Soft Matter under Pressure: Pushing Particle-Field Molecular Dynamics to the Isobaric Ensemble

Abstract

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.

Learning Force Field Parameters from Differentiable Particle-Field Molecular Dynamics

“…Notably, in the same region, the stretching, and bending terms provide larger contributions to the pressure unbalance than with the BO model. 23 This is consistent with the sharper distribution of the polar heads reported in the density profiles (Fig. (dashed line) due to field, bond and angle terms.…”

“…As previously shown using BO-optimized parameters for DPPC in HhPF simulations, the main features of ∆P (z) could be reproduced without directly introducing any related information in the learning function. 23 Fig. 5 reports the lateral pressure profile for the same lipid obtained from simulations using parameters by ∂-HyMD, also in comparison with previously reported data.…”

“…(dashed line) due to field, bond and angle terms. On the right, total pressure differences calculated in this work (solid line), and HhPF, hPF, and united atom (UA) curves are taken from ref 23 .…”

“…The approach is very general and has the advantage over bottom-up coarse-graining approaches in that it can incorporate both experimental and all-atom data, as exemplified in a recent work, where the loss function to parameterize dipalmitoyl-phosphatidylcholine (DPPC) phospholipid bilayers included both the computationally-determined density profiles and the experimental value of the area-per-lipid. 23 BO provides a state-of-the-art algorithm for optimizing costly fitness functions without access to gradients in low-dimensional parameter spaces. 24 However, this approach becomes problematic when the number of particle species S increases, resulting in a large S(S − 1)/2-dimensional parameter space, or, even worse when also including intramolecular bonded parameters into the optimization problem.…”

“…Figure5: On the left, contributions to the pressure difference in the normal and lateral directions to the membrane (∆P ), across a DPPC bilayer simulated with the parameters optimized in this paper (solid line) and with previous BO parameters from Sen et al23 (dashed line) due to field, bond and angle terms. On the right, total pressure differences calculated in this work (solid line), and HhPF, hPF, and united atom (UA) curves are taken from ref23 .…”