On the calculation of equilibrium thermodynamic properties from molecular dynamics

The purpose of statistical mechanics is to provide a route to the calculation of macroscopic properties of matter from their constituent microscopic components. It is well known that the macrostates emerge as ensemble averages of microstates. However, this is more often stated than implemented in computer simulation studies. Here we consider foundational aspects of statistical mechanics which are overlooked in most textbooks and research articles that purport to compute macroscopic behaviour from microscopic descriptions based on classical mechanics and show how due attention to these issues leads in directions which have not been widely appreciated in the field of molecular dynamics simulation

An efficient, localised approach for the simulation of elastic blood vessels using the lattice Boltzmann method

Many numerical studies of blood flow impose a rigid wall assumption due to the simplicity of its implementation compared to a full coupling with a solid mechanics model. In this paper, we present a localised method for incorporating the effects of elastic walls into blood flow simulations using the lattice Boltzmann method implemented by the open-source code HemeLB. We demonstrate that our approach is able to more accurately capture the flow behaviour expected in elastic walled vessels than ones with rigid walls. Furthermore, we show that this can be achieved with no loss of computational performance and remains strongly scalable on high performance computers. We finally illustrate that our approach captures the same trends in wall shear stress distribution as those observed in studies using a rigorous coupling between fluid dynamics and solid mechanics models to solve flow in personalised vascular geometries. These results demonstrate that our model can be used to efficiently and effectively represent flows in elastic blood vessels

When we can trust computers (and when we can't)

With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the domains of science and engineering which are relatively simple and firmly grounded in theory, these methods are indeed powerful. Even so, the availability of code, data and documentation, along with a range of techniques for validation, verification and uncertainty quantification, are essential for building trust in computer-generated findings. When it comes to complex systems in domains of science that are less firmly grounded in theory, notably biology and medicine, to say nothing of the social sciences and humanities, computers can create the illusion of objectivity, not least because the rise of big data and machine-learning pose new challenges to reproducibility, while lacking true explanatory power. We also discuss important aspects of the natural world which cannot be solved by digital means. In the long term, renewed emphasis on analogue methods will be necessary to temper the excessive faith currently placed in digital computation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'

Principles governing control of aggregation and dispersion of aqueous graphene oxide

Controlling the structure of graphene oxide (GO) phases and their smaller analogues, graphene (oxide) quantum dots (GOQDs), is vitally important for any of their widespread intended applications: highly ordered arrangements of nanoparticles for thin-film or membrane applications of GO, dispersed nanoparticles for composite materials and three-dimensional porous arrangements for hydrogels. In aqueous environments, it is not only the chemical composition of the GO flakes that determines their morphologies; external factors such as pH and the coexisting cations also influence the structures formed. By using accurate models of GO that capture the heterogeneity of surface oxidation and very large-scale coarse-grained molecular dynamics that can simulate the behaviour of GO at realistic sizes of GOQDs, the driving forces that lead to the various morphologies in aqueous solution are resolved. We find the morphologies are determined by a complex interplay between electrostatic, [Formula: see text]-[Formula: see text] and hydrogen bonding interactions. Assembled morphologies can be controlled by changing the degree of oxidation and the pH. In acidic aqueous solution, the GO flakes vary from fully aggregated over graphitic domains to partial aggregation via hydrogen bonding between hydroxylated domains, leading to the formation of planar extended flakes at high oxidation ratios and stacks at low oxidation ratios. At high pH, where the edge carboxylic acid groups are deprotonated, electrostatic repulsion leads to more dispersion, but a variety of aggregation behaviour is surprisingly still observed: over graphitic regions, via hydrogen bonding and "face-edge" interactions. Calcium ions cause additional aggregation, with a greater number of "face-face" and "edge-edge" aggregation mechanisms, leading to irregular aggregated structures. "Face-face" aggregation mechanisms are enhanced by the GO flakes possessing distinct domains of hydroxylated and graphitic regions, with [Formula: see text]-[Formula: see text] and hydrogen bonding interactions prevalent between these regions on aggregated flakes respectively. These findings furnish explanations for the aggregation characteristics of GO and GOQDs, and provide computational methods to design directed synthesis routes for self-assembled and associated applications

Mechanism of Exfoliation and Prediction of Materials Properties of Clay-Polymer Nanocomposites from Multiscale Modeling

We describe the mechanism that leads to full exfoliation and dispersion of organophilic clays when mixed with molten hydrophilic polymers. This process is of fundamental importance for the production of clay-polymer nanocomposites with enhanced materials properties. The chemically specific nature of our multiscale approach allows us to probe how chemistry, in combination with processing conditions, produces such materials properties at the mesoscale and beyond. In general agreement with experimental observations, we find that a higher grafting density of charged quaternary ammonium surfactant ions promotes exfoliation, by a mechanism whereby the clay sheets slide transversally over one another. We can determine the elastic properties of these nanocomposites; exfoliated and partially exfoliated morphologies lead to substantial enhancement of the Young's modulus, as found experimentally

