Dynamics Sampling in Transition Pathway Space

The minimum energy pathway contains important information describing the transition between two states on a potential energy surface (PES). Chain-of-states methods were developed to efficiently calculate minimum energy pathways connecting two stable states. In the chain-of-states framework, a series of structures are generated and optimized to represent the minimum energy pathway connecting two states. However, multiple pathways may exist connecting two existing states and should be identified to obtain a full view of the transitions. Therefore, we developed an enhanced sampling method, named as the direct pathway dynamics sampling (DPDS) method, to facilitate exploration of a PES for multiple pathways connecting two stable states as well as addition minima and their associated transition pathways. In the DPDS method, molecular dynamics simulations are carried out on the targeting PES within a chain-of-states framework to directly sample the transition pathway space. The simulations of DPDS could be regulated by two parameters controlling distance among states along the pathway and smoothness of the pathway. One advantage of the chain-of-states framework is that no specific reaction coordinates are necessary to generate the reaction pathway, because such information is implicitly represented by the structures along the pathway. The chain-of-states setup in a DPDS method greatly enhances the sufficient sampling in high-energy space between two end states, such as transition states. By removing the constraint on the end states of the pathway, DPDS will also sample pathways connecting minima on a PES in addition to the end points of the starting pathway. This feature makes DPDS an ideal method to directly explore transition pathway space. Three examples demonstrate the efficiency of DPDS methods in sampling the high-energy area important for reactions on the PES

Identifying Key Residues for Protein Allostery through Rigid Residue Scan

Allostery is a ubiquitous process for protein regulatory activity in which a binding event can change a protein’s function carried out at a distal site. Despite intensive theoretical and experimental investigation of protein allostery in the past five decades, effective methods have yet to be developed that can systematically identify key residues involved in allosteric mechanisms. In this study, we propose the rigid residue scan as a systematic approach to identify important allosteric residues. The third PDZ domain (PDZ3) in the postsynaptic density 95 protein (PSD-95) is used as a model system, and each amino acid residue is treated as a single rigid body during independent molecular dynamics simulations. Various indices based on cross-correlation matrices are used, which allow for two groups of residues with different functions to be identified. The first group is proposed as “switches” that are needed to “turn on” the binding effect of protein allostery. The second group is proposed as “wire residues” that are needed to propagate energy or information from the binding site to distal locations within the same protein. Among the nine residues suggested as important for PDZ3 intramolecular communication in this study, eight have been reported as critical for allostery in PDZ3. Therefore, the rigid residue scan approach is demonstrated to be an effective method for systemically identifying key residues in protein intramolecular communication and allosteric mechanisms

Heat maps of individual residue entropic contribution under rigid residue perturbation for unbound (left) and bound (right) states.

<p>The entropic contribution from each residue in unperturbed simulations (with index as 0 in both plots) is set as reference.</p

Right- and Left-Handed Helices, What is in between? Interconversion of Helical Structures of Alternating Pyridinedicarboxamide/<i>m</i>‑(phenylazo)azobenzene Oligomers

Some unnatural polymers/oligomers have been designed to adopt a well-defined, compact, three-dimensional folding capability. Azobenzene units are common linkages in these oligomer designs. Two alternating pyridinedicarboxamide/<i>m</i>-(phenylazo)­azobenzene oligomers that can fold into both right- and left-handed helices were studied computationally in order to understand their dynamical properties. Helical structures were shown to be the global minima among the many different conformations generated from the Monte Carlo simulations, and extended conformations have higher potential energies than compact ones. To understand the interconversion process between right- and left-handed helices, replica-exchange molecular dynamic (REMD) simulations were performed on both oligomers, and with this method, both right- and left-handed helices were successfully sampled during the simulations. REMD trajectories revealed twisted conformations as intermediate structures in the interconversion pathway between the two helical forms of these azobenzene oligomers. This mechanism was observed in both oligomers in current study and occurred locally in the larger oligomer. This discovery indicates that the interconversion between helical structures with different handedness goes through a compact and partially folded structure instead of globally unfold and extended structure. This is also verified by the nudged elastic band (NEB) calculations. The temperature weighted histogram analysis method (T-WHAM) was applied on the REMD results to generate contour maps of the potential of mean force (PMF). Analysis showed that right- and left-handed helices are equally sampled in these REMD simulations. In large oligomers, both right- and left-handed helices can be adopted by different parts of the molecule simultaneously. The interconversion between two helical forms can occur in the middle of the helical structure and not necessarily at the termini of the oligomer

Rigid Residue Scan Simulations Systematically Reveal Residue Entropic Roles in Protein Allostery

<div><p>Intra-protein information is transmitted over distances via allosteric processes. This ubiquitous protein process allows for protein function changes due to ligand binding events. Understanding protein allostery is essential to understanding protein functions. In this study, allostery in the second PDZ domain (PDZ2) in the human PTP1E protein is examined as model system to advance a recently developed rigid residue scan method combining with configurational entropy calculation and principal component analysis. The contributions from individual residues to whole-protein dynamics and allostery were systematically assessed via rigid body simulations of both unbound and ligand-bound states of the protein. The entropic contributions of individual residues to whole-protein dynamics were evaluated based on covariance-based correlation analysis of all simulations. The changes of overall protein entropy when individual residues being held rigid support that the rigidity/flexibility equilibrium in protein structure is governed by the La Châtelier’s principle of chemical equilibrium. Key residues of PDZ2 allostery were identified with good agreement with NMR studies of the same protein bound to the same peptide. On the other hand, the change of entropic contribution from each residue upon perturbation revealed intrinsic differences among all the residues. The quasi-harmonic and principal component analyses of simulations without rigid residue perturbation showed a coherent allosteric mode from unbound and bound states, respectively. The projection of simulations with rigid residue perturbation onto coherent allosteric modes demonstrated the intrinsic shifting of ensemble distributions supporting the population-shift theory of protein allostery. Overall, the study presented here provides a robust and systematic approach to estimate the contribution of individual residue internal motion to overall protein dynamics and allostery.</p></div

Key residues recognized based on protein entropic response to rigid body perturbation.

<p>Key residues recognized based on protein entropic response to rigid body perturbation.</p

RMSD for the unperturbed (no rigid residue perturbation) molecular dynamics simulations of both unbound and bound PDZ2.

<p>The RMSD is determined relative to the initial simulation structure of each simulation.</p

Distribution of unperturbed states projected onto a 2D surface using two PC1 modes.

<p>Only one set of 30 ns trajectories are used for sake of consistency with RRS simulations.</p

Average entropic response from each residue in all RRS simulations.

<p>Average entropic response from each residue in all RRS simulations.</p

Distributions of density of states for unperturbed unbound and bound states.

<p>Distributions of density of states for unperturbed unbound and bound states.</p