James F. Dama

Fitting coarse-grained distribution functions through an iterative force-matching method

An iterative coarse-graining method is developed for systematically converting an atomistic force field to a model at lower resolution that is able to accurately reproduce the distribution functions defined in the coarse-grained potential. The method starts from the multiscale coarse-graining (MS-CG) approach, and it iteratively refines the distribution functions using repeated applications of the MS-CG algorithm. It is justified on the basis of the force matching normal equation, which can be considered a discrete form of the Yvon-Born-Green equation in liquid state theory. Numerical results for molecular systems involving pairwise nonbonded and three-body bonded interactions are obtained, and comparison with other approaches in literature is provided.

Coarse-grained simulation reveals key features of HIV-1 capsid self-assembly

The maturation of HIV-1 viral particles is essential for viral infectivity. During maturation, many copies of the capsid protein (CA) self-assemble into a capsid shell to enclose the viral RNA. The mechanistic details of the initiation and early stages of capsid assembly remain to be delineated. We present coarse-grained simulations of capsid assembly under various conditions, considering not only capsid lattice self-assembly but also the potential disassembly of capsid upon delivery to the cytoplasm of a target cell. The effects of CA concentration, molecular crowding, and the conformational variability of CA are described, with results indicating that capsid nucleation and growth is a multi-stage process requiring well-defined metastable intermediates. Generation of the mature capsid lattice is sensitive to local conditions, with relatively subtle changes in CA concentration and molecular crowding influencing self-assembly and the ensemble of structural morphologies.

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

Transition-Tempered Metadynamics: Robust, Convergent Metadynamics via On-the-Fly Transition Barrier Estimation.

Well-tempered metadynamics has proven to be a practical and efficient adaptive enhanced sampling method for the computational study of biomolecular and materials systems. However, choosing its tunable parameter can be challenging and requires balancing a trade-off between fast escape from local metastable states and fast convergence of an overall free energy estimate. In this article, we present a new smoothly convergent variant of metadynamics, transition-tempered metadynamics, that removes that trade-off and is more robust to changes in its own single tunable parameter, resulting in substantial speed and accuracy improvements. The new method is specifically designed to study state-to-state transitions in which the states of greatest interest are known ahead of time, but transition mechanisms are not. The design is guided by a picture of adaptive enhanced sampling as a means to increase dynamical connectivity of a models state space until percolation between all points of interest is reached, and it uses the degree of dynamical percolation to automatically tune the convergence rate. We apply the new method to Brownian dynamics on 48 random 1D surfaces, blocked alanine dipeptide in vacuo, and aqueous myoglobin, finding that transition-tempered metadynamics substantially and reproducibly improves upon well-tempered metadynamics in terms of first barrier crossing rate, convergence rate, and robustness to the choice of tuning parameter. Moreover, the trade-off between first barrier crossing rate and convergence rate is eliminated: the new method drives escape from an initial metastable state as fast as metadynamics without tempering, regardless of tuning.

Designing free energy surfaces that match experimental data with metadynamics.

Creating models that are consistent with experimental data is essential in molecular modeling. This is often done by iteratively tuning the molecular force field of a simulation to match experimental data. An alternative method is to bias a simulation, leading to a hybrid model composed of the original force field and biasing terms. We previously introduced such a method called experiment directed simulation (EDS). EDS minimally biases simulations to match average values. In this work, we introduce a new method called experiment directed metadynamics (EDM) that creates minimal biases for matching entire free energy surfaces such as radial distribution functions and phi/psi angle free energies. It is also possible with EDM to create a tunable mixture of the experimental data and free energy of the unbiased ensemble with explicit ratios. EDM can be proven to be convergent, and we also present proof, via a maximum entropy argument, that the final bias is minimal and unique. Examples of its use are given in the construction of ensembles that follow a desired free energy. The example systems studied include a Lennard-Jones fluid made to match a radial distribution function, an atomistic model augmented with bioinformatics data, and a three-component electrolyte solution where ab initio simulation data is used to improve a classical empirical model.

The Theory of Ultra-Coarse-Graining. 2. Numerical Implementation.

The increasing interest in the modeling of complex macromolecular systems in recent years has spurred the development of numerous coarse-graining (CG) techniques. However, many of the CG models are constructed assuming that all details beneath the resolution of CG degrees of freedom are fast and average out, which sets limits on the resolution of feasible coarse-grainings and on the range of applications of the CG models. Ultra-coarse-graining (UCG) makes it possible to construct models at any desired resolution while accounting for discrete conformational or chemical changes within the CG sites that can modulate the interactions between them. Here, we discuss the UCG methodology and its numerical implementation. We pay particular attention to the numerical mechanism for including state transitions between different conformations within CG sites because this has not been discussed previously. Using a simple example of 1,2-dichloroethane, we demonstrate the ability of the UCG model to reproduce the multiconfigurational behavior of this molecular liquid, even when each molecule is modeled with only one CG site. The methodology can also be applied to other molecular liquids and macromolecular systems with time scale separation between conformational transitions and other intramolecular motions and rotations.

Exploring Valleys without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust On-the-Fly Bias Domain Restriction.

