arXiv subjects

Takahiro Sakaue

Publications and source records attributed to Takahiro Sakaue.

At least 19 recordsLinked to original sources

arXiv2026

The Polymer Physics of Kinetoplast DNA as a Polymerised Membrane

We analyze the conformational and dynamical properties of the kinetoplast DNA (kDNA), a massive sheet-like structure made from thousands of circular DNA molecules, found in the mitochondrion of certain parasites. The connectivity between circular DNA molecules is achieved by topological linking, hence, the kDNA may be regarded as a naturally occurring two-dimensional version of Olympic gels, whose physical properties are yet to be understood. We propose that the basic aspects in the large scale behaviors of kDNA could be described by the physics of polymerized membrane. Our analysis indicates the relevance of the hydrodynamic interactions in the dynamics of kDNA in aqueous solution. We demonstrate that the predicted dynamical scaling scenario captures various experimental data recently obtained from {\it in vitro} imaging experiments in a unified manner. We also provide an estimate for the in-plane elastic modulus of kDNA, whose magnitude agrees well with recent measurements.

cond-mat.soft↗

arXiv2026

Violation of the method of images in non-Markovian processes and its connection to stochastic thermodynamics

We discuss a failure of the wide-spread method of images solution to describe the time evolution of probability distribution in diffusive processes with memory. For a path that touches a target during stochastic evolution, we define its conjugate twin of reflected path and show that their path probability ratio obeys a relation analogous to the fluctuation theorem. For systems reducible to the generalized Langevin equation with the fluctuation-dissipation relation, we suggest thermodynamic interpretation of the processes, which provides a quantitative basis as well as an intuitive physical picture on how and why the method of images breaks down for non-Markovian processes.

cond-mat.stat-mech↗

arXiv2026

Compounding formula approach to chromatin and active polymer dynamics

Active polymers are ubiquitous in nature, and often kicked by persistent noises that break detailed balance. In order to capture the out-of-equilibrium dynamics of such active polymers, we propose a simple yet reliable analytical framework based on a compounding formula. Connecting polymeric dynamics to the isolated monomeric behavior via the notion of tension propagation, the formula allows us to clarify rich scaling scenarios alongside corresponding intuitive physical pictures. We demonstrate distinctive transient and steady-state scalings due to the non-Markovian nature of the active noise. Aside from a paradigmatic example of an active Rouse polymer, we expect the framework to be applicable to wide variety of spatially extended systems including more general polymers (crumpled globule, semiflexible polymers etc), fluctuation of growing interface, and an array of particles in single-file configuration.

cond-mat.soft↗

arXiv2026

Physics of active polymers: scaling analysis via a compounding formula

Active polymeric systems exhibit a rich spectrum of non-equilibrium phenomena arising from stochastic forces that explicitly break detailed balance. Despite the rapid growth of experimental and numerical studies, analytical progress remains limited. To date, theoretical understanding relies largely on variants of the active Rouse model, whose formal solutions, though exact, are often obscured by summations over Rouse modes and therefore provide limited direct physical insight. In this work, we develop a transparent scaling theory that captures the tagged-monomer mean-squared displacement (MSD) in active polymers through a compounding formula: the MSD of a monomer in the chain is expressed as that of an isolated active particle, modulated by a connectivity factor encoding tension propagation along the polymer backbone. This approach isolates the role of activity from that of polymer connectivity and reveals the emergent dynamical regimes in a physically intuitive manner. We test the scaling predictions against exact calculations for a broad class of generalized active polymer models driven by diverse noise statistics. The agreement demonstrates the robustness of the scaling framework across microscopic details. Our results provide a simple and extensible theoretical structure that can be applied to complex and analytically intractable active polymer systems, thereby offering a unifying perspective on non-equilibrium polymer dynamics.

cond-mat.soft↗

arXiv2025

Note on two-point mean square displacement

When probe molecules of interest are embedded in a container or aggregate under stochastic motion, one needs to rely on the so-called two-point mean square displacement (MSD) measurement to extract the intrinsic mobility of the probes. We discuss two versions, based on the time series of relative vector or distance between two probes, and summarize their basic properties compared to the standard MSD. We also propose a way to extract (i) the non-Gaussianity in the displacement statistics and (ii) the motional correlation between probes from the two-point MSD. The results are presented not only for independent probes, but also for intramolecular probes within a long polymer, which could be useful in quantifying the dynamics of chromatin loci in living cell nucleus.

