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

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

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

Unbalanced Langmuir kinetics affects TASEP dynamical transitions: mean-field theory

In a previous study we developed a mean-field theory of dynamical transitions for the totally-asymmetric simple-exclusion process (TASEP) with open boundaries and Langmuir kinetics, in the so-called balanced regime, characterized by equal binding and unbinding rates. Here we show that simply including the possibility of unbalanced rates gives rise to an unexpectedly richer dynamical phase diagram. In particular, the current work predicts an unusual type of dynamical transition, which exhibits certain similarities with first-order phase transitions of equilibrium systems. We also point out that different types of dynamical transition are accompanied by different structural changes in the (mean-field) relaxation spectrum.Comment: 32 pages, 8 figure

An Ising-Like model for protein mechanical unfolding

The mechanical unfolding of proteins is investigated by extending the Wako-Saito-Munoz-Eaton model, a simplified protein model with binary degrees of freedom, which has proved successful in describing the kinetics of protein folding. Such a model is generalized by including the effect of an external force, and its thermodynamics turns out to be exactly solvable. We consider two molecules, the 27th immunoglobulin domain of titin and protein PIN1. In the case of titin we determine equilibrium force-extension curves and study nonequilibrium phenomena in the frameworks of dynamic loading and force clamp protocols, verifying theoretical laws and finding the position of the kinetic barrier which hinders the unfolding of the molecule. The PIN1 molecule is used to check the possibility of computing the free energy landscape as a function of the molecule length by means of an extended form of the Jarzynski equality.Comment: 4 pages + appendi

The exploding-reflector concept for ground-penetrating-radar modeling

The simulation of a stacked radargram requires the calculation of a set of common-source experiments and application of the standard processing sequence. To reduce computing time, a zero-offset stacked section can be obtained with a single simulation, by using the exploding-reflector concept and the so-called non-reflecting wave equation. This non-physical modification of the wave equation implies a constant impedance model to avoid multiple reflections, which are, in principle, absent from stacked sections and constitute unwanted artifacts in migration processes. Magnetic permeability is used as a free parameter to obtain a constant impedance model and avoid multiple reflections. The reflection strength is then implicit in the source strength. Moreover, the method generates normal-incidence reflections, i.e. those having identical downgoing and upgoing wave paths.Exploding reflector experiments provide correct travel times of diffraction and reflection events, in contrast to the plane-wave method

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

Optimality in Self-Organized Molecular Sorting

We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations of a lattice-gas realization of the model and with experimental observations. The efficiency of the distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal conditions are realized in living cells