arXiv subjects

Macoto Kikuchi

Publications and source records attributed to Macoto Kikuchi.

At least 19 recordsLinked to original sources

arXiv2026

Funnel-like protein energy landscapes emerge from functional evolution under thermal fluctuations

Foldable proteins exhibit funnel-like energy landscapes, but their evolution under selection for function remains unclear. We study this in a lattice protein model, defining fitness as the equilibrium probability of a fixed active-site motif and using multicanonical sequence sampling. At intermediate temperature, rare high-fitness sequences show funnel-like energy and double-well free-energy landscapes. At very low temperature, abundant high-fitness sequences retain glass-like landscapes. Thus, thermal fluctuations turn a local functional requirement into a global structural constraint.

physics.bio-ph↗

arXiv2023

Emergence of cooperative bistability and robustness of gene regulatory networks

Gene regulatory networks (GRNs) are complex systems in which many genes regulate mutually to adapt the cell state to environmental conditions. In addition to function, the GRNs possess several kinds of robustness. This robustness means that systems do not lose their functionality when exposed to disturbances such as mutations or noise, and is widely observed at many levels in living systems. Both function and robustness have been acquired through evolution. In this respect, GRNs utilized in living systems are rare among all possible GRNs. In this study, we explored the fitness landscape of GRNs and investigated how robustness emerged in highly-fit GRNs. We considered a toy model of GRNs with one input gene and one output gene. The difference in the expression level of the output gene between two input states, "on" and "off", was considered as fitness. Thus, the determination of the fitness of a GRN was based on how sensitively it responded to the input. We employed the multicanonical Monte Carlo method, which can sample GRNs randomly in a wide range of fitness levels, and classified the GRNs according to their fitness. As a result, the following properties were found: (1) Highly-fit GRNs exhibited bistability for intermediate input between "on" and "off". This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. (3) GRNs that were robust against mutations were not extremely rare among the highly-fit GRNs. This implies that mutational robustness is readily acquired through the evolutionary process.

q-bio.MN↗

arXiv2023

Phenotype selection due to mutational robustness

The mutation-selection mechanism of Darwinian evolution gives rise not only to adaptation to environmental conditions but also to the enhancement of robustness against mutations. When two or more phenotypes have the same fitness value, the robustness distribution for different phenotypes can vary. Thus, we expect that some phenotypes are favored in evolution and that some are hardly selected because of a selection bias for mutational robustness. In this study, we investigated this selection bias for phenotypes in a model of gene regulatory networks (GRNs) using numerical simulations. The model had one input gene accepting a signal from the outside and one output gene producing a target protein, and the fitness was high if the output for the full signal was much higher than that for no signal. The model exhibited three types of responses to changes in the input signal: monostable, toggle switch, and one-way switch. We regarded these three response types as three distinguishable phenotypes. We constructed a randomly generated set of GRNs using the multicanonical Monte Carlo method originally developed in statistical physics and compared it to the outcomes of evolutionary simulations. One-way switches were strongly suppressed during evolution because of their lack of mutational robustness. By examining one-way switch GRNs in detail, we found that mutationally robust GRNs obtained by evolutionary simulations and non-robust GRNs obtained by McMC have different network structures. While robust GRNs have a common core motif, non-robust GRNs lack this motif. The bistability of non-robust GRNs is considered to be realized cooperatively by many genes, and these cooperative genotypes have been suppressed by evolution.

q-bio.PE↗

arXiv2022

Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution

The aim of this paper is two-fold. First, we propose a new computational method to investigate the particularities of evolution. Second, we apply this method to a model of gene regulatory networks (GRNs) and explore the evolution of mutational robustness and bistability. Living systems have developed their functions through evolutionary processes. To understand the particularities of this process theoretically, evolutionary simulation (ES) alone is insufficient because the outcomes of ES depend on evolutionary pathways. We need a reference system for comparison. An appropriate reference system for this purpose is an ensemble of the randomly sampled genotypes. However, generating high-fitness genotypes by simple random sampling is difficult because such genotypes are rare. In this study, we used the multicanonical Monte Carlo method developed in statistical physics to construct a reference ensemble of GRNs and compared it with the outcomes of ES. We obtained the following results. First, mutational robustness was significantly higher in ES than in the reference ensemble at the same fitness level. Second, the emergence of a new phenotype, bistability, was delayed in evolution. Third, the bistable group of GRNs contains many mutationally fragile GRNs compared with those in the non-bistable group. This suggests that the delayed emergence of bistability is a consequence of the mutation-selection mechanism.

