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Robustness and plasticity are essential features that allow biological systems to cope with complex and variable environments. In a constant environment, robustness, i.e., insensitivity of phenotypes, is expected to increase, whereas plasticity, i.e., the changeability of phenotypes, tends to diminish. Under a variable environment, existence of plasticity will be relevant. The robustness and plasticity, on the other hand, are related to phenotypic variances. As phenotypic variances decrease with the increase in robustness to perturbations, they are expected to decrease through the evolution. However, in nature, phenotypic fluctuation is preserved to a certain degree. One possible cause for this is environmental variation, where one of the most important "environmental" factors will be inter-species interactions. As a first step toward investigating phenotypic fluctuation in response to an inter-species interaction, we present the study of a simple two-species system that comprises hosts and parasites. Hosts are expected to evolve to achieve a phenotype that optimizes fitness. Then, the robustness of the corresponding phenotype will be increased by reducing phenotypic fluctuations. Conversely, plasticity tends to evolve to avoid certain phenotypes that are attacked by parasites. By using a dynamic model of gene expression for the host, we investigate the evolution of the genotype-phenotype map and of phenotypic variances. If the host-parasite interaction is weak, the fittest phenotype of the host evolves to reduce phenotypic variances. In contrast, if there exists a sufficient degree of interaction, the phenotypic variances of hosts increase to escape parasite attacks. For the latter case, we found two strategies: if the noise in the stochastic gene expression is below a certain threshold, the phenotypic variance increases via genetic diversification, whereas above this threshold, it is increased mediated by noise-induced phenotypic fluctuation. We examine how the increase in the phenotypic variances caused by parasite interactions influences the growth rate of a single host, and observed a trade-off between the two. Our results help elucidate the roles played by noise and genetic mutations in the evolution of phenotypic fluctuation and robustness in response to host-parasite interactions., Competing Interests: The authors have declared that no competing interests exist.

Microbial communities display remarkable diversity, facilitated by the secretion of chemicals that can create new niches. However, it is unclear why cells often secrete even essential metabolites after evolution. Based on theoretical results indicating that cells can enhance their own growth rate by leaking even essential metabolites, we show that such "leaker" cells can establish an asymmetric form of mutualism with "consumer" cells that consume the leaked chemicals: the consumer cells benefit from the uptake of the secreted metabolites, while the leaker cells also benefit from such consumption, as it reduces the metabolite accumulation in the environment and thereby enables further secretion, resulting in frequency-dependent coexistence of multiple microbial species. As supported by extensive simulations, such symbiotic relationships generally evolve when each species has a complex reaction network and adapts its leakiness to optimize its own growth rate under crowded conditions and nutrient limitations. Accordingly, symbiotic ecosystems with diverse cell species that leak and exchange many metabolites with each other are shaped by cell-level adaptation of leakiness of metabolites. Moreover, the resultant ecosystems with entangled metabolite exchange are resilient against structural and environmental perturbations. Thus, we present a theory for the origin of resilient ecosystems with diverse microbes mediated by secretion and exchange of essential chemicals., Competing Interests: The authors have declared that no competing interests exist.

Microbial cells generally leak various metabolites including those necessary to grow. Why cells secrete even essential chemicals so often is, however, still unclear. Based on analytical and numerical calculations, we show that if the intracellular metabolism includes multibody (e.g., catalytic) reactions, leakage of essential metabolites can promote the leaking cell's growth. This advantage is typical for most metabolic networks via "flux control" and "growth-dilution" mechanisms, as a general consequence of the balance between synthesis and growth-induced dilution with autocatalytic reactions. We further argue that this advantage may lead to a novel form of symbiosis among diverse cells.

