Steering a solute between coexisting solvation states: Revisiting nonequilibrium work relations and the calculation of free energy differences

Computational methods and theory for ion channel research

Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Force probe simulations using an adaptive resolution scheme

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations.

Density-functional-theory approach to the Hamiltonian adaptive resolution simulation method

In the Hamiltonian adaptive resolution simulation method (H-AdResS) it is possible to simulate coexisting atomistic (AT) and ideal gas representations of a physical system that belong to different subdomains within the simulation box. The Hamiltonian includes a field that bridges both models by smoothly switching on (off) the intermolecular potential as particles enter (leave) the AT region. In practice, external one-body forces are calculated and applied to enforce a reference density throughout the simulation box, and the resulting external potential adds up to the Hamiltonian. This procedure suggests an apparent dependence of the final Hamiltonian on the system's thermodynamic state that challenges the method's statistical mechanics consistency. In this paper, we explicitly include an external potential that depends on the switching function. Hence, we build a grand canonical potential for this inhomogeneous system to find the equivalence between H-AdResS and density functional theory (DFT). We thus verify that the external potential inducing a constant density profile is equal to the system's excess chemical potential. Given DFT's one-to-one correspondence between external potential and equilibrium density, we find that a Hamiltonian description of the system is compatible with the numerical implementation based on enforcing the reference density across the simulation box. In the second part of the manuscript, we focus on assessing our approach's convergence and computing efficiency concerning various model parameters, including sample size and solute concentrations. To this aim, we compute the excess chemical potential of water, aqueous urea solutions and Lennard-Jones (LJ) mixtures. The results' convergence and accuracy are convincing in all cases, thus emphasising the method's robustness and capabilities.

From adaptive resolution to molecular dynamics of open systems

ABSTRACT

We provide an overview of the Adaptive Resolution Simulation method (AdResS) based on discussing its basic principles and presenting its current numerical and theoretical developments. Examples of applications to systems of interest to soft matter, chemical physics, and condensed matter illustrate the method's advantages and limitations in its practical use and thus settle the challenge for further future numerical and theoretical developments.