arXiv subjects

A. Maritan

Publications and source records attributed to A. Maritan.

31 records · Page 2Linked to original sources

arXiv2001

Modeling of protein interaction networks

We introduce a graph generating model aimed at representing the evolution of protein interaction networks. The model is based on the hypotesis of evolution by duplications and divergence of the genes which produce proteins. The obtained graphs shows multifractal properties recovering the absence of a characteristic connectivity as found in real data of protein interaction networks. The error tolerance of the model to random or targeted damage is in very good agreement with the behavior obtained in real protein networks analysis. The proposed model is a first step in the identification of the evolutionary dynamics leading to the development of protein functions and interactions.

cond-mat.stat-mech↗

arXiv2001

Deciphering the folding kinetics of transmembrane helical proteins

Nearly a quarter of genomic sequences and almost half of all receptors that are likely to be targets for drug design are integral membrane proteins. Understanding the detailed mechanisms of the folding of membrane proteins is a largely unsolved, key problem in structural biology. Here, we introduce a general model and use computer simulations to study the equilibrium properties and the folding kinetics of a $C_α$-based two helix bundle fragment (comprised of 66 amino-acids) of Bacteriorhodopsin. Various intermediates are identified and their free energy are calculated toghether with the free energy barrier between them. In 40% of folding trajectories, the folding rate is considerably increased by the presence of non-obligatory intermediates acting as traps. In all cases, a substantial portion of the helices is rapidly formed. This initial stage is followed by a long period of consolidation of the helices accompanied by their correct packing within the membrane. Our results provide the framework for understanding the variety of folding pathways of helical transmembrane proteins.

cond-mat.stat-mech↗

arXiv2001

Dynamical scaling of the DNA unzipping transition

We report studies of the equilibrium and the dynamics of a general set of lattice models which capture the essence of the force-induced or mechanical DNA unzipping transition. Besides yielding the whole equilibrium phase diagram in the force vs temperature plane, which reveals the presence of an interesting re-entrant unzipping transition for low T, these models enable us to characterize the dynamics of the process starting from a non-equilibrium initial condition. The thermal melting of the DNA strands displays a model dependent time evolution. On the contrary, our results suggest that the dynamical mechanism for the unzipping by force is very robust and the scaling behaviour does not depend on the details of the description we adopt.

cond-mat.soft↗

arXiv1999

A novel iterative strategy for protein design

We propose and discuss a novel strategy for protein design. The method is based on recent theoretical advancements which showed the importance to treat carefully the conformational free energy of designed sequences. In this work we show how computational cost can be kept to a minimum by encompassing negative design features, i.e. isolating a small number of structures that compete significantly with the target one for being occupied at low temperature. The method is succesfully tested on minimalist protein models and using a variety of amino acid interaction potentials.

cond-mat.stat-mech↗

arXiv1999

Heteropolymers in a Solvent at an Interface

Exact bounds are obtained for the quenched free energy of a polymer with random hydrophobicities in the presence of an interface separating a polar from a non polar solvent. The polymer may be ideal or have steric self-interactions. The bounds allow to prove that a ``neutral'' random polymer is localized near the interface at any temperature, whereas a ``non-neutral'' chain is shown to undergo a delocalization transition at a finite temperature. These results are valid for a quite general a priori probability distribution for both independent and correlated hydrophobic charges. As a particular case we consider random AB-copolymers and confirm recent numerical studies.

cond-mat.stat-mech↗

arXiv1998

Swollen-Collapsed Transition in Random Hetero-Polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continnuum counterpart has been proposed by T. Garel, L. Leibler and H. Orland {J. Phys. II France 4, 2139 (1994)]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary $θ$-point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed.

cond-mat.stat-mech↗

arXiv1998

Correlation functions by Cluster Variation Method for Ising model with NN, NNN and Plaquette interactions

