Biological and synthetic membranes: What can be learned from a coarse-grained description?
Introduction
The incredible complexity of biological systems combined with their immediate importance makes them the most recent subject for the application of the coarse-grained models of soft condensed matter physics [1], [2], [3]. While developed earlier for the elucidation of the statics and dynamics of melts and solutions of very long and uniform polymers [4], [5], [6], [7], [8], [9], [10], [11], coarse-grained models seem particularly well suited to the study of biological constituents [12], [13], [14], [15], [16], [17], such as the heteropolymers DNA and RNA, as well as relatively short-chain lipids which comprise all biological membranes.
Systems of polymers and of lipids share many common features, and exhibit universal collective phenomena, those which involve many molecules [13]. Examples of such phenomena include thermodynamic phase transitions, e.g., the main chain transition in lipid bilayers from a fluid, liquid crystalline to a gel phase [18], [19], and the lateral phase separation which appears to be implicated in “raft” formation in the plasma membrane [20], [21], [22], [23], as well as thermally activated processes such as vesicle fusion and fission [24], [25], [26], [27], [28], [29], [30], important in endocytosis and exocytosis, and electroporation [31], [32], [33], [34], [35] used in the micro-encapsulation of drugs and drug-delivery systems [36], [37].
Since collective phenomena involve many molecules and entail large length and time scales—10–1000 nm and –ms, respectively—details of the structure and dynamics on short, atomistic length scales are often irrelevant, and the behavior is dictated by only a small number of key properties, e.g., the amphiphilic nature of the molecule. This imparts a large degree of universality to the collective phenomena. These terms are borrowed from the theory of critical phenomena [38]. However the clear separation in length, time and energy scales assumed by this approach, is often missing in membrane systems. Thus the universality of collective phenomena, or the ability of coarse-grained models to describe collective phenomena, cannot be taken for granted. It is important, therefore, to compare the behavior of different experimental realizations among each other and with the results of coarse-grained models.
In the following we shall highlight some recent developments in this active research area in which many new models and computational techniques are being developed. We do not attempt to provide a comprehensive overview of this rapidly evolving field, but rather try to give an introduction both to the basic concepts involved in creating a coarse-grained model, and to the simulation techniques specific to membranes and interfaces. We shall emphasize the connection to polymer science whenever appropriate. In particular, we will also discuss application of field-theoretic techniques to calculate membrane properties. These techniques employ very similar coarse-grained models as do the particle-based simulation schemes, and they permit the calculation of free energies, and free energy barriers, which are often difficult to obtain in computer simulations. An application of coarse-grained models in the context of computer simulations and field-theoretic techniques is illustrated by the study of membrane fusion, a choice biased by our own research focus on this area.
Many important applications are not covered by this manuscript. Most notably we do not discuss important progress in the study of collective phenomena exhibited by single molecules, as in the folding of a protein [39], [40], [41] or the processes that ensue when a protein is inserted into a membrane [42], [43], [44], [45], [46], or those exhibited by assemblies of a small number of molecules, as in the formation and subsequent function of a channel [47], [48], [49]. In our view, details of the specific molecular architecture are very important for these processes, and they lack the type of universality which undergirds the application of coarse-grained models.
In the next section we place coarse-grained models in the context of atomistic ones that deal with molecular details, and of phenomenological Hamiltonians that do not retain the notion of individual molecules. We then discuss briefly a selection of simulation and self-consistent field techniques utilized for coarse-grained models of membranes. We illustrate the combination of computer simulation and field-theoretic approach with the example of membrane fusion. The paper closes with an outlook on further exciting, and open, questions in this area.
Section snippets
Atomistic modeling, coarse-grained models and phenomenological Hamiltonians
Processes in membranes evolve on vastly different scales of time, length and energy. Consequently a variety of membrane models and computational techniques have been devised to investigate specific questions at these different scales. We divide them roughly into atomistic, coarse-grained, and phenomenological models as illustrated in Fig. 1.
Motivation and open questions
One example of a collective phenomenon in membranes is the fusion of two apposing lipid bilayers. It is a basic ingredient in a multitude of important biological processes ranging from synaptic release, viral infection, endo- and exocytosis, trafficking within the cell, and fertilization [24], [25], [26], [27], [28], [29], [30]. The fusion process can be roughly divided into two steps [30]: first the two membranes to be fused are brought into close apposition. Fusion peptides embedded in the
Conclusion and outlook
We hope that we have demonstrated that coarse-grained models are a valuable tool for investigating universal collective phenomena in bilayer membranes. These models bridge the gap between atomistic simulations that are limited to rather small time and length scales, and phenomenological models that ignore much of the internal structure of the bilayer. They allow for direct insights into processes that involve many lipids and take place on time scales of milliseconds and length scales of
Acknowledgments
It is a great pleasure to acknowledge stimulating discussions with V. Frolov. We also acknowledge K. Ch. Daoulas, S. J. Marrink and H. Noguchi for a critical reading of the manuscript. Financial support was provided by the Volkswagen Foundation and the NFS under grants DMR-0140500 and 0503752. The simulations were performed at the von Neumann Institute for Computing at Jülich, Germany.
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