ALAS2 gene mutations cause X-linked sideroblastic anemia. The presence of ring sideroblasts in a patient's bone marrow is the hallmark of sideroblastic anemia, but the precise mechanisms underlying sideroblast formation are largely unknown. Using a genome-editing system, a mutation was introduced in the erythroid-specific enhancer of the ALAS2 gene in HUDEP2 cells, which were derived from human umbilical stem cells and can produce erythrocytes. The established cell line, termed HA2low, expressed less ALAS2 mRNA than did wild-type cells, even after erythroid differentiation. Although the mRNA expression of α-globin, β-globin, and the mitochondrial iron importer mitoferrin-1 was induced similarly in wild-type and HA2low cells, hemoglobinization of differentiated cells was limited in HA2low cells compared with wild-type cells. Importantly, Prussian blue staining revealed that approximately one-third of differentiated HA2low cells exhibited intracellular iron deposition and these cells looked like ring sideroblasts. Electron microscopy confirmed that the mitochondria in HA2low cells contained high-density deposits that might contain iron. Ring sideroblastic cells appeared among HA2low cells only after differentiation, whereas the induced expression of mitochondrial ferritin was observed in both cell types during differentiation. These results suggest that the induction of mitochondrial ferritin expression might be essential for, but not the primary cause of, ring sideroblast formation. Our results also suggest that the insufficient supply of protoporphyrin IX due to ALAS2 deficiency in combination with increased iron import into mitochondria during erythroid differentiation results in the formation of ring sideroblasts. Furthermore, HA2low cells are a useful tool for characterizing ring sideroblasts in vitro., (Copyright © 2018. Published by Elsevier Inc.)

A reduction in high-dimensional phenotypic states to a few degrees of freedom is essential to understand biological systems. Here, we show evolutionary robustness causes such reduction which restricts possible phenotypic changes in response to a variety of environmental conditions. First, global protein expression changes in Escherichia coli after various environmental perturbations were shown to be proportional across components, across different types of environmental conditions. To examine if such dimension reduction is a result of evolution, we analyzed a cell model-with a huge number of components, that reproduces itself via a catalytic reaction network-and confirmed that common proportionality in the concentrations of all components is shaped through evolutionary processes. We found that the changes in concentration across all components in response to environmental and evolutionary changes are constrained to the changes along a one-dimensional major axis, within a huge-dimensional state space. On the basis of these observations, we propose a theory in which such constraints in phenotypic changes are achieved both by evolutionary robustness and plasticity and formulate this proposition in terms of dynamical systems. Accordingly, broad experimental and numerical results on phenotypic changes caused by evolution and adaptation are coherently explained.

A most important property of biochemical systems is robustness. Static robustness, e.g., homeostasis, is the insensitivity of a state against perturbations, whereas dynamics robustness, e.g., homeorhesis, is the insensitivity of a dynamic process. In contrast to the extensively studied static robustness, dynamics robustness, i.e., how a system creates an invariant temporal profile against perturbations, is little explored despite transient dynamics being crucial for cellular fates and are reported to be robust experimentally. For example, the duration of a stimulus elicits different phenotypic responses, and signaling networks process and encode temporal information. Hence, robustness in time courses will be necessary for functional biochemical networks. Based on dynamical systems theory, we uncovered a general mechanism to achieve dynamics robustness. Using a three-stage linear signaling cascade as an example, we found that the temporal profiles and response duration post-stimulus is robust to perturbations against certain parameters. Then analyzing the linearized model, we elucidated the criteria of when signaling cascades will display dynamics robustness. We found that changes in the upstream modules are masked in the cascade, and that the response duration is mainly controlled by the rate-limiting module and organization of the cascade's kinetics. Specifically, we found two necessary conditions for dynamics robustness in signaling cascades: 1) Constraint on the rate-limiting process: The phosphatase activity in the perturbed module is not the slowest. 2) Constraints on the initial conditions: The kinase activity needs to be fast enough such that each module is saturated even with fast phosphatase activity and upstream changes are attenuated. We discussed the relevance of such robustness to several biological examples and the validity of the above conditions therein. Given the applicability of dynamics robustness to a variety of systems, it will provide a general basis for how biological systems function dynamically.

Protein motors, such as kinesins and dyneins, bind to a microtubule and travel along it in a specific direction. Previously, it was thought that the directionality for a given motor was constant in the absence of an external force. However, the directionality of the kinesin-5 Cin8 was recently found to change as the number of motors that bind to the same microtubule is increased. Here, we introduce a simple mechanical model of a microtubule-sliding assay in which multiple motors interact with the filament. We show that, due to the collective phenomenon, the directionality of the motor changes (e.g., from minus- to plus- end directionality), depending on the number of motors. This is induced by a large diffusive component in the directional walk and by the subsequent frustrated motor configuration, in which multiple motors pull the filament in opposite directions, similar to a game of tug-of-war. A possible role of the dual-directional motors for the mitotic spindle formation is also discussed. Our framework provides a general mechanism to embed two conflicting tasks into a single molecular machine, which works context-dependently.

