Molecular Simulations and Biomembranes

From Biophysics to Function

By Mark S.P. Sansom, Philip C. Biggin

The Royal Society of Chemistry

Copyright © 2010 Royal Society of Chemistry
All rights reserved.
ISBN: 978-0-85404-189-3

Contents

Chapter 1 Methods and Parameters for Membrane Simulations D. Peter Tieleman, 1,
Chapter 2 Lateral Pressure Profiles in Lipid Membranes: Dependence on Molecular Composition O. H. Samuli Ollila and Ilpo Vattulainen, 26,
Chapter 3 Coarse-grained Molecular Dynamics Simulations of Membrane Proteins Sarah Rouse, Timothy Carpenter and Mark S. P. Sansom, 56,
Chapter 4 Passive Permeation Across Lipid Bilayers: a Literature Review Mario Orsi and Jonathan W. Essex, 76,
Chapter 5 Implicit Membrane Models For Peptide Folding and Insertion Studies Martin B. Ulmschneider and Jakob P. Ulmschneider, 91,
Chapter 6 Multi-scale Simulations of Membrane Sculpting by N-BAR Domains Ying Yin, Anton Arkhipov and Klaus Schulten, 146,
Chapter 7 Continuum Electrostatics and Modeling of K+ Channels Janice L. Robertson, Vishwanath Jogini and Benoît Roux, 177,
Chapter 8 Computational Approaches to Ionotropic Glutamate Receptors Ranjit Vijayan, Bogdan Iorga and Philip C. Biggin, 203,
Chapter 9 Molecular Dynamics Studies of Outer Membrane Proteins: a Story of Barrels Syma Khalid and Marc Baaden, 225,
Chapter 10 Molecular Mechanisms of Active Transport Across the Cellular Membrane Po-Chao Wen, Zhijian Huang, Giray Enkavi, Yi Wang, James Gumbart and Emad Tajkhorshid, 248,
Chapter 11 Molecular Dynamics Studies of the Interactions Between Carbon Nanotubes and Biomembranes E. Jayne Wallace and Mark S. P. Sansom, 287,
Subject Index, 306,

CHAPTER 1

Methods and Parameters for Membrane Simulations

D. PETER TIELEMAN

Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4, Canada

1.1 Introduction

Computer simulation is a powerful approach to studying the properties of models of biological membranes. Because lipids have a certain degree of intrinsic disorder in biologically relevant states, direct structural and spectroscopic experimental methods necessarily average over a large number of different lipid conformations. Experimental methods to study membrane proteins are also complicated by their lipid environment. Although much progress has been made, experimental structural, dynamic and functional data on membrane proteins lag behind water-soluble proteins. In principle, simulation can be used to track the behaviour of individual atoms, with the potential for very high-resolution information, provided that the simulation models are sufficiently accurate for the properties of interest.

Biomolecular simulation, initially focused on proteins, has matured into a widely used method over the past 30 years, while more recently simulations of lipids have made significant progress. Figure 1.1 gives a graphical view of a typical simulation setup for simulating a bilayer, in this case a mixture of several lipids with a peptide. Review articles in 1994 and 1997 could still be comprehensive, but after that the field became too large and even reviews of sub-topics such as membrane protein simulations are now rarely comprehensive. A recent book volume gives a good overview of the state of the field, with a broad range of chapters. Other recent reviews include reviews on membrane protein simulations, simulations including cholesterol and simulations involving significant changes in the basic bilayer structure, including lipid defects, pores, domain formation, phase transitions and curvature.

Biomolecular simulation in general is a combination of an interaction model to describe the interactions between atoms or molecules and a sampling algorithm to explore this model numerically, using the methods of statistical mechanics. Molecular dynamics (MD) simulation is the most commonly used method, but not the only one. Because most other methods are important primarily to explore interaction models that contain less detail (coarse-grained models), this chapter will focus exclusively on MD simulation. In molecular dynamics, the force field consists of the equations chosen to model the potential energy and their associated parameters, while the standard sampling algorithm is a numerical solution of classical equations of motion based on the forces given by the energy function. The general form of the potential energy is a sum of terms similar to

[MATHEMATICAL EXPRESSION OMITTED] (1.1)

The potential function V depends on r, the position vector of particles in the system, expressed in terms of distances (rij and b – b0) and angles θ, φ and ψ between atoms. Despite occasional extra terms in some force fields, the functional form of the potential function is essentially the same in all common force fields, so that they are not fundamentally different. Indeed, the potential function embodies the most serious assumptions and will provide an upper limit to the accuracy of any parameter set to describe the interactions between atoms.

