Lipid membranes computer simulation

MD simulations of model membrane systems have provided a unique view of lipid interactions at a molecular level of resolution [21], Due to the inherent fluidity and heterogeneity in lipid membranes, computer simulation is an attractive tool. MD simulations allow us to obtain structural, dynamic, and energetic information about model lipid membranes. Comparing calculated structural properties from our simulations to experimental values, such as areas and volumes per lipid, and electron density profiles, allows validation of our models. With molecular resolution, we are able to probe lipid-lipid interactions at a level difficult to achieve experimentally. 

Once the significant components of the system have been chosen, a computational domain is then defined to enclose them. The geometry of the simulation box must define a volume that realistically encloses the physics of the system, with boundary conditions mimicking the effects of the larger, real system being modeled. Within the ion channel framework, only a small fraction of the cellular lipid membrane is simulated thus, the dimension of the computational domain is minimized to reduce the computational burden. Consequently, the boundary conditions must be chosen carefully so that unwanted computational artifacts are not introduced into the simulation results. 

Interactions between macromolecules (protems, lipids, DNA,.. . ) or biological structures (e.g. membranes) are considerably more complex than the interactions described m the two preceding paragraphs. The sum of all biological mteractions at the molecular level is the basis of the complex mechanisms of life. In addition to computer simulations, direct force measurements [98], especially the surface forces apparatus, represent an invaluable tool to help understand the molecular interactions in biological systems. 

Simple considerations show that the membrane potential cannot be treated with computer simulations, and continuum electrostatic methods may constimte the only practical approach to address such questions. The capacitance of a typical lipid membrane is on the order of 1 j.F/cm-, which corresponds to a thickness of approximately 25 A and a dielectric constant of 2 for the hydrophobic core of a bilayer. In the presence of a membrane potential the bulk solution remains electrically neutral and a small charge imbalance is distributed in the neighborhood of the interfaces. The membrane potential arises from... 

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a probe molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical... 

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. 

Pohorille, A., New, M. H., Schweighofer, K. and Wilson, M. A. (1999). Insights from computer simulations into the interactions of small molecules with lipid bilayers. In Membrane Permeability, Vol. 48 100 Years Since Ernest Overton, eds. Deamer, D. W., Kleinzeller, A. and Fambrough, D. M., Academic Press, San Diego pp. 50-76. 

Wong-Ekkabut, J., Baoukina, S., Triampo, W., Tang, I.M., Tieleman, D.P., Monticelli, L. Computer simulation study of fullerene translocation through lipid membranes. Nat. Nanotechnol. 2008, 3, 363-8. 

This chapter will not review all of the published studies, but instead will focus on examples of computer simulations of phospholipid membrane systems ranging from simple models through descriptions of lipid and water in full atomic detail to complex membranes containing small solutes, lipids, and proteins. The chapter is aimed at medicinal chemists who are interested in drug-phospholipid interactions. Before discussing the results of different simulations, the currently applied methodologies will briefly be described. 

Overall, the mechanisms associated with dynamic processes in lipid systems are complex and are understood rather poorly, although the combination of experiments and computer simulations has improved the situation recently. As an example, let us consider a more concrete situation, the formation of pores in a cell membrane and its significance for cellular functions. 

Keywords Block copolymers, Coarse-grained models, Collective phenomena. Computer simulation, Fusion, Lipid membranes, Monte Carlo techniques, Poly-mersome, Pore formation, Self-assembly, Self consistent field theory, Vesicle... 

Fig. 6 Plot of membrane tension t as a function of dilation for a wide range of copolymer amphiphiles as extracted from MD simulations. The computational models, derived from systematic coarse-graining (black symbols), show nearly the same dilational behavior marked by the solid line. The slope of the line, ka, is very close to experimental measurements performed on giant vesicles 0colored symbols). Experimental data for a dimyristoyl phosphatidylcholine lipid membrane are also shown. The point of membrane lysis as observed experimentally for selected lipid and polymersome systems is also shown in the plot with green and red stars, respectively. Reprinted by permission from Macmillan Publishers Ltd Nature Materials, Ref. [85], copyright (2004)...

Conformational Analysis, R. Brasseur, Ed., CRC Press, Boca Raton, FL, 1990, pp. 3-84. Computer Simulation of Cooperative Phenomena in Lipid Membranes. 

In Chapter 5 the Penn State group of K. V. Damodaran and Kenneth M. Merz Jr. review lipid systems. Merz s research in computational chemistry spans the range from applied bonding theory of small organic molecules to simulations of biophysical processes. Membranes are an important component of living systems and are now the focus of much research. An overview of computer simulation of lipid systems is warranted. It is to be noted that this is the first chapter in Review in Computational Chemistry that discusses a class of molecules rather than a technique of computation. As time progresses we will... 

We have illustrated here how modelling and simulation can be applied to the understanding of membrane protein structure and function and the effect of peptides on lipid ordering. Evidently these calculations are but a small start towards understanding membrane protein structure and function at atomic detail, and the range of application is strongly limited by the availability of complementary experimental structural information. However, as described here, experiment has already furnished information of sufficient quality that a variety of atomic-detail computational techniques can usefully be applied. Future computer simulation research aimed at understanding functional photocycles. 

Santo KP, Berkowitz ML (2014) Shock wave induced collapse of arrays of nanobubbles located next to a lipid membrane coarse-grained computer simulations. J Phys Chem B. doi 10.1021/jp505720d... 

It is clear that the motions (translational and rotational) of water molecules near a lipid bilayer membrane are restricted. Nevertheless, they exhibit rich dynamic behavior [3]. Mueh of the information has come recently from computer simulations, which, as mentioned before, allow detailed follow-up of motion of individual water molecules. 

Proteins distort or disrupt membranes, which in turn act back on proteins. Strucmral perturbations contribute to protein function and are among the most important sources of membrane-induced interactions between proteins. Unfortunately, perturbations or transformations of lipid bilayers due to proteins are very difficult to probe experimentally [225]. Complementary theoretical and computer simulation studies can help to elucidate the role of the lipid bilayer in processes such as protein aggregation and function. 

Despite the fact that main focus has always been on ion channels, the influence of physiologically most relevant ions (such as Na", K", Cl , Ca, or Mg" ) on model lipid membranes was also studied in considerable detail [21-24]. Additionally, other ions, such as Li", Cs", NH4, Ba" ", La" ", F , Br , I , NO3, and SCN , were also investigated [24-26] in order to elucidate the factors influencing the specific ionic effects observed. This specificity has been known from measurements to be more pronounced for anions than for cations consequently, more experimental data are available for the former ions [26-29]. Computer simulations are, however, typically more focused on cations, since a proper description of the effects of larger anions often requires the use of resource-consuming polarizable force... 

H.L. Scott, E. Jakobsson, and S. Subramaniam. Simulations of lipid membranes with atomic resolution. Comput. Phys., 12 (1998) 328-334. 

---