Direction dependent mechanical unfolding and Green Fluorescent Protein as a force sensor

An Ising--like model of proteins is used to investigate the mechanical unfolding of the Green Fluorescent Protein along different directions. When the protein is pulled from its ends, we recover the major and minor unfolding pathways observed in experiments. Upon varying the pulling direction, we find the correct order of magnitude and ranking of the unfolding forces. Exploiting the direction dependence of the unfolding force at equilibrium, we propose a force sensor whose luminescence depends on the applied force.Comment: to appear in Phys Rev

Downhill versus two-state protein folding in a statistical mechanical model

The authors address the problem of downhill protein folding in the framework of a simple statistical mechanical model, which allows an exact solution for the equilibrium and a semianalytical treatment of the kinetics. Focusing on protein 1BBL, a candidate for downhill folding behavior, and comparing it to the WW domain of protein PIN1, a two-state folder of comparable size, the authors show that there are qualitative differences in both the equilibrium and kinetic properties of the two molecules. However, the barrierless scenario which would be expected if 1BBL were a true downhill folder is observed only at low enough temperature.Comment: 20 pages, 13 figure

Protein mechanical unfolding: a model with binary variables

A simple lattice model, recently introduced as a generalization of the Wako--Sait\^o model of protein folding, is used to investigate the properties of widely studied molecules under external forces. The equilibrium properties of the model proteins, together with their energy landscape, are studied on the basis of the exact solution of the model. Afterwards, the kinetic response of the molecules to a force is considered, discussing both force clamp and dynamic loading protocols and showing that theoretical expectations are verified. The kinetic parameters characterizing the protein unfolding are evaluated by using computer simulations and agree nicely with experimental results, when these are available. Finally, the extended Jarzynski equality is exploited to investigate the possibility of reconstructing the free energy landscape of proteins with pulling experiments

Equilibrium properties and force-driven unfolding pathways of RNA molecules

The mechanical unfolding of a simple RNA hairpin and of a 236--bases portion of the Tetrahymena thermophila ribozyme is studied by means of an Ising--like model. Phase diagrams and free energy landscapes are computed exactly and suggest a simple two--state behaviour for the hairpin and the presence of intermediate states for the ribozyme. Nonequilibrium simulations give the possible unfolding pathways for the ribozyme, and the dominant pathway corresponds to the experimentally observed one.Comment: Main text + appendix, to appear in Phys. Rev. Let

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-{\gamma} where {\gamma} values lie in between 1.42 and 2.35

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.Comment: 27 pages, 7 figure

Cluster variation - Pade` approximants method for the simple cubic Ising model

The cluster variation - Pade` approximant method is a recently proposed tool, based on the extrapolation of low/high temperature results obtained with the cluster variation method, for the determination of critical parameters in Ising-like models. Here the method is applied to the three-dimensional simple cubic Ising model, and new results, obtained with an 18-site basic cluster, are reported. Other techniques for extracting non-classical critical exponents are also applied and their results compared with those by the cluster variation - Pade` approximant method.Comment: 8 RevTeX pages, 3 PostScript figure

On the low-temperature phase of the three-state antiferromagnetic Potts model on the simple cubic lattice

The three-state antiferromagnetic Potts model on the simple cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free energy difference between the broken-sublattice-symmetry and the permutationally-symmetric-sublattices phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.Comment: 4 pages REVTeX + 2 PostScript figures, to be published in Phys. Rev. E as a Rapid Communicatio

An exactly solvable model for a beta-hairpin with random interactions

I investigate a disordered version of a simplified model of protein folding, with binary degrees of freedom, applied to an ideal beta-hairpin structure. Disorder is introduced by assuming that the contact energies are independent and identically distributed random variables. The equilibrium free-energy of the model is studied, performing the exact calculation of its quenched value and proving the self-averaging feature.Comment: 9 page

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.Comment: 4 pages, 2 figure