arXiv subjects

Alessandro Pelizzola

Publications and source records attributed to Alessandro Pelizzola.

At least 19 recordsLinked to original sources

arXiv2024

Totally asymmetric simple exclusion process with local resetting and open boundary conditions

We study a totally asymmetric simple exclusion process with open boundary conditions and local resetting at the injection node. We investigate the stationary state of the model, using both mean-field approximation and kinetic Monte Carlo simulations, and identify three regimes, depending on the way the resetting rate scales with the lattice size. The most interesting regime is the intermediate resetting one, as in the case of periodic boundary conditions. In this regime we find pure phases and phase separation phenomena, including a low-density/high-density phase separation, which was not possible with periodic boundary conditions. We discuss density profiles, characterizing bulk regions and boundary layers, and nearest-neighbour covariances, finding a remarkable agreement between mean-field and simulation results. The stationary state phase diagram is mapped out analytically at the mean-field level, but we conjecture that it may be exact in the thermodynamic limit. We also briefly discuss the large resetting regime, which exhibits an inverse characteristic length scale diverging logarithmically with the lattice size.

cond-mat.stat-mech↗

arXiv2023

Interaction vs inhomogeneity in a periodic TASEP

We study the non-equilibrium steady states in a totally-asymmetric simple-exclusion process with periodic boundary conditions, also incorporating (i) an extra (nearest-neighbour) repulsive interaction and (ii) hopping rates characterized by a smooth spatial inhomogeneity. We make use of a generalized mean-field approach (at the level of nearest-neighbour pair clusters), in combination with kinetic Monte Carlo simulations. It turns out that the so-called shock phase can exhibit a lot of qualitatively different subphases, including multiple-shock phases, and a minimal-current shock phase. We argue that the resulting, considerably rich phase diagram should be relatively insensitive to minor details of either interaction or spatial inhomogeneity. As a consequence, we also expect that our results help elucidate the nature of shock subphases detected in previous studies.

cond-mat.stat-mech↗

arXiv2021

Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA/protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly-interacting thermal bath. Notably, this 'kinetic' temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple 4-state Markov model which describes the long-time behaviour of the RNA molecule.

cond-mat.stat-mech↗

arXiv2018

Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory

We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries, in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate, at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by providing rigorous bounds, which become tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones, in the symmetric case of equal binding/unbinding rates. The theory predicts a dynamical transition to occur in this case as well.

cond-mat.stat-mech↗

arXiv2017

Cluster approximations for the TASEP: stationary state and dynamical transition

We develop and test cluster approximations, which generalize simple mean--field by taking into account more and more local correlations, for the Totally Asymmetric Simple Exclusion Process with open boundaries. We consider in detail the pair and triplet approximations, discussing the improvements with respect to mean field in various steady state properties. Moreover, we analyze the recently discovered dynamical transition, describing how the spectrum of the relaxation matrix changes at the transition.

cond-mat.stat-mech↗

arXiv2017

Variational approximations for stochastic dynamics on graphs

We investigate different mean-field-like approximations for stochastic dynamics on graphs, within the framework of a cluster-variational approach. In analogy with its equilibrium counterpart, this approach allows one to give a unified view of various (previously known) approximation schemes, and suggests quite a systematic way to improve the level of accuracy. We compare the different approximations with Monte Carlo simulations on a reversible (susceptible-infected-susceptible) discrete-time epidemic-spreading model on random graphs.

cond-mat.stat-mech↗

arXiv2014

Six vertex model with domain-wall boundary conditions in the Bethe-Peierls approximation

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available.

cond-mat.stat-mech↗

arXiv2014

Generalized belief propagation for the magnetization of the simple cubic Ising model

A new approximation of the cluster variational method is introduced for the three-dimensional Ising model on the simple cubic lattice. The maximal cluster is, as far as we know, the largest ever used in this method. A message-passing algorithm, generalized belief propagation, is used to minimize the variational free energy. Convergence properties and performance of the algorithm are investigated. The approximation is used to compute the spontaneous magnetization, which is then compared to previous results. Using the present results as the last step in a sequence of three cluster variational approximations, an extrapolation is obtained which captures the leading critical behaviour with a good accuracy.

cond-mat.stat-mech↗

arXiv2013

Variational approximations for stationary states of Ising-like models

We introduce a new variational approach to the stationary state of kinetic Ising-like models. The approach is based on the cluster expansion of the entropy term appearing in a functional which is minimized by the system history. We rederive a known mean-field theory and propose a new method, here called diamond approximation, which turns out to be more accurate and faster than other methods of comparable computational complexity.

