Efficient Computer Simulations of Protein-Peptide Binding Using Weighted Ensemble Sampling

Molecular dynamics simulations can, in principle, provide detailed views of protein-protein association processes. However, these processes frequently occur on timescales inaccessible on current computing resources. These are not particularly slow processes, but rather they are rare — fast but infrequent. The weighted ensemble (WE) sampling approach provides a way to exploit this separation of timescales and focus computing power efficiently on rare events. In this work, it is demonstrated that WE sampling can be used to efficiently obtain kinetic rate constants, pathways, and energy landscapes of molecular association processes. Chapter 1 of this dissertation further discusses the need for enhanced sampling techniques like the WE approach. In Chapter 2, WE sampling is used to study the kinetics of association of four model molecular recognition systems (methane/methane, Na+/Cl–, methane/benzene, and K+/18-crown-6 ether) using molecular dynamics (MD) simulations in explicit water. WE sampling reproduces straightforward “brute force” results while increasing the efficiency of sampling by up to three orders of magnitude. Importantly, the efficiency of WE simulation increases with increasing complexity of the systems under consideration. In Chapter 3, weighted ensemble Brownian dynamics (BD) simulations are used to explore the association between a 13-residue fragment of the p53 tumor suppressor and the MDM2 oncoprotein. The association rates obtained compare favorably with experiment. By directly comparing both flexible and pre-organized variants of p53, it is shown that the “fly-casting” effect, by which natively unstructured proteins may increase their association rates, is not significant in MDM2-p53 peptide binding. Including hydrodynamic interactions in the simulation model dramatically alters the association rate, indicating that the detailed motion of solvent may have substantial effects on the kinetics of protein-protein association. In Chapter 4, an all-atom molecular dynamics simulation of p53-MDM2 binding is described. We obtain an association rate that agrees with the experimental value. The free energy landscape of binding is “funnel-like”, downhill after the initial encounter between p53 and MDM2. Together, the studies described here establish that WE sampling is highly effective in simulating rare molecular association events

Simultaneous computation of dynamical and equilibrium information using a weighted ensemble of trajectories

Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many non-equilibrium processes can be described by suitable subsets of the equilibrium ensemble. Here, we employ the "weighted ensemble" (WE) simulation protocol [Huber and Kim, Biophys. J., 1996] to generate equilibrium trajectory ensembles and extract non-equilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance. The procedure formally allows estimation of kinetic rates between arbitrary states chosen after the simulation, along with their equilibrium populations. We also describe a related history-dependent matrix procedure for estimating equilibrium and non-equilibrium observables when phase space has been divided into arbitrary non-Markovian regions, whether in WE or ordinary simulation. In this proof-of-principle study, these methods are successfully applied and validated on two molecular systems: explicitly solvated methane association and the implicitly solvated Ala4 peptide. We comment on challenges remaining in WE calculations

Simulations of the Alternating Access Mechanism of the Sodium Symporter Mhp1

AbstractSodium coupled cotransporters of the five-helix inverted repeat (5HIR) superfamily use an alternating access mechanism to transport a myriad of small molecules across the cell membrane. One of the primary steps in this mechanism is the conformational transition from a state poised to bind extracellular substrates to a state that is competent to deliver substrate to the cytoplasm. Here, we construct a coarse-grained model of the 5HIR benzylhydantoin transporter Mhp1 that incorporates experimental structures of the outward- and inward-open states to investigate the mechanism of this conformational change. Using the weighted ensemble path-sampling method, we rigorously sample the outward- to inward-facing transition path ensemble. The transition path ensemble reveals a heterogeneous set of pathways connecting the two states and identifies two modes of transport: one consistent with a strict alternating access mechanism and another where decoupling of the inner and outer gates causes the transient formation of a continuous permeation pathway through the transporter. We also show that the conformational switch between the outward- and inward-open states results from rigid body motions of the hash motif relative to the substrate bundle, supporting the rocking bundle hypothesis. Finally, our methodology provides the groundwork for more chemically detailed investigations of the alternating mechanism

Efficient Atomistic Simulation of Pathways and Calculation of Rate Constants for a Protein–Peptide Binding Process: Application to the MDM2 Protein and an Intrinsically Disordered p53 Peptide

The characterization of protein binding processes  with all of the key conformational changes  has been a grand challenge in the field of biophysics. Here, we have used the weighted ensemble path sampling strategy to orchestrate molecular dynamics simulations, yielding atomistic views of protein–peptide binding pathways involving the MDM2 oncoprotein and an intrinsically disordered p53 peptide. A total of 182 independent, continuous binding pathways were generated, yielding a <i>k</i>_on that is in good agreement with experiment. These pathways were generated in 15 days using 3500 cores of a supercomputer, substantially faster than would be possible with “brute force” simulations. Many of these pathways involve the anchoring of p53 residue F19 into the MDM2 binding cleft when forming the metastable encounter complex, indicating that F19 may be a kinetically important residue. Our study demonstrates that it is now practical to generate pathways and calculate rate constants for protein binding processes using atomistic simulation on typical computing resources

WESTPA: An Interoperable, Highly Scalable Software Package for Weighted Ensemble Simulation and Analysis

The weighted ensemble (WE) path sampling approach orchestrates an ensemble of parallel calculations with intermittent communication to enhance the sampling of rare events, such as molecular associations or conformational changes in proteins or peptides. Trajectories are replicated and pruned in a way that focuses computational effort on underexplored regions of configuration space while maintaining rigorous kinetics. To enable the simulation of rare events at any scale (e.g., atomistic, cellular), we have developed an open-source, interoperable, and highly scalable software package for the execution and analysis of WE simulations: WESTPA (The Weighted Ensemble Simulation Toolkit with Parallelization and Analysis). WESTPA scales to thousands of CPU cores and includes a suite of analysis tools that have been implemented in a massively parallel fashion. The software has been designed to interface conveniently with any dynamics engine and has already been used with a variety of molecular dynamics (e.g., GROMACS, NAMD, OpenMM, AMBER) and cell-modeling packages (e.g., BioNetGen, MCell). WESTPA has been in production use for over a year, and its utility has been demonstrated for a broad set of problems, ranging from atomically detailed host–guest associations to nonspatial chemical kinetics of cellular signaling networks. The following describes the design and features of WESTPA, including the facilities it provides for running WE simulations and storing and analyzing WE simulation data, as well as examples of input and output

Fretting about FRET: Correlation between κ and R

Molecular dynamics simulations were used to examine the structural dynamics of two fluorescent probes attached to a typical protein, hen egg-white lysozyme (HEWL). The donor probe (D) was attached via a succinimide group, consistent with the commonly-used maleimide conjugation chemistry, and the acceptor probe (A) was bound into the protein as occurs naturally for HEWL and the dye Eosin Y. The 〈κ2〉 is found to deviate significantly from the theoretical value and high correlation between the orientation factor κ and the distance R is observed. The correlation is quantified using several possible fixed A orientations and correlation as high as 0.80 is found between κ and R and as high as 0.68 between κ2 and R. The presence of this correlation highlights the fact that essentially all fluorescence-detected resonance energy transfer studies have assumed that κ and R are independent—an assumption that is clearly not justified in the system studied here. The correlation results in the quantities 〈κ2R−6〉 and 〈κ2〉 〈R−6〉 differing by a factor of 1.6. The observed correlation between κ and R is caused by the succinimide linkage between the D and HEWL, which is found to be relatively inflexible