Lipid continuum model

Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility-diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section. 

Systems with structure pose problems for continuum models. Examples include surfactants, block copolymers, lipids, and amphiphilic molecules in general. Ad hoc models are used to predict surface packing and phase behavior, but the incorporation... 

Another important class of materials which can be successfully described by mesoscopic and continuum models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different environments. Lipid molecules, for instance, comprise a polar head that likes an aqueous environment and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

In summary, continuum models of membranes have been instrumental to understand the physical properties of lipid assemblies and they have dramatically helped the development of this research field. They nowadays represent a gold standard to interpret both in vitro and in vivo experiments and to test the accuracy of bottom-up microscopic approaches on large-scale membrane properties. Yet, despite massively elaborated mathematical attempts to incorporate microscopic details into the equations, the inevitable assumptions that are intrinsic of phenomenological approaches prevent a faithful and accurate description of the chemical properties of lipid assemblies. 

To overcome the intrinsic limitations of continuum models to investigate the chemical properties of lipid and membranes, molecular simulations are an obvious and powerful alternative methodology. The first MD simulations of lipid assemblies date back to the early and all... 

To reconcile this apparent contradiction the membrane skeleton fence and anchored transmembrane picket model was proposed (54). According to this model, transmembrane proteins anchored to and lined up along the membrane skeleton (fence) effectively act as a row of posts for the fence against the free diffusion of lipids (Fig. 11). This model is consistent with the observation that the hop rate of transmembrane proteins increases after the partial removal of the cytoplasmic domain of transmembrane proteins, but it is not affected by the removal of the major fraction of the extracellular domains of transmembrane proteins or extracellular matrix. Within the compartment borders, membrane molecules undergo simple Brownian diffusion. In a sense, the Singer-Nicolson model is adequate for dimensions of about 10 x lOnm, the special scale of the original cartoon depicted by the authors in 1972. However, beyond such distances simple extensions of the fluid mosaic model fail and a substantial paradigm shift is required from a two-dimensional continuum fluid to the compartmentalized fluid. 

The most widely applicable model of membrane structure which allows for the physicochemical properties of membrane lipids and proteins and accounts for the dynamic nature and versatility of membranes is the fluid mosaic model (Figure 15.3). According to this the membrane is composed of a two-dimensional array of phospholipid and globular protein molecules in which the protein molecules are floating in a phospholipid continuum. About 70-80% of the protein molecules are integral proteins, which are held in association with the lipid bilayer by hydrophobic interactions. They, like the lipids, are amphiphilic and form an essential part of the structure. Other proteins known as peripheral or surface proteins can be dissociated from the membrane by the addition of salts. From this it is concluded that they are... 

Static modeling and energy minimization studies have been used to relate IR data and the orientation of molecules in membranes. A number of studies have used continuum approaches to mimic membrane properties. These have defined the membrane and water as regions having different dielectric constants. A recent study used a three-phase model including a hydrogen bonding potential. Lattice-based approaches have been used to study the influence of solutes on the phase transition of membranes and solute placement as a function of lipid surface area. Lattice-based approaches... 

As CG simulations of lipids and membranes become more and more widespread and accessible ( routine ), it is easier to lose track of how a specific model has been parameterized and of its main capabilities and limitations. We will thus briefly review the history of CG modelling approaches to study lipid assemblies and we will especially focus on the most popular CG force fields that are somewhat able to retain chemical accuracy, providing a direct link between atomistic properties of lipid bilayers and mesoscale properties of membranes that can be investigated using continuum approaches. 

The main advantage of particle-based models over continuum treatments is their capability of being able to describe simultaneously membrane curvature and lipid chemistry, as well as their interplay how do specific lipids promote/prevent curvature stresses And how do lipids respond to curvature stresses, for example by partitioning between the inner and the outer monolayer of highly curved vesicles ... 

The most promising approaches in this context appear to be those CG models that are able to retain the key aspects of protein and lipid chemistry while still being sufficiently computationally-efficient to investigate large-scale processes that have been traditionally investigated with more drastic coarse-graining approaches or with continuum methodologies. 

Kessel A, Musafia B, Ben-Tal N. Continuum solvent model studies of the interactions of an anticonvulsant drug with a lipid bilayer. Biophys. J. 2001 80 2536-2545. 

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