Middle-way flexible docking: Pose prediction using mixed-resolution Monte Carlo in estrogen receptor α.

There is a vast gulf between the two primary strategies for simulating protein-ligand interactions. Docking methods significantly limit or eliminate protein flexibility to gain great speed at the price of uncontrolled inaccuracy, whereas fully flexible atomistic molecular dynamics simulations are expensive and often suffer from limited sampling. We have developed a flexible docking approach geared especially for highly flexible or poorly resolved targets based on mixed-resolution Monte Carlo (MRMC), which is intended to offer a balance among speed, protein flexibility, and sampling power. The binding region of the protein is treated with a standard atomistic force field, while the remainder of the protein is modeled at the residue level with a Go model that permits protein flexibility while saving computational cost. Implicit solvation is used. Here we assess three facets of the MRMC approach with implications for other docking studies: (i) the role of receptor flexibility in cross-docking pose prediction; (ii) the use of non-equilibrium candidate Monte Carlo (NCMC) and (iii) the use of pose-clustering in scoring. We examine 61 co-crystallized ligands of estrogen receptor α, an important cancer target known for its flexibility. We also compare the performance of the MRMC approach with Autodock smina. Adding protein flexibility, not surprisingly, leads to significantly lower total energies and stronger interactions between protein and ligand, but notably we document the important role of backbone flexibility in the improvement. The improved backbone flexibility also leads to improved performance relative to smina. Somewhat unexpectedly, our implementation of NCMC leads to only modestly improved sampling of ligand poses. Overall, the addition of protein flexibility improves the performance of docking, as measured by energy-ranked poses, but we do not find significant improvements based on cluster information or the use of NCMC. We discuss possible improvements for the model including alternative coarse-grained force fields, improvements to the treatment of solvation, and adding additional types of NCMC moves.

Computational Estimation of Microsecond to Second Atomistic Folding Times.

Despite the development of massively parallel computing hardware including inexpensive graphics processing units (GPUs), it has remained infeasible to simulate the folding of atomistic proteins at room temperature using conventional molecular dynamics (MD) beyond the microsecond scale. Here, we report the folding of atomistic, implicitly solvated protein systems with folding times τ ranging from ∼10 µs to ∼100 ms using the weighted ensemble (WE) strategy in combination with GPU computing. Starting from an initial structure or set of structures, WE organizes an ensemble of GPU-accelerated MD trajectory segments via intermittent pruning and replication events to generate statistically unbiased estimates of rate constants for rare events such as folding; no biasing forces are used. Although the variance among atomistic WE folding runs is significant, multiple independent runs are used to reduce and quantify statistical uncertainty. Folding times are estimated directly from WE probability flux and from history-augmented Markov analysis of the WE data. Three systems were examined: NTL9 at low solvent viscosity (yielding τf = 0.8-9 µs), NTL9 at water-like viscosity (τf = 0.2-2 ms), and Protein G at low viscosity (τf = 3-200 ms). In all cases, the folding time, uncertainty, and ensemble properties could be estimated from WE simulation; for Protein G, this characterization required significantly less overall computing than would be required to observe a single folding event with conventional MD simulations. Our results suggest that the use and calibration of force fields and solvent models for precise estimation of kinetic quantities is becoming feasible.

Identification of an Electrostatic Ruler Motif for Sequence-Specific Binding of Collagenase to Collagen.

Sequence-specific cleavage of collagen by mammalian collagenase plays a pivotal role in cell function. Collagenases are matrix metalloproteinases that cleave the peptide bond at a specific position on fibrillar collagen. The collagenase Hemopexin-like (HPX) domain has been proposed to be responsible for substrate recognition, but the mechanism by which collagenases identify the cleavage site on fibrillar collagen is not clearly understood. In this study, Brownian dynamics simulations coupled with atomic-detail and coarse-grained molecular dynamics simulations were performed to dock matrix metalloproteinase-1 (MMP-1) on a collagen IIIα1 triple helical peptide. We find that the HPX domain recognizes the collagen triple helix at a conserved R-X11-R motif C-terminal to the cleavage site to which the HPX domain of collagen is guided electrostatically. The binding of the HPX domain between the two arginine residues is energetically stabilized by hydrophobic contacts with collagen. From the simulations and analysis of the sequences and structural flexibility of collagen and collagenase, a mechanistic scheme by which MMP-1 can recognize and bind collagen for proteolysis is proposed.

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 nonequilibrium 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, 70, 97-110] to generate equilibrium trajectory ensembles and extract nonequilibrium 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 nonequilibrium 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.

Molecular dynamic simulation studies on the effect of one residue chain staggering on the structure and stability of heterotrimeric collagen-like peptides with interruption.

A systematic molecular dynamics (MD) simulation has been carried out on collagen-like peptides with different combinations of interruptions in the Gly-X(AA) -Y(AA) repeats. Although experimental studies have been carried out to elucidate the structural consequences of homotrimeric collagen-like peptides, this is the first report on the structural effect on the heterotrimeric models with G4G and G1G breaks present simultaneously in the constituent chains with difference in one residue chain staggering. The results reveal that the axial registry of the interrupted region changes significantly from that of conventional triple helical peptide without interruption. Further, results from MD simulations show the formation of a kink in the interrupted region of the triple-helical peptides. The conformational analysis reveals that the interruption in the Gly-X(AA) -Y(AA) pattern in these peptides induces ß-strand conformation in triple helical peptides. The conventional hydrogen bonds in the interrupted triad are affected and new nonconventional H-bonds are formed in the triple helical structure, and as a result interrupted region becomes locally fragile. MM-PBSA calculations on the different systems clearly suggest that the binding affinity varies marginally due to one residue staggering. However, it is found from the structural parameters that hydrogen-bonding pattern differs significantly due to the difference in the staggering of chains.