Simulations of ion channeling

The interactions of several peptides with phospholipids have been studied by computer simulation. Emphasis has been given to several aspects of protein-phospholipid interactions, including the way of association and orientational preference of peptides in contact with a bilayer, the effect of phospholipids on the preference and stability of helical conformations, and the effect of the inserted peptide on the structure and dynamics of the phospholipids. These investigations have been extended to bundles of helices and even whole pore-forming proteins. In particular, the simulation of ion channels and of peptides with antimicrobial action has attracted a great deal of attention in theoretical studies. 

The simulation of ion channels and other pore-forming peptides and proteins at atomic detail is nowadays also possible. With the increase in computational power, these complex systems have attracted much more interest, and several simulations have been reported. Very often, only the transmembrane segments of the channel-forming proteins are included in the simulation to reduce the size and complexity of the system. The simulated systems range from synthetic model ion channels to a bacterial porine protein. 

Equations [18], [54], and [55] constitute a system of three equations with three unknowns, and this system is solved numerically on one-, two-or three-dimensional domains. For the sake of simplicity, we will discuss the one-dimensional case (the equations are easily extended to three-dimensional). Although finite element methods have been used extensively for the solution of Eqs. [18], and [55] in solid state electronics, flux-based approaches for the simulation of ion channels rely primarily on finite difference schemes. 

Reservoir Boundaries in Brownian Dynamics Simulations of Ion Channels. 

Whereas the main challenge for the first bilayer simulations has been to obtain stable bilayers with properties (e.g., densities) which compare well with experiments, more and more complex problems can be tackled nowadays. For example, lipid bilayers were set up and compared in different phases (the fluid, the gel, the ripple phase) [67,68,76,81]. The formation of large pores and the structure of water in these water channels have been studied [80,81], and the forces acting on lipids which are pulled out of a membrane have been measured [82]. The bilayer systems themselves are also becoming more complex. Bilayers made of complicated amphiphiles such as unsaturated lipids have been considered [83,84]. The effect of adding cholesterol has been investigated [85,86]. An increasing number of studies are concerned with the important complex of hpid/protein interactions [87-89] and, in particular, with the structure of ion channels [90-92]. 

Standard molecular mechanics (MM) force fields have been developed that provide a good description of protein structure and dynamics,21 but they cannot be used to model chemical reactions. Molecular dynamics simulations are very important in simulations of protein folding and unfolding,22 an area in which they complement experiments and aid in interpretation of experimental data.23 Molecular dynamics simulations are also important in drug design applications,24 and particularly in studies of protein conformational changes,25,26 simulations of the structure and function of ion channels and other membrane proteins,27-29 and in studies of biological macromolecular assemblies such as F-l-ATPase.30... 

Schirmer, T., and Phale, P. S. (1999). Brownian dynamics simulation of ion flow through porin channels./ Mol. Biol. 294, 1159-1167. 

PISEMA spectra of ion channel proteins (A) crystal structure and (B) simulated PISEMA spectrum of a 10.2 kDa KcsA monomer (97 residues), a K+ channel of S. lividans (PDB ID 1BL8) (C) crystal structure and (ID) simulated PISEMA spectrum of a monomeric 50.3 kDa (473 residues) CLC chloride channel from E. coli (PDB ID IKPK). 

Simulation studies in the area of membrane transport have been limited to simplified representations. Simulations of ion carriers or channels with the explicit inclusion of lipid and solvent molecules have not appeared as yet. Early... 

MD simulations of ionophore/channel molecules intercalated into a lipid bilayer would require a large number of lipid molecules to ensure that the ionophore/channel molecule does not interact with its periodic images. Still, comparisons between boundary and bulk lipids may have to be done from independent simulations to get an accurate view of how these molecules affea bilayer dynamics. Typical channels like gramicidin show ion transport times of —10 s, which is a time scale that is presently unattainable in typical MD simulations. However, one can obtain insights into the molecular aspects of the energy barriers involved in the translocation of small molecules and ions from PMF calculations, particularly when there is no ambiguity about the path of the solute movement. Moreover, short time scale (10 s) simulations can... 