As cells grow and divide under a given environment, they become crowded and resources are limited, as seen in bacterial biofilms and multicellular aggregates. These cells often show strong interactions through exchanging chemicals, as evident in quorum sensing, to achieve mutualism and division of labor. Here, to achieve stable division of labor, three characteristics are required. First, isogenous cells differentiate into several types. Second, this aggregate of distinct cell types shows better growth than that of isolated cells without interaction and differentiation, by achieving division of labor. Third, this cell aggregate is robust with respect to the number distribution of differentiated cell types. Indeed, theoretical studies have thus far considered how such cooperation is achieved when the ability of cell differentiation is presumed. Here, we address how cells acquire the ability of cell differentiation and division of labor simultaneously, which is also connected with the robustness of a cell society. For this purpose, we developed a dynamical-systems model of cells consisting of chemical components with intracellular catalytic reaction dynamics. The reactions convert external nutrients into internal components for cellular growth, and the divided cells interact through chemical diffusion. We found that cells sharing an identical catalytic network spontaneously differentiate via induction from cell-cell interactions, and then achieve division of labor, enabling a higher growth rate than that in the unicellular case. This symbiotic differentiation emerged for a class of reaction networks under the condition of nutrient limitation and strong cell-cell interactions. Then, robustness in the cell type distribution was achieved, while instability of collective growth could emerge even among the cooperative cells when the internal reserves of products were dominant. The present mechanism is simple and general as a natural consequence of interacting cells with limited resources, and is consistent with the observed behaviors and forms of several aggregates of unicellular organisms., Competing Interests: The authors have declared that no competing interests exist.

Evolution is often conceived as changes in the properties of a population over generations. Does this notion exhaust the possible dynamics of evolution? Life is hierarchically organized, and evolution can operate at multiple levels with conflicting tendencies. Using a minimal model of such conflicting multilevel evolution, we demonstrate the possibility of a novel mode of evolution that challenges the above notion: individuals ceaselessly modify their genetically inherited phenotype and fitness along their lines of descent, without involving apparent changes in the properties of the population. The model assumes a population of primitive cells (protocells, for short), each containing a population of replicating catalytic molecules. Protocells are selected towards maximizing the catalytic activity of internal molecules, whereas molecules tend to evolve towards minimizing it in order to maximize their relative fitness within a protocell. These conflicting evolutionary tendencies at different levels and genetic drift drive the lineages of protocells to oscillate endlessly between high and low intracellular catalytic activity, i.e. high and low fitness, along their lines of descent. This oscillation, however, occurs independently in different lineages, so that the population as a whole appears stationary. Therefore, ongoing evolution can be hidden behind an apparently stationary population owing to conflicting multilevel evolution., (© 2016 The Authors.)

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 reciprocity 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 coefficient. 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.

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Cells change their internal state to adapt to environmental changes, and evolve in response to the new conditions. The phenotype changes first via adaptation in response to environmental changes, and then through mutational changes in the genomic sequence, followed by selection in evolution. Here, we analysed simulated adaptive evolution using a simple cell model consisting of thousands of intracellular components, and found that the changes in their concentrations by adaptation are proportional to those by evolution across all the components, where the proportion coefficient between the two agreed well with the change in the growth rate of a cell. Furthermore, we demonstrate that the phenotypic variance in concentrations of cellular components due to (non-genetic) noise and to genomic alternations is proportional across all components. This implies that the specific phenotypes that are highly evolvable were already given by non-genetic fluctuations. These global relationships in cellular states were also supported by phenomenological theory based on steady reproduction and transcriptome analysis of laboratory evolution in Escherichia coli. These findings demonstrate that a possible evolutionary change in phenotypic state is highly restricted. Our results provide a basis for the development of a quantitative theory of plasticity and robustness in phenotypic evolution., (© 2015 The Author(s) Published by the Royal Society. All rights reserved.)

Cells generally convert external nutrient resources to support metabolism and 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 nonequilibrium thermodynamics. The minimal entropy production per unit-cell growth is found to be achieved at a nonzero nutrient uptake rate rather than at a quasistatic 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.

