We present HylleraasMD (HyMD), a comprehensive implementation of the recently proposed Hamiltonian formulation of hybrid particle-field molecular dynamics (hPF). The methodology is based on tunable, grid-independent length-scale of coarse graining, obtained by filtering particle densities in reciprocal space. This enables systematic convergence of energies and forces by grid refinement, also eliminating non-physical force aliasing. Separating the time integration of fast modes associated with internal molecular motion, from slow modes associated with their density fields, we implement the first time-reversible hPF simulations. HyMD comprises the optional use of explicit electrostatics, which, in this formalism, corresponds to the long-range potential in Particle-Mesh Ewald. We demonstrate the ability of HhPF to perform simulations in the microcanonical and canonical ensembles with a series of test cases, comprising lipid bilayers and vesicles, surfactant micelles, and polypeptide chains, comparing our results to established literature. An on-the-fly increase of the characteristic coarse graining length significantly speeds up dynamics, accelerating self-diffusion and leading to expedited aggregation. Exploiting this acceleration, we find that the time scales involved in the self-assembly of polymeric structures can lie in the tens to hundreds of picoseconds instead of the multi microsecond regime observed with comparable coarse-grained models.

The hybrid particle-field molecular dynamics method is an efficient alternative to standard particlebased coarse grained approaches. In this work, we propose an automated protocol for optimisation of the effective parameters that define the interaction energy density functional, based on Bayesian optimisation. The machine-learning protocol makes use of an arbitrary fitness function defined upon a set of observables of relevance, which are optimally matched by an iterative process. Employing phospholipid bilayers as test systems, we demonstrate that the parameters obtained through our protocol are able to reproduce reference data better than currently employed sets derived by Flory-Huggins models. The optimisation procedure is robust and yields physically sound values. Moreover, we show that the parameters are satisfactorily transferable among chemically analogous species. Our protocol is general, and does not require heuristic a posteriori rebalancing. Therefore it is particularly suited for optimisation of reliable hybrid particle-field potentials of complex chemical mixtures, and extends the applicability corresponding simulations to all those systems for which calibration of the density functionals may not be done via simple theoretical models.

Hamiltonian hybrid particle−field molecular dynamics is a computationally efficient method to study large soft matter systems. In this work, we extend this approach to constant-pressure (NPT) simulations. We reformulate the calculation of internal pressure from the density field by taking into account the intrinsic spread of the particles in space, which naturally leads to a direct anisotropy in the pressure tensor. The anisotropic contribution is crucial for reliably describing the physics of systems under pressure, as demonstrated by a series of tests on analytical and monatomic model systems as well as realistic water/lipid biphasic systems. Using Bayesian optimization, we parametrize the field interactions of phospholipids to reproduce the structural properties of their lamellar phases, including area per lipid, and local density profiles. The resulting model excels in providing pressure profiles in qualitative agreement with all-atom modeling, and surface tension and area compressibility in quantitative agreement with experimental values, indicating the correct description of long-wavelength undulations in large membranes. Finally, we demonstrate that the model is capable of reproducing the formation of lipid droplets inside a lipid bilayer.

Molecular dynamics (MD) is a computational methodology in which the dynamical behavior of systems of interacting atoms and molecules is investigated by integrating the corresponding classical equations of motion. The analysis of the molecular trajectories yields an incredibly powerful computational microscope with atomic resolution. While prominent examples of molecular dynamics involving all-atom models exist, many systems operate on time-and lengths scales too large, precluding the use of such an approach. The intrinsic complexity of biological soft-matter systems has necessitated the development of coarse-grained (CG) MD models wherein groups of atoms are treated as individual entities. To probe experimentally relevant length-(nm-µm) and time-(ps-ms) scales, further reduction of computational complexity may be warranted through the removal of explicit particle-particle interactions in favor of particle-density field interactions. Such hybrid particle-field (hPF) models recast the interactions between particle pairs into a system of free particles interacting with an external potential dependent on the density, in analogy with self-consistent field theories.HylleraasMD (named after our affiliate centre, the Hylleraas Centre for Quantum Molecular Sciences) (HyMD) is a Python package capable of highly parallel hPF-MD simulations of a wide range of surfactants and other biological systems in a CG representation. At present, it is the only open-source implementation of the hPF formalism freely available to computational researchers.

Hamiltonian hybrid particle-field molecular dynamics is a computationally efficient method to study large soft matter systems. In this work, we extend this approach to constant pressure (NPT) simulations. We reformulate the calculation of internal pressure from the density field by taking into account the intrinsic spread of the particles in space, which naturally lead to a direct anisotropy in the pressure tensor. The anisotropic contribution is crucial for reliably describing the physics of systems under pressure, demonstrated by a series of tests on analytical and monoatomic model systems as well as realistic water/lipid biphasic systems. Using Bayesian optimization, we parameterise the field interactions of phospholipids to reproduce the structural properties of their lamellar phases, including area per lipid, and local density profiles. The resulting model excels in providing pressure profiles in qualitative agreement with all-atom modeling, surface tension, and area compressibility in quantitative agreement with experimental values, indicating the correct description of long wavelength undulations in large membranes. Finally, we demonstrate that the model is capable of reproducing the formation of lipid droplets inside a lipid bilayer.