Measuring friction from simulations of folded graphene sheets.

We ran molecular dynamics simulations of folded graphene sheets and present a procedure to measure the sliding friction in these systems based on the rate of decay of a damped harmonic oscillator. This procedure allowed us to study the effect that the size, geometry, and the temperature of the graphene sheet had on the ability to propagate the initial fold and the rate at which it settles to a final "fully folded" equilibrium state. We offer simple rationalizations for the relationships between the initial geometries of our simulations and the friction values that emerge.

Interplay of multiple clusters and initial interface positioning for forward flux sampling simulations of crystal nucleation.

Forward flux sampling (FFS) is a path sampling technique widely used in computer simulations of crystal nucleation from the melt. In such studies, the order parameter underpinning the progress of the FFS algorithm is often the size of the largest crystalline nucleus. In this work, we investigate the effects of two computational aspects of FFS simulations, using the prototypical Lennard-Jones liquid as our computational test bed. First, we quantify the impact of the positioning of the liquid basin and first interface in the space of the order parameter. In particular, we demonstrate that these choices are key to ensuring the consistency of the FFS results. Second, we focus on the frequently encountered scenario where the population of crystalline nuclei is such that there are multiple clusters of size comparable to the largest one. We demonstrate the contribution of clusters other than the largest cluster to the initial flux; however, we also show that they can be safely ignored for the purposes of converging a full FFS calculation. We also investigate the impact of different clusters merging, a process that appears to be facilitated by substantial spatial correlations-at least at the supercooling considered here. Importantly, all of our results have been obtained as a function of system size, thus contributing to the ongoing discussion on the impact of finite size effects on simulations of crystal nucleation. Overall, this work either provides or justifies several practical guidelines for performing FFS simulations that can also be applied to more complex and/or computationally expensive models.

Can molecular dynamics be used to simulate biomolecular recognition?

There are many problems in biochemistry that are difficult to study experimentally. Simulation methods are appealing due to direct availability of atomic coordinates as a function of time. However, direct molecular simulations are challenged by the size of systems and the time scales needed to describe relevant motions. In theory, enhanced sampling algorithms can help to overcome some of the limitations of molecular simulations. Here, we discuss a problem in biochemistry that offers a significant challenge for enhanced sampling methods and that could, therefore, serve as a benchmark for comparing approaches that use machine learning to find suitable collective variables. In particular, we study the transitions LacI undergoes upon moving between being non-specifically and specifically bound to DNA. Many degrees of freedom change during this transition and that the transition does not occur reversibly in simulations if only a subset of these degrees of freedom are biased. We also explain why this problem is so important to biologists and the transformative impact that a simulation of it would have on the understanding of DNA regulation.

A fully quantum-mechanical treatment for kaolinite.

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculations that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate the static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included, the dynamic properties of the material change substantially.

Combining Machine Learning and Enhanced Sampling Techniques for Efficient and Accurate Calculation of Absolute Binding Free Energies.

Calculating absolute binding free energies is challenging and important. In this paper, we test some recently developed metadynamics-based methods and develop a new combination with a Hamiltonian replica-exchange approach. The methods were tested on 18 chemically diverse ligands with a wide range of different binding affinities to a complex target; namely, human soluble epoxide hydrolase. The results suggest that metadynamics with a funnel-shaped restraint can be used to calculate, in a computationally affordable and relatively accurate way, the absolute binding free energy for small fragments. When used in combination with an optimal pathlike variable obtained using machine learning or with the Hamiltonian replica-exchange algorithm SWISH, this method can achieve reasonably accurate results for increasingly complex ligands, with a good balance of computational cost and speed. An additional benefit of using the combination of metadynamics and SWISH is that it also provides useful information about the role of water in the binding mechanism.

Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification.

Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometimes lack material-specific descriptions. Here, we provide a comprehensive framework for constructing a continuum picture from an atomistic simulation of homogeneous nucleation. We use this framework to determine the equilibrium shape of the solid nucleus that forms inside bulk liquid for a Lennard-Jones potential. From this shape, we then extract the anisotropy of the solid-liquid interfacial free energy, by performing a reverse Wulff construction in the space of spherical harmonic expansions. We find that the shape of the nucleus is nearly spherical and that its anisotropy can be perfectly described using classical models.

Using Data-Reduction Techniques to Analyze Biomolecular Trajectories.

This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function as well as practical issues such as landmark selection and how these algorithms can be used when the data to be analyzed comes from enhanced sampling trajectories. In the later part a comparison between the results obtained by applying various algorithms to two sets of sample data is performed and discussed. This section is then followed by a summary of how one algorithm in particular, sketch-map, has been applied to a range of problems. The chapter concludes with a discussion on the directions that we believe this field is currently moving.

Analyzing and Biasing Simulations with PLUMED.

This chapter discusses how the PLUMED plugin for molecular dynamics can be used to analyze and bias molecular dynamics trajectories. The chapter begins by introducing the notion of a collective variable and by then explaining how the free energy can be computed as a function of one or more collective variables. A number of practical issues mostly around periodic boundary conditions that arise when these types of calculations are performed using PLUMED are then discussed. Later parts of the chapter discuss how PLUMED can be used to perform enhanced sampling simulations that introduce simulation biases or multiple replicas of the system and Monte Carlo exchanges between these replicas. This section is then followed by a discussion on how free-energy surfaces and associated error bars can be extracted from such simulations by using weighted histogram and block averaging techniques.

Using Dimensionality Reduction to Analyze Protein Trajectories.

In recent years the analysis of molecular dynamics trajectories using dimensionality reduction algorithms has become commonplace. These algorithms seek to find a low-dimensional representation of a trajectory that is, according to a well-defined criterion, optimal. A number of different strategies for generating projections of trajectories have been proposed but little has been done to systematically compare how these various approaches fare when it comes to analysing trajectories for biomolecules in explicit solvent. In the following paper, we have thus analyzed a molecular dynamics trajectory of the C-terminal fragment of the immunoglobulin binding domain B1 of protein G of Streptococcus modeled in explicit solvent using a range of different dimensionality reduction algorithms. We have then tried to systematically compare the projections generated using each of these algorithms by using a clustering algorithm to find the positions and extents of the basins in the high-dimensional energy landscape. We find that no algorithm outshines all the other in terms of the quality of the projection it generates. Instead, all the algorithms do a reasonable job when it comes to building a projection that separates some of the configurations that lie in different basins. Having said that, however, all the algorithms struggle to project the basins because they all have a large intrinsic dimensionality.

Insights into mechanochemical reactions at the molecular level: simulated indentations of aspirin and meloxicam crystals.

Although solvent-free mechanochemical synthesis continues to gain ever greater importance, the molecular scale processes that occur during such reactions remain largely uncharacterised. Here, we apply computational modelling to indentations between particles of crystals of aspirin and meloxicam under a variety of conditions to mimic the early stages of their mechanochemical cocrystallisation reaction. The study also extends to the effects of the presence of small amounts of solvent. It is found that, despite the solid crystalline nature of the reactants and the presence of little or no solvent, mixing occurs readily at the molecular level even during relatively low-energy collisions. When indented crystals are subsequently drawn apart, a connective neck formed by a mixture of the reactant molecules is observed, suggesting plastic-like behaviour of the reacting materials. Overall the work reveals some striking new insights including (i) relatively facile mixing of crystals under solvent-free conditions, (ii) no appreciable local temperature increases, (iii) localised amorphisation at the contact region and neck of the reacting crystals, and (iv) small amounts of solvent have relatively little effect during this early stage of the reaction, suggesting that their accelerating effect on the reaction may be exerted at later stages.

Solvation Effects on Dissociative Electron Attachment to Thymine.

Ionizing radiation can excite the cellular medium to produce secondary electrons that can subsequently cause damage to DNA. The damage is believed to occur via dissociative electron attachment (DEA). In DEA, the electron is captured by a molecule in a resonant antibonding state and a transient negative ion is formed. If this ion survives against electron autodetachment, then bonds within the molecule may dissociate as energy is transferred from the electronic degrees of freedom into vibrational modes of the molecule. We present a model for studying the effect that transferring kinetic energy into the vibrational modes of a molecule in this way has on a DNA nucleobase. We show that when the base is in an aqueous environment, dissociation is affected by interactions with the surrounding water molecules. In particular, hydrogen bonding between the nucleobase and the solvent can suppress the dissociative channel.

Building maps in collective variable space.

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables (CVs). The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work, we discuss how auxiliary variables can be mapped in CV space. We show that maps of auxiliary variables allow one to analyze both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyze the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.

Using Intrinsic Surfaces To Calculate the Free-Energy Change When Nanoparticles Adsorb on Membranes.

A reaction coordinate that can be used when investigating binding to dynamical surfaces with molecular dynamics is introduced. This coordinate measures the distance between the adsorbate and an isocontour in a density field. Furthermore, the coordinate is continuous so simulation biases that are a function of this coordinate can be added to the Hamiltonian to increase the rate of adsorption/desorption. The efficacy of this new coordinates is demonstrated by performing metadynamics simulations to measure the strength with which a hydrophilic nanoparticle binds to a lipid bilayer. An investigation of the binding mechanism that is performed using the coordinate demonstrates that the lipid bilayer undergoes a series of concerted changes in structure as the nanoparticle binds.

Nucleation of Molecular Crystals Driven by Relative Information Entropy.

Simulating nucleation of molecular crystals is extremely challenging for all but the simplest cases. The challenge lies in formulating effective order parameters that are capable of driving the transition process. In recent years, order parameters based on molecular pair-functions have been successfully used in combination with enhanced sampling techniques to simulate nucleation of simple molecular crystals. However, despite the success of these approaches, we demonstrate that they can fail when applied to more complex cases. In fact, we show that order parameters based on molecular pair-functions, while successful at nucleating benzene, fail for paracetamol. Hence, we introduce a novel approach to formulate order parameters. In our approach, we construct reduced dimensional distributions of relevant quantities on the fly and then quantify the difference between these distributions and selected reference distributions. By computing the distribution of different quantities and by choosing different reference distributions, it is possible to systematically construct an effective set of order parameters. We then show that our new order parameters are capable of driving the nucleation of ordered states and, in particular, the form I crystal of paracetamol.