Cellular memory, which allows cells to retain information from their environment, is important for a variety of cellular functions, such as adaptation to external stimuli, cell differentiation, and synaptic plasticity. Although posttranslational modifications have received much attention as a source of cellular memory, the mechanisms directing such alterations have not been fully uncovered. It may be possible to embed memory in multiple stable states in dynamical systems governing modifications. However, several experiments on modifications of proteins suggest long-term relaxation depending on experienced external conditions, without explicit switches over multi-stable states. As an alternative to a multistability memory scheme, we propose "kinetic memory" for epigenetic cellular memory, in which memory is stored as a slow-relaxation process far from a stable fixed state. Information from previous environmental exposure is retained as the long-term maintenance of a cellular state, rather than switches over fixed states. To demonstrate this kinetic memory, we study several models in which multimeric proteins undergo catalytic modifications (e.g., phosphorylation and methylation), and find that a slow relaxation process of the modification state, logarithmic in time, appears when the concentration of a catalyst (enzyme) involved in the modification reactions is lower than that of the substrates. Sharp transitions from a normal fast-relaxation phase into this slow-relaxation phase are revealed, and explained by enzyme-limited competition among modification reactions. The slow-relaxation process is confirmed by simulations of several models of catalytic reactions of protein modifications, and it enables the memorization of external stimuli, as its time course depends crucially on the history of the stimuli. This kinetic memory provides novel insight into a broad class of cellular memory and functions. In particular, applications for long-term potentiation are discussed, including dynamic modifications of calcium-calmodulin kinase II and cAMP-response element-binding protein essential for synaptic plasticity.

Biological systems have often to perform binary decisions under highly dynamic and noisy environments, such as during cell-fate determination. These decisions can be implemented by two main bifurcation mechanisms based on the transitions from either monostability or oscillation to bistability. We compare these two mechanisms by using stochastic models with time-varying fields and by establishing asymptotic formulas for the choice probabilities. Different scaling laws for decision sensitivity with respect to noise strength and signal timescale are obtained, supporting a role for oscillatory dynamics in performing noise-robust and temporally tunable binary decision-making. This result provides a rationale for recent experimental evidences showing that oscillatory expression of proteins often precedes binary cell-fate decisions.

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.

A simple cell model consisting of a gene regulatory network with epigenetic feedback regulation is studied to evaluate the effect of epigenetic dynamics on adaptation and evolution. We find that, the type of epigenetic dynamics considered enables a cell to adapt to unfamiliar environmental changes, for which no regulatory program has been prepared, through noise-driven selection of a cellular state with a high growth rate. Furthermore, we demonstrate that the inclusion of epigenetic regulation promotes evolutionary development of a regulatory network that can respond to environmental changes in a fast and precise manner. These results strongly suggest that epigenetic feedback regulation in gene expression dynamics provides a significant increase in fitness by engendering an increase in cellular plasticity during adaptation and evolution.

In both randomly moving Dictyostelium and mammalian cells, phosphatidylinositol (3,4,5)-trisphosphate and F-actin are known to propagate as waves at the membrane and act to push out the protruding edge. To date, however, the relationship between the wave geometry and the patterns of amoeboid shape change remains elusive. Here, by using phase map analysis, we show that morphology dynamics of randomly moving Dictyostelium discoideum cells can be characterized by the number, topology, and position of spatial phase singularities, i.e., points that represent organizing centers of rotating waves. A single isolated singularity near the cellular edge induced a rotational protrusion, whereas a pair of singularities supported a symmetric extension. These singularities appeared by strong phase resetting due to de novo nucleation at the back of preexisting waves. Analysis of a theoretical model indicated excitability of the system that is governed by positive feedback from phosphatidylinositol (3,4,5)-trisphosphate to PI3-kinase activation, and we showed experimentally that this requires F-actin. Furthermore, by incorporating membrane deformation into the model, we demonstrated that geometries of competing waves explain most of the observed semiperiodic changes in amoeboid morphology.

Circadian clocks--ubiquitous in life forms ranging from bacteria to multicellular 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. Here 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. The steps with the highest activation energy rate-limit the cycle when 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 the common enzyme. We show that this change in free enzyme abundance compensates 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 mechanism 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.

A simple cell model consisting of a catalytic reaction network is studied to show that cellular states are self-organized in a critical state for achieving optimal growth; we consider the catalytic network dynamics over a wide range of environmental conditions, through the spontaneous regulation of nutrient transport into the cell. Furthermore, we find that the adaptability of cellular growth to reach a critical state depends only on the extent of environmental changes, while all chemical species in the cell exhibit correlated partial adaptation. These results are in remarkable agreement with the recent experimental observations of the present cells.

