The Volumetric Properties of the Transition State Ensemble for Protein Folding

Hydrostatic pressure together with the temperature is an important environmental variable that plays an essential role in biological adaptation of extremophilic organisms. In particular, the effects of hy-drostatic pressure on the rates of the protein folding/unfolding reaction are determined by the magni-tude and sign of the activation volume changes. Here we provide computational description of the ac-tivation volume changes for folding/unfolding reaction, and compare them with the experimental data for six different globular proteins. We find that the volume of the transition state ensemble is always in-between the folded and unfolded states. Based on this, we conclude that hydrostatic pressure will invariably slow down protein folding and accelerate protein unfolding.

Evolution of dynamical networks enhances catalysis in a designer enzyme

Activation heat capacity is emerging as a crucial factor in enzyme thermoadaptation, as shown by non-Arrhenius behaviour of many natural enzymes1,2. However, its physical origin and relationship to evolution of catalytic activity remain uncertain. Here, we show that directed evolution of a computationally designed Kemp eliminase introduces dynamical changes that give rise to an activation heat capacity absent in the original design3. Extensive molecular dynamics simulations show that evolution results in the closure of solvent exposed loops and better packing of the active site with transition state stabilising residues. Remarkably, these changes give rise to a correlated dynamical network involving the transition state and large parts of the protein. This network tightens the transition state ensemble, which induces an activation heat capacity and thereby nonlinearity in the temperature dependence. Our results have implications for understanding enzyme evolution (e.g. in explaining the role of distal mutations and evolutionary tuning of dynamical responses) and suggest that integrating dynamics with design and evolution will accelerate the development of efficient novel enzymes.

Sampling the Folding Transition State Ensemble in a Tube-Like Model of Protein

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformational root-mean-square deviation (RMSD) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using the umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

Sampling the Folding Transition State Ensemble in a Tube-like Model of Protein

We used the tube model with Go-like potential for native contacts to study the folding transition of a designed three-helix bundle and a designed protein G-like structure. It is shown that both proteins in this model are two-state folders with a cooperative folding transition coincided with the collapse transition. We defined the transition states as protein conformations in a small region around the saddle point on a free energy surface with the energy and the conformationalroot mean square deviation (rmsd) from the native state as the coordinates. The transition state region on the free energy surface then was sampled by using umbrella sampling technique. We show that the transition state ensemble is broad consisting of different conformations that have different folded and unfolded elements.

Dissecting the energetics of subunit rotation in the ribosome

The accurate expression of proteins requires the ribosome to efficiently undergo elaborate conformational rearrangements. The most dramatic of these motions is subunit rotation, which is necessary for tRNA molecules to transition between ribosomal binding sites. While rigid-body descriptions provide a qualitative picture of the process, obtaining quantitative mechanistic insights requires one to account for the relationship between molecular flexibility and collective dynamics. Using simulated rotation events, we assess the quality of experimentally-accessible measures for describing the collective displacement of the ~ 4000-residue small subunit. For this, we ask whether each coordinate is able to identify the underlying free-energy barrier and transition state ensemble (TSE). We find that intuitive structurally-motivated coordinates (e.g. rotation angle, inter-protein distances) can distinguish between the endpoints, though they are poor indicators of barrier-crossing events, and they underestimate the free-energy barrier. In contrast, coordinates based on inter-subunit bridges can identify the TSE. We additionally verify that the committor probability for the putative TSE configurations is 0.5, a hallmark feature of any transition state. In terms of structural properties, these calculations implicate a transition state in which flexibility allows for asynchronous rearrangements of the bridges as the ribosome adopts a partially-rotated orientation. These calculations provide a theoretical foundation, upon which experimental techniques may precisely quantify the energy landscape of the ribosome.

Analysis of Two-State Folding Using Parabolic Approximation I: Hypothesis

A model which treats the denatured and native conformers of spontaneously-folding fixed two-state systems as being confined to harmonic Gibbs energy-wells has been developed. Within the assumptions of this model the Gibbs energy functions of the denatured (DSE) and the native state (NSE) ensembles are described by parabolas, with the mean length of the reaction coordinate (RC) being given by the temperature-invariant denaturant m value. Consequently, the ensemble-averaged position of the transition state ensemble (TSE) along the RC, and the ensemble-averaged Gibbs energy of the TSE are determined by the intersection of the DSE and the NSE-parabolas. The equations derived enable equilibrium stability and the rate constants to be rationalized in terms of the mean and the variance of the Gaussian distribution of the solvent accessible surface area of the conformers in the DSE and the NSE. The implications of this model for protein folding are discussed.