Nelson A. Alves

Partition function zeros and finite size scaling of helix-coil transitions in a polypeptide.

We report on multicanonical simulations of the helix-coil transition of a polypeptide. The nature of this transition was studied by calculating partition function zeros and the finite size scaling of various quantities. New estimates for critical exponents are presented.

Unveiling community structures in weighted networks.

Random walks on simple graphs in connection with electrical resistor networks lead to the definition of Markov chains with transition probability matrix in terms of electrical conductances. We extend this definition to an effective transition matrix Pij to account for the probability of going from vertex i to any vertex j of the original connected graph G. Also, we present an algorithm based on the definition of this effective transition matrix among vertices in the network to extract a topological feature related to the manner by which graph G has been organized. This topological feature corresponds to the communities in the graph.

Solution effects and the order of the helix–coil transition in polyalanine

We study helix–coil transitions in an all-atom model of polyalanine. Molecules of up to length 30 residues are investigated by multicanonical simulations. Results from two implicit solvent models are compared with each other and with that from simulations in gas phase. While the helix–coil transition is in all three models a true thermodynamic phase transition, we find that its strength is reduced by the protein–solvent interaction term. The order of the helix–coil transition depends on the details of the solvation term.

Helix formation and folding in an artificial peptide

We study the relation between α-helix formation and folding for a simple artificial peptide, Ala10–Gly5–Ala10. Our data rely on multicanonical Monte Carlo simulations where the interactions among all atoms are taken into account. The free-energy landscape of the peptide is evaluated for various temperatures. Our data indicate that folding of this peptide is a two-step process. In the first step two α-helices are formed which afterwards re-arrange themselves into a U-like structure.

Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation

We explore the initial conditions in short-time critical dynamics to propose an alternative way to evaluate the dynamic exponent z. Estimates are obtained with high precision for the 2D Ising model and the 2D Potts model with three and four states by performing heat-bath Monte Carlo simulations.

Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at an early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are z=2.215(2) and theta=-0.53(2).

Yang–Lee zeros and the helix–coil transition in a continuum model of polyalanine

We calculate the Yang–Lee zeros for characteristic temperatures of the helix–coil transition in a continuum model of polyalanine. The distribution of these zeros differs from predictions of the Zimm–Bragg theory and supports recent claims that polyalanine exhibits a true phase transition. New estimates for critical exponents are presented and the relation of our results to the Lee–Yang theorem is discussed.

Numerical comparison of two approaches for the study of phase transitions in small systems.

We compare two recently proposed methods for the characterization of phase transitions in small systems. The validity and usefulness of these approaches are studied for the cases of the q=4 and q=5 Potts model, i.e., systems where a thermodynamic limit and exact results exist. Guided by this analysis we then discuss the helix-coil transition in polyalanine, an example of structural transitions in biological molecules.

Communication: multicanonical entropy-like solution of statistical temperature weighted histogram analysis method.

A multicanonical update relation for calculation of the microcanonical entropy S(micro)(E) by means of the estimates of the inverse statistical temperature β(S), is proposed. This inverse temperature is obtained from the recently proposed statistical temperature weighted histogram analysis method (ST-WHAM). The performance of ST-WHAM concerning the computation of S(micro)(E) from canonical measures, in a model with strong free-energy barriers, is also discussed on the basis of comparison with the multicanonical simulation estimates.

Global persistence exponent of the two-dimensional Blume-Capel model

The global persistence exponent theta(g) is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value theta(g)=1.080(4) is found at the tricritical point.