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 a 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.

The transactivation response element (TAR) DNA-binding protein-43 (TDP-43) is a nuclear protein that normally regulates transcription and splicing. Abnormal accumulation of insoluble inclusions containing TDP-43 has been recently reported in the affected tissues of amyotrophic lateral sclerosis (ALS) patients. Here, we show that intracellular aggregation of TDP-43 can be triggered by transduction of fibrillar aggregates prepared from in vitro functional TDP-43. Sarkosyl is found to be incapable of solubilizing those intracellularly seeded aggregates of TDP-43, which is consistent with the observation that TDP-43 inclusions in ALS patients are sarkosyl-insoluble. In addition, intracellular seeding in our cell models reproduces ubiquitination of TDP-43 aggregates, which is another prominent feature of TDP-43 inclusions in ALS patients. Although it has been so far difficult to initiate disease-associated changes of TDP-43 using cultured cell models, we propose that a seeding reaction is a key to construct a model to monitor TDP-43 pathologies.

In 1905, Albert Einstein proposed that the forces that cause the random Brownian motion of a particle also underlie the resistance to macroscopic motion when a force is applied. This insight, of a coupling between fluctuation (stochastic behavior) and responsiveness (non-stochastic behavior), founded an important branch of physics. Here we argue that his insight may also be relevant for understanding evolved biological systems, and we present a 'fluctuation-response relationship' for biology. The relationship is consistent with the idea that biological systems are similarly canalized to stochastic, environmental, and genetic perturbations. It is also supported by in silico evolution experiments, and by the observation that 'noisy' gene expression is often both more responsive and more 'evolvable'. More generally, we argue that in biology there is (and always has been) an important role for macroscopic theory that considers the general behavior of systems without concern for their intimate molecular details.

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 of dynamics, rapid-burst-type oscillation and a slow cycle were discovered; depending on the initial conditions, these two 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.

Regeneration phenomena are ubiquitous in nature and are studied in a variety of experiments. Positional information and feedback-loop hierarchy are theories that have been proposed to explain ordering rules in regeneration; however, some regeneration phenomena violate the rules derived from them. In particular, grafted junction stumps with the same value/hierarchy sometimes lead to one extra segmented portion, termed segmented regeneration. To present a unified description of all insect leg regeneration phenomena, we propose a theoretical mechanism for regeneration without postulating positional information, by using a model that consists of intracellular reaction dynamics of chemical concentrations, cell-to-cell interactions, and an increase in cell number. As a normal developmental process, successive differentiation from pluripotent cells appears, as described by transition from cells with intracellular chaotic dynamics to those with oscillatory or fixed-point dynamics. By assigning chaotic and nonchaotic cell types to corresponding positions instead of positional information, intercalary, segmented, and tarsus regeneration are explained coherently. With this assignment of pluripotency to chaotic dynamics, a unified description of regeneration is obtained with some predictive value for new experiments., (Copyright (c) 2009 Wiley-Liss, Inc.)

Background: During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells., Presentation of the Hypothesis: To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic) oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency., Testing the Hypothesis: To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS) analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can examine whether the loss of pluripotency is accompanied by a loss of oscillation., Implications of the Hypothesis: Recovery of pluripotency from determined cells is a long-standing aspiration, from both scientific and clinical perspectives. Our hypothesis suggests a feasible route to recover the potential to differentiate, i.e., by increasing the variety of expressed genes to restore chaotic expression dynamics, as is consistent with the recent generation of induced pluripotent stem (iPS) cells.

