The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes

Citation: Orsi M, Essex JW ( The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes Mario Orsi 0 Jonathan W. Essex 0 Franca Fraternali, King9s College London, United Kingdom 0 School of Chemistry, University of Southampton , Southampton , United Kingdom A new coarse-grain model for molecular dynamics simulation of lipid membranes is presented. Following a simple and conventional approach, lipid molecules are modeled by spherical sites, each representing a group of several atoms. In contrast to common coarse-grain methods, two original (interdependent) features are here adopted. First, the main electrostatics are modeled explicitly by charges and dipoles, which interact realistically through a relative dielectric constant of unity (Er~1). Second, water molecules are represented individually through a new parametrization of the simple Stockmayer potential for polar fluids; each water molecule is therefore described by a single spherical site embedded with a point dipole. The force field is shown to accurately reproduce the main physical properties of single-species phospholipid bilayers comprising dioleoylphosphatidylcholine (DOPC) and dioleoylphosphatidylethanolamine (DOPE) in the liquid crystal phase, as well as distearoylphosphatidylcholine (DSPC) in the liquid crystal and gel phases. Insights are presented into fundamental properties and phenomena that can be difficult or impossible to study with alternative computational or experimental methods. For example, we investigate the internal pressure distribution, dipole potential, lipid diffusion, and spontaneous self-assembly. Simulations lasting up to 1.5 microseconds were conducted for systems of different sizes (128, 512 and 1058 lipids); this also allowed us to identify size-dependent artifacts that are expected to affect membrane simulations in general. Future extensions and applications are discussed, particularly in relation to the methodology's inherent multiscale capabilities. - Over the past decade, coarse-grain (CG) modeling has become an increasingly popular approach to the simulation of membrane systems [14]. In fact, in recent years, we have developed our own CG model, characterized by two interdependent features which are normally absent from alternative CG force fields [5,6]. First, the fundamental lipid electrostatics were captured using charges and dipoles, interacting realistically with each other through a relative dielectric constant of unity (Er~1). Second, we described water molecules individually using the soft sticky dipole (SSD) potential [7]. These characteristics proved advantageous in a number of important areas. For example, we were able to model the dipole potential, an extremely important property [812] which is very problematic to measure experimentally [13] and to simulate by alternative CG approaches [14]. Moreover, our model could be coupled straightforwardly with a standard atomistic force field in a multiscale (dualresolution) fashion, allowing the atomistically-detailed treatment of selected parts of the simulation while retaining the CG speed advantage for the surrounding environment [15,16]. Full details of our original methodology, and specific comparisons with alternative approaches, can be found in recent publications [6,17,18]. Despite the encouraging results obtained, our original model also showed a number of limitations. In particular, we recently identified issues related to the Gay-Berne potential [1921], which was used to model the lipid tail sites as ellipsoids [5,6,22]. Preliminary studies, aimed at simulating lipid bilayers in the solid (gel) phase, showed the formation of highly interdigitated structures bearing no resemblance to the desired phase (unpublished data). Gel-phase lipids play important roles in many structures (such as the skin) and phenomena (such as microdomain formation), and hence they should ideally be present in a lipid force field. More generally, the Gay-Berne model has a rather complex analytical form, and comprises six independent parameters (for comparison, the popular Lennard-Jones potential is defined by only two parameters); as in any model, it is important to question the need for elaborate components when simpler alternatives are available. We therefore decided to substitute the Gay-Berne representation with the simpler conventional LennardJones potential, which is used to model lipid tails in most alternative CG models [14]; as shown in this paper, this new representation is indeed capable of reproducing realistic gel phases, while retaining excellent performances in the (biologically prevalent) liquid-crystalline state. Another issue in our original model was that, to capture the hydrophobic effect, the strength of the Lennard-Jones dispersion energy between hydrophilic (water and headgroup) and hydrophobic (tail) sites had to be scaled down with respect to the values determined through the LorentzBerthelot (LB) formulae [23]. The LB combination rules are potential energy Uij of an interacting pair i,j can be expressed as: with UiLjJ the Lennard-Jones term and Uimjm the dipole-dipole term. Both interactions are truncated, that is, they are set to zero for interparticle distances larger than a cutoff radius rc [23]. In molecular dynamics, a well-known problem arising from truncating the interactions is the introduction of a discontinuity in the potential and its derivative (the force); this can affect the energy of the system and induce artifacts in the motion of the particles. This issue can be tackled by altering the form of the potential so that both the potential energy and its derivative go to zero at the cutoff distance [23,33]. We have therefore adopted a shifted-force form of the Lennard-Jones potential [34]: simple and physically intuitive, and hence advantageous; in fact, they are commonly used in atomistic force fields [24,25]. Unfortunately (and in common with other CG models), without ad hoc modifications to the LB rules, preassembled bilayers simulated with our original model were unstable, and dispersions of lipids and water would not self-assemble into membrane structures. The need to resort to such alterations of the general mixing rules was rather unexpected, as one would hope that an accurate water model (such as the SSD [7]), together with an explicit description of the lipid electrostatics, would prove sufficient to capture the hydrophobic effect. Interestingly, it now appears that this issue is associated with the Gay-Berne tails, in relation to their interaction with the Lennard-Jones potentials of headgroups and water. In fact, we show in this work that for the new model (where the Gay-Berne components have been replaced by Lennard-Jones terms), the stability and self-assembly of membranes is achieved without the need to modify the LB rules as described above; the hydrophobic effect no longer needs to be enforced through arbitrary deviations from the LB formulae, but is now an inherent property (...truncated)