In practice, the parameters in equation (1.1) are generally stored in data files with lists corresponding to each term in the sum. The force field includes a list of particle types corresponding to the different types of atoms that occur in a system of interest. For example, the carbon atom in a methyl group CH3 and in a carbonyl group C=O can be described by two different particle types with two different charges [q in equation (1.1)] and potentially different Lennard-Jones parameters (ε, σ), and also specific bonds, angles and dihedral parameters. The Lennard-Jones parameters may be different for each pair of different atom types or they may be systematically derived from parameters attached to a single type of atom. The force field also includes a list of parameters to describe bonds (force constant kb, equilibrium bond length b0), angles (force constant kθ, equilibrium angle θ0), dihedrals (force constant kθ, phase angle θ0, multiplicity n ) to describe rotation around a central bond and improper dihedrals (force constant kψ, equilibrium angle ψ0) to enforce certain specific geometries such as planar or tetrahedral groups. Combined, these parameters describe all combinations of different particle types necessary to model a particular molecule or class of molecules, e.g. proteins, nucleic acids or lipids, or in several modern force fields nearly every molecule one can think of.

The scale of the systems that have been studied continues to increase with increasing computer power and with more efficient simulation software. The range of applications has become extremely broad, but generally a reasonable limit on simulations at the moment is 106 particles, corresponding to ca. 5000 all-atom lipids or ca. 50 000 lipids in coarse-grained models. Simulation times of hundreds of nanoseconds have become routine in simple bilayer simulations, while microsecond simulations for all-atom and millisecond simulations at the coarse-grained level are pushing current limits. In terms of both time and length scales, although more prominently in time scale (which increases linearly with computer power), simulations can now probe into the microscopic regime, allowing a direct bridge to new classes of experiments such as vesicle aspiration, fluorescence imaging and atomic force microscopy (AFM) measurements.

This chapter briefly reviews the main technical choices that have to be made in simulations of lipids and membrane proteins. Most of this material is based on a number of publications from the author’s group and collaborators: on electrostatics and algorithmic choices, on force field issues for lipids and membrane proteins and on creating starting structures and a number of other issues. The goal is not to provide a comprehensive literature review, but to indicate which technical choices are considered important. For an informed decision on any of these, a broader consultation of the literature is essential.

It is assumed that simulation is a sensible approach for a particular problem, but this is not a given. In fact, the most important decision in a simulation project is likely whether a given problem is suitable for computer simulation at all. The answer to this question will depend on the problem itself – are models available that are sufficiently accurate to address the problem? Is there a possible link to experimental data? Is it likely enough sampling can be obtained with a sufficiently detailed model, given the available computational resources? Are there experimental approaches that are likely to give more insight or that are easier routes to answering a particular question? Once the decision has been made to attempt simulations, the remaining choices are important but of a more technical nature.

1.2 Force Fields/Descriptions of Interactions

The force field is the description of interactions between atoms in the simulation system. Equation (1.1) gives a typical classical potential function which combines with the (many) parameters for each type of interaction in the equation to form the force field. Strictly, there are additional modifiers, which affect the pairs of particles for which interactions are actually calculated (modulated by neighbour searching details, cut-offs, lattice sums, periodic boundary conditions and long-range corrections), the form of the interaction potential (shift or switch functions) and external influences including temperature and pressure control algorithms and potentially additional terms such as external electric fields. Several of these will be discussed in more detail below.

Different force fields exist that are fundamentally similar, but have their own strengths and weaknesses. Because the parameters are empirical, there is no unique solution for an optimal set of parameters. Hence there is a certain degree of experience and judgement involved in picking force fields and interpreting results from simulations.

Most current force fields contain terms for all atoms, while there continues to be a subset that uses ‘united’ atoms, in which non-polar hydrogens are grouped together with a carbon atom to make effective ‘CH1’, ‘CH2’ or ‘CH3’ atoms. In biomolecular simulation in general, other levels of detail exist, ranging from ab initio quantum mechanics to very coarse-grained models that represent, for example, an entire amino acid by a single interaction site. For lipid simulations, two intermediate levels are likely to be important. Towards more detail, modifications of classical force fields to include explicitly electronic polarizability have seen significant progress in several groups and the first simulations of lipid bilayers using (partially) polarizable force fields have begun to appear in the literature.

Towards less detail and longer time and length scales, there has been significant progress in developing coarse-grained models that average over a number of atoms, interacting through effective potentials that reproduce the average interactions of the details that have been left out. An example is the MARTINI model of Marrink and co-workers, in which on average four non-hydrogen atoms are replaced by an effective particle type that is parameterized on the properties of a library of small organic molecules. A range of other methods exist, some of which are much coarser (and computationally cheaper), but the rest of this chapter is focused on classical atomistic simulations only.

