Bilayer membranes, simulations

In special cases (as in colloidal solutions) some particles can be considered as essential and other particles as irrelevant , but in most cases the essential space will itself consist of collective degrees of freedom. A reaction coordinate for a chemical reaction is an example where not a particle, but some function of the distance between atoms is considered. In a simulation of the permeability of a lipid bilayer membrane for water [132] the reaction coordinate was taken as the distance, in the direction perpendicular to the bilayer, between the center of mass of a water molecule and the center of mass of the rest of the system. In proteins (see below) a few collective degrees of freedom involving all atoms of the molecule, describe almost all the... 

The first dynamical simulation of a protein based on a detailed atomic model was reported in 1977. Since then, the uses of various theoretical and computational approaches have contributed tremendously to our understanding of complex biomolecular systems such as proteins, nucleic acids, and bilayer membranes. By providing detailed information on biomolecular systems that is often experimentally inaccessible, computational approaches based on detailed atomic models can help in the current efforts to understand the relationship of the strucmre of biomolecules to their function. For that reason, they are now considered to be an integrated and essential component of research in modern biology, biochemistry, and biophysics. 

A final example of the simulation of a complex system is a series of MD simulations of bilayer membranes. Membranes are crucial constituents of living organisms they are the scene for many important biological processes. Experimental data are known for model systems for example for the system sodium decanoate, decanol and water that forms smectic liquid crystalline structures at room temperature, with the lipids organized in bilayers. 

Chiu, S. W., Clark, M., Balaji, V., Subramaniam, S., Scott, H. L. and Jakobsson, E. (1995). Incorporation of surface tension into molecular dynamics simulation of an interface a fluid phase lipid bilayer membrane, Biophys. J., 69,1230-1245. 

Goetz, R. and Lipowsky, R. (1998). Computer simulations of bilayer membranes self-assembly and interfacial tension, J. Chem. Phys., 108, 7397-7409. 

Bassolino-Klimas, D., Alper, H. E. and Stouch, T. R. (1993). Solute diffusion in lipid bilayer membranes an atomic level study by molecular dynamics simulation,... 

The other major limitation of membrane simulations is the time and length scale we are able to simulate. We are currently able to reach a microsecond, but tens to hundreds of nanosecond simulations are more common, especially in free energy calculations. The slow diffusion of lipids means we are not able to observe many biologically interesting phenomena using equilibrium simulations. For example, we would not observe pore formation in an unperturbed bilayer system during an equilibrium simulation, and even pore dissipation is at the limits of current computational accessibility. 

Although it is clear that complex lipids can be synthesized under laboratory simulations using pure reagents, the list of required ingredients does not seem plausible under prebiotic conditions. Therefore, it is unlikely that early membranes were composed of complex lipids such as phospholipids and cholesterol. Instead, there must have been a source of simpler amphiphilic molecules capable of self-assembly into membranes. One possibility is lipidlike fatty acids and fatty alcohols, which are products of FTT simulations of prebiotic geochemistry [12] and are also present in carbonaceous meteorites. Furthermore, as will be discussed later, these compounds form reasonably stable lipid bilayer membranes by self-assembly from mixtures (Fig. 4a). 

The exact dimensions of a phospholipid bilayer membrane in terms of the in-plane area and the height of the lipid molecules as well as the thickness of the water layer that is associated with them is dependent on the chemical identity of the phospholipid head group, the length and the degree of saturation of the acyl chains, and the degree of hydration. This information may be obtained from a combination of small-angle X-ray diffraction by MLV or oriented multi-bilayer samples of phospholipids in excess water, electron and/or neutron density profiles across lipid bilayers, and atomic level molecular dynamics simulations of hydrated lipid bilayers. H-NMR studies on selectively deuter-ated phospholipids have also been important in elucidating acyl... 

FIGURE 14.2 Molecular dynamics simulation of the diffusion of benzene within a hydrated lipid bilayer membrane. Benzene molecules are shown as Corey-Pauling-Koltun (CPK) models atoms in the phospholipid head groups are shown as ball and stick models and hydrocarbon chains and water molecules as dark and light stick models, respectively. (Reproduced with permission from Bassolino-Klinaas D, Alper HE, Stouch TR. Biochemistry 1993 32 12624-37.)... 

As noted previously, real membranes are characterized by nonuniform free-energy profiles for bilayer permeation. Consequently, molecular dynamics simulations have been used to treat the motion of a solute through a bilayer membrane. These calculations accurately reproduce experimentally estimated values of diffusion 143]. However, because this approach is mathematically complex, it has been applied only to the permeation of relatively small molecules. Approximate methods have been developed based on a simple kinetic scheme for the diffusion of solute molecules M in a four compartment system ... 

D. Bassolino-Klimas, H. E. Alper and T. R. Stouch, Solute Diffusion in Lipid Bilayer Membranes An Atomic Level Study by Molecular Dynamics Simulation, Biochemistry 32 (1993) 12624. 

In summary, quantum mechanics attempts to model the position or distribution of the electrons or bonds, while mtv lecular mechanics attempts to model the positions of the nuclei or atoms. Quantum mechanics calculations are used commonly to generate or verify molecular mechanics parameters. Larger. structures can be studied hy use of molecular mechanics, and with. simulation techniques such as molecular dynamics, the behavior of drugs in solution or even in pas.sage through bilayer membranes can he studied. 

Seelig A and J Seelig 1974 The Dynamics Structure of Fatty Acyl Chains in a Phospholipid Bilayer Measured by Deuterium Magnetic Resonance Biochemistry 13-4839-4845 Stouch T R 1993 Lipid Membrane Structure and Dynamics Studied by All-atom Molecular Dynamics Simulations of Hydrated Phospholipid Bilayers. Molecular Simulation 10-335-362. 

For the study of drug membrane interactions and of the influence of drug structure and membrane composition, artificial membranes simulating especially mammalian membranes can easily be prepared because of the readiness of phospholipids to form automatically lipid bilayers, i.e. their tendency for self-association in water. The macroscopic structure of dispersions of phospholipids depends on the type of lipids and on the water content. The structure and properties of self-assembled phospholipids in excess water have been described [32], and the mechanism of liposome formation has been reviewed [33]. While the individual components, i.e. the membrane proteins and lipids, are composted of atoms and covalent bonds, their association with each other to produce membrane structures is governed largely by the hydrophobic effect This hydrophobic effect is derived from the structure of water and the interaction of other components with the water structure. Because of their enormous hydrogen-bonding capacity, water molecules adopt a structure in both the liquid and the solid state. 

Free Energy of Cell-Penetrating Peptide through Lipid Bilayer Membrane Coarse-Grained Model Simulation... 

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