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- Xinjian Liu
- Ivan Korotkin
- Zhonghao Rao
- [...]
- I Korotkin

The thermostat-consistent fully coupled molecular dynamics-generalised fluctuating hydrodynamics method is developed for non-equilibrium water flow simulations. The model allows for strong coupling between the atomistic and the continuum hydrodynamics representations of water and shows an improved stability in comparison with the previous formulations of similar multiscale methods. Numerical results are demonstrated for a periodic nano-scale Poiseuille flow problem with SPC/E water. The computed time-averaged velocity profiles are compared with the analytical solution, and the thermal velocity fluctuations are well reproduced in comparison with the Equilibrium Molecular Dynamics (EMD) simulation. Several options to account for the long-range electrostatics interactions available in GROMACS are incorporated in the model and compared. It is demonstrated that the suggested non-equilibrium multiscale model is a factor of 4 to 18 faster in comparison with the standard all-atom equilibrium molecular dynamics model for the same computational domain size.

For atomistic scale-resolving simulations of peptide diffusion, which are representative of molecular sorting in micro-fluidic device, a hybrid Fluctuating Hydrodynamics-Molecular Dynamics (FH/MD) model is implemented based on the two-phase flow analogy framework. Thanks to the used framework, in comparison with existing simulations in the literature, the suggested model captures inter-atomic forces between the peptides and the surrounding shell of water atoms at atomistic resolution while concurrently taking into account the non-uniform flow effect. In comparison with previous applications of the hybrid two-phase flow analogy method, multiple moving atomic-resolution zones are implemented for the first time here. The moving zones comprise one and two peptides solvated in water with a Poiseuille flow applied, where each diffusing peptide and the surrounding water shell are dynamically resolved. The models are validated in comparison with the pure all-atom molecular dynamics simulations for the no flow case and then used to investigate how the flow rate and the starting location of peptides in the parabolic flow profile affect their lateral migration over a range of flow Reynolds numbers. It is estimated that for the Poiseuille flows considered, the FH/MD model is 2 to 20 times faster in comparison with the conventional all-atom non-equilibrium molecular dynamics simulations.

The previously developed multiscale method for concurrently coupling atomistic and continuum hydrodynamic representations of the same chemical substance is extended to consistently incorporate the Langevin-type thermostat equations in the model. This allows not only to preserve the mass and momentum conservation laws based on the two-phase flow analogy modelling framework but also to capture the correct local fluctuations and temperature in the pure atomistic region of the hybrid model. Numerical results for the test problem of equilibrium isothermal fluctuations of SPC/E water are presented. Advantages of using local thermostat equations adjusted for the multi-resolution model for accurately capturing of the local water density in the atomistic part of the hybrid simulation domain are discussed. Comparisons with the reference pure all-atom molecular dynamics simulations in GROMACS show that the suggested hybrid models are by a factor of 5 to 20 faster depending on the simulation domain size.

A new hybrid multiscale model that incorporates both continuum fluid dynamics effects including thermal fluctuations and molecular dynamics is developed for accurate force calculation on a silica tip of the moving needle of an Atomic Force Microscopy (AFM) device near a mica substrate wall. By smoothly coupling the atomic and continuum representations of the AFM problem, the multiscale model is able to bridge atomistic-continuum scales thereby providing a practical solution for how to simulate the effect of the slowing moving tip relevant for the experiment while preserving atomistic water/material interface interaction details. Parameters of the multiscale model are validated in comparison with the standard all-atom Molecular Dynamics model for the stationary case. By systematically varying the cantilever velocity, the modelling reveals that the effect of the continuum flow induced by the cantilever motion should be taken into account once the AFM tip speed reaches 1 m/s.

Supramolecular chemistry offers an exciting opportunity to assemble materials with molecular precision. However, there remains an unmet need to turn molecular self-assembly into functional materials and devices. Harnessing the inherent properties of both disordered proteins and graphene oxide (GO), we report a disordered protein-GO co-assembling system that through a diffusion-reaction process and disorder-to-order transitions generates hierarchically organized materials that exhibit high stability and access to non-equilibrium on demand. We use experimental approaches and molecular dynamics simulations to describe the underlying molecular mechanism of formation and establish key rules for its design and regulation. Through rapid prototyping techniques, we demonstrate the system’s capacity to be controlled with spatio-temporal precision into well-defined capillary-like fluidic microstructures with a high level of biocompatibility and, importantly, the capacity to withstand flow. Our study presents an innovative approach to transform rational supramolecular design into functional engineering with potential widespread use in microfluidic systems and organ-on-a-chip platforms.

