Anomalous relaxation and self-organization in non-equilibrium processes

We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find, that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify two types of self-organization, cooperative and anti-cooperative, which lead to fast and slow relaxation, respectively. We give a qualitative explanation for the behavior of the stretched exponent in different parameter ranges. We emphasize that this is a system exhibiting stretched-exponential relaxation without explicit disorder or frustration.Comment: submitted to PR

An experimental survey of the transition between two-state and downhill protein folding scenarios

A kinetic and thermodynamic survey of 35 WW domain sequences is used in combination with a model to discern the energetic requirements for the transition from two-state folding to downhill folding. The sequences used exhibit a 600-fold range of folding rates at the temperature of maximum folding rate. Very stable proteins can achieve complete downhill folding when the temperature is lowered sufficiently below the melting temperature, and then at even lower temperatures they become two-state folders again because of cold denaturation. Less stable proteins never achieve a sufficient bias to fold downhill because of the onset of cold denaturation. The model, considering both heat and cold denaturation, reveals that to achieve incipient downhill folding (barrier <3 RT) or downhill folding (no barrier), the WW domain average melting temperatures have to be ≥50°C for incipient downhill folding and ≥90°C for downhill folding

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively