Satisfying the fluctuation theorem in free-energy calculations with Hamiltonian replica exchange

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

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.

Generalized Scalable Multiple Copy Algorithms for Molecular Dynamics Simulations in NAMD

Computational methodologies that couple the dynamical evolution of a set of replicated copies of a system of interest offer powerful and flexible approaches to characterize complex molecular processes. Such multiple copy algorithms (MCAs) can be used to enhance sampling, compute reversible work and free energies, as well as refine transition pathways. Widely used examples of MCAs include temperature and Hamiltonian-tempering replica-exchange molecular dynamics (T-REMD and H-REMD), alchemical free energy perturbation with lambda replica-exchange (FEP/λ-REMD), umbrella sampling with Hamiltonian replica exchange (US/H-REMD), and string method with swarms-of-trajectories conformational transition pathways. Here, we report a robust and general implementation of MCAs for molecular dynamics (MD) simulations in the highly scalable program NAMD built upon the parallel programming system Charm++. Multiple concurrent NAMD instances are launched with internal partitions of Charm++ and located continuously within a single communication world. Messages between NAMD instances are passed by low-level point-to-point communication functions, which are accessible through NAMD's Tcl scripting interface. The communication-enabled Tcl scripting provides a sustainable application interface for end users to realize generalized MCAs without modifying the source code. Illustrative applications of MCAs with fine-grained inter-copy communication structure, including global lambda exchange in FEP/λ-REMD, window swapping US/H-REMD in multidimensional order parameter space, and string method with swarms-of-trajectories were carried out on IBM Blue Gene/Q to demonstrate the versatility and massive scalability of the present implementation.

New estimators for calculating solvation entropy and enthalpy and comparative assessments of their accuracy and precision

We present two new methods for estimating the entropy and enthalpy decomposition of free energy calculations. These methods are based on temperature derivatives of the Bennett Acceptance Ratio and the Multistate Bennett Acceptance Ratio estimators, respectively. We test the accuracy of these new estimators using a simple one-dimensional model. A detailed assessment of their performance is reported by studying the solvation of N-methylacetamide. Finally, we quantify the free energies of solvation for 11 model compounds using the OPLS-AA force field and a variation of this force field. Thermodynamic decompositions of these calculated free energies are obtained to highlight the utility of these quantities for refining force field parameters by comparing computed free energies and their decompositions to their experimental counterparts.

Replica exchange with nonequilibrium switches

We introduce a replica exchange (parallel tempering) method in which attempted configuration swaps are generated using nonequilibrium work simulations. By effectively increasing phase space overlap, this approach mitigates the need for many replicas. We illustrate our method by using a model system and show that it is able to achieve the computational efficiency of ordinary replica exchange, using fewer replicas.

Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Aggregation of expanded polyglutamine tracts is associated with nine different neurodegenerative diseases, including Huntington's disease. Experiments and computer simulations have demonstrated that monomeric forms of polyglutamine molecules sample heterogeneous sets of collapsed structures in water. The current work focuses on a mechanistic characterization of polyglutamine homodimerization as a function of chain length and temperature. These studies were carried out using molecular simulations based on a recently developed continuum solvation model that was designed for studying conformational and binding equilibria of intrinsically disordered molecules such as polyglutamine systems. The main results are as follows: Polyglutamine molecules form disordered, collapsed globules in aqueous solution. These molecules spontaneously associate at conditions approaching those of typical in vitro experiments for chains of length N>/=15. The spontaneity of these homotypic associations increases with increasing chain length and decreases with increasing temperature. Similar and generic driving forces govern both collapse and spontaneous homodimerization of polyglutamine in aqueous milieus. Collapse and dimerization maximize self-interactions and reduce the interface between polyglutamine molecules and the surrounding solvent. Other than these generic considerations, there do not appear to be any specific structural requirements for either chain collapse or chain dimerization; that is, both collapse and dimerization are nonspecific in that disordered globules form disordered dimers. In fact, it is shown that the driving force for intermolecular associations is governed by spontaneous conformational fluctuations within monomeric polyglutamine. These results suggest that polyglutamine aggregation is unlikely to follow a homogeneous nucleation mechanism with the monomer as the critical nucleus. Instead, the results support the formation of disordered, non-beta-sheet-like soluble molten oligomers as early intermediates--a proposal that is congruent with recent experimental data.