cond-mat.stat-mech↗

arXiv2012

Folding transitions in three-dimensional space with defects

A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed in terms of Ising-like variables with nearest-neighbor and plaquette interactions in the hexagonal lattice; its phase diagram is determined by the Cluster Variation Method. The results found by varying the curvature and defect energy show that the introduction of defects turns the first-order crumpling transitions of the model without defects into continuous transitions. New phases also appear by decreasing the energy cost of defects and the behavior of their densities has been analyzed.

cond-mat.stat-mech↗

arXiv2012

Effects of confinement on thermal stability and folding kinetics in a simple Ising-like model

In cellular environment, confinement and macromulecular crowding play an important role on thermal stability and folding kinetics of a protein. We have resorted to a generalized version of the Wako-Saito-Munoz-Eaton model for protein folding to study the behavior of six different protein structures confined between two walls. Changing the distance 2R between the walls, we found, in accordance with previous studies, two confinement regimes: starting from large R and decreasing R, confinement first enhances the stability of the folded state as long as this is compact and until a given value of R; then a further decrease of R leads to a decrease of folding temperature and folding rate. We found that in the low confinement regime both unfolding temperatures and logarithm of folding rates scale as R-γ where γ values lie in between 1.42 and 2.35.

physics.bio-ph↗

arXiv2011

Palette-colouring: a belief-propagation approach

We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call "palette-colouring", has been recently addressed as a basic example of problem arising in the context of distributed data storage. Even though it has not been proved to be NP complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach, at the cost of increased computational effort. We also investigate the emergence of a satisfiable to unsatisfiable "phase transition" as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ("thermodynamic") limit.

cond-mat.stat-mech↗

arXiv2011

Analysis of the Equilibrium and Kinetics of the Ankyrin Repeat Protein Myotrophin

We apply the Wako-Saito-Munoz-Eaton model to the study of Myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model, that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild type protein despite the presence of a non-trivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, folding and unfolding pathway appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

q-bio.BM↗

arXiv2007

Rate Determining Factors in Protein Model Structures

Previous research has shown a strong correlation of protein folding rates to the native state geometry, yet a complete explanation for this dependence is still lacking. Here we study the rate-geometry relationship with a simple statistical physics model, and focus on two classes of model geometries, representing ideal parallel and antiparallel structures. We find that the logarithm of the rate shows an almost perfect linear correlation with the "absolute contact order", but the slope depends on the particular class considered. We discuss these findings in the light of experimental results.

q-bio.BM↗

arXiv2006

Rigorous results on the local equilibrium kinetics of a protein folding model

A local equilibrium approach for the kinetics of a simplified protein folding model, whose equilibrium thermodynamics is exactly solvable, was developed in [M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important properties of this approach are (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, (iii) the equilibration rate is an upper bound of the exact one and (iv) computational complexity is polynomial in the number of variables. Moreover, (v) this method is equivalent to another approximate approach to the kinetics: the path probability method. In this paper we give detailed rigorous proofs for the above results.

cond-mat.stat-mech↗

arXiv2006

Kinetics of the Wako-Saito-Munoz-Eaton Model of Protein Folding

We consider a simplified model of protein folding, with binary degrees of freedom, whose equilibrium thermodynamics is exactly solvable. Based on this exact solution, the kinetics is studied in the framework of a local equilibrium approach, for which we prove that (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, and (iii) the folding rate is an upper bound of the exact one. The kinetics is compared to the exact one for a small peptide and to Monte Carlo simulations for a longer protein, then rates are studied for a real protein and a model structure.

cond-mat.stat-mech↗

arXiv2005

Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models

The cluster variation method (CVM) is a hierarchy of approximate variational techniques for discrete (Ising--like) models in equilibrium statistical mechanics, improving on the mean--field approximation and the Bethe--Peierls approximation, which can be regarded as the lowest level of the CVM. In recent years it has been applied both in statistical physics and to inference and optimization problems formulated in terms of probabilistic graphical models. The foundations of the CVM are briefly reviewed, and the relations with similar techniques are discussed. The main properties of the method are considered, with emphasis on its exactness for particular models and on its asymptotic properties. The problem of the minimization of the variational free energy, which arises in the CVM, is also addressed, and recent results about both provably convergent and message-passing algorithms are discussed.

cond-mat.stat-mech↗

arXiv2002

Exact Solution of the Munoz-Eaton Model for Protein Folding

A transfer-matrix formalism is introduced to evaluate exactly the partition function of the Munoz-Eaton model, relating the folding kinetics of proteins of known structure to their thermodynamics and topology. This technique can be used for a generic protein, for any choice of the energy and entropy parameters, and in principle allows the model to be used as a first tool to characterize the dynamics of a protein of known native state and equilibrium population. Applications to a $β$-hairpin and to protein CI-2, with comparisons to previous results, are also shown.

cond-mat.stat-mech↗