Water confined by hydrophilic materials shows unique transport properties compared to bulk water thereby offering new opportunities for development of nano-fluidic devices. Recent experimental and numerical studies showed that nano-confined water undergoes liquid-to-solid phase-like transitions depending on the degree of confinement. In the case of water confined by graphene layers, the Van der Waals forces are known to deform the graphene layers, whose bending leads to further non-uniform confinement effects. Despite the extensive studies of nano-confined water at equilibrium conditions, the interplay between the confinement and rheological water properties, such as viscosity, slip length and normal stress differences under shear flow conditions, is poorly understood. The current investigation uses a validated all-atom non-equilibrium molecular dynamics model to simultaneously analyse continuum transport and atomistic structure properties of water in a slit between two moving graphene walls under Couette flow conditions. A range of different slit widths and velocity strain rates are considered. It is shown that under the sub-nanometer confinement, water loses its rotational symmetry of a Newtonian fluid. In such conditions, water transforms into ice, where the atomistic structure is completely insensitive to the applied shear force and which behaves like a frozen slab sliding between the graphene walls. This leads to the shear viscosity increase, although not as dramatic as the normal force increase that contributes to the increased friction force reported in previous experimental studies. On the other end of the spectra, for flows at large velocity strain rates in moderate to large slits between the graphene walls, water is in the liquid state and reveals a shear thinning behavior. In this case, water exhibits a constant slip length on the wall, which is typical of liquids in the vicinity of hydrophobic surfaces.

Water confined by hydrophilic materials shows unique hydrodynamics properties compared to bulk water, offering a new point of view for development of the nano-fluidic devices. Recent experimental and numerical studies showed that nano-confined water undergoes liquid-to-solid phase transitions depending on the degree of confinement. In case of water confined by graphene layers, it is further shown that water atoms cause the graphene layers to deform that creates a non-uniform confinement effect. Despite the extensive studies of water confined by graphene walls at equilibrium conditions, the interplay between the confinement and rheological water properties such as viscosity and slip length under non-uniform flow conditions is poorly understood. The current investigation uses a validated all-atom non-equilibrium molecular dynamics model to simultaneously analyse hydrodynamic and structure properties in a water volume confined between the two moving graphene walls in accordance with the Couette flow conditions. A range of slit widths and velocity strain rates are considered. Results of the modelling reveal a direct link between the rheological properties of water confined by graphene layers and its atomistic structure. Viscosity coefficient is shown to have a significant anisotropy in the direction normal to the wall and in the tangential direction. Furthermore, the loss of rotational symmetry in-plane normal to the shear as well as a sliding solid-like behaviour of water are reported under the strong confinement. In such conditions, water transforms into ice where atomistic structure is completely insensitive to the shear force applied. On the other end of the spectra, for flow in moderate to large slits between the graphene walls, water reveals a shear thinning behaviour at large velocity strain rates. In this case it also exhibits a constant partial-slip condition on the wall, which is typical of liquids in the vicinity of hydrophobic surfaces.

The hybrid Molecular Dynamics-Fluctuating Hydrodynamics model is extended for multi-resolution simulations of molecular diffusion in water under a steady shear flow. Cases of water self-diffusion and a small protein diffusion in water are considered. For the switched-off flow effect, the model is validated in comparison with the reference all-atom equilibrium molecular dynamics solution. With the flow effect included, the multiscale model correctly captures the meanflow velocity distribution as well as the difference between mean square deviations in different directions with respect to the flow in accordance with the diffusion theory. Results of the simulations are analysed in the context of using hydrodynamic flow gradients for molecular diffusion focusing.