cond-mat.soft↗

arXiv2024

Phase separation in soft repulsive polymer mixtures: foundation and implication for chromatin organization

Given the wide range of length scales, the analysis of polymer systems often requires coarse-graining, for which various levels of description may be possible depending on the phenomenon under consideration. Here, we provide a super-coarse grained description, where polymers are represented as a succession of mesosopic soft beads which are allowed to overlap with others. We then investigate the phase separation behaviors in a mixture of such homopolymers based on mean-field theory, and discuss universal aspects of the miscibility phase diagram in comparison with the numerical simulation. We also discuss an extension of our analysis to mixtures involving random copolymers, which might be interesting in the context of chromatin organization in a cell nucleus.

cond-mat.soft↗

arXiv2024

Method of Filtration in first passage time problems

Statistics of stochastic processes are crucially influenced by the boundary conditions. In one spatial dimension, for example, the first passage time distribution in semi-infinite space (one absorbing boundary) is markedly different from that in a finite interval with two absorbing boundaries. Here, we propose a method, which we refer to as a method of filtration, that allows us to construct the latter from only the knowledge of the former. We demonstrate that our method yields two solution forms, a method of eigenfunction expansion-like form and a method of image-like form. In particular, we argue that the latter solution form is a generalization of the method of image applicable to a stochastic process for which the method of image generally does not work, e.g., the Ornstein-Uhlenbeck process.

math-ph↗

arXiv2024

Chromatin remodeling due to transient-link-and-pass activity enhances subnuclear dynamics

Spatiotemporal coordination of chromatin and subnuclear compartments is crucial for cells. Numerous enzymes act inside nucleus\textemdash some of those transiently link and pass two chromatin segments. Here we study how such an active perturbation affects fluctuating dynamics of an inclusion in the chromatic medium. Using numerical simulations and a versatile effective model, we categorize inclusion dynamics into three distinct modes. The transient-link-and-pass activity speeds up inclusion dynamics by affecting a slow mode related to chromatin remodeling, viz., size and shape of the chromatin meshes.

physics.bio-ph↗

arXiv2024

Mechanisms of DNA-mediated allostery

Proteins often regulate their activities via allostery - or action at a distance - in which the binding of a ligand at one binding site influences the affinity for another ligand at a distal site. Although less studied than in proteins, allosteric effects have been observed in experiments with DNA as well. In these experiments two or more proteins bind at distinct DNA sites and interact indirectly with each other, via a mechanism mediated by the linker DNA molecule. We develop a mechanical model of DNA/protein interactions which predicts three distinct mechanisms of allostery. Two of these involve an enthalpy-mediated allostery, while a third mechanism is entropy driven. We analyze experiments of DNA allostery and highlight the distinctive signatures allowing one to identify which of the proposed mechanisms best fits the data.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium diffusion of active particles bound to a semi-flexible polymer network: simulations and fractional Langevin equation

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question is to quantitatively explain how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active particle is connected with multiple semi-flexible filaments. Our Langevin dynamics simulations show that the active cross-linker displays super- and sub-diffusive athermal motion with a time-dependent anomalous exponent $α$. In such viscoelastic feedback, the active particle always has superdiffusion with $α=3/2$ at times shorter than the self-propulsion time ($τ_A$). At times greater than $τ_A$, the subdiffusion emerges with $α$ bounded between $1/2$ and $3/4$. Remarkably, the active subdiffusion is reinforced as the active propulsion (Pe) is more vigorous. In the high-Pe limit, the athermal fluctuation in the stiff filament eventually leads to $α=1/2$, which can be misinterpreted with the thermal Rouse motion in a flexible chain. We demonstrate that the motion of active particles cross-linking a network of semi-flexible filaments can be governed by a fractional Langevin equation combined with fractional Gaussian noise and an Ornstein-Uhlenbeck noise. We analytically derive the velocity autocorrelation function and mean-squared displacement of the model, explaining their scaling relations as well as the prefactors. We find that there exist the threshold Pe ($\mathrm{Pe}^*$) and cross-over times ($τ^*$ and $τ^\dagger$) above which the active viscoelastic dynamics emerge on the timescales of $τ^* \lesssim t \lesssim τ^\dagger$. Our study may provide a theoretical insight into various nonequilibrium active dynamics in intracellular viscoelastic environments.

