Kunihiko Kaneko

Long-range correlation and partial 1/fα spectrum in a noncoding DNA sequence

Mutual information function, which is an alternative to correlation function for symbolic sequences, and a symbolic spectrum are calculated for a human DNA sequence containing mostly intron segments, those that do not code for proteins. It is observed that the mutual information function of this sequence decays very slowly, and the correlation length is extremely long (at least 800 bases). The symbolic spectrum of the sequence at very low frequencies can be approximated by 1/fα, where f is the frequency and α ranges from 0.5 to 0.85. It is suggested that the existence of the repetitive patterns in the sequence is mainly responsible for the observed long-range correlation. A possible connection between this long-range correlation and those in music notes is also briefly discussed.

A Dynamical-Systems View of Stem Cell Biology

During development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Stem cells, however, keep their potential to both proliferate and differentiate. A very important issue then is to understand the characteristics that distinguish stem cells from other cell types and allow them to conduct stable proliferation and differentiation. Here, we review relevant dynamical-systems approaches to describe the state transition between stem and differentiated cells, with an emphasis on fluctuating and oscillatory gene expression levels, as these represent the specific properties of stem cells. Relevance between recent experimental results and dynamical-systems descriptions of stem cell differentiation is also discussed.

Evolution of Robustness to Noise and Mutation in Gene Expression Dynamics

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

Ubiquity of log-normal distributions in intra-cellular reaction dynamics

The discovery of two fundamental laws concerning cellular dynamics with recursive growth is reported. Firstly, the chemical abundances measured over many cells were found to obey a log-normal distribution and secondly, the relationship between the average and standard deviation of the abundances was found to be linear. The ubiquity of these laws was explored both theoretically and experimentally. By means of a model with a catalytic reaction network, the laws were shown to exist near a critical state with efficient self-reproduction. Additionally, by measuring distributions of fluorescent proteins in bacteria cells, the ubiquity of log-normal distribution of protein abundances was confirmed. Relevance of these findings to cellular function and biological plasticity is briefly discussed.

Oscillatory Protein Expression Dynamics Endows Stem Cells with Robust Differentiation Potential

The lack of understanding of stem cell differentiation and proliferation is a fundamental problem in developmental biology. Although gene regulatory networks (GRNs) for stem cell differentiation have been partially identified, the nature of differentiation dynamics and their regulation leading to robust development remain unclear. Herein, using a dynamical system modeling cell approach, we performed simulations of the developmental process using all possible GRNs with a few genes, and screened GRNs that could generate cell type diversity through cell-cell interactions. We found that model stem cells that both proliferated and differentiated always exhibited oscillatory expression dynamics, and the differentiation frequency of such stem cells was regulated, resulting in a robust number distribution. Moreover, we uncovered the common regulatory motifs for stem cell differentiation, in which a combination of regulatory motifs that generated oscillatory expression dynamics and stabilized distinct cellular states played an essential role. These findings may explain the recently observed heterogeneity and dynamic equilibrium in cellular states of stem cells, and can be used to predict regulatory networks responsible for differentiation in stem cell systems.

Noise-driven growth rate gain in clonal cellular populations

Significance Differences between individuals exist even in the absence of genetic differences, e.g., in identical twins. Over the last decade, experiments have shown that even genetically identical microbes exhibit large cell-to-cell differences. In particular, the timing of cell division events is highly variable between single bacterial cells. The effect of this variability on long-term growth and survival of bacteria, however, remains elusive. Here, we present a striking finding showing that a bacterial population grows faster on average than its constituent cells. To explain this counterintuitive result, we present a mathematical model that precisely predicts our measurements. Furthermore, we show an empirical growth law that constrains the maximal growth rate of Escherichia coli. Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a “speed limit” for proliferation.

Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness

Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.

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

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.

Fluctuation and response in biology

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.

Dynamical systems modeling of Continuous Flash Suppression

Continuous Flash Suppression (CFS) is a technique in which a stationary image in one eye can be reliably suppressed by rapid presentation of different flashing images in the other. In this paper we address why flashing stimuli modulate the visibility of the stimuli. We determine, in particular, which type of neural network is sufficient for the modulation of the dominance duration, assuming that elemental units are endowed with reciprocal inhibition and adaptation. We show that the model introduced by Wilson (2007) reproduces flash suppression, which is considered to be involved in CFS, but does not reproduce CFS. We then extend the model by including a stimulus feature dimension. With this extension, we found that the model accounts for the modulation of visibility observed in CFS. In addition, this model captured some defining characteristics of CFS such as dependence on flash interval and the depth of suppression. Our findings suggest that a network with inhibition and adaptation including feature dimension provides a crucial mechanism for the modulation of the dominance duration in CFS.