Tunable, mixed-resolution modeling using library-based Monte Carlo and graphics processing units

From quantum to subcellular scales: multi-scale simulation approaches and the SIRAH force field

Modern molecular and cellular biology profits from astonishing resolution structural methods, currently even reaching the whole cell level. This is encompassed by the development of computational methods providing a deep view into the structure and dynamics of molecular processes happening at very different scales in time and space. Linking such scales is of paramount importance when aiming at far-reaching biological questions. Computational methods at the interface between classical and coarse-grained resolutions are gaining momentum with several research groups dedicating important efforts to their development and tuning. An overview of such methods is addressed herein, with special emphasis on the SIRAH force field for coarse-grained and multi-scale simulations. Moreover, we provide proof of concept calculations on the implementation of a multi-scale simulation scheme including quantum calculations on a classical fine-grained/coarse-grained representation of double-stranded DNA. This opens the possibility to include the effect of large conformational fluctuations in chromatin segments on, for instance, the reactivity of particular base pairs within the same simulation framework.

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 Gō 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.

Multifidelity Analysis for Predicting Rare Events in Stochastic Computational Models of Complex Biological Systems

Rare events such as genetic mutations or cell-cell interactions are important contributors to dynamics in complex biological systems, eg, in drug-resistant infections. Computational approaches can help analyze rare events that are difficult to study experimentally. However, analyzing the frequency and dynamics of rare events in computational models can also be challenging due to high computational resource demands, especially for high-fidelity stochastic computational models. To facilitate analysis of rare events in complex biological systems, we present a multifidelity analysis approach that uses medium-fidelity analysis (Monte Carlo simulations) and/or low-fidelity analysis (Markov chain models) to analyze high-fidelity stochastic model results. Medium-fidelity analysis can produce large numbers of possible rare event trajectories for a single high-fidelity model simulation. This allows prediction of both rare event dynamics and probability distributions at much lower frequencies than high-fidelity models. Low-fidelity analysis can calculate probability distributions for rare events over time for any frequency by updating the probabilities of the rare event state space after each discrete event of the high-fidelity model. To validate the approach, we apply multifidelity analysis to a high-fidelity model of tuberculosis disease. We validate the method against high-fidelity model results and illustrate the application of multifidelity analysis in predicting rare event trajectories, performing sensitivity analyses and extrapolating predictions to very low frequencies in complex systems. We believe that our approach will complement ongoing efforts to enable accurate prediction of rare event dynamics in high-fidelity computational models.

Hybrid All-Atom/Coarse-Grained Simulations of Proteins by Direct Coupling of CHARMM and PRIMO Force Fields

Hybrid all-atom/coarse-grained (AA/CG) simulations of proteins offer a computationally efficient compromise where atomistic details are only applied to biologically relevant regions while benefiting from the speedup of treating the remaining parts of a given system at the CG level. The recently developed CG model, PRIMO, allows a direct coupling with an atomistic force field with no additional modifications or coupling terms and the ability to carry out dynamic simulations without any restraints on secondary or tertiary structures. A hybrid AA/CG scheme based on combining all-atom CHARMM and coarse-grained PRIMO representations was validated via molecular dynamics and replica exchange simulations of soluble and membrane proteins. The AA/CG scheme was also tested in the calculation of the free energy profile for the transition from the closed to the open state of adenylate kinase via umbrella sampling molecular dynamics method. The overall finding is that the AA/CG scheme generates dynamics and energetics that are qualitatively and quantitatively comparable to AA simulations while offering the computational advantages of coarse-graining. This model opens the door to challenging applications where high accuracy is required only in parts of large biomolecular complexes.

Improvements, trends, and new ideas in molecular docking: 2012-2013 in review

Molecular docking is a computational method for predicting the placement of ligands in the binding sites of their receptor(s). In this review, we discuss the methodological developments that occurred in the docking field in 2012 and 2013, with a particular focus on the more difficult aspects of this computational discipline. The main challenges and therefore focal points for developments in docking, covered in this review, are receptor flexibility, solvation, scoring, and virtual screening. We specifically deal with such aspects of molecular docking and its applications as selection criteria for constructing receptor ensembles, target dependence of scoring functions, integration of higher-level theory into scoring, implicit and explicit handling of solvation in the binding process, and comparison and evaluation of docking and scoring methods.

