Enhanced sampling in molecular dynamics using metadynamics, replica-exchange, and temperature-acceleration

We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods. \ua9 2013 by the author; licensee MDPI, Basel, Switzerland

Transferable neural networks for enhanced sampling of protein dynamics

Variational auto-encoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single non-linear embedding. In this work, we illustrate how this non-linear latent embedding can be used as a collective variable for enhanced sampling, and present a simple modification that allows us to rapidly perform sampling in multiple related systems. We first demonstrate our method is able to describe the effects of force field changes in capped alanine dipeptide after learning a model using AMBER99. We further provide a simple extension to variational dynamics encoders that allows the model to be trained in a more efficient manner on larger systems by encoding the outputs of a linear transformation using time-structure based independent component analysis (tICA). Using this technique, we show how such a model trained for one protein, the WW domain, can efficiently be transferred to perform enhanced sampling on a related mutant protein, the GTT mutation. This method shows promise for its ability to rapidly sample related systems using a single transferable collective variable and is generally applicable to sets of related simulations, enabling us to probe the effects of variation in increasingly large systems of biophysical interest.Comment: 20 pages, 10 figure

Determination of protein structural ensembles using cryo-electron microscopy.

Achieving a comprehensive understanding of the behaviour of proteins is greatly facilitated by the knowledge of their structures, thermodynamics and dynamics. All this information can be provided in an effective manner in terms of structural ensembles. A structural ensemble can be obtained by determining the structures, populations and interconversion rates for all the main states that a protein can occupy. To reach this goal, integrative methods that combine experimental and computational approaches provide powerful tools. Here we focus on cryo-electron microscopy, which has become over recent years an invaluable resource to bridge the gap from order to disorder in structural biology. In this review, we provide a perspective of the current challenges and opportunities in determining protein structural ensembles using integrative approaches that can combine cryo-electron microscopy data with other available sources of information, along with an overview of the tools available to the community

Making the best of a bad situation: a multiscale approach to free energy calculation

Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space one is then able to sample efficiently and reconstruct the free energy landscape. In methods like metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the non-ideal situation of a system in which some slow modes are not accelerated. We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture

Free-energy landscape of polymer-crystal polymorphism

Polymorphism rationalizes how processing can control the final structure of a material. The rugged free-energy landscape and exceedingly slow kinetics in the solid state have so far hampered computational investigations. We report for the first time the free-energy landscape of a polymorphic crystalline polymer, syndiotactic polystyrene. Coarse-grained metadynamics simulations allow us to efficiently sample the landscape at large. The free-energy difference between the two main polymorphs, $\alpha$ and $\beta$, is further investigated by quantum-chemical calculations. The two methods are in line with experimental observations: they predict $\beta$ as the more stable polymorph at standard conditions. Critically, the free-energy landscape suggests how the $\alpha$ polymorph may lead to experimentally observed kinetic traps. The combination of multiscale modeling, enhanced sampling, and quantum-chemical calculations offers an appealing strategy to uncover complex free-energy landscapes with polymorphic behavior.Comment: 10 pages, 4 figure

CO2 packing polymorphism under pressure: mechanism and thermodynamics of the I-III polymorphic transition

In this work we describe the thermodynamics and mechanism of CO$_2$ polymorphic transitions under pressure from form I to form III combining standard molecular dynamics, well-tempered metadynamics and committor analysis. We find that the phase transformation takes place through a concerted rearrangement of CO$_2$ molecules, which unfolds via an anisotropic expansion of the CO$_2$ supercell. Furthermore, at high pressures we find that defected form I configurations are thermodynamically more stable with respect to form I without structural defects. Our computational approach shows the capability of simultaneously providing an extensive sampling of the configurational space, estimates of the thermodynamic stability and a suitable description of a complex, collective polymorphic transition mechanism