Upon their exit from mitosis, mammalian cells enter a G(1) phase during which they acutely sense all sorts of environmental stimuli. On the basis of these signals that they first need to decipher and integrate, they decide whether to undergo division, differentiation, senescence or apoptosis. We questioned whether, despite the complexity of the G(1) regulatory network, simple organizing principles might be identified that could explain how specific input signals are converted into appropriate cell fates. For this purpose, we formulated a mathematical model of the G(1) regulatory network using a simplified description of activities linked to signal transduction, cell growth, cell division and cell death. Bifurcation analysis of the model revealed the existence of multistability between several attractor states corresponding to G(0)-arrest, G(1)-arrest, S-phase entry and apoptosis cell fates. We further unravelled interlinked feedback and feedforward loops within the G(1) regulatory network that drive the signal-dependent transition between G(0) arrest and the other cell fates. Initially, exit from G(0) and progression in early G(1) entail growth factor-dependent activation of an upstream positive feedback loop that activates the cell-growth machinery. Once ribosome synthesis is restored in G(1), a competition develops between a downstream positive feedback loop, which, upon activation, triggers S phase entry, and stress-activated pathways that promote G(1) arrest. If S phase entry prevails over G(1) arrest, cells are sensitized to apoptosis due to stress-induced activation of pro-apoptotic pathways or repression of pro-survival pathways. Thus, the choice between the four possible cell fates in the G(1) phase relies on the flexibly interlinked growth-activatory and division-activatory modules, certain components of which have antagonistic effects on pathways involved in driving apoptosis and G(1) arrest. The final outcome ultimately depends on the context-dependent coordination between the cell-growth and cell-division processes.

We propose a principle of consistency between different hierarchical levels of biological systems. Given a consistency between molecule replication and cell reproduction, universal statistical laws on cellular chemical abundances are derived and confirmed experimentally. They include a power law distribution of gene expressions, a lognormal distribution of cellular chemical abundances over cells, and embedding of the power law into the network connectivity distribution. Second, given a consistency between genotype and phenotype, a general relationship between phenotype fluctuations by genetic variation and isogenic phenotypic fluctuation by developmental noise is derived. Third, we discuss the chaos mechanism for stem cell differentiation with autonomous regulation, resulting from a consistency between cell reproduction and growth of the cell ensemble.

How can a microorganism adapt to a variety of environmental conditions despite the existence of a limited number of signal transduction mechanisms? We show that for any growing cells whose gene expression fluctuate stochastically, the adaptive cellular state is inevitably selected by noise, even without a 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 nonadaptive 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 mechanisms 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.

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.

An equation describing the evolution of phenotypic distribution is derived using methods developed in statistical physics. The equation is solved by using the singular perturbation method, and assuming that the number of bases in the genetic sequence is large. Applying the equation to the mutation-selection model by Eigen provides the critical mutation rate for the error catastrophe. Phenotypic fluctuation of clones (individuals sharing the same gene) is introduced into this evolution equation. With this formalism, it is found that the critical mutation rate is sometimes increased by the phenotypic fluctuations, i.e., noise can enhance robustness of a fitted state to mutation. Our formalism is systematic and general, while approximations to derive more tractable evolution equations are also discussed.

Chemotaxis is ubiquitously performed by bacteria. They sense and move toward a region with a higher concentration of an attractive chemical by changing the rate of tumbling for random walk. We numerically studied several models with internal adaptive dynamics to examine the validity of the condition for chemotaxis proposed by Oosawa and Nakaoka [J. Theor. Biol. 66, 747 (1977)], which states that the time scale of tumbling frequency must be smaller than that of adaptation and greater than that of sensing. Suitable renormalization of the time scales showed that the condition holds for a variety of environments and for both short- and long-term behavior.

Characterizing a cell state by measuring the degree of gene expression as well as its noise has gathered much attention. The distribution of such state values (e.g., abundances of some proteins) over cells has been measured, and is not only a result of intracellular process, but is also influenced by the growth in cell number that depends on the state. By incorporating the growth-death process into the standard Fokker-Planck equation, a nonlinear temporal evolution equation of distribution is derived and then solved by means of eigenfunction expansions. This general formalism is applied to the linear relaxation case. First, when the growth rate of a cell increases linearly with the state value x, the shift of the average x due to the growth effect is shown to be proportional to the variance of x and the relaxation time, similar to the biological fluctuation-response relationship. Second, when there is a threshold value of x for growth, the existence of a critical growth rate, represented again by the variance and the relaxation time, is demonstrated. The relevance of the results to the analysis of biological data on the distribution of cell states, as obtained for example by flow cytometry, is discussed.

The dynamical systems theory of morphogenesis is surveyed, in which positional information is generated through intracellular reaction dynamics and cell-cell interaction. Cells differentiate because of these dynamics. In addition, these differentiated cells form an ordered spatial pattern, which further stabilizes the cellular states, leading to robust morphogenesis and irreversibility in the differentiation. Induction, community effect, gastrulation and activin-controlled artificial tissue-genesis are discussed from the perspective of this theory and the relevance of dynamics of cellular plasticity is stressed.

Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relation to the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics and considering the division and death of cells, the development of cells is studied. Cell differentiation process is found to occur through instability in transient dynamics and cell-cell interaction. In long-term behavior, extinction of multiple cells is repeated, which leads to itinerancy over successive quasi-stable multi-cellular states consisting of different types of cells. By defining the plasticity of a cellular state, it is shown that the plasticity of cells decreases before the extinction of most cell types, from which diversity and plasticity are later recovered. In the following, a decrease of plasticity occurs again, leading to the next extinction. This cycle of diversification and extinction is repeated. Relevance of our results to development and evolution is briefly discussed.

The dose calculation system IMAGINE is being developed keeping in mind remotely supporting external radiation therapy using photon beams. The system is expected to provide an accurate picture of the dose distribution in a patient body, using a Monte Carlo calculation that employs precise models of the patient body and irradiation head. The dose calculation will be performed utilising super-parallel computing at the dose calculation centre, which is equipped with the ITBL computer, and the calculated results will be transferred through a network. The system is intended to support the quality assurance of current, widely carried out radiotherapy and, further, to promote the prevalence of advanced radiotherapy. Prototypes of the modules constituting the system have already been constructed and used to obtain basic data that are necessary in order to decide on the concrete design of the system. The final system will be completed in 2007.

A general relationship between fluctuation and response in a biological system is presented. The fluctuation is given by the variance of some quantity, whereas the response is given as the average change of that quantity for a given parameter change. We propose a relationship where the two are proportional, in a similar way to the fluctuation-dissipation theorem in physics. By studying an evolution experiment where fluorescence of protein in bacteria increases, we confirm our relation by observing a positive correlation between the speed of fluorescence evolution and the phenotypic fluctuation of the fluorescence over clone bacteria. The generality of the relationship as well as its relevance to evolution is discussed.

The origin and robustness of morphogenesis are studied by dynamical system modeling of a cell society, in which cells possessing internal chemical reaction dynamics interact with each other through their mutual interaction with diffusive chemicals in a two-dimensional medium. It is found that stem-type cells differentiate into various cell types (where a cell 'type' is defined by a type of intra-cellular dynamics) due to a dynamic instability caused by cell-cell interactions in a manner described by the isologous diversification theory. The differentiations are spatially regulated by the concentration of chemicals in the medium, while the chemical concentrations are locally influenced by the intra-cell dynamics. Through this reciprocal relationship, chemical concentrations come to exhibit spatial variation as differentiated cell types begin to emerge, and as a result the regulation exercised by the chemical concentrations become spatially inhomogeneous. This reinforces the process of differentiation, through which spatial patterns of differentiated cells appear. Within this reciprocal relationship, the concentration gradients are read and interpreted by the cell as positional information. A spatial order of cells realized in this process represents a stable state of the system governed by this reciprocal relationship, and that the developmental process through which this state is realized is robust with respect to perturbations. The dependence of the morphogenesis on history and the community effect in cell differentiation are also discussed.

The autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as an extinction of molecule species alternately in the autocatalytic reaction loop. Phase transition to this state with changes of the system size and flow is studied, while a single-molecule switch of the molecule distributions is reported. The relevance of the results to intracellular processes is briefly discussed.

By introducing a dynamical system model of a multicellular system, it is shown that an organism with a variety of differentiated cell types and a complex pattern emerges through cell-cell interactions even without postulating any elaborate control mechanism. Such an organism is found to maintain a larger growth speed as an ensemble, by achieving a cooperative use of resources, than do simple homogeneous cells, which behave "selfishly." This suggests that the emergence of multicellular organisms with complex organization is a necessity in evolution. According to our theoretical model, there initially appear multipotent stem cells, which undergo stochastic differentiation to other cell types. With development and differentiation, both the chemical diversity and the complexity of intra-cellular dynamics are decreased, as a general consequence of our system. Robustness of the developmental process is also confirmed.

Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems can exhibit complex pattern formation with spontaneous cell differentiation. Such systems employ a "cooperative" use of resources and maintain a larger growth speed than simple cell systems, which exist in a homogeneous state and behave "selfishly." The relevance of the diversity of chemicals and reaction dynamics to the growth of a multicellular organism is demonstrated. Chaotic biochemical dynamics are found to provide the multipotency of stem cells.

