Discontinuous Molecular Dynamics Simulations Of Protein Folding Based Upon All-atom Models

Protein folding is a challenging subject in natural science.In the era of post-'human genome project' and mature genetic engineering,it becomes more required to understand the relationship between structure,function,and folding mechanism of proteins.One of the underlying important approaches is computer simulation.As a bio-macromolecule,protein could be regarded as a special chain composed of 20 amino acid residues.The problem of protein folding could also be regarded as how a special polymer changes its conformation from a flexible coil to a relative compact globule with a specific ordered spatial structure.The empirical force-field-based all-atom model demands a remarkable computer resource.On the other hand,the highly simplified coarse-grained model based on a united-atom representation of the amino acid could only explore the general aspects of protein folding.In fact,some studies have reported that even using the complicated description of the force field for a simplified model,it is still impossible to disclose the specific folding pathways as indicated by all-atom models.And some experiments indicate that the side-chain packing plays a dominant role for the stabilities of proteins. Thus we adopt a model between simple models that are foldable-but-nonspecific and all-atom models that are specific-but-demanding.The model considers all heavy atoms and polar hydrogen atoms,but the interactions between atoms are simplified by the square-well potential.Involving the whole side-chain,the model could thus describe the self-avoiding effects;at the same time square-well potential used for the van der Waals interactions and hydrogen bond is beneficial for save of CPU time and making the discontinuous molecular dynamics(DMD) simulation feasible.We also called this model the all-atom model.In contrast to Monte Carlo(MC) method,a DMD simulation could obtain the more refined protein native structure and more exact kinetic process of folding from a coil to a specific 3-dimensional structure.Gōmodel was used in our DMD simulations.There is a region locating between folded and unfolded state called transition state ensemble(TSE).A two-state small protein affords a good model to studies of TSE.While the folding mechanism ofα-helix is well understood with the investigations of nucleation and propagation and helix-helix interactions,the dynamics ofβ-hairpins is less characterized because the completion and stability ofβ-folds are based on the formation of hydrophobic interactions or hydrogen bonds between residues more separated in sequence.Proteins are folded in water.Simulation of a bio-macromolecule in the presence of explicit solvent molecules is computationally expensive;various implicit solvent models have thus been developed. While various implicit solvent models have been well developed based on continuous potentials,none is available for models based on discontinuous potentials in the formulism of DMD.This Ph.D thesis focuses on the folding of a triple-stranded anti-parallel[3-sheet protein,Pin1 WW domain.The thermodynamics and kinetics as well as the folding mechanisms are investigated in detail.TSE is especially discussed.Another aspect of the thesis is to develop a new off-lattice implicit solvent model for DMD simulations.The main achievements are summarized as follows:1.We study the folding thermodynamics and kinetics of the Pinl WW domain, a three-strandedβ-sheet protein,by using all-atom DMD simulations at various temperatures with a Gōmodel.Near the folding transition temperature,the protein exhibits a two-state folding kinetics between coil and native state indicated by heat capacity,energy distribution and free energy profile.A good agreement between our simulations and the experimental measurements by Gruebele group has been found. The simulation also reveals that the folding pathways at high temperatures and at low temperatures are much different,and an intermediate state at a low temperature is predicted.That low-temperature kinetic intermediate has a formed hairpinβ2-β3.At its folding transition temperature,folding and unfolding is reversible,and hairpinβ1-β2 is formed first.In the unfolding process at higher temperature,hairpinβ2-β3 is dissociated at first.Theoretical results are compared with other simulation results as well as available experimental data.This study confirms that specific side-chain packing in an all-atom Gōmodel can yield a reasonable prediction of specific folding kinetics for a given protein.2.Besides different folding pathways at different temperatures,the folding mechanism of an individualβ-hairpin is also found temperature-dependent.The turn zipper model and the hydrophobic collapse model originally developed for a singleβ-hairpin in the literatures are confirmed to be justified in describingβ-hairpins in Pinl WW domain.We find that the mechanism for folding a specific hairpin is independent of whether it folds first or second,but the formation process is significantly dependent on temperature.More specifically,hairpinβ1-β2 folds via the turn-zipper model at a low temperature,that is,the turn nucleate first and sequential hydrogen bonds formed beginning at the turn and zipping along to the end of the hairpin;and the hydrophobic collapse model at a high temperature,that is,the early hydrophobic collapse at the end of hairpin is stabilized and triggers hairpin formation. The folding of hairpin 132-133 follows the turn-zipper model at both temperatures. Loop 1 connecting hairpin 131-132 is much longer than loop 2 connectingβ2-β3(six residues in the former vs.four ones in the later).The change of folding mechanisms is interpreted by the interplay between contact stability(enthalpy) and loop lengths (entropy),the effect of which is temperature-dependent.3.During the last decade,the probability of folding before unfolding P_fold = 0.5 has been a modem and "standard" criterion to capture TSE of a protein in computer simulations.We however got to oppugn this gold criterion in our hard and time consuming simulations.Recently,a report upon the discussion of "P" versus "Q" encourages us since Wolynes and his coworkers have recalled the validity of the fraction of native contacts Q compared to "P" as a reaction coordinate to judge the TSE of protein on the smooth landscape.To assess the superiority of P_fold,we have compared it with various other criteria in this thesis based upon our all-atom DMD simulations of the Pinl WW domain.The TSEs obtained from different "P","Q" and "R" criteria agree with each other and also with the experimental measurements by the Gruebele group.By analyzing an unsymmetrical free energy profile in an imagined folding experiment,we illustrate that P_fold = 0.5 is NOT a rigorous criterion and the exact value of P_fold associated with TSE is,if not impossible,very hard to be predicted.Under such a circumstance,we prefer trying time-saving criteria first and strongly suggest the combinatory approach.Q-R-plots with Q and two principal components in the best-plane projection of conformation space for a folding trajectory (R1 and R2) as the three structural coordinates were especially recommended.The classification of all criteria employed and improved so far is finally performed. 4.An off-lattice implicit solvent model for DMD simulations is suggested,and confirmed via examination of a single 64-mer self-avoiding homopolymer in a given bead-bead attraction but a variety of bead-solvent interactions.The solvents are treated as ghost solvent "particles" in order to meet the requirements of the DMD algorithm.The solvent accessibility of a specific bead is equivalent to the insertion probability of ghost solvent around that bead.The modified bead-bead square-well potential would involve the components of bead-solvent interaction and solvent accessible probability.Both coil-globule transition and liquid-solid transitions are reproduced with a reasonable trend upon change of bead-solvent interactions.We first found a two-state coil-globule transition for a flexible homopolymer at very good solvent as well as at low temperatures.The characteristic of economic CPU cost of DMD is still kept aider the introduction of the implicit solvent.The present simple model is promising in studies of synthetic polymers and proteins,while some limitations of our model have also been mentioned.