Multiscale (re)modeling of lipid bilayer membranes

Abstract

Many phenomena of biological membranes are inherently multi-scalar: their observation and description requires very different length and time-scales. Especially membrane remodeling processes that are essential for many important cellular activities, such as endo- and exocytosis, cell division, infection, immune response or cell-cell communication, involve large scale morphological changes of the membrane, which are initiated and controlled by molecular scale interactions. The large-scale behavior of the membrane is intimately coupled to the atomic detail of the system, so that for a successful model, the contributions at all scales have to be included. This chapter gives an overview of the computational methods used to model lipid bilayer membranes and their interactions with proteins and other molecules at different levels of resolution. Then strategies to connect the models at different scales in order to provide a multi-resolution picture are described. Methods to quantify free energy changes associated with complex collective rearrangement are outlined. The last sections summarize examples for the application of these methods to pore formation, reshaping membranes into buds and membrane tubes as well as membrane fusion.

Introduction

Lipid membranes are the first point of contact of any molecule or material entering a cell, and form some of the cell's most important structural components. They provide a barrier separating biological cells from their surroundings as well as the different compartments and organelles within the cell. Their function as cell or compartment boundaries requires structural integrity. At the same time, the cell has to communicate with its surroundings and nutrients and other molecules are transported in and out of the cell under precise regulation. Only few molecules cross the membrane by passive diffusion [1]. Instead, small molecules are transported with the help of transmembrane proteins [2], [3]. Transport of larger cargo involves the endocytosis-exocytosis pathway, in which cargo is enclosed by the cell membrane to form buds and vesicles, which in turn can fuse with a target membrane to release their cargo at the opposite side [4], [5]. Thus, biological function requires lipid membranes to be dynamic structures that constantly undergo morphological changes and remodeling, including processes such as pore formation, budding, fusion and fission.

Besides these dynamic shape changes, a large variety of membrane shapes are formed and maintained in different parts and organelles of the cell, ranging from nearly flat regions to highly curved spheres, tubes or discs. Intriguing examples are the complex combinations of disks and tubes that form in the endoplasmic reticulum or the Golgi and the formation of membrane tubes as seen for instance in filopodia and mitochondria, or as tubular connections between cells, facilitating cell-cell communication and intracellular transport [6], [7], [8].

The biological membranes forming these cellular structures are complex entities with compositions containing many lipid types, which may be asymmetrically distributed between the two monolayers, and cholesterol, as well as a large number of proteins. These can either have transmembrane domains embedded in the bilayer or be attached to one of the leaflets [9], [10]. The shapes and morphological changes observed in the cell are tightly coupled to this complex composition and regulated by protein complexes. In addition, the lipid composition is linked to local curvature and plays an important role in signaling and controlling protein action through specific interactions [456].

However, even much simpler membrane model systems, which do not contain any proteins, can exhibit a large number of complex shapes, confirming that membrane remodeling is, at its core, a lipid-based process. Giant unilamellar vesicles (GUVs) with a much simpler lipid composition are often utilized to understand membrane properties and their relation to vesicle shape and membrane remodeling [11]. These vesicles have sizes of 1–100 μm and serve as well-established model systems with a strongly reduced complexity and well-defined physical properties.

The description and understanding of the structural features and the reshaping of lipid membranes involves multiple scales. Whereas the bilayer thickness corresponds to only about the length of two molecules, typically 4–5 nm, the lateral dimension of the bilayer structures covers scales of 100 nm to over 100 μm. Similarly, processes such as pore formation or membrane fusion will start locally and initially only involve a couple of lipids molecules, yet they result in large scale structural changes of the whole membrane. The interactions of the proteins and protein complexes that govern and regulate membrane shapes with the lipids or with other proteins are often highly specific and require a detailed model to capture the relevant features. However, for their role in membrane remodeling proteins often form large aggregates and complex scaffolds such as the basket like structures of clathrin driven endocytosis [12], [13], the large spirals built by ESCRT complexes [14] or the assembly of BAR domain containing proteins on tubular necks [15], [16]. Often the working mechanism and aggregation of these proteins is in turn directly coupled to membrane composition, raft formation, or the large scale curvature of the membrane [17]. These processes take place on length and time scales typically much larger than 100 ns and 100 nm.

In addition to the range of length scales, many membrane processes represent single events and involve transient structures and fast dynamics, so that their observation requires both high spatial and temporal resolution. This poses a considerable challenge for their investigation, so that many open questions about the molecular mechanisms and energetics remain.

To address these limitations, molecular modeling tools are often applied to bring insights to the mechanisms of membrane processes and to support or oppose structural interpretations of experimental data. Over the last decades, molecular simulations have become a fundamental tool for investigating bio-molecular systems which offers simultaneous spatial and temporal resolution far beyond the reach of experimental methods. For membranes, they can provide a molecular scale picture of the bilayer structure, and can therefore resolve and predict different intermediate steps of the membrane remodeling processes as well as identify some of the key interactions involved.

However simulation models come with their own set of restrictions. One is the accuracy of the molecular model, i.e. its ability to correctly reproduce experimentally measurable properties. The simulation models involve many adjustable and interdependent parameters for the potential functions governing interactions between atoms and molecules, which are generally referred to as a force field. Simulation results depend sensitively on the force field parameters and their development and optimization is an ongoing and iterative effort. Another limitation, are the length and timescales that can be modeled at high levels of resolution. Despite the continuous growth in computational power and the development of efficient algorithms, simulations resolving the system at the atomistic scale are typically limited to μs timescales and systems sizes of about a hundred thousand atoms [18]. Though a few examples exceeding these limits can be found in the literature [19], [20], [21], [22], these typically require a specialized computer hardware [21], [22] or computational resources beyond what is available to most researchers. These limitations still place the simulation of large-scale membrane-remodeling processes out of reach for models with all-atom resolution.

Strategies to overcome these difficulties involve either the use of coarse-grained (CG) models, with fewer degrees of freedom, or the development of enhanced sampling methods which bias the system's energy landscape [23]. The most widely used examples for these are umbrella sampling [24], [25] or metadynamics [26], which force the system out of equilibrium, along a chosen reaction coordinate.

Enhanced sampling can provide valuable insights to interactions and processes that can be studied locally using small bilayer patches, such as the interactions of small molecules with the membrane or pore and stalk formation. Other problems, that involve large-scale rearrangements of the membrane such as budding, fission or fusion require modeling large membrane segments and complex topologies and require the use of CG models that group several atoms together into effective interaction sites, at the cost of some chemical detail. At even larger scales, a number of mesoscopic membrane models have been developed, in which the resolution is below that of individual lipid molecules. These models use a quasi-particle description of the membrane, often complimented with the use of vector or continuum fields to represent local properties of the membrane or its local environment [27], [28], [29], [30], [31].

Ideally, the resolution of the description used would be tunable to combine the benefits of the different representations, and supplement more efficient models locally with high accuracy. Several schemes to achieve a coupling between the different scales have been developed. These can work either sequentially to derive interactions between CG sites from a higher resolution system or alternatively to zoom in on certain features, or they can combine a higher resolution model for the most sensitive parts of the structure with a CG model for the rest of the system.

The following sections give an overview of membrane models at different levels of resolution, and of different approaches used to provide connections and couple the hierarchy of scales into a multiscale picture of membrane protein systems. Finally, some membrane simulation studies of remodeling processes including pore formation, budding and tube formation as well as membrane fusion are summarized.