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'

Development and performance of a HemeLB GPU code for human-scale blood flow simulation

In recent years, it has become increasingly common for high performance computers (HPC) to possess some level of heterogeneous architecture - typically in the form of GPU accelerators. In some machines these are isolated within a dedicated partition, whilst in others they are integral to all compute nodes - often with multiple GPUs per node - and provide the majority of a machine's compute performance. In light of this trend, it is becoming essential that codes deployed on HPC are updated to execute on accelerator hardware. In this paper we introduce a GPU implementation of the 3D blood flow simulation code HemeLB that has been developed using CUDA C++. We demonstrate how taking advantage of NVIDIA GPU hardware can achieve significant performance improvements compared to the equivalent CPU only code on which it has been built whilst retaining the excellent strong scaling characteristics that have been repeatedly demonstrated by the CPU version. With HPC positioned on the brink of the exascale era, we use HemeLB as a motivation to provide a discussion on some of the challenges that many users will face when deploying their own applications on upcoming exascale machines

Principles Governing Control of Aggregation and Dispersion of Graphene and Graphene Oxide in Polymer Melts

Controlling the structure of graphene and graphene oxide (GO) phases is vitally important for any of its widespread intended applications: highly ordered arrangements of nanoparticles are needed for thin‐film or membrane applications of GO, dispersed nanoparticles for composite materials, and 3D porous arrangements for hydrogels. By combining coarse‐grained molecular dynamics and newly developed accurate models of GO, the driving forces that lead to the various morphologies are resolved. Two hydrophilic polymers, poly(ethylene glycol) (PEG) and poly(vinyl alcohol) (PVA), are used to illustrate the thermodynamically stable morphologies of GO and relevant dispersion mechanisms. GO self‐assembly can be controlled by changing the degree of oxidation, varying from fully aggregated over graphitic domains to intercalated assemblies with polymer bilayers between sheets. The long‐term stability of a dispersion is extremely important for many commercial applications of GO composites. For any degree of oxidation, GO does not disperse in PVA as a thermodynamic equilibrium product, whereas in PEG dispersions are only thermodynamically stable for highly oxidized GO. These findings—validated against the extensive literature on GO systems in organic solvents—furnish quantitative explanations for the empirically unpredictable aggregation characteristics of GO and provide computational methods to design directed synthesis routes for diverse self‐assemblies and applications

Large-scale binding affinity calculations on commodity compute clouds

In recent years, it has become possible to calculate binding affinities of compounds bound to proteins via rapid, accurate, precise and reproducible free energy calculations. This is imperative in drug discovery as well as personalized medicine. This approach is based on molecular dynamics (MD) simulations and draws on sequence and structural information of the protein and compound concerned. Free energies are determined by ensemble averages of many MD replicas, each of which requires hundreds of cores and/or GPU accelerators, which are now available on commodity cloud computing platforms; there are also requirements for initial model building and subsequent data analysis stages. To automate the process, we have developed a workflow known as the binding affinity calculator. In this paper, we focus on the software infrastructure and interfaces that we have developed to automate the overall workflow and execute it on commodity cloud platforms, in order to reliably predict their binding affinities on time scales relevant to the domains of application, and illustrate its application to two free energy methods

The influence of base pair tautomerism on single point mutations in aqueous DNA

The relationship between base pair hydrogen bond proton transfer and the rate of spontaneous single point mutations at ambient temperatures and pressures in aqueous DNA is investigated. By using an ensemble-based multiscale computational modelling method, statistically robust rates of proton transfer for the A:T and G:C base pairs within a solvated DNA dodecamer are calculated. Several different proton transfer pathways are observed within the same base pair. It is shown that, in G:C, the double proton transfer tautomer is preferred, while the single proton transfer process is favoured in A:T. The reported range of rate coefficients for double proton transfer is consistent with recent experimental data. Notwithstanding the approximately 1000 times more common presence of single proton transfer products from A:T, observationally there is bias towards G:C to A:T mutations in a wide range of living organisms. We infer that the double proton transfer reactions between G:C base pairs have a negligible contribution towards this bias for the following reasons: (i) the maximum half-life of the G*:C* tautomer is in the range of picoseconds, which is significantly smaller than the milliseconds it takes for DNA to unwind during replication, (ii) statistically, the majority of G*:C* tautomers revert back to their canonical forms through a barrierless process, and (iii) the thermodynamic instability of the tautomers with respect to the canonical base pairs. Through similar reasoning, we also deduce that proton transfer in the A:T base pair does not contribute to single point mutations in DNA