Coupled monolayer models

In this article, we will focus in particular on the so-called coupled monolayer models [18,20-26,28,29], where membranes are described as stacks of two sheets (monolayers), each with their own elastic parameters. Mraiolayers are bound to each other by a local harmonic potential that accounts for the areal compressibility of lipids within the membrane and their constant volume [22, 28]. Li et al. have recently compared the elastic properties of amphiphilic bilayers with those of the corresponding monolayers within a numerical self-consistent field study of... 

In the case where the membrane is deformed, the deformation profiles can be compared to a variety of theories [16,17,27, 33, 245-247]. Both in coarse-grained [30,234] and atomistic [248] simulations, it was reported that membrane thickness profiles as a function of the distance to the protein are not strictly monotonic, but exhibit a weakly oscillatory behavior. This feature is not compatible with membrane models that predict an exponential decay [16,17,27], but it is nicely captured by the coupled elastic monolayer models discussed earlier [22, 28, 30]. Coarsegrained simulations of the Lenz model showed that the coupled monolayer models describe the profile data at a quantitative level, with almost no fit parameters except the boundary conditions [30, 244]. 

The ionic profile of the metal was modeled as a step function, since it was anticipated that it would be much narrower than the electronic profile, and the distance dx from this step to the beginning of the water monolayer, which reflects the interaction