Implicit membrane models

Ulmschneider, J.P., Ulmschneider, M.B. Folding simulations of the transmembrane helix of virus protein U in an implicit membrane model. J. Chem. Theory Comput. 2007, 3, 2335 16. 

The non-polar component of the solvation free energy is especially important for implicit membrane models as it decreases from a significant positive contribution in aqueous solvent to near zero at the center of the phospholipid bilayer. Without a non-polar term, even hydrophobic solutes would in fact prefer the high-dielectric environment where the electrostatic solvation free energy is more favorable than in a low-dielectric medium. The functional form of the non-polar term may follow a simple switching function [79,80], a calculated free energy insertion profile for molecular oxygen [82,84], or may be parameterized as well with respect to simulation or experimental data. 

FIGURE 6.3 Optimized effective dielectric profiles and non-polar profiles to be used in implicit membrane model. 

Implicit membrane models have been used successfully in simulation of membrane proteins [9] and in folding studies of membrane-bound peptides [88-90]. Furthermore, applications of implicit membrane models as scoring functions and in MMGB/SA-type free energy calculations for membrane-bound biomolecules are conceivable [91]. 

Tanizaki, S., Feig, M. Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model. J. Phys. Chem. B 2006,110,548-56. 

Membrane environment. Membranes are large structures, translocation of molecular structures through membranes may involve significant conformational changes, and so these systems are natural candidates for implicit solvent modeling. One of the challenges here is accurate and computationally facile representation of the complex dielectric environment that, in the case of membranes, includes solvent, solute, and the membrane, all with different dielectric properties. Corrections to the GB model have been introduced [45-47] to account for the effects of variable dielectric environment. Other implicit membrane models, not based on the GB, have also been proposed [48]. 

FIGURE 6.2 Amino acid side chain analog insertion profiles with explicit (red) and implicit (purple, black) membrane models. The explicit lipid profiles were calculated with the OPLS force field [87], implicit profiles were calculated with both CHARMM [92] and OPLS force fields [93]. Experimental water-cyclohexane transfer free energies [85] are indicated as red dots. 

Spassov, V.Z., Yan, L., Szalma, S. Introducing an implicit membrane in Generalized Bom/solvent accessibUity continuum solvent models. J. Phys. Ghem. B 2002,106, 8726-38. 

This interpretation of velocities and the resulting additional terms are in fact erroneous as we have shown in Ref. [24], and amount to double accounting. The BFM was on the other hand shown to implicitly contain the viscous terms, i.e. the Schloegl equation [24]. The new membrane model developments presented in this Chapter are therefore based on the correct and rational BFM framework. 

In a related paper, Ikeda et al. has presented a combined use of replica-exchange MD and solid-state MAS NMR spectral simulations for determining the structure and orientation of membrane-bound peptide." First, an ensemble of low energy structures of mastoparan-X, a wasp venom peptide, in lipid bilayers was generated by replica exchange molecular dynamics (REMD) simulation with the implicit membrane/solvent model. Next, peptide structures compatible with experimental chemical shifts of C,, Cp and C carbons were selected from the ensemble. Chemical shifts of C, alone were sufficient for the selection with backbone rmsd s of 0.8 A from the experimentally determined structure. The dipolar couplings between the peptide protons and lipid nuclei were obtained from the C-... 

Many CG models have been developed and used in the past two decades, and not surprisingly, applications have been focusing primarily on the phenomenon of self-assembly and the equilibrium between phases. To some extent, all models that simplify the chemical structure of a macromolecule to focus on its physical properties can be considered as CG models of varied complexity. However, a marked distinction between these models is whether the solvent is modeled implicitly as a continuous medium interacting only with the solute, or explicitly as an ensemble of particles that also interact with each other. For brevity, we discuss only the latter kind of models because the competition between intermolecular forces is crucial to simulate self-assembly. For the purpose of modeling the mechanical properties of membranes and other known stmctures, implicit solvent models are relatively accurate [28, 29] and are typically lower in computational cost than explicit solvent models. 

Despite the success of the comparatively simple models presented so far, they implicitly assume that the skin barrier may be modeled by a homogeneous membrane—which implies that the properties of the barrier do not change with depth and that there exists only a single pathway through the barrier. Obviously, skin is not a homogeneous membrane and therefore in several studies the simple model was extended to include several subsequent skin layers. In addition, possible transport along hair follicles and sweat ducts, for example, was sometimes included. 

The CNMMR model with laminar flow liquid stream in the annular region consists of three ordinary differential equations for the gas in the tube core and two partial differential equations for the liquid in the annular region. These equations are coupled through the diffusion-reaction equations inside the membrane and boundary conditions. The model can be solved by first discretizing the liquid-phase mass balance equations in the radial direction by the orthogonal collocation technique. The resulting equations are then solved by a semi-implicit integration procedure [Harold etal., 1989]. 

The Dusty Gas Model (DGM) is one of the most suitable models to describe transport through membranes [11]. It is derived for porous materials from the generalised Maxwell-Stefan equations for mass transport in multi-component mixtures [1,2,47]. The advantage of this model is that convective motion, momentum transfer as well as drag effects are directly incorporated in the equations (see also Section 9.2.4.2 and Fig. 9.12). Although this model is fundamentally more correct than a description in terms of the classical Pick model, DGM/Maxwell-Stefan models )deld implicit transport equations which are more difficult to solve and in many cases the explicit Pick t)q>e models give an adequate approximation. For binary mixtures the DGM model can be solved explicitly and the Fickian type of equations are obtained. Surface diffusion is... 

Tanizaki, S., Feig, M. A Generalized Bom formalism for heterogeneous dielectric environments Application to the implicit modeling of biological membranes. J. Ghem. Phys. 2005,122,12470-6. 

---