1.2.1 Current Atomistic Force Fields

Major force fields commonly used in MD simulations of biomolecules include AMBER, CHARMM, GROMOS and OPLS. Parameters in each force field are supposed to be internally consistent, but this is not necessarily true between different force fields and may not be true between different force field versions from the same family. Most major force fields have developed a specific set of parameters for apolar solvents, common organic molecules and common phospholipids (typically at least DPPC, POPC and DOPC). However, only two phospholipid force fields are in common use today: an all-atom force field that is part of the official CHARMM distribution and a united-atom force field by Berger et al., created by combining parameters taken from united-atom versions of OPLS and AMBER with some modifications to charges and lipid chain parameters and bonded parameters based on an older version of GROMOS. Both CHARMM-based lipids and Berger lipids reproduce the available experimental information on the structure and dynamics of phospholipid bilayers reasonably well, particularly for the experimentally well-studied phosphatidylcholine lipids, and in our opinion there is no compelling experimental information that indicates that either force field is substantially better, although their errors differ. In addition to these two force fields, there has been recent progress in developing GROMOS96-based lipids, AMBER parameters to describe lipids and modifications of CHARMM parameters, and there are several modifications of older force fields.

Only CHARMM currently provides a full set of parameters for all types of biomolecules, but recent GROMOS96 and AMBER developments are moving in that direction. Other choices of lipid parameters require combining these parameters with other parameter sets, unless one is interested in pure lipids. However, even in that case it is a problem to develop new lipids – phosphatidylcholine lipids have been the traditional ‘test’ lipid, but other head-groups such as phosphatidylserine and phosphatidylglycerol require specific groups that look like a peptide or carbohydrate force field, respectively, while modifying lipid chains requires parameters for (poly-)unsaturated bonds and common types of other lipids such as sphingomyelin, ceramide, cardiolipin and sterols require a broad range of chemical groups.

1.2.2 Development of Force Field Parameters

The parameterization of all lipid force fields is typically based on ab initio and other calculations on molecules mimicking lipid fragments, such as dimethyl phosphate and liquid alkanes, combined with parameterization based on density and thermodynamic parameters for long-chain alkanes. Lipids are complex molecules but share a limited number of functional groups, so that a building block approach similar to proteins seems sensible. Detailed structural and thermodynamic information on complete phospholipids is scarce, but more readily available for well-chosen model compounds. High-level quantum mechanics calculations have a high computational cost and are limited in size and cannot deal accurately with solvation phenomena. This general approach assumes that bond, angle and dihedral parameters and also charge distributions in model compounds such as dimethyl phosphate and butane are reasonably close to those of phospholipids.

In practice, lipid force fields continue to have issues when parameters that work well for the model compounds are combined for use in full bilayers. Ad hoc adjustments can improve the results for a single lipid or class of lipids (phosphatidylcholine), but this often runs counter to chemical intuition and in practice such adjustments have often turned out not to be transferable to other lipids, such as the closely related phosphatidylethanolamine and phosphatidylserine lipids. For example, Chiu et al. have reparameterized GROMOS-based lipids to give the right area for PC and Sonne et al. have shown that is possible partially to solve the area per lipid problem of CHARMM27 by treating DPPC molecules as a whole and not as a sum of building blocks. A key problem appears to be that lipid bilayers are extremely sensitive to an accurate balance between water– water, water–lipid and lipid–lipid interactions, at different levels along the bilayer normal.

A significant additional problem is that it is difficult to test a lipid model. Although it is fairly easy to make sure a particular lipid model produces, for example, the area or molecular volume of DMPC, this does not mean that ‘trivial’ modifications such as adding or removing two carbons on the alkane chains also give accurate results; area and volume contain relatively little information and may be reproduced even if the actual distribution of atoms in the system is very different from experiment; and more important chemical changes such as changing the CH3 groups of the PC headgroup into H-atoms to make a phosphatidylethanolamine headgroup are rarely accurate based on a model optimized for DMPC.

A number of different issues complicate the systematic development of lipid models. First, equilibration times for small one-component bilayers are tens of nanoseconds and to obtain statistically accurate areas or other properties may take several times that. This makes it hard to test, modify, etc., parameters. A second problem is that there are few experimental data on most lipids that are useful for testing parameters. Areas per lipid, chain order parameters and density profiles (or form factors) are useful and essential, but are only available for a handful of lipids. Lipid properties change with temperature and hydration level, both of which are difficult to obtain accurately experimentally and expensive to test across a wide range of lipids. Phase diagrams can be measured experimentally and are obviously biologically relevant, but it is a major challenge to use these in testing simulation parameters. As simulations become more sophisticated or longer, more properties, such as mechanical properties, come within reach, but it remains to be seen how critical these are as test cases.

(Continues…)Excerpted from Molecular Simulations and Biomembranes by Mark S.P. Sansom, Philip C. Biggin. Copyright © 2010 Royal Society of Chemistry. Excerpted by permission of The Royal Society of Chemistry.
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