Specific and nonspecific collapse in protein folding funnels

Experiments with fast folding proteins are beginning to address the relationship between collapse and folding. We investigate how different scenarios for folding can arise depending on whether the folding and collapse transitions are concurrent or whether a nonspecific collapse precedes folding. Many earlier studies have focused on the limit in which collapse is fast compared to the folding time; in this work we focus on the opposite limit where, at the folding temperature, collapse and folding occur simultaneously. Real proteins exist in both of these limits. The folding mechanism varies substantially in these two regimes. In the regime of concurrent folding and collapse, nonspecific collapse now occurs at a temperature below the folding temperature (but slightly above the glass transition temperature).     

A semi-analytical description of protein folding that incorporates detailed geometrical information

Much has been done to study the interplay between geometric and energetic effects on the protein folding energy landscape. Numerical techniques such as molecular dynamics simulations are able to maintain a precise geometrical representation of the protein. Analytical approaches, however, often focus on the energetic aspects of folding, including geometrical information only in an average way. Here, we investigate a semi-analytical expression of folding that explicitly includes geometrical effects. We consider a Hamiltonian corresponding to a Gaussian filament with structure-based interactions. The model captures local features of protein folding often averaged over by mean-field theories, for example, loop contact formation and excluded volume. We explore the thermodynamics and folding mechanisms of beta-hairpin and alpha-helical structures as functions of temperature and Q, the fraction of native contacts formed. Excluded volume is shown to be an important component of a protein Hamiltonian, since it both dominates the cooperativity of the folding transition and alters folding mechanisms. Understanding geometrical effects in analytical formulae will help illuminate the consequences of the approximations required for the study of larger proteins.     

Effective stochastic dynamics on a protein folding energy landscape

We present an approach to protein folding kinetics using stochastic reaction-coordinate dynamics, in which the effective drift velocities and diffusion coefficients are determined from microscopic simulation data. The resultant Langevin equation can then be used to directly simulate the folding process. Here, we test this approach by applying it to a toy two-state dynamical system and to a funnellike structure-based (Go-type) model. The folding time predictions agree very well with full simulation results. Therefore, we have in hand a fast numerical tool for calculating the folding kinetic properties, even when full simulations are not feasible. In addition, the local drift and diffusion coefficients provide an alternative way to compute the free energy profile in cases where only local sampling can be achieved.     

Pseudo-steady-state solutions for solidification in a wedge

Polubarinova-Kochina's analytical differential equation methodis used to determine the pseudo-steady-state solution to problemsinvolving the freezing (solidification) of wedges of liquidwhich are initially at their fusion temperature. In particular,we consider four distinct problems for wedges which are: freezingwith the same constant boundary temperature, freezing with thesame constant boundary heat fluxes, freezing with distinct constantboundary temperatures and freezing with distinct constant fluxesat the boundaries. For the last two problems, a Heun's differentialequation with an unknown singularity is derived, which in bothcases admits a particularly elegant simple solution for thespecial case when the wedge angle is . The moving boundariesobtained are shown pictorially.     

Determination of the water geometry in violuric acid monohydrate with a Monte Carlo simulation

The positions and orientations of water molecules in violuric acid crystals have been determined with the Metropolis Monte Carlo method. The interaction potentials between water and violuric acid needed in the simulation have been developed using ab initio calculations corrected for the basis set superposition error with the C.P. technique and fitted to atom-atom pairwise potentials. The agreement between experimental data and simulation results is good, proving that the interaction potentials can be used with confidence.