The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit.

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fitted using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.

Extracting the interfacial free energy and anisotropy from a smooth fluctuating dividing surface.

Interfaces between different materials and phases play a crucial role in many physical and chemical phenomena. When performing simulations of matter at the atomic scale, however, it is often not trivial to characterize these interfaces, particularly when they are rough or diffuse. Here we discuss a generalization of a construction, due to Willard and Chandler, that allows one to obtain a smooth dividing surface that follows the irregular, ever changing shape of these fluctuating interfaces. We show how this construction can be used to study the surface that separates a solid material from its melt and how analyses of the Fourier modes for the capillary fluctuations of this instantaneous dividing surface can be performed. This particular analysis is useful as one can compute the specific free energy excess of the interface, and its dependence on orientation relative to the bulk phases, from the average amplitude of the Fourier modes. We therefore discuss the efficiency of this approach, both in terms of system size and statistical sampling.

Interactions between low energy electrons and DNA: a perspective from first-principles simulations.

DNA damage caused by irradiation has been studied for many decades. Such studies allow us to better assess the dangers posed by radiation, and to increase the efficiency of the radiotherapies that are used to combat cancer. A full description of the irradiation process involves multiple size and time scales. It starts with the interaction of radiation-either photons or swift ions-and the biological medium, which causes electronic excitation and ionisation. The two main products of ionising radiation are thus electrons and radicals. Both of these species can cause damage to biological molecules, in particular DNA. In the long run, this molecular level damage can prevent cells from replicating and can hence lead to cell death. For a long time it was assumed that the main actors in the damage process were the radicals. However, experiments in a seminal paper by the group of Leon Sanche in 2000 showed that low-energy electrons (LEE), such as those generated when ionising biological targets, can also cause bond breaks in biomolecules, and strand breaks in plasmid DNA in particular (Boudaiffa et al 2000 Science 287 1658-60). These results prompted a significant amount of experimental and theoretical work aimed at elucidating the role played by LEE in DNA damage. In this Topical Review we provide a general overview of the problem. We discuss experimental findings and theoretical results hand in hand with the aim of describing the physics and chemistry that occurs during the process of radiation damage, from the initial stages of electronic excitation, through the inelastic propagation of electrons in the medium, the interaction of electrons with DNA, and the chemical end-point effects on DNA. A very important aspect of this discussion is the consideration of a realistic, physiological environment. The role played by the aqueous solution and the amino acids from the histones in chromatin must be considered. Moreover, thermal fluctuations must be incorporated when studying these phenomena. Hence, a special place in this Topical Review is occupied by our recent first-principles molecular dynamics simulations that address the issue of how the environment favours or prevents LEEs from causing damage to DNA. We finish by summarising the conclusions achieved so far, and by suggesting a number of possible directions for further study.

Analyzing and Driving Cluster Formation in Atomistic Simulations.

In this paper a set of computational tools for identifying the phases contained in a system composed of atoms or molecules is introduced. The method is rooted in graph theory and combines atom centered symmetry functions, adjacency matrices, and clustering algorithms to identify regions of space where the properties of the system constituents can be considered uniform. We show how this method can be used to define collective variables and how these collective variables can be used to enhance the sampling of nucleation events. We then show how this method can be used to analyze simulations of crystal nucleation and growth by using it to analyze simulations of the nucleation of the molecular crystal urea and simulations of nucleation in a semiconducting alloy. The semiconducting alloy example we discuss is particular challenging as multiple nucleation centers are formed. We show, however, that our algorithm is able to detect the grain boundaries in the resulting polycrystal.

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite.

Most ice in nature forms because of impurities which boost the exceedingly low nucleation rate of pure supercooled water. However, the microscopic details of ice nucleation on these substances remain largely unknown. Here, we have unraveled the molecular mechanism and the kinetics of ice formation on kaolinite, a clay mineral playing a key role in climate science. We find that the formation of ice at strong supercooling in the presence of this clay is about 20 orders of magnitude faster than homogeneous freezing. The critical nucleus is substantially smaller than that found for homogeneous nucleation and, in contrast to the predictions of classical nucleation theory (CNT), it has a strong two-dimensional character. Nonetheless, we show that CNT describes correctly the formation of ice at this complex interface. Kaolinite also promotes the exclusive nucleation of hexagonal ice, as opposed to homogeneous freezing where a mixture of cubic and hexagonal polytypes is observed.

Porous Organic Cages for Sulfur Hexafluoride Separation.

A series of porous organic cages is examined for the selective adsorption of sulfur hexafluoride (SF6) over nitrogen. Despite lacking any metal sites, a porous cage, CC3, shows the highest SF6/N2 selectivity reported for any material at ambient temperature and pressure, which translates to real separations in a gas breakthrough column. The SF6 uptake of these materials is considerably higher than would be expected from the static pore structures. The location of SF6 within these materials is elucidated by X-ray crystallography, and it is shown that cooperative diffusion and structural rearrangements in these molecular crystals can rationalize their superior SF6/N2 selectivity.