We consider the procedure for calculating the pair correlation function in the context of the Cluster Variation Methods. As specific cases, we study the pair correlation function in the paramagnetic phase of the Ising model with nearest neighbors, next to the nearest neighbors and plaquette interactions in two and three dimensions. In presence of competing interactions, the so called disorder line separates in the paramagnetic phase a region where the correlation function has the usual exponential behavior from a region where the correlation has an oscillating exponentially damped behavior. In two dimensions, using the plaquette as the maximal cluster of the CVM approximation, we calculate the phase diagram and the disorder line for a case where a comparison is possible with results known in literature for the eight-vertex model. In three dimensions, in the CVM cube approximation, we calculate the phase diagram and the disorder line in some cases of particular interest. The relevance of our results for experimental systems like mixtures of oil, water and surfactant is also discussed.

cond-mat.stat-mech↗

arXiv1997

Inverse design of proteins with hydrophobic and polar amino acids

A two amino acid (hydrophobic and polar) scheme is used to perform the design on target conformations corresponding to the native states of twenty single chain proteins. Strikingly, the percentage of successful identification of the nature of the residues benchmarked against naturally occurring proteins and their homologues is around 75 % independent of the complexity of the design procedure. Typically, the lowest success rate occurs for residues such as alanine that have a high secondary structure functionality. Using a simple lattice model, we argue that one possible shortcoming of the model studied may involve the coarse-graining of the twenty kinds of amino acids into just two effective types.

cond-mat.stat-mech↗

arXiv1997

Protein design in a lattice model of hydrophobic and polar amino acids

A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional lattice structures. Previous studies employing a sequence-space Monte-Carlo technique resulted in the successful design of one sequence in ten attempts. The present work also entails the exploration of conformations that compete significantly with the target structure for being its ground state. The design procedure is successful in all the ten cases.

cond-mat.stat-mech↗

arXiv1996

An Analytical and Numerical Study of Optimal Channel Networks

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the optimal configurations. The fractal character of river networks is reflected in the power law behaviour of various quantities characterising the morphology of the basin. In the context of a finite size scaling Ansatz, the exponents describing the power law behaviour are calculated exactly and show mean field behaviour, except for two limiting values of a parameter characterizing the dissipated energy, for which the system belongs to different universality classes. Two modified versions of the model, incorporating quenched disorder are considered: the first simulates heterogeneities in the local properties of the soil, the second considers the effects of a non-uniform rainfall. In the region of mean field behaviour, the model is shown to be robust to both kinds of perturbations. In the two limiting cases the random rainfall is still irrelevant, whereas the heterogeneity in the soil properties leads to new universality classes. Results of a numerical analysis of the model are reported that confirm and complement the theoretical analysis of the global minimum. The statistics of the local minima are found to more strongly resemble observational data on real rivers.

cond-mat.stat-mech↗

arXiv1996

Stochastic Growth Equations and Reparametrization Invariance

It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach provides a particularly transparent way to obtain continuum growth equations for interfaces. It is straightforward to derive equations which describe the coarse grained evolution of discrete lattice models and analyze their small gradient expansion. In this way, the authors identify the basic mechanisms which lead to the most commonly used growth equations. The advantages of this formulation of growth processes is that it allows one to go beyond the frequently used no-overhang approximation. The reparametrization invariant form also displays explicitly the conservation laws for the specific process and all the symmetries with respect to space-time transformations which are usually lost in the small gradient expansion. Finally, it is observed, that the knowledge of the full equation of motion, beyond the lowest order gradient expansion, might be relevant in problems where the usual perturbative renormalization methods fail.

cond-mat↗

arXiv1995

Multi-interaction mean-field renormalization group

We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of different sublattices of the given lattice and it generates as many flow equations as coupling constants without arbitrary truncations on the renormalized Hamiltonian. We obtain good results for the test case of Ising systems with an additional second-neighbor coupling in two and three dimensions. An application of the method is also done to a morphological model of interacting surfaces introduced recenlty by Likos, Mecke and Wagner [J. Chem. Phys. {\bf{102}}, 9350 (1995)]. PACS: 64.60.Ak, 64.60.Fr, 05.70.Jk

cond-mat↗

arXiv1993

Cluster Variation Approach to the Random-Anisotropy Blume-Emery-Griffiths Model

The random--anisotropy Blume--Emery--Griffiths model, which has been proposed to describe the critical behavior of $^3$He--$^4$He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high $^3$He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the $λ$ line.

cond-mat↗