Metadynamics is an enhanced sampling method designed to flatten free energy surfaces uniformly. However, the highest-energy regions are often irrelevant to study and dangerous to explore because systems often change irreversibly in unforeseen ways in response to driving forces in these regions, spoiling the sampling. Introducing an on-the-fly domain restriction allows metadynamics to flatten only up to a specified energy level and no further, improving efficiency and safety while decreasing the pressure on practitioners to design collective variables that are robust to otherwise irrelevant high energy driving. This paper describes a new method that achieves this using sequential on-the-fly estimation of energy wells and redefinition of the metadynamics hill shape, termed metabasin metadynamics. The energy level may be defined a priori or relative to unknown barrier energies estimated on-the-fly. Altering only the hill ensures that the method is compatible with many other advances in metadynamics methodology. The hill shape has a natural interpretation in terms of multiscale dynamics, and the computational overhead in simulation is minimal when studying systems of any reasonable size, for instance proteins or other macromolecules. Three example applications show that the formula is accurate and robust to complex dynamics, making metadynamics significantly more forgiving with respect to CV quality and thus more feasible to apply to the most challenging biomolecular systems.

On the representability problem and the physical meaning of coarse-grained models.

In coarse-grained (CG) models where certain fine-grained (FG, i.e., atomistic resolution) observables are not directly represented, one can nonetheless identify indirect the CG observables that capture the FG observables dependence on CG coordinates. Often, in these cases it appears that a CG observable can be defined by analogy to an all-atom or FG observable, but the similarity is misleading and significantly undermines the interpretation of both bottom-up and top-down CG models. Such problems emerge especially clearly in the framework of the systematic bottom-up CG modeling, where a direct and transparent correspondence between FG and CG variables establishes precise conditions for consistency between CG observables and underlying FG models. Here we present and investigate these representability challenges and illustrate them via the bottom-up conceptual framework for several simple analytically tractable polymer models. The examples provide special focus on the observables of configurational internal energy, entropy, and pressure, which have been at the root of controversy in the CG literature, as well as discuss observables that would seem to be entirely missing in the CG representation but can nonetheless be correlated with CG behavior. Though we investigate these problems in the framework of systematic coarse-graining, the lessons apply to top-down CG modeling also, with crucial implications for simulation at constant pressure and surface tension and for the interpretations of structural and thermodynamic correlations for comparison to experiment.

Solvent Free Ionic Solution Models from Multiscale Coarse-Graining.

Solvent free models for aqueous ionic solutions are derived using the multiscale coarse-graining (MS-CG) method to obtain many-body potentials of mean force and generalized Langevin equations to propagate the model in time. The resulting models are compared to other implicit solvent models for aqueous NaCl in terms of both sampling efficiency and accuracy. First, the equilibrium structural properties of the models are compared, and then the temperature dependence of the interion potentials of mean force are determined to obtain the pairwise entropy associated with the effective ionic interactions. After validating the equilibrium behavior of the new models, the dynamical properties are investigated using generalized Langevin equation dynamics simulations. The dynamical properties can be put into better agreement with the original atomistic models by introducing an exponential memory kernel to account for the strong coupling between the ions and their water solvation shells.

Simulating Protein Mediated Hydrolysis of ATP and Other Nucleoside Triphosphates by Combining QM/MM Molecular Dynamics with Advances in Metadynamics

The protein mediated hydrolysis of nucleoside triphosphates such as ATP or GTP is one of the most important and challenging biochemical reactions in nature. The chemical environment (water structure, catalytic metal, and amino acid residues) adjacent to the hydrolysis site contains hundreds of atoms, usually greatly limiting the amount of the free energy sampling that one can achieve from computationally demanding electronic structure calculations such as QM/MM simulations. Therefore, the combination of QM/MM molecular dynamics with the recently developed transition-tempered metadynamics (TTMetaD), an enhanced sampling method that can provide a high-quality free energy estimate at an early stage in a simulation, is an ideal approach to address the biomolecular nucleoside triphosphate hydrolysis problem. In this work the ATP hydrolysis process in monomeric and filamentous actin is studied as an example application of the combined methodology. The performance of TTMetaD in these demanding QM/MM simulations is compared with that of the more conventional well-tempered metadynamics (WTMetaD). Our results show that TTMetaD exhibits much better exploration of the hydrolysis reaction free energy surface in two key collective variables (CVs) during the early stages of the QM/MM simulation than does WTMetaD. The TTMetaD simulations also reveal that a key third degree of freedom, the O-H bond-breaking and proton transfer from the lytic water, must be biased for TTMetaD to converge fully. To perturb the NTP hydrolysis dynamics to the least extent and to properly focus the MetaD free energy sampling, we also adopt here the recently developed metabasin metadynamics (MBMetaD) to construct a self-limiting bias potential that only applies to the lytic water after its nucleophilic attack of the phosphate of ATP. With these new, state-of-the-art enhanced sampling metadynamics techniques, we present an effective and accurate computational strategy for combining QM/MM molecular dynamics simulation with free energy sampling methodology, including a means to analyze the convergence of the calculations through robust numerical criteria.