46 research outputs found
Chaos in spin glasses revealed through thermal boundary conditions
We study the fragility of spin glasses to small temperature perturbations
numerically using population annealing Monte Carlo. We apply thermal boundary
conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal
boundary conditions all eight combinations of periodic versus antiperiodic
boundary conditions in the three spatial directions are present, each appearing
in the ensemble with its respective statistical weight determined by its free
energy. We show that temperature chaos is revealed in the statistics of
crossings in the free energy for different boundary conditions. By studying the
energy difference between boundary conditions at free-energy crossings, we
determine the domain-wall fractal dimension. Similarly, by studying the number
of crossings, we determine the chaos exponent. Our results also show that
computational hardness in spin glasses and the presence of chaos are closely
related.Comment: 4 pages, 4 figure
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, âonâ and âoffâ, 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 âonâ and âoffâ. This means that such GRNs responded to two input states by using different fixed points of dynamics. This bistability emerges necessarily as fitness increases. (2) These highly-fit GRNs were robust against noise because of their bistability. In other words, noise robustness is a byproduct of high fitness. (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. These properties are universal irrespective of the evolutionary pathway, because the results do not rely on evolutionary simulation.Nagata S., Kikuchi M..(2020) Emergence of cooperative bistability and robustness of gene regulatory networks. PLoS Computational Biology 16(6): 1007969. doi: 10.1371/journal.pcbi.1007969
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.Kaneko T., Kikuchi M.. (2022) Evolution enhances mutational robustness and suppresses the emergence of a new phenotype: A new computational approach for studying evolution. PLoS Computational Biology 18(1): e1009796. doi: 10.1371/journal.pcbi.1009796
How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
The dynamics and structure of nonequilibrium liquids, driven by
non-conservative forces which can be either external or internal, generically
hold the signature of the net dissipation of energy in the thermostat. Yet,
disentangling precisely how dissipation changes collective effects remains
challenging in many-body systems due to the complex interplay between driving
and particle interactions. First, we combine explicit coarse-graining and
stochastic calculus to obtain simple relations between diffusion, density
correlations and dissipation in nonequilibrium liquids. Based on these results,
we consider large-deviation biased ensembles where trajectories mimic the
effect of an external drive. The choice of the biasing function is informed by
the connection between dissipation and structure derived in the first part.
Using analytical and computational techniques, we show that biasing
trajectories effectively renormalizes interactions in a controlled manner, thus
providing intuition on how driving forces can lead to spatial organization and
collective dynamics. Altogether, our results show how tuning dissipation
provides a route to alter the structure and dynamics of liquids and soft
materials.Comment: 21 pages, 7 figure
A large deviation theory perspective on nanoscale transport phenomena
Understanding transport processes in complex nanoscale systems, like ionic
conductivities in nanofluidic devices or heat conduction in low dimensional
solids, poses the problem of examining fluctuations of currents within
nonequilibrium steady states and relating those fluctuations to nonlinear or
anomalous responses. We have developed a systematic framework for computing
distributions of time integrated currents in molecular models and relating
cumulants of those distributions to nonlinear transport coefficients. The
approach elaborated upon in this perspective follows from the theory of
dynamical large deviations, benefits from substantial previous formal
development, and has been illustrated in several applications. The framework
provides a microscopic basis for going beyond traditional hydrodynamics in
instances where local equilibrium assumptions break down, which are ubiquitous
at the nanoscale.Comment: Small revisions for clarit
Effective driven dynamics for one-dimensional conditioned Langevin processes in the weak-noise limit
In this work we focus on fluctuations of time-integrated observables for a
particle diffusing in a one-dimensional periodic potential in the weak-noise
asymptotics. Our interest goes to rare trajectories presenting an atypical
value of the observable, that we study through a biased dynamics in a
large-deviation framework. We determine explicitly the effective
probability-conserving dynamics which makes rare trajectories of the original
dynamics become typical trajectories of the effective one. Our approach makes
use of a weak-noise path-integral description in which the action is minimised
by the rare trajectories of interest. For `current-type' additive observables,
we find the emergence of a propagative trajectory minimising the action for
large enough deviations, revealing the existence of a dynamical phase
transition at a fluctuating level. In addition, we provide a new method to
determine the scaled cumulant generating function of the observable without
having to optimise the action. It allows one to show that the weak-noise and
the large-time limits commute in this problem. Finally, we show how the biased
dynamics can be mapped in practice to an effective driven dynamics, which takes
the form of a driven Langevin dynamics in an effective potential. The
non-trivial shape of this effective potential is key to understand the link
between the dynamical phase transition in the large deviations of current and
the standard depinning transition of a particle in a tilted potential