q-bio.MN↗

arXiv2016

The interplay of intrinsic disorder and macromolecular crowding on α-synuclein fibril formation

α-synuclein (α-syn) is an intrinsically disordered protein which is considered to be one of the causes of Parkinson's disease. This protein forms amyloid fibrils when in a highly concentrated solution. The fibril formation of α-syn is induced not only by increases in α-syn concentration but also by macromolecular crowding. In order to investigate the coupled effect of the intrinsic disorder of α-syn and macromolecular crowding, we construct a lattice gas model of α-syn in contact with a crowding agent reservoir based on statistical mechanics. The main assumption is that α-syn can be expressed as coarse-grained particles with internal states coupled with effective volume; and disordered states are modeled by larger particles with larger internal entropy than other states. Thanks to the simplicity of the model, we can exactly calculate the number of conformations of crowding agents, and this enables us to prove that the original grand canonical ensemble with a crowding agent reservoir is mathematically equivalent to a canonical ensemble without crowding agents. In this expression, the effect of macromolecular crowding is absorbed in the internal entropy of disordered states; it is clearly shown that the crowding effect reduces the internal entropy. Based on Monte Carlo simulation, we provide scenarios of crowding-induced fibril formation. We also discuss the recent controversy over the existence of helically folded tetramers of α-syn, and suggest that macromolecular crowding is the key to resolving the controversy.

q-bio.BM↗

arXiv2013

Structural flexibility of intrinsically disordered proteins induces stepwise target recognition

An intrinsically disordered protein (IDP) lacks a stable three-dimensional structure, while it folds into a specific structure when it binds to a target molecule. In some IDP-target complexes, not all target binding surfaces are exposed on the outside, and intermediate states are observed in their binding processes. We consider that stepwise target recognition via intermediate states is a characteristic of IDP binding to targets with "hidden" binding sites. To investigate IDP binding to hidden target binding sites, we constructed an IDP lattice model based on the HP model. In our model, the IDP is modeled as a chain and the target is modeled as a highly coarse-grained object. We introduced motion and internal interactions to the target to hide its binding sites. In the case of unhidden binding sites, a two-state transition between the free states and a bound state is observed, and we consider that this represents coupled folding and binding. Introducing hidden binding sites, we found an intermediate bound state in which the IDP forms various structures to temporarily stabilize the complex. The intermediate state provides a scaffold for the IDP to access the hidden binding site. We call this process multiform binding. We conclude that structural flexibility of IDPs enables them to access hidden binding sites, and this is a functional advantage of IDPs.

q-bio.BM↗

arXiv2013

Robustness Leads Close to the Edge of Chaos in Coupled Map Networks: toward the understanding of biological networks

Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations (perturbations in dynamics), as well as systems which are robust against mutation (perturbations in network structure). To achieve such a design, we apply a multicanonical Monte Carlo method. Analysis based on the maximum Lyapunov exponent and parameter sensitivity shows that systems with marginal stability, which are regarded as systems at the edge of chaos, emerge when robustness against network perturbations is required. This emergence of the edge of chaos is a self-organization phenomenon and does not need a fine tuning of parameters.

q-bio.MN↗

arXiv2013

How to estimate the number of self-avoiding walks over 10^100? Use random walks

Counting the number of N-step self-avoiding walks (SAWs) on a lattice is one of the most difficult problems of enumerative combinatorics. Once we give up calculating the exact number of them, however, we have a chance to apply powerful computational methods of statistical mechanics to this problem. In this paper, we develop a statistical enumeration method for SAWs using the multicanonical Monte Carlo method. A key part of this method is to expand the configuration space of SAWs to random walks, the exact number of which is known. Using this method, we estimate a number of N-step SAWs on a square lattice, c_N, up to N=256. The value of c_256 is 5.6(1)*10^108 (the number in the parentheses is the statistical error of the last digit) and this is larger than one googol (10^100).