Tunable Coarse Graining for Monte Carlo Simulations of Proteins via Smoothed Energy Tables: Direct and Exchange Simulations

Many commonly used coarse-grained models for proteins are based on simplified interaction sites and consequently may suffer from significant limitations, such as the inability to properly model protein secondary structure without the addition of restraints. Recent work on a benzene fluid (Lettieri S.; Zuckerman D. M.J. Comput. Chem.2012, 33, 268-275) suggested an alternative strategy of tabulating and smoothing fully atomistic orientation-dependent interactions among rigid molecules or fragments. Here we report our initial efforts to apply this approach to the polar and covalent interactions intrinsic to polypeptides. We divide proteins into nearly rigid fragments, construct distance and orientation-dependent tables of the atomistic interaction energies between those fragments, and apply potential energy smoothing techniques to those tables. The amount of smoothing can be adjusted to give coarse-grained models that range from the underlying atomistic force field all the way to a bead-like coarse-grained model. For a moderate amount of smoothing, the method is able to preserve about 70-90% of the α-helical structure while providing a factor of 3-10 improvement in sampling per unit computation time (depending on how sampling is measured). For a greater amount of smoothing, multiple folding-unfolding transitions of the peptide were observed, along with a factor of 10-100 improvement in sampling per unit computation time, although the time spent in the unfolded state was increased compared with less smoothed simulations. For a β hairpin, secondary structure is also preserved, albeit for a narrower range of the smoothing parameter and, consequently, for a more modest improvement in sampling. We have also applied the new method in a "resolution exchange" setting, in which each replica runs a Monte Carlo simulation with a different degree of smoothing. We obtain exchange rates that compare favorably to our previous efforts at resolution exchange (Lyman E.; Zuckerman D. M.J. Chem. Theory Comput.2006, 2, 656-666).

Hamiltonian Switch Metropolis Monte Carlo Simulations for Improved Conformational Sampling of Intrinsically Disordered Regions Tethered to Ordered Domains of Proteins

There is growing interest in the topic of intrinsically disordered proteins (IDPs). Atomistic Metropolis Monte Carlo (MMC) simulations based on novel implicit solvation models have yielded useful insights regarding sequence-ensemble relationships for IDPs modeled as autonomous units. However, a majority of naturally occurring IDPs are tethered to ordered domains. Tethering introduces additional energy scales and this creates the challenge of broken ergodicity for standard MMC sampling or molecular dynamics that cannot be readily alleviated by using generalized tempering methods. We have designed, deployed, and tested our adaptation of the Nested Markov Chain Monte Carlo sampling algorithm. We refer to our adaptation as Hamiltonian Switch Metropolis Monte Carlo (HS-MMC) sampling. In this method, transitions out of energetic traps are enabled by the introduction of an auxiliary Markov chain that draws conformations for the disordered region from a Boltzmann distribution that is governed by an alternative potential function that only includes short-range steric repulsions and conformational restraints on the ordered domain. We show using multiple, independent runs that the HS-MMC method yields conformational distributions that have similar and reproducible statistical properties, which is in direct contrast to standard MMC for equivalent amounts of sampling. The method is efficient and can be deployed for simulations of a range of biologically relevant disordered regions that are tethered to ordered domains.

Paramagnetic metal ions in pulsed ESR distance distribution measurements

The use of pulsed electron spin resonance (ESR) to measure interspin distance distributions has advanced biophysical research. The three major techniques that use pulsed ESR are relaxation rate based distance measurements, double quantum coherence (DQC), and double electron electron resonance (DEER). Among these methods, the DEER technique has become particularly popular largely because it is easy to implement on commercial instruments and because programs are available to analyze experimental data. Researchers have widely used DEER to measure the structure and conformational dynamics of molecules labeled with the methanethiosulfonate spin label (MTSSL). Recently, researchers have exploited endogenously bound paramagnetic metal ions as spin probes as a way to determine structural constraints in metalloproteins. In this context Cu(2+) has served as a useful paramagnetic metal probe at X-band for DEER based distance measurements. Sample preparation is simple, and a coordinated-Cu(2+) ion offers limited spatial flexibility, making it an attractive probe for DEER experiments. On the other hand, Cu(2+) has a broad absorption ESR spectrum at low temperature, which leads to two potential complications. First, the Cu(2+)-based DEER time domain data has lower signal to noise ratio compared with MTSSL. Second, accurate distance distribution analysis often requires high-quality experimental data at different external magnetic fields or with different frequency offsets. In this Account, we summarize characteristics of Cu(2+)-based DEER distance distribution measurements and data analysis methods. We highlight a novel application of such measurements in a protein-DNA complex to identify the metal ion binding site and to elucidate its chemical mechanism of function. We also survey the progress of research on other metal ions in high frequency DEER experiments.