arXiv subjects

Namiko Mitarai

Publications and source records attributed to Namiko Mitarai.

At least 19 recordsLinked to original sources

arXiv2023

Sustainable Diversity of Phage-Bacteria Systems

Bacteriophages are central to microbial ecosystems for balancing bacterial populations and promoting evolution by applying strong selection pressure. Here we review some of the known aspects that modulate phage-bacteria interaction in a way that naturally promotes their coexistence. We focus on the modulations that arise from structural, physical, or physiological constraints. We argue they should play roles in many phage-bacteria systems providing sustainable diversity.

q-bio.PE↗

arXiv2021

A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined

Numerous living systems are hierarchically organised, whereby replicating components are grouped into reproducing collectives -- e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by $N$) and the mutation rate of components ($m$) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing $N$ or $m$ accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: $Nm^α$ is a constant, where scaling exponent $α$ depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although $N$ and $m$ have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if $m$ is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically-organised replicating systems.

q-bio.PE↗

arXiv2020

When to wake up? The optimal waking-up strategies for starvation-induced persistence

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time exhibits a discontinuous transition when the severeness of the antibiotic is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.

physics.bio-ph↗

arXiv2020

Dynamics of bacterial populations under the feast-famine cycles

Bacterial populations in natural conditions are expected to experience stochastic environmental fluctuations, and in addition, environments are affected by bacterial activities since they consume substrates and excrete various chemicals. We here study possible outcomes of population dynamics and evolution under the repeated cycle of substrate-rich conditions and starvation, called the "feast-famine cycle", by a simple stochastic model with the trade-off relationship between the growth rate and the growth yield or the death rate. In the model, the feast (substrate-rich) period is led by a stochastic substrate addition event, while the famine (starvation) period is evoked because bacteria use the supplied substrate. Under the repeated feast-famine cycle, the bacterial population tends to increase the growth rate, even though that tends to decrease the total population size due to the trade-off. Analysis of the model shows that the ratio between the growth rate and the death rate becomes the effective fitness of the population. Hence, the functional form of the trade-off between the growth and death rate determines if the bacterial population eventually goes extinct as an evolutionary consequence. We then show that the increase of the added substrate in the feast period can drive the extinction faster. Overall, the model sheds light on non-trivial possible outcomes under repeated feast-famine cycles.

q-bio.PE↗

arXiv2019

Finite response time in stripe formation by bacteria with density-suppressed motility

Genetically engineered bacteria to increase the tumbling frequency of the run-and-tumble motion for the higher local bacterial density form visible stripe pattern composed of successive high and low density regions on an agar plate. We propose a model that includes a simplified regulatory dynamics of the tumbling frequency in individual cells to clarify the role of finite response time. We show that the time-delay due to the response dynamics results in the instability in a homogeneous steady state allowing a pattern formation. For further understanding, we propose a simplified two-state model that allows us to describe the response time dependence of the instability analytically. We show that the instability occurs at long wave length as long as the response time is comparable with the tumbling timescale and the non-linearity of the response function to the change of the density is high enough. The minimum system size to see the instability grows with the response time $τ$, proportional to $\sqrtτ$ in the large delay limit.

q-bio.CB↗

arXiv2017

Deterministic extinction by mixing in cyclically competing species

We consider a cyclically competing species model on a ring with global mixing at finite rate, which corresponds to the well-known Lotka-Volterra equation in the limit of infinite mixing rate. Within a perturbation analysis of the model from the infinite mixing rate, we provide analytical evidence that extinction occurs deterministically at sufficiently large but finite values of the mixing rate for any species number $N\ge3$. Further, by focusing on the cases of rather small species numbers, we discuss numerical results concerning the trajectories toward such deterministic extinction, including global bifurcations caused by changing the mixing rate.