A new implementation of the hybrid molecular dynamics – hydrodynamics methods based on the analogy with two-phase flows is developed that takes into account the feedback of molecular dynamics on hydrodynamics consistently. The consistency is achieved by deriving a discrete system of fluctuating hydrodynamic equations which solution converges to the locally averaged molecular dynamics field exactly in terms of the locally averaged fields. The new equations can be viewed as a generalisation of the classical continuum Landau-Lifshitz Fluctuating Hydrodynamics model in statistical mechanics to include a smooth transition from large-scale continuum hydrodynamics that obeys a Gaussian statistics to all-atom molecular dynamics. Similar to the classical Landau-Lifshitz Fluctuating Hydrodynamics model, the suggested Generalised Landau-Lifshitz Fluctuating Hydrodynamics equations are too complex for analytical solution, hence, a computational scheme for solving these equations is suggested. The scheme is implemented in a popular open-source molecular dynamics code GROMACS and numerical examples are provided for liquid argon simulations in equilibrium conditions and under macroscopic flow effects.

Simulations of complete virus capsid at atomistic details have been performed using standard molecular dynamics as well as original hybrid molecular dynamics/hydrodynamics methodologies. The results show that the capsid is stable in water solution at room temperature and ions composition similar to physiological conditions. Detailed analysis of the flow of water molecules and ions through the capsid's wall is performed. It demonstrates that ions do not cross the capsid shell, while water exhibits substantial flows in both directions. This behaviour can be classified as a semipermeable membrane and may play a role in mechanical properties of the virus particle.

A novel framework for modelling biomolecular systems at multiple scales in space and time simultaneously is described. The atomistic molecular dynamics representation is smoothly connected with a statistical continuum hydrodynamics description. The system behaves correctly at the limits of pure molecular dynamics (hydrodynamics) and at the intermediate regimes when the atoms move partly as atomistic particles, and at the same time follow the hydrodynamic flows. The corresponding contributions are controlled by a parameter, which is defined as an arbitrary function of space and time, thus, allowing an effective separation of the atomistic ‘core’ and continuum ‘environment’. To fill the scale gap between the atomistic and the continuum representations our special purpose computer for molecular dynamics, MDGRAPE-4, as well as GPU-based computing were used for developing the framework. These hardware developments also include interactive molecular dynamics simulations that allow intervention of the modelling through force-feedback devices.

A new implementation of the hybrid molecular dynamics-hydrodynamics methods based on the analogy with two-phase flows is developed that takes into account the feedback of molecular dynamics on hydrodynamics consistently. The consistency is achieved by deriving a generalised system of fluctuating hydrodynamic equations which solution converges to the locally averaged molecular dynamics field exactly. The method is implemented in a popular open-source molecular dynamics code GROMACS and numerical examples are provided for liquid argon simulations in equilibrium conditions and under macroscopic flow effects.

A triple-scale model of a molecular liquid, where atomistic, coarse-grained, and hydrodynamic descriptions of the same substance are consistently combined, is developed. Following the two-phase analogy method, the continuum and discrete particle representations of the same substance are coupled together in the framework of conservation laws for mass and momentum that are treated as effective phases of a nominally two-phase flow. The effective phase distribution, which governs the model resolution locally, is a user defined function. In comparison with the previous models of this kind in the literature which used the classical Molecular Dynamics (MD) for the particulate phase, the current approach uses the Adaptive Resolution Scheme (AdResS) and stochastic integration to smoothen the particle transition from non-bonded atom dynamics to hydrodynamics. Accuracy and robustness of the new AdResS-Fluctuating Hydrodynamics (FH) model for water at equilibrium conditions is compared with the previous implementation of the two-phase analogy model based on the MD-FH method. To demonstrate that the AdResS-FH method can accurately support hydrodynamic fluctuations of mass and momentum, a test problem of high-frequency acoustic wave propagation through a small hybrid computational domain region is considered.

A hybrid Molecular Dynamics/ Fluctuating Hydrodynamics framework based on the analogy with two-phase hydrodynamics has been extended to dynamically tracking the feature of interest at all-atom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package GROMACS and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment.

A new 3D implementation of a hybrid model based on the analogy with two-phase
hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the
method is to smoothly combine the atomistic description in the Molecular Dynamics (MD) zone
with the Landau-Lifshitz Fluctuating Hydrodynamics (LL-FH) representation in the rest of the
system in the framework of macroscopic conservation laws through the use of a single ‘zoom-in’
user-defined function s that has the meaning of a partial concentration in the two-phase analogy
model. In comparison with our previous works, the implementation has been extended to full 3D
simulations for a range of atomistic models in GROMACS from argon to water in equilibrium
conditions with a constant or a spatially variable function s. Preliminary results of simulating the
diffusion of a small peptide in water are also reported.