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Hybrid Particle-Field Approach Including Electrostatics for Large-Scale Simulations of Biological Systems

Periodic Reporting for period 1 - HYPERBIO (Hybrid Particle-Field Approach Including Electrostatics for Large-Scale Simulations of Biological Systems)

Reporting period: 2016-09-01 to 2018-08-31

Biochemical/biophysical processes are very diverse, and they may occur at different time scales (from femtoseconds to seconds) and may require propagation over different sizes (from few Angstroms over nano- or micro- metres). Such broad extension of both the time- and size- scales poses a unique set of problems to the computational scientists in building models of the biological matter on physical principles. In recent years, Milano and Kawakatsu [J. Chem. Phys. 2009, 130, 214106; 2010, 133, 214102] reformulated the hybrid particle-field (hPF) method within molecular dynamics (hPF-MD) framework. The hPF-MD was validated for different molecular models including molecular surfactants, atomistic models of polymers, and bio membranes. This project was aimed at implementation of electrostatics into hPF-MD where the field explicitly takes into account both particle and charge densities. The overall objectives of the project are listed below. Each objective is considered as a separate work package (WP).

1.The first objective of the proposal was to implement electrostatics into OCCAM software (WP1). The new code would be tested for its efficiency and performance in both serial and parallel implementations.

2.The second objective was the application of hPF-MD to realistic soft matter models (WP2). We aimed to validate the models for charged amphiphile systems and investigate the ability of hPF-MD in describing both the structural and dynamic properties of those charged systems. Our goal was to address the structure and assembly of complex ipopolysaccharide (LPS) membranes. In fact, we started our study with coarse grained models for simple charged amphiphile systems such as palmitoyloleoylphosphatidylglycerol (POPG) lipid bilayer and sodium dodecyl sulfate (SDS) surfactant in aqueous environment.

3.Our original plan for WP3 was to extend the charge-field formalism to incorporate dipole-field and dipole-dipole interactions for the description of proteins in a field approach compatible with CG method proposed by Michele Cascella and coworkers. On the contrary, we preferred to concentrate our efforts to introduce spatially resolved dielectric which depends on the local density of the different molecular species. This step is crucial for the better treatment of electrostatics in complex phase separated systems like biological membranes comprised of complex polyelectrolytes. In WP3, we also aimed at the introduction of protocols to perform simulations of tensionless bio membranes by considering an interaction energy due to surface tension in particle-field formalism.

We introduced a series of methods in particle-field formalism to compute the electrostatic energy and forces for a mesoscopic system in the condensed phase, described with molecular resolution. The methods are inexpensive, robust and are able to reproduce the correct electrostatic features for dipolar/charged lipid membranes. A pressure tensor is derived in particle field formalism to perform simulations on tensionless bio membranes to study major conformational changes like membrane curvature, disruption and pore formation.
WP1(01/09/2016 - 30/04/2017): This period was particularly dedicated to the efficient implementation of the grid based electrostatic solvers into the OCCAM software and on quality check of the code. The code has been developed and tested on model polyelectrolyte system. A parallel version of the code is developed, and the efficiency of the code has been tested.
WP2 (01/05/2017 - 31/12/2017): By using the OCCAM code, we tested and developed models for POPG and SDS. Our work showed how our new implementation of grid based electrostatic solvers for particle field simulation can be used to investigate realistic models of polyelectrolyte soft matter systems. We demonstrated that the hPF-MD approach can treat amphiphilic systems either in extended aggregates, like lipid bilayers, or in finite micellar forms. . This work has been published in the Journal of Chemical Theory and Computation and was selected for the the cover page of the issue. As part of the continuation work on SDS self-assembly, we provided a theoretical explanation for the transition of spherical micelles to cylindrical aggregates (shown in Fig.1) in presence of ions. This manuscript is under preparation now.
WP3(01/01/2018 - 31/08/2018): A theoretical framework has been developed to compute the polarization forces through local dielectric permittivity. We do this by introducing a spatially resolved dielectric that depends on the local density of the different molecular species. We employed a finite difference scheme to solve generalized Poisson equation iteratively using the Successive over relaxation method (SOR). This has been implemented into OCCAM and tested for ion permeability in oil/water system and lipid membranes. This work is crucial for the better treatment of electrostatics in complex phase separated systems. The manuscript on this work is finished and about to be submitted. Alongside, the derivation of the pressure tensor for amphiphile mono/bi layers in hPF formalism has been performed and implemented in OCCAM.

A series of methods are developed for rigorous and accurate treatment of electrostatics. This work opens the possibility of using hPF schemes to investigate major biological processes that are dominated by such interactions-for example ion-membrane permeation, membrane electroporation, protein/protein and protein/membrane interactions. This project has delivered two publications in reputed journals, one manuscript to be submitted and two are under preparation.
Before the project, the hPF-MD method was limited to study uncharged/neutral soft matter systems due to the lack of explicit treatment of electrostatics. This remained a major hindrance preventing hPF-MD simulations of complex biomolecular systems comprised of polyelectrolytes. We introduced a series of methods to treat electrostatics in hPF formalism. We calibrated particle field models for different polyelectrolyte systems. Our first implementation based on Ewald summation technique points out the importance of carefully calibrating dielectric value in studies that aim to determine dynamic and structural properties of soft matter assemblies. We have not only overcome this problem by introducing spatially resolved dielectric but also improved the method by developing the theoretical framework which introduces polarizing media and thus polarization forces. The new theory and its implementation in hPF formalism is rigorous and accurate compared to the conventional methods for treating electrostatics. Also, the derivation of the pressure tensor made possible the studies on membrane deformation. The ability of the hPF models to treat explicit electrostatics in good agreement with experiments opens the possibility of simulating efficiently biological moieties where the polyelectrolyte character is dominant, for example, combining it to proposed models of polypeptides with explicit electrostatics. Thus, the new PF formulation is a door opener for simulations of complex biological systems beyond the time- and length scales affordable today. The methods and theory developed are general and can be used to simulate any complex multiphase biosystem. This project is helpful in broadening the pathway for field-based simulations and the potential impact of the outcome is long term.