellular environment in 3D lattice space, and executed Monte Carlo simulation. By changing the relative amount of non-reactive obstacles in the simulation space, we tested the effect of the level of crowdedness to the molecular mobility and reaction processes. Our results showed that molecules demonstrated anomalous diffusion correlating to the restriction level of the reaction space. Reaction processes also showed distinct characteristics, that is increase of reaction rate at the beginning of reactions, with the decrease of the reaction rate at later time frame of reactions. Our results suggested that the anomalous behaviors at singe molecule level in vivo could bring an essential difference to the reaction processes and the results.

The cellular and intracellular dynamics are intrinsically stochastic and dynamic. However, whole biological system such as a cell or our body can function very robustly and stably even though they are composed of these stochastic reactions. To account for this riddling relation between macroscopic robustness and microscopic stochasticity, I propose a mechanism that information relevant for stable and reliable operation of a biological system is embedded in apparently stochastic and noisy behavior of their components. To show validity of this possibility, I demonstrates that information can actually be decoded from apparently noisy signal when it is processed by an appropriate dynamics derived by Bayes' rule. Next, I investigate biological relevance of this possibility by showing that several intracellular networks can implement this decoding dynamics. Finally, by focusing its dynamical properties, I show the mechanism how the derived dynamics can separate information and noise.

Microscopic biological processes have extraordinary complexity and variety at the sub-cellular, intra-cellular, and multi-cellular levels. In dealing with such complex phenomena, conceptual and theoretical frameworks are crucial, which enable us to understand seemingly different intra- and inter-cellular phenomena from unified viewpoints. Decision-making is one such concept that has attracted much attention recently. Since a number of cellular behavior can be regarded as processes to make specific actions in response to external stimuli, decision-making can cover and has been used to explain a broad range of different cellular phenomena [Balázsi et al. (Cell 144(6):910, 2011), Zeng et al. (Cell 141(4):682, 2010)]. Decision-making is also closely related to cellular information-processing because appropriate decisions cannot be made without exploiting the information that the external stimuli contain. Efficiency of information transduction and processing by intra-cellular networks determines the amount of information obtained, which in turn limits the efficiency of subsequent decision-making. Furthermore, information-processing itself can serve as another concept that is crucial for understanding of other biological processes than decision-making. In this work, we review recent theoretical developments on cellular decision-making and information-processing by focusing on the relation between these two concepts.

A variety of cellular functions are robust even to substantial intrinsic and extrinsic noise in intracellular reactions and the environment that could be strong enough to impair or limit them. In particular, of substantial importance is cellular decision-making in which a cell chooses a fate or behavior on the basis of information conveyed in noisy external signals. For robust decoding, the crucial step is filtering out the noise inevitably added during information transmission. As a minimal and optimal implementation of such an information decoding process, the autocatalytic phosphorylation and autocatalytic dephosphorylation (aPadP) cycle was recently proposed. Here, we analyze the dynamical properties of the aPadP cycle in detail. We describe the dynamical roles of the stationary and short-term responses in determining the efficiency of information decoding and clarify the optimality of the threshold value of the stationary response and its information-theoretical meaning. Furthermore, we investigate the robustness of the aPadP cycle against the receptor inactivation time and intrinsic noise. Finally, we discuss the relationship among information decoding with information-dependent actions, bet-hedging and network modularity.

The biological function of noise-induced symmetry breaking (NISB) is still unclear even though it may potentially occur in noisy intracellular systems. In this work, I demonstrate that information decoding from a noisy signal is a potential biological function of NISB by revealing that NISB naturally emerges from an optimal information-decoding dynamics and that several intracellular networks can be identified with the information-decoding dynamics. I also propose a mean first passage time profile as a way to experimentally identify NISB.

Decision making in a noisy and dynamically changing environment is a fundamental task for a cell. To choose appropriate decisions over time, a cell must be equipped with intracellular kinetics that can conduct dynamic and efficient decision making. By using the theory of sequential inference, I demonstrate that dynamic Bayesian decision making can be implemented by an intracellular kinetics with a dual positive feedback structure. I also show that the combination of linear instantaneous and nonlinear stationary sensitivities to the input dominantly contributes to decision making efficiency, and that the state-dependent sensitivity change further suppresses noisy response. The statistical principles underlying these two factors are further clarified to be a log-likelihood-dependent quantification of the input information and uncertainty-dependent sensitivity control.

Single-cell-level behaviors of cells are typically inferred from ensemble measurements. However, such inferences implicitly assume a biological version of ergodicity: the percentage of cells in a state is identical to the probability to find a cell in that state. While the ergodicity does not always hold, it has been rarely tested. Here, we reveal that the ergodicity does not necessarily hold even for simple toggle switches and that apparent stabilities of the switches are due to a balance between single-cell-level biased stabilities and growth rates differences. Therefore, verification of the ergodicity and reconstructing single-cell-level behaviors are crucial for understanding intracellular systems.

Understanding the information processing ability of signal transduction pathways is of great importance because of their crucial roles in triggering various cellular responses. Despite continuing theoretical investigation, some important aspects of signal transduction such as a transient response and its connection to stochasticity originating from a small number of molecules have not yet been well understood. It is, however, through these aspects that unexpected and nontrivial properties of the information processing emerge. In this article, we analyze the transient behavior of a simple signaling cascade by taking into account the stochasticity originating from the small number of molecules. We identify several properties of the signaling cascade that emerge as a result of the interplay between the stochasticity and transient dynamics of the cascade. We specifically demonstrate that each step of the cascade has an optimal number of signaling molecules at which the average signal amplitude becomes maximal. We further investigate the connection between a finite number of molecules and the ability of the cascade to discriminate between true and error signals, which cannot be inferred from deterministic descriptions. The implications of our results are discussed from both biological and mathematical viewpoints.