The Origin of Nonmonotonic Complex Behavior and the Effects of Nonnative Interactions on the Diffusive Properties of Protein Folding

Abstract

We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.

Analyzing the effect of homogeneous frustration in protein folding

“…Simulations employing structure‐based models show a strong correlation of the calculated folding rates with free‐energy barriers . Simulations have also shown how important it is to consider the diffusion coefficient as being dependent on the reaction coordinate to improve the accuracy of the folding rate prediction . Folding rates have excellent correlation with dimensionless parameters related to protein topology, such as the contact order …”

“…In principle, the existence of frustration hinders folding kinetics and stability. However, studies show that a low degree of frustration helps the protein‐folding process …”

“…This aspect is hard to control in protein computational models. On the other hand, energetic frustration is associated with the energy interaction between monomers and can be simulated by adding interaction terms to the potential energy function …”

What protein folding teaches us about biological function and molecular machines

“…From a theoretical perspective, algorithms have been developed and employed to extract D r from simulations, ranging from Bayesian analysis of equilibrium trajectories [31], to fitting dynamics to the short-time solution of the Fokker-Planck equation [35], to applying quasi-harmonic approximations [36]. Approaches have also been developed for extracting the scale of roughness from pulling experiments [37], and FRET measurements have implicated a dependence of D on protein compaction [38].…”

Microscopic aspects of Stretched Exponential Relaxation (SER) in homogeneous molecular and network glasses and polymers

“…themes of inhomogeneities and the competing influences of shortand long-range interactions are now appearing in some simulations of folding of small proteins (~100 amino acids). Thus [55] studied the folding of a 66 amino acid beta barrel protein known to follow simple two-state kinetics with a single transition state. They found two interesting results: restriction of the ensemble of folding paths to a tube in contact space (1) enhanced the contact homogeneity of the transition state, and (2) enhanced the diffusion constant near the folded state.…”