cond-mat.stat-mech↗

arXiv2013

Multicanonical simulation of the Domb-Joyce model and the Go model: new enumeration methods for self-avoiding walks

We develop statistical enumeration methods for self-avoiding walks using a powerful sampling technique called the multicanonical Monte Carlo method. Using these methods, we estimate the numbers of the two dimensional N-step self-avoiding walks up to N=256 with statistical errors. The developed methods are based on statistical mechanical models of paths which include self-avoiding walks. The criterion for selecting a suitable model for enumerating self-avoiding walks is whether or not the configuration space of the model includes a set for which the number of the elements can be exactly counted. We call this set a scale fixing set. We selected the following two models which satisfy the criterion: the Go model for lattice proteins and the Domb-Joyce model for generalized random walks. There is a contrast between these two models in the structures of the configuration space. The configuration space of the Go model is defined as the universal set of self-avoiding walks, and the set of the ground state conformation provides a scale fixing set. On the other hand, the configuration space of the Domb-Joyce model is defined as the universal set of random walks which can be used as a scale fixing set, and the set of the ground state conformation is the same as the universal set of self-avoiding walks. From the perspective of enumeration performance, we conclude that the Domb-Joyce model is the better of the two. The reason for the performance difference is partly explained by the existence of the first-order phase transition of the Go model.

cond-mat.stat-mech↗

arXiv2008

Structural Fluctuations of Microtubule Binding Site of KIF1A in Different Nucleotide States

How molecular motors like Kinesin regulates the affinity to the rail protein in the process of ATP hydrolysis remains to be uncovered. To understand the regulation mechanism, we investigate the structural fluctuation of KIF1A in different nucleotide states that are realized in the ATP hydrolysis process by molecular dynamics simulations of Go-like model. We found that "alpha4 helix", which is a part of the microtubule (MT) binding site, changes its fluctuation systematically according to the nucleotide states. In particular, the frequency of large fluctuations of alpha4 strongly correlates with the affinity of KIF1A for microtubule. We also show how the strength of the thermal fluctuation and the interaction with the nucleotide affect the dynamics of microtubule binding site. These results suggest that KIF1A regulates the affinity to MT by changing the flexibility of alpha4 helix according to the nucleotide states.

q-bio.BM↗

arXiv2007

Free-Energy Landscape of Kinesin by a Realistic Lattice Model

Structural fluctuations in the thermal equilibrium of the kinesin motor domain are studied using a lattice protein model with Go interactions. By means of the multi-self-overlap ensemble (MSOE) Monte Carlo method and the principal component analysis (PCA), the free-energy landscape is obtained. It is shown that kinesins have two subdomains that exhibit partial folding/unfolding at functionally important regions: one is located around the nucleotide binding site and the other includes the main microtubule binding site. These subdomains are consistent with structural variability that was reported recently based on experimentally-obtained structures. On the other hand, such large structural fluctuations have not been captured by B-factor or normal mode analyses. Thus, they are beyond the elastic regime, and it is essential to take into account chain connectivity for studying the function of kinesins.

q-bio.BM↗

arXiv2006

Structural Change of Myosin Motor Domain and Nucleotide Dissociation

We investigated the structural relaxation of myosin motor domain from the pre-power stroke state to the near-rigor state using molecular dynamics simulation of a coarse-grained protein model. To describe the structural change, we propose a "dual Go-model," a variant of the Go-like model that has two reference structures. The nucleotide dissociation process is also studied by introducing a coarse-grained nucleotide in the simulation. We found that the myosin structural relaxation toward the near-rigor conformation cannot be completed before the nucleotide dissociation. Moreover, the relaxation and the dissociation occurred cooperatively when the nucleotide was tightly bound to the myosin head. The result suggested that the primary role of the nucleotide is to suppress the structural relaxation.

q-bio.BM↗

arXiv2006

Thermodynamics of aggregation of two proteins

We investigate aggregation mechanism of two proteins in a thermodynamically unambiguous manner by considering the finite size effect of free energy landscape of HP lattice protein model. Multi-Self-Overlap-Ensemble Monte Carlo method is used for numerical calculations. We find that a dimer can be formed spontaneously as a thermodynamically stable state when the system is small enough. It implies the possibility that the aggregation of proteins in a cell is triggered when they are confined in a small region by, for example, being surrounded by other macromolecules.We also find that the dimer exhibits a transition between unstable state and metastable state in the infinite system.

q-bio.BM↗

arXiv2005

Diversity in Free Energy Landscape of Proteins with the Same Native Topology

In order to elucidate the role of the native state topology and the stability of subdomains in protein folding, we investigate free energy landscape of human lysozyme, which is composed of two subdomains, by Monte Carlo simulations. A realistic lattice model with Go-like interaction is used. We take the relative interaction strength (stability, in other word) of two subdomains as a variable parameter and study the folding process. A variety of folding process is observed and we obtained a phase diagram of folding in terms of temperature and the relative stability. Experimentally-observed diversity in folding process of c-type lysozimes is thus understood as a consequence of the difference in the relative stability of subdomains.

q-bio.BM↗

arXiv2004

Emergence of a Barchan Belt in a Unidirectional Flow: Experiment and Numerical Simulation

We observed time evolution of dune fields in a water tank experiment and simulated it by using a simple model without taking complex fluid dynamics into account. The initial sand bed changed its form into transverse ripples, that is, dunes with straight crest lines perpendicular to the flow direction. Then the crescentic shaped dunes called barchans emerged from transverse ripples.

cond-mat.soft↗

arXiv2000

Cluster Analysis of the Ising Model and Universal Finite-Size Scaling

The recent progress in the study of finite-size scaling (FSS) properties of the Ising model is briefly reviewed. We calculate the universal FSS functions for the Binder parameter $g$ and the magnetization distribution function $p(m)$ for the Ising model on $L_1 \times L_2$ two-dimensional lattices with tilted boundary conditions. We show that the FSS functions are universal for fixed sets of the aspect ratio $L_1/L_2$ and the tilt parameter. We also study the percolating properties of the Ising model, giving attention to the effects of the aspect ratio of finite systems. We elucidate the origin of the complex structure of $p(m)$ for the system with large aspect ratio by the multiple-percolating-cluster argument.

cond-mat.stat-mech↗

arXiv1999

Shape Effects of Finite-Size Scaling Functions for Anisotropic Three-Dimensional Ising Models

The finite-size scaling functions for anisotropic three-dimensional Ising models of size $L_1 \times L_1 \times aL_1$ ($a$: anisotropy parameter) are studied by Monte Carlo simulations. We study the $a$ dependence of finite-size scaling functions of the Binder parameter $g$ and the magnetization distribution function $p(m)$. We have shown that the finite-size scaling functions for $p(m)$ at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing $a$ from 1. We also study the finite-size scaling near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional anisotropy. We have found the three-dimensional and two-dimensional finite-size scaling behavior depending on the parameter which is fixed; a unified view of 3D and 2D finite-size scaling behavior has been obtained for the anisotropic 3D Ising models.

cond-mat.stat-mech↗

arXiv1999

Multi-Self-Overlap Ensemble for protein folding: ground state search and thermodynamics

Long chains of the HP lattice protein model are studied by the Multi-Self-Overlap Ensemble(MSOE) Monte Carlo method, which was developed recently by the authors. MSOE successfully finds the lowest energy states reported before for sequences of the chain length $N=42\sim 100$ in two and three dimensions. Moreover, MSOE realizes the lowest energy state that ever found in a case of N=100. Finite-temperature properties of these sequences are also investigated by MSOE. Two successive transitions are observed between the native and random coil states. Thermodynamic analysis suggests that the ground state degeneracy is relevant to the order of the transitions in the HP model.

cond-mat.soft↗