cond-mat.soft↗

arXiv2023

First passage time statistics of non-Markovian random walker: Onsager's regression hypothesis approach

First passage time plays a fundamental role in dynamical characterization of stochastic processes. Crucially, our current understanding on the problem is almost entirely relies on the theoretical formulations, which assume the processes under consideration are Markovian, despite abundant non-Markovian dynamics found in complex systems. Here we introduce a simple and physically appealing analytical framework to calculate the first passage time statistics of non-Markovian walkers grounded in a fundamental principle of nonequilibrium statistical physics that connects the fluctuations in stochastic system to the macroscopic law of relaxation. Pinpointing a crucial role of the memory in the first passage time statistics, our approach not only allows us to confirm the non-trivial scaling conjectures for fractional Brownian motion, but also provides a formula of the first passage time distribution in the entire time scale, and establish the quantitative description of the position probability distribution of non-Markovian walkers in the presence of absorbing boundary.

cond-mat.stat-mech↗

arXiv2022

Mechanical properties of Nucleic Acids and the non-local Twistable Wormlike Chain model

Mechanical properties of nucleic acids play an important role in many biological processes which often involve physical deformations of these molecules. At sufficiently long length scales (say above $\sim 20-30$ base pairs) the mechanics of DNA and RNA double helices is described by a homogeneous Twistable Wormlike Chain (TWLC), a semiflexible polymer model characterized by twist and bending stiffnesses. At shorter scales this model breaks down for two reasons: the elastic properties become sequence-dependent and the mechanical deformations at distal sites gets coupled. We discuss in this paper the origin of the latter effect using the framework of a non-local Twistable Wormlike Chain (nlTWLC). We show, by comparing all-atom simulations data for DNA and RNA double helices, that the non-local couplings are of very similar nature in these two molecules: couplings between distal sites are strong for tilt and twist degrees of freedom and weak for roll. We introduce and analyze a simple double-stranded polymer model which clarifies the origin of this universal distal couplings behavior. In this model, referred to as the ladder model, a nlTWLC description emerges from the coarsening of local (atomic) degrees of freedom into angular variables which describe the twist and bending of the molecule. Differently from its local counterpart, the nlTWLC is characterized by a length-scale-dependent elasticity. Our analysis predicts that nucleic acids are mechanically softer at the scale of a few base pairs and are asymptotically stiffer at longer length scales, a behavior which matches experimental data.

cond-mat.stat-mech↗

arXiv2022

Coarse-graining DNA: Symmetry, non-local elasticity and persistence length

While the behavior of double stranded DNA at mesoscopic scales is fairly well understood, less is known about its relation to the rich mechanical properties in the base-pair scale, which is crucial, for instance, to understand DNA-protein interactions and the nucleosome diffusion mechanism. Here, by employing the rigid base pair model, we connect its microscopic parameters to the persistence length. Combined with all-atom molecular dynamic simulations, our scheme identifies relevant couplings between different degrees of freedom at each coarse-graining step. This allows us to clarify how the scale dependence of the elastic moduli is determined in a systematic way encompassing the role of previously unnoticed off site couplings between deformations with different parity.

cond-mat.soft↗

arXiv2021

How enzymatic activity is involved in chromatin organization

Spatial organization of chromatin plays a critical role in genome regulation. Various types of affinity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways. Here, we construct a polymer physics model following the mechanistic scheme of Topoisomerase-II, an enzyme resolving topological constraints of chromatin, and investigate its role on interphase chromatin organization. Our computer simulations demonstrate Topoisomerase-II's ability to phase separate chromatin into eu- and heterochromatic regions with a characteristic wall-like organization of the euchromatic regions. Exploiting a mean-field framework, we argue that the ability of the euchromatic regions crossing each other due to enzymatic activity of Topoisomerase-II induces this phase separation. Motivated from a recent experimental observation on different structural states of the eu- and the heterochromatic units, we further extend our model to a bidisperse setting and show that the characteristic features of the enzymatic activity driven phase separation survives there. The existence of these characteristic features, even under the non-localized action of the enzyme, highlights the critical role of enzymatic activity in chromatin organization, and points out the importance of further experiments along this line.

