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We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
The differing ability of polypeptide conformations to act as the native state of proteins has long been rationalized in terms of differing kinetic accessibility or thermodynamic stability. Building on the successful applications of physical…
The remarkable accuracy and versatility of single-molecule techniques make possible new measurements that are not feasible in bulk assays. Among these, the precise estimation of folding free energies using fluctuation theorems in…
Using the Gaussian Ansatz for the monomer-monomer correlation functions we derive a set of the self-consistent equations for determination of the conformational state in the bead-and-spring copolymer model. The latter is based on the…
We present a method for determining the free energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting…
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and…
A model of self-avoiding walk with suitable constraints on self-attraction is developed to describe the conformational behaviour of a single stranded short DNA molecule that form hairpin structure. Using exact enumeration method we…
In this study we evaluate, at full atomic detail, the folding processes of two small helical proteins, the B domain of protein A and the Villin headpiece. Folding kinetics are studied by performing a large number of ab initio Monte Carlo…
Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central…
We investigate the formation of beta-sheet structures in proteins without taking into account specific sequence-dependent hydrophobic interactions. To accomplish this, we introduce a model which explicitly incorporates both solvation…
We present the results of a self-consistent, unified molecular dynamics study of simple model heteropolymers in the continuum with emphasis on folding, sequence design and the determination of the interaction parameters of the effective…
The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to…
The theory of transition between $\alpha$-helix, $\beta$-sheet and random coil conformation of a protein is discussed through a simple model, that includes both short and long-range interactions. Besides the bonding parameter and helical…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…
We investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent $\alpha$ > 0, when the correlated sequence is given by another independent renewal set with loop exponent…
We use a generalization of Hoeffding's inequality to show concentration results for the free energy of disordered pinning models, assuming only that the disorder has a finite exponential moment. We also prove some concentration inequalities…
The stability of a $\beta$-sheeted conformation and its transition into a random coil are studied with a 2D lattice biopolymer model. At low temperature and low external force, the polymer folds back and forth on itself and forms a…
Proteins are minimally frustrated polymers. However, for realistic protein models non-native interactions must be taken into account. In this paper we analyze the effect of non-native interactions on the folding rate and on the folding free…