q-bio.PE↗

arXiv2017

Characterization of phase transitions in a model ecosystem of sessile species

We consider a model ecosystem of sessile species competing for space. In particular, we consider the system introduced in [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)] where species compete according to a fixed interaction network with links determined by a Bernoulli process. In the limit of a small introduction rate of new species, the model exhibits a discontinuous transition from a high-diversity state to a low-diversity state as the interaction probability between species, $γ$, is increased from zero. Here we explore the effects of finite introduction rates and system-size on the phase transition by utilizing efficient parallel computing. We find that the low state appears for $γ>γ_c$. As $γ$ is increased further, the high state approaches to the low state, suggesting the possibility that the two states merge at a high $γ$. We find that the fraction of time spent in the high state becomes longer with higher introduction rates, but the availability of the two states is rather insensitive to the value of the introduction rate. Furthermore we establish a relation between the introduction rate and the system size, which preserves the probability for the system to remain in the high-diversity state.

q-bio.PE↗

arXiv2016

Bifurcation of Transition Paths Induced by Coupled Bistable Systems

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example, and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.

q-bio.MN↗

arXiv2016

Three is much more than two in coarsening dynamics of cyclic competitions

The classical game of rock-paper-scissors have inspired experiments and spatial model systems that address robustness of biological diversity. In particular the game nicely illustrates that cyclic interactions allow multiple strategies to coexist for long time intervals. When formulated in terms of a one-dimensional cellular automata, the spatial distribution of strategies exhibits coarsening with algebraically growing domain size over time, while the two-dimensional version allows domains to break and thereby opens for long-time coexistence. We here consider a quasi-one-dimensional implementation of the cyclic competition, and study the long-term dynamics as a function of rare invasions between parallel linear ecosystems. We find that increasing the complexity from two to three parallel subsystems allows a transition from complete coarsening to an active steady state where the domain size stays finite. We further find that this transition happens irrespective of whether the update is done in parallel for all sites simultaneously, or done randomly in sequential order. In both cases the active state is characterized by localized bursts of dislocations, followed by longer periods of coarsening. In the case of the parallel dynamics, we find that there is another phase transition between the active steady state and the coarsening state within the three-line system when the invasion rate between the subsystems is varied. We identify the critical parameter for this transition, and show that the density of active boundaries have critical exponents that are consistent with the directed percolation universality class. On the other hand, numerical simulations with the random sequential dynamics suggest that the system may exhibit an active steady state as long as the invasion rate is finite.

nlin.CG↗

arXiv2015

Dynamic competition between transcription initiation and repression: Role of nonequilibrium steps in cell-to-cell heterogeneity

Transcriptional repression may cause transcriptional noise by a competition between repressor and RNA polymerase binding. Although promoter activity is often governed by a single limiting step, we argue here that the size of the noise strongly depends on whether this step is the initial equilibrium binding or one of the subsequent unidirectional steps. Overall, we show that nonequilibrium steps of transcription initiation systematically increase the cell-to-cell heterogeneity in bacterial populations. In particular, this allows also weak promoters to give substantial transcriptional noise.

q-bio.MN↗

arXiv2015

Food web assembly rules

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

q-bio.PE↗

arXiv2014

Fixation in cyclically competing species on a directed graph with quenched disorder

A simple model of cyclically competing species on a directed graph with quenched disorder is proposed as an extension of the rock-paper-scissors model. By assuming that the effects of loops in a directed random graph can be ignored in the thermodynamic limit, it is proved for any finite disorder that the system fixates to a frozen configuration when the species number $s$ is larger than the spatial connectivity $c$, and otherwise stays active. Nontrivial lower and upper bounds for the persistence probability of a site never changing its state are also analytically computed. The obtained bounds and numerical simulations support the existence of a phase transition as a function of disorder for $1<c_l(s)\le c <s$, with a $s$-dependent threshold of the connectivity $c_l(s)$.

cond-mat.stat-mech↗

arXiv2014

Disturbance accelerates the transition from low- to high- diversity state in a model ecosystem