physics.bio-ph↗

arXiv2021

Fold analysis of crumpled sheet using micro computed tomography

Hand crumpled paper balls involve intricate structure with a network of creases and vertices, yet show simple scaling properties, which suggests self-similarity of the structure. We investigate the internal structure of crumpled papers by the micro computed tomography (micro-CT) without destroying or unfolding them. From the reconstructed three dimensional data, we examine several power laws for the crumpled square sheets of paper of the sizes $L=50\sim 300$ mm, and obtain the mass fractal dimension $D_M = 2.7\pm 0.1$ by the relation between the mass and the radius of gyration of the balls, and the fractal dimension $2.5\lesssim d_f \lesssim 2.8$ for the internal structure of each crumpled paper ball by the box counting method in the real space and the structure factors in the Fourier space; The data for the paper sheets are consistent with $D_M = d_f$, suggesting that the self-similarity in the structure of each crumpled ball gives rise to the similarity among the balls with different sizes. We also examine the cellophane sheets and the aluminium foils of the size $L=200$ mm and obtain $2.6\lesssim d_f\lesssim 2.8$ for both of them. The micro-CT also allows us to reconstruct 3-d structure of a line drawn on the crumpled sheets of paper. The Hurst exponent for the root mean square displacement along the line is estimated as $H\approx 0.9$ for the length scale shorter than the scale of the radius of gyration, beyond which the line structure becomes more random with $H\sim 0.5$.

cond-mat.soft↗

arXiv2021

Quantifying the mobility of chromatin during embryogenesis: Nuclear size matters

Chromatin moves dynamically inside the cell nucleus, and its motion is often correlated with gene functions such as DNA recombination and transcription. A recent study has shown that during early embryogenesis of the nematode, Caenorhabiditis elegans, the chromatin motion markedly decreases. However, the underlying mechanism for this transition has yet to be elucidated. We systematically investigated the impact of nuclear size to demonstrate that it is indeed a decisive factor in chromatin mobility. To this end, we established a method to quantify chromatin motion inside the nucleus, while excluding the contribution of the movement of the nucleus itself, which allowed us to extract the intrinsic mean-squared displacement (iMSD) of individual chromosomal loci in moving nuclei from the correlated motion of two loci. We show that a simple theoretical description, which takes into account the topological constraints of chromatin polymers, can quantitatively describe the relationship between the nucleus size and the chromatin motion in vivo. Our results emphasize a regulatory role of nuclear size in restricting chromatin motion, and a generic polymer physics model plays a guiding role in capturing this essential feature.

physics.bio-ph↗

arXiv2020

Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers

Understanding how entanglements affect the behaviour of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatio-temporal entanglement structures from the pair-wise displacement correlation of entangled chains. By applying this method to large-scale Molecular Dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainment between entangled chains. We show that DEA is a powerful and sensitive probe that reveals previously unnoticed, and architecture-dependent, spatio-temporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis which provides previously under-appreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyse the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.

cond-mat.soft↗

arXiv2020

Persistence Homology Of Entangled Rings

Topological constraints (TCs) between polymers determine the behaviour of complex fluids such as creams, oils and plastics. Most of the polymer solutions used every day life employ linear chains; their behaviour is accurately captured by the reptation and tube theories which connect microscopic TCs to macroscopic viscoelasticity. On the other hand, polymers with non-trivial topology, such as rings, hold great promise for new technology but pose a challenging problem as they do not obey standard theories; additionally, topological invariance -- i.e. the fact that rings must remain unknotted and unlinked if prepared so -- precludes any serious analytical treatment. Here we propose an unambiguous, parameter-free algorithm to characterise TCs in polymeric solutions and show its power in characterising TCs of entnagled rings. We analyse large-scale molecular dynamics (MD) simulations via persistent homology, a key mathematical tool to extract robust topological information from large datasets. This method allows us to identify ring-specific TCs which we call "homological threadings" (H-threadings) and to connect them to the polymers' behaviour. It also allows us to identify, in a physically appealing and unambiguous way, scale-dependent loops which have eluded precise quantification so far. We discover that while threaded neighbours slowly grow with the rings' length, the ensuing TCs are extensive also in the asymptotic limit. Our proposed method is not restricted to ring polymers and can find broader applications for the study of TCs in generic polymeric materials.

cond-mat.soft↗