Nonadditive interactions in protein folding: the zipper model of cytochrome C

How the Proximal Pocket May Influence the Enantiospecificities of Chloroperoxidase-Catalyzed Epoxidations of Olefins

Chloroperoxidase-catalyzed enantiospecific epoxidations of olefins are of significant biotechnological interest. Typical enantiomeric excesses are in the range of 66%-97% and translate into free energy differences on the order of 1 kcal/mol. These differences are generally attributed to the effect of the distal pocket. In this paper, we show that the influence of the proximal pocket on the electron transfer mechanism in the rate-limiting event may be just as significant for a quantitatively accurate account of the experimentally-measured enantiospecificities.

Chloroperoxidase-Catalyzed Epoxidation of Cis-β-Methylstyrene: NH-S Hydrogen Bonds and Proximal Helix Dipole Change the Catalytic Mechanism and Significantly Lower the Reaction Barrier

Proximal hydrogen bonding of the axial sulfur with the backbone amides (NH-S) is a conserved feature of heme-thiolate enzymes such as chloroperoxidase (CPO) and cytochrome P450 (P450). In CPO, the effect of NH-S bonds is amplified by the dipole moment of the proximal helix. Our gas-phase DFT studies show that the proximal pocket effect significantly enhances CPO's reactivity toward the epoxidation of olefinic substrates. Comparison of models with and without proximal pocket residues shows that with them, the barrier for Cβ-O bond formation is lowered by about ∼4.6 kcal/mol, while Cα-O-Cβ ring closure becomes barrierless. The dipole moment of the proximal helix was estimated to contribute 1/3 of the decrease, while the rest is attributed to the effect of NH-S bonds. The decrease of the reaction barrier correlates with increased electron density transfer to residues of the proximal pocket. The effect is most pronounced on the doublet spin surface and involves a change in the electron-transfer mechanism. A full enzyme QMMM study on the doublet spin surface gives about the same barrier as the gas-phase DFT study. The free-energy barrier was estimated to be in agreement with the experimental results for the CPO-catalyzed epoxidation of styrene.

Controlling dissociation channels of gas-phase protein complexes using charge manipulation

Coarse-grained simulations with charge hopping were performed for a positively charged tetrameric transthyretin (TTR) protein complex with a total charge of +20. Charges were allowed to move among basic amino acid sites as well as N-termini. Charge distributions and radii of gyration were calculated for complexes simulated at two temperatures, 300 and 600 K, under different scenarios. One scenario treated the complex in its normal state allowing charge to move to any basic site. Another scenario blocked protonation of all the N-termini except one. A final scenario used the complex in its normal state but added a basic-site containing tether (charge tag) near the N-terminus of one chain. The differences in monomer unfolding and charging were monitored in all three scenarios and compared. The simulation results show the importance of the N-terminus in leading the unfolding of the monomer units; a process that follows a zipper-like mechanism. Overall, experimentally modifying the complex by adding a tether or blocking the protonation of N-termini may give the potential for controlling the unraveling and subsequent dissociation of protein complexes.

Thermodynamics of protein folding using a modified Wako-Saitô-Muñoz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model's thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.

Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin

We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

A random walk sampling algorithm allows the extraction of the density of states distribution in energy-reaction coordinate space. As a result, the temperature dependences of thermodynamic quantities such as relative energy, entropy, and heat capacity can be calculated using first-principles statistical mechanics. The strategies for optimal convergence of the algorithm and control of its accuracy are proposed. We show that the saturation of the error [Q. Yan and J. J. de Pablo, Phys. Rev. Lett. 90, 035701 (2003); E. Belardinelli and V. D. Pereyra, J. Chem. Phys. 127, 184105 (2007)] is due to the use of histogram flatness as a criterion of convergence. An application of the algorithm to methane dimer hydrophobic interactions is presented. We obtained a quantitatively accurate energy-entropy decomposition of the methane dimer cavity potential. The presented results confirm the previous results, and they provide new information regarding the thermodynamics of hydrophobic interactions. We show that the finite-difference approximation, which is widely used in molecular dynamic simulations for the energy-entropy decomposition of a free energy potential, can lead to a significant error.