The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically removes individuals from the system, and the created empty sites are re-colonized by neighbouring species. We show that the stable high-diversity state, maintained by occasional cyclic species interactions that create isolated patches of meta-populations, is robust against small disturbance. We further demonstrate that finite disturbance can accelerate the transition from the low- to high-diversity state by helping creation of small patches through diffusion of boundaries between species with stand-off relation.

q-bio.PE↗

arXiv2013

Control of ribosome traffic by position-dependent choice of synonymous codons

Messenger RNA encodes a sequence of amino acids by using codons. For most amino acids there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the messenger RNA (mRNA) but also might have an effect on nearby ribosomes by affecting the appearance of "traffic jams" where multiple ribosomes collide and form queues. To test this "context effect" further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild type sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the wild type sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.

q-bio.SC↗

arXiv2013

Experimental observation of shear thickening oscillation

We report experimental observation of the shear thickening oscillation, i.e. the spontaneous macroscopic oscillation in the shear flow of severe shear thickening fluid. The shear thickening oscillation is caused by the interplay between the fluid dynamics and the shear thickening, and has been predicted theoretically by the present authors using a phenomenological fluid dynamics model for the dilatant fluid, but never been reported experimentally. Using a density-matched starch-water mixture, in the cylindrical shear flow of a few centimeters flow width, we observed strong vibrations of the frequency around 20 Hz, which is consistent with our theoretical prediction.

physics.flu-dyn↗

arXiv2013

Entrainment of noise-induced and limit cycle oscillators under weak noise

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed point is linearly stable with complex eigenvalues and addition of noise gives oscillations around the fixed point with fluctuating amplitude. We investigate how each class of model behaves under the external periodic forcing, taking the well-studied van der Pol equation as an example. We find that, when the forcing is additive, the noise-induced oscillator can show only one-to-one entrainment to the external frequency, in contrast to the limit cycle oscillator which is known to entrain to any ratio. When the external forcing is multiplicative, on the other hand, the noise-induced oscillator can show entrainment to a few ratios other than one-to-one, while the limit cycle oscillator shows entrain to any ratio. The noise blurs the entrainment in general, but clear entrainment regions for limit cycles can be identified as long as the noise is not too strong.

q-bio.QM↗

arXiv2012

Circuit architecture explains functional similarity of bacterial heat shock responses

Heat shock response is a stress response to temperature changes and a consecutive increase in amounts of unfolded proteins. To restore homeostasis, cells upregulate chaperones facilitating protein folding by means of transcription factors (TF). We here investigate two heat shock systems: one characteristic to gram negative bacteria, mediated by transcriptional activator sigma32 in E. coli, and another characteristic to gram positive bacteria, mediated by transcriptional repressor HrcA in L. lactis. We construct simple mathematical model of the two systems focusing on the negative feedbacks, where free chaperons suppress sigma32 activation in the former, while they activate HrcA repression in the latter. We demonstrate that both systems, in spite of the difference at the TF regulation level, are capable of showing very similar heat shock dynamics. We find that differences in regulation impose distinct constrains on chaperone-TF binding affinities: the binding constant of free sigma32 to chaperon DnaK, known to be in 100 nM range, set the lower limit of amount of free chaperon that the system can sense the change at the heat shock, while the binding affinity of HrcA to chaperon GroE set the upper limit and have to be rather large extending into the micromolar range.

physics.bio-ph↗

arXiv2012

Emergence of diversity in a model ecosystem

The biological requirements for an ecosystem to develop and maintain species diversity are in general unknown. Here we consider a model ecosystem of sessile and mutually excluding organisms competing for space [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)]. The competition is controlled by an interaction network with fixed links chosen by a Bernoulli process. New species are introduced in the system at a predefined rate. In the limit of small introduction rates, the system becomes bistable and can undergo a phase transition from a state of low diversity to high diversity. We suggest that patches of isolated meta-populations formed by the collapse of cyclic relations are essential for the transition to the state of high diversity.

q-bio.PE↗