To understand an architecture of a living system, "Tile Automaton" is introduced as an abstract model of chemical reaction of molecules scattered over a space. The model consists of tiles of various shapes that stand for molecules. The chemical reaction, induced by the collisions of tiles, is represented by the change of the tile shapes. The rules for reaction are deterministic, and the evolution of the system strongly depends on mutual spatial relationship among tiles. The evolution often leads to self-organization of a "factory," a set of tiles that produces tiles continuously and keeps its structure. Several interesting phenomena, such as a deformation or a division of a factory, are also observed. It is proposed that the formation of the factory is due to the interference between different aspects of tiles - the shape and the motion. The concept of "entanglement" is introduced as a mechanism of living systems.

The origin of multicellular organisms and the mechanism of development in cell societies are studied by choosing a model with intracellular biochemical dynamics allowing for oscillations, cell-cell interaction through diffusive chemicals on a two-dimensional grid, and state-dependent cell adhesion. Cells differentiate due to a dynamical instability, as described by our "isologous diversification" theory. A fixed spatial pattern of differentiated cells emerges, where spatial information is sustained by cell-cell interactions. This pattern is robust against perturbations. With an adequate cell adhesion force, active cells are release that form the seed of a new generation of multicellular organisms, accompanied by death of the original multicellular unit as a halting state. It is shown that the emergence of multicellular organisms with differentiation, regulation, and life cycle is not an accidental event, but a natural consequence in a system of replicating cells with growth.

A dynamic model for cell differentiation, where cells with internal chemical reaction dynamics interact with each other and replicate was studied. It led to spontaneous differentiation of cells and determination, as discussed in the isologous diversification. The following features of the differentiation were obtained: (1) hierarchical differentiation from a 'stem' cell to other cell types, with the emergence of the interaction-dependent rules for differentiation; (2) global stability of an ensemble of cells consisting of several cell types, that were sustained by the emergent, autonomous control on the rate of differentiation; (3) existence of several cell colonies with different cell-type distributions. The results provide a novel viewpoint on the origin of a complex cell society, while relevance to some biological problems, especially to the hemopoietic system, is also discussed.

An isologous diversification theory for cell differentiation is processed, based on simulations of interacting cells with biochemical networks and the cell division process following consumption of some chemicals. According to the simulations of the interaction-based dynamical systems model, the following scenario of the cell differentiation is proposed. (1) Up to some threshold number, divisions bring about almost identical cells with synchronized biochemical oscillations. (2) As the number is increased, the oscillations lose synchrony, leading to groups of cells with different phases of oscillations. (3) Amplitudes of oscillation and averaged chemical compositions start to differ by groups of cells. The differentiated behavior of states is transmitted to daughter cells. (4) Recursivity is formed so that the daughter cells keep the identical chemical character. This "memory" is made possible through the transfer of initial conditions. (5) Successive differentiation proceeds. The mechanism of tumor cell formation, origin of stem cells, anomalous differentiation by transplantations, apoptosis and other features of cell differentiation process are also discussed, with some novel predictions.

Estrogen receptors are key elements in the mechanisms of action of estrogenic hormones. Models of how estrogens and their receptors interact and subsequently modify gene expression should be reevaluated to explain new data currently available. The following review discusses nuclear localization, DNA binding, and protein structural changes of the estrogen receptor induced by estrogen binding. We also discuss how these phenomena relate to the induction of changes in gene expression.

A lung model was constructed to examine the effects of the following factors on the phase IV of a single-breath N2 washout: the lung's elasticity change with age, closing pressure (CP), regional volume (Volr) distribution, pleural pressure, and gradient (Grad). The analysis revealed 1) when the CP was assumed to be + 1.0 cmH2O, predicted changes in closing capacity (CC) due to alterations in elasticity agreed with previous experimental results for individuals above 40 yr; for younger age groups, the predicted values were apparently larger, suggesting the CP may be near zero; 2) difference in Volr distribution alone caused alterations in CC and the slope of phase IV; 3) for 1 cmH2O elevation of CP, closing capacity /total lung capacity (CC/TLC) was predicted to increase about 8%; 4) for 0.1 cmHiO/cm Grad increase, CC/TLC was predicted to rise approximately 7%. In conclusion, multiple factors affect phase IV.