This paper presents systematic molecular dynamics modelling of Na-montmorillonite subjected to uniaxial compression and unidirectional shearing. An initial 3D model of a single-cell Na-montmorillonite structure is established using the Build Crystal module. The space group is C2/m, and COMPASS force fields are applied. Hydration analysis of Na-montmorillonite has been performed to validate the simulation procedures, where the number of absorbed water molecules varied with respect to the various lattice parameters. A series of uniaxial compression stress σzz and unidirectional shear stress τxy values are applied to the Na-montmorillonite structure. It is shown that the lattice parameter and hydration degree exhibit significant influence on the stress–strain relationship of Na-montmorillonite. The ultimate strain increases with increases in the lattice parameter but decreases in the number of water molecules. For saturated Na-montmorillonite, more water molecules result in a stiffer clay mineral under uniaxial compression and unidirectional shearing.

Uniaxial and isothermal compression tests of kaolinite were carried out using molecular dynamics simulations. Five different temperatures (300, 400, 500, 600 and 700 K) and pressures ranging from 0.0001 to 50 GPa were selected to study the temperature and pressure effects on the mechanical properties of kaolinite. As kaolinite may undergo a phase transition at ~1572 K, a highest temperature of 700 K was chosen to avoid such structural change. The Young's modulus, strength and elastic constants of kaolinite under various temperatures were calculated, and the relative change of the elastic constant C33 with temperature was found to be almost 12 times greater than the relative change of the interlayer constant C11. The microstructures under various compressive strains were tracked and they exhibited various failure modes in three directions. The temperature and pressure effects on the mechanical properties of three crystal directions were analysed. The results showed that the Young's modulus of the z-direction is the most affected by temperature; however, the influence of temperature on the strengths of the three crystal directions was the same. In addition, the structure of the z-direction was the most sensitive to temperature under the same hydrostatic pressure due to the weak interactions between layers.

The adsorption mechanisms of hazardous gas molecules such as NH3, H2S and SO2 on sepiolite have not yet been elucidated. Therefore, molecular dynamics (MD) simulations were employed to investigate the adsorption behaviour of sepiolite towards NH3, H2S and SO2. A calculation model for sepiolite containing structural and zeolitic water molecules was constructed in this study. The adsorption sites and molecular configurations of the hazardous gases in the sepiolite channels were studied. The radial distribution function was employed to evaluate the interactions between the gas molecules and sepiolite. The results show that the order of adsorption capacity of sepiolite for the gases is as follows: SO2 > H2S > NH3. These three types of gas molecules absorbed in the channel nanopores of sepiolite exhibit different atomic configurations. The diffusion coefficients of the gas molecules in the channels decreased in the following order: NH3 > H2S > SO2. In addition, the diffusion coefficients were affected significantly by the ratio of the number of gas/water molecules. This study provides new perspectives for understanding the molecular processes responsible for the adsorption properties of sepiolite.

It is well known that the Poiseuille mass flow rate along microchannels shows a stationary point as the fluid density decreases, referred to as the Knudsen minimum. Surprisingly, if the flow characteristic length is comparable to the molecular size, the Knudsen minimum disappears, as reported for the first time by Wu et al. (J. Fluid Mech., vol. 794, 2016, pp. 252–266). However, there is still no fundamental understanding why the mass flow rate monotonically increases throughout the entire range of flow regimes. Although diffusion is believed to dominate the fluid transport at the nanoscale, here we show that the Fick's first law fails in capturing this behaviour, and so diffusion alone is insufficient to explain this confined flow phenomenon. Rather, we show that the Knudsen minimum disappears in tight confinements because the decay of the mass flow rate due to the decreasing density effects is overcome by the enhancing contribution to the flow provided by the fluid velocity slip at the wall.

The systematic development of coarse-grained (CG) models via the Mori–Zwanzig projector operator formalism requires the explicit description of a deterministic drift term, a dissipative memory term and a random fluctuation term. The memory and fluctuating terms are related by the fluctuation–dissipation relation and are more challenging to sample and describe than the drift term due to complex dependence on space and time. This work proposes a rational basis for a Markovian data-driven approach to approximating the memory and fluctuating terms. We assumed a functional form for the memory kernel and under broad regularity hypothesis, we derived bounds for the error committed in replacing the original term with an approximation obtained by its asymptotic expansions. These error bounds depend on the characteristic time scale of the atomistic model, representing the decay of the autocorrelation function of the fluctuating force; and the characteristic time scale of the CG model, representing the decay of the autocorrelation function of the momenta of the beads. Using appropriate parameters to describe these time scales, we provide a quantitative meaning to the observation that the Markovian approximation improves as they separate. We then proceed to show how the leading-order term of such expansion can be identified with the Markovian approximation usually considered in the CG theory. We also show that, while the error of the approximation involving time can be controlled, the Markovian term usually considered in CG simulations may exhibit significant spatial variation. It follows that assuming a spatially constant memory term is an uncontrolled approximation which should be carefully checked. We complement our analysis with an application to the estimation of the memory in the CG model of a one-dimensional Lennard–Jones chain with different masses and interactions, showing that even for such a simple case, a non-negligible spatial dependence for the memory term exists.

One major challenge for a continuum model to describe nanoscale confined fluid flows is the lack of a boundary condition that can capture molecular-scale slip behaviours. In this work, we propose a molecular-kinetic boundary condition to model the fluid–surface and fluid–fluid molecular interactions using the Lennard–Jones type potentials, and add a mean-field force to the momentum equation. This new boundary condition is then applied to investigate the nanoscale Couette and Poiseuille flows using the generalised hydrodynamic model developed by Guo et al. (Phys. Fluids, volume 18, issue 6, 2006a, 067107). The accuracy of our model is validated by molecular dynamics simulations and other models for a broad range of parameters including density, shear rate, wettability and channel width. Our simulation results reveal some unexpected and unintuitive slip behaviours at the nanoscale, including the epitaxial layering structure of fluids and the slip length minimum. The slip length minimum, which is analogous to the Knudsen minimum, can be explained by competing fluid–solid and fluid–fluid molecular interactions as density varies. A new scaling law is proposed for the slip length to account for not only the competing effect between the fluid–solid and fluid–fluid molecular interactions, but also many other physical mechanisms including the competition between the fluid internal potential energy and kinetic energy, and the confinement effect. While the slip length is nearly constant at the low shear rates, it increases rapidly at the high shear rates due to friction reduction. These molecular-scale slip behaviours are caused by energy corrugations at the fluid–solid interface where strong fluid–solid and fluid–fluid molecular interactions interplay.

In this paper, slip at liquid–liquid interfaces is studied focusing on the ubiquitous case in which a third species (e.g. a gas) is present. Non-equilibrium molecular dynamics simulations demonstrate that the contaminant species accumulate at the liquid–liquid interface, enriching it and affecting momentum transfer in a non-trivial fashion. The Navier boundary condition is seen to apply at this interface, accounting for slip between the liquids. Opposite trends are observed for soluble and poorly soluble species, with the slip length decreasing with concentration in the first case and significantly increasing in the latter. Two regimes are found, one in which the liquid–liquid interface is altered by the third species but changes in slip length remain limited to molecular sizes (intrinsic slip). In the second regime, further accumulation of non-soluble gas at the interface gives rise to a gaseous layer replacing the liquid–liquid interface; in this case, the apparent slip lengths are one order of magnitude larger and grow linearly with the layer width as captured quantitatively by a simple three-fluids model. Overall, results show that the presence of a third species considerably enriches the slip phenomenology both calling for new experiments and opening the door to novel strategies to control liquid–liquid slip, e.g. in liquid infused surfaces.

Coarse-grained (CG) modelling with the Martini force field has come of age. By combining a variety of bead types and sizes with a new mapping approach, the newest version of the model is able to accurately simulate large biomolecular complexes at millisecond timescales. In this perspective, we discuss possible applications of the Martini 3 model in drug discovery and development pipelines and highlight areas for future development. Owing to its high simulation efficiency and extended chemical space, Martini 3 has great potential in the area of drug design and delivery. However, several aspects of the model should be improved before Martini 3 CG simulations can be routinely employed in academic and industrial settings. These include the development of automatic parameterisation protocols for a variety of molecule types, the improvement of backmapping procedures, the description of protein flexibility and the development of methodologies enabling efficient sampling. We illustrate our view with examples on key areas where Martini could give important contributions such as drugs targeting membrane proteins, cryptic pockets and protein–protein interactions and the development of soft drug delivery systems.

Biomolecular recognition including binding of small molecules, peptides and proteins to their target receptors plays a key role in cellular function and has been targeted for therapeutic drug design. However, the high flexibility of biomolecules and slow binding and dissociation processes have presented challenges for computational modelling. Here, we review the challenges and computational approaches developed to characterise biomolecular binding, including molecular docking, molecular dynamics simulations (especially enhanced sampling) and machine learning. Further improvements are still needed in order to accurately and efficiently characterise binding structures, mechanisms, thermodynamics and kinetics of biomolecules in the future.

Copper is a trace element vital to many cellular functions. Yet its abnormal levels are toxic to cells, provoking a variety of severe diseases. The high affinity copper transporter 1 (CTR1), being the main in-cell copper [Cu(I)] entry route, tightly regulates its cellular uptake via a still elusive mechanism. Here, all-atoms simulations unlock the molecular terms of Cu(I) transport in eukaryotes disclosing that the two methionine (Met) triads, forming the selectivity filter, play an unprecedented dual role both enabling selective Cu(I) transport and regulating its uptake rate thanks to an intimate coupling between the conformational plasticity of their bulky side chains and the number of bound Cu(I) ions. Namely, the Met residues act as a gate reducing the Cu(I) import rate when two ions simultaneously bind to CTR1. This may represent an elegant autoregulatory mechanism through which CTR1 protects the cells from excessively high, and hence toxic, in-cell Cu(I) levels. Overall, our outcomes resolve fundamental questions in CTR1 biology and open new windows of opportunity to tackle diseases associated with an imbalanced copper uptake.

Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions.

Scattering kernel models for gas–solid interaction are crucial for rarefied gas flows and microscale flows. However, most existing models depend on certain accommodation coefficients (ACs). We propose here to construct a data-based model using molecular dynamics (MD) simulation and machine learning. The gas–solid interaction is first modelled by 100 000 MD simulations of a single gas molecule reflecting on the wall surface, which is fulfilled by GPU parallel technology. The results showed a correlation of the reflection velocity with the incidence velocity in the same direction, and also revealed correlations that may exist in different directions, which are neglected by the traditional gas–solid interaction model. Inspired by the sophisticated Cercignani–Lampis–Lord (CLL) model, two improved scattering kernels were constructed to better reproduce the probability density of velocity determined from MD simulation. The first one adopts variable ACs which depend on the incidence velocity and the second one combines three CLL-like kernels. All the parameters in the improved kernels are automatically chosen by the machine learning method. Compared with the numerical experiments of a molecular beam, the reconstructed scattering kernels are basically consistent with the MD results.

The behaviour of a fluid at the interface with a solid boundary is affected, to a large extent, by the potential landscape imposed on the fluid by the solid. Fluid slip at the interface with a solid boundary is modelled here as forced Brownian motion in a periodic potential landscape. The resulting model goes beyond simple transition-state-theory approaches and uses well-defined atomistic parameters to capture the salient features of the slip process in both the linear and nonlinear forcing regimes, yielding excellent agreement with molecular dynamics simulation results, as well as previous modelling results. An explicit expression for the Navier slip coefficient in terms of molecular-level system parameters is derived.

Bitter taste is sensed by bitter taste receptors (TAS2Rs) that belong to the G protein-coupled receptor (GPCR) superfamily. In addition to bitter taste perception, TAS2Rs have been reported recently to be expressed in many extraoral tissues and are now known to be involved in health and disease. Despite important roles of TAS2Rs in biological functions and diseases, no crystal structure is available to help understand the signal transduction mechanism or to help develop selective ligands as new therapeutic targets. We report here the three-dimensional structure of the fully activated TAS2R4 human bitter taste receptor predicted using the GEnSeMBLE complete sampling method. This TAS2R4 structure is coupled to the gustducin G protein and to each of several agonists. We find that the G protein couples to TAS2R4 by forming strong salt bridges to each of the three intracellular loops, orienting the activated Gα5 helix of the Gα subunit to interact extensively with the cytoplasmic region of the activated receptor. We find that the TAS2Rs exhibit unique motifs distinct from typical Class A GPCRs, leading to a distinct activation mechanism and a less stable inactive state. This fully activated bitter taste receptor complex structure provides insight into the signal transduction mechanism and into ligand binding to TAS2Rs.

Molecular dynamics simulations with a repulsive Lennard-Jones potential are employed to understand the bifurcation scenario and the resulting patterns in compressible Taylor–Couette flow of a dense gas, with the inner cylinder rotating ($\omega _i>0$) and the outer one at rest ($\omega _o=0$). The steady-state flow patterns are presented in terms of a phase diagram in the ($\omega _i,\varGamma$) plane, where $\varGamma =h/\delta$ is the aspect ratio, $h$ is the height of the cylinders and $\delta =R_o-R_i$ is the gap between the outer and inner cylinders, and the underlying bifurcation scenario is analysed as a function of $\omega _i$ for different $\varGamma$. Considerable density stratification is found along both radial and axial directions in the Taylor-vortex regime of a dense gas, which makes the present system fundamentally different from its incompressible analogue. In the circular Couette flow regime, the stratifications remain small and the predicted critical Reynolds number for the onset of Taylor vortices matches well with that of its incompressible counterpart. The emergence of asymmetric Taylor vortices at $\varGamma >1$ is found to occur via saddle-node bifurcations, resulting in hysteresis loops in the bifurcation diagrams that are characterized in terms of the net circulation or the maximum radial velocity or the axial density contrast as order parameters. For $\varGamma \leq 1$ with reflecting axial boundary conditions, the primary bifurcation yields a single-vortex state which is connected to a two-roll branch via saddle-node bifurcations; however, changing to stationary (no-slip) endwalls yields a new state, which consists of two large symmetric vortices near the inner cylinder coexisting with an irregular pattern near the stationary outer cylinder. It is shown that the endwall conditions and the fluid compressibility play crucial roles on the genesis of asymmetric and stratified vortices and the related multiplicity of states in the Taylor-vortex regime of a dense gas.

The discovery of governing equations from data is revolutionizing the development of some research fields, where the scientific data are abundant but the well-characterized quantitative descriptions are probably scarce. In this work, we propose to combine the direct simulation Monte Carlo (DSMC) method, which is a popular molecular simulation tool for gas flows, and machine learning to discover the governing equations for fluid dynamics. The DSMC method does not assume any macroscopic governing equations a priori but just relies on the model of molecular interactions at the microscopic level. The data generated by DSMC are utilized to derive the underlying governing equations using a sparse regression method proposed recently. We demonstrate that this strategy is capable of deriving a variety of equations in fluid dynamics, such as the momentum equation, diffusion equation, Fokker–Planck equation and vorticity transport equation. The data-driven discovery not only provides the right forms of the governing equations, but also determines accurate values of the transport coefficients such as viscosity and diffusivity. This work proves that data-driven discovery combined with molecular simulations is a promising and alternative method to derive governing equations in fluid dynamics, and it is expected to pave a new way to establish the governing equations of non-equilibrium flows and complex fluids.