The binary collision approximation (BCA) model was the first to be used in computer simulations of ion-solid interactions (Bredov et al, 1958). The usefulness of computer simulations was further demonstrated by Robinson and Oen (1963) during their discovery of the channeling effect. Computer simulations based on the BCA model in essence fall into two categories, those that assume a crystalline structure of the solid and those that, as in calculations based on the TRIM code, assume a randomized or structureless target. 

While they provide considerable insight into aspects of ion-channel behavior, and the relation between structure and function, the approaches outlined in Section II.B.l have their drawbacks. The reliability of the force fields, the real time length of the simulations,... 

Note that many of the molecules produced have few internal polar fimctional groups to which ions may bind. Instead, it is more likely that ion-water-channel interactions escort the ion through the pore. To that end. many of the models can then be viewed as methods to pull water into the lipidic core of a bilayer membrane and thereby stabilize ions in transport. Recent studies of molecular dynamics simulations of ion transportation in human aquaporin-1 and in the bacterial glycerol facilitator GlpF revealed the key role of water in the stabilization of ions in transit and in the molecular selectivity of channels. Synthetic compoxmds form less-defined stmctures than these complex proteins but apparently act as efficiently as more complex natural materials. It is likely that continued study of synthetic systems will continue to reveal the general details underlying all transport processes. 

The remaining part of the introduction will be devoted to the description of the simulative environment required to model the operation of ion channels. 

After choosing an adequate model for each different component of the system and integrating them into a final atomistic model that will be simulated, an important issue is the selection of a discretization scheme to implement the computer representation of the ion channel and its environment. Within the framework of a computer experiment, the adjective realistic is strictly related to the phenomena one wants to study, and to the resolution required to reproduce those phenomena. The basic idea for modeling many-body systems is to build a set of rules that apply to each component and let the system evolve dynamically. Ensemble and time averages are then computed to obtain observables that are compared with experiment to validate the model. A characteristic of ion channel systems is that the measurable quantities of direct biological interest evolve in times up to 12 orders of magnitude larger than the smallest atomic or molecular relaxation times (milliseconds versus femtoseconds). In comparison, solid state many-body systems collectively relax in a faster fashion, and the difference between the microscopic... 

The self-consistent nature of the simulation approaches described in this chapter requires frequent solutions of Poisson s equation the potential profiles from one step to the next are very similar to each other because the changes in the charge distribution between two consecutive solutions are very small (but very important for the particle dynamics). The current potential profile can thus generally be used as a good initial guess for the next solution, which makes iterative methods a natural choice within the framework of self-consistent simulation programs. In addition, memory issues (other than pure performance) make the choice of iterative methods appealing in the field of ion channel simulations. 

Several approaches for the simulation of ionic charge transport in protein channels have been presented in the previous sections. It should be clear from this discussion that none of the mentioned methods can supply a complete and self-contained description of the full functionality of ion channels starting from piu ely structural information. For this reason, methods based on a hierarchy of simulative approaches, rather than on a specific method, are becoming more and more popular. 

The recent development of high-resolution experimental techniques allows for the structural analysis of protein channels with unprecedented detail. However, the fundamental problem of relating the structure of ion channels to their function is a formidable task. This chapter describes some of the most popular simulation approaches used to model channel systems. Particle-based approaches such as Brownian and molecular dynamics will continue to play a major role in the study of protein channels and in validating the results obtained with the extremely fast continuum models. Research in the area of atomistic simulations will focus mainly on the force-field schemes used in the ionic dynamics simulation engines. In particular, polar interactions between the various components of the system need to be computed with algorithms that are more accurate than those currently used. The effects of the local polarization fields need to be accounted for explicitly and, at the same time, efficiently. Continuum models will remain attractive for their efficiency in depicting the electrostatic landscape of protein channels. Both Poisson-Boltzmann and Poisson-Nemst-Plank solvers will continue to be used to... 

J. Breed, R. Sankararamakrisnan, I.D. Kerr, and M.S.P. Sansom. Molecular dynamics simulations of water within models of ion channels. Biophys. J., 70 (1996) 1643-1661. 

With the rapid development of computational resources, simulations of large systems like lipid bilayers with membrane proteins are feasibled - Patel and coworkers have been developing a polarizable force field for biomembranes to study the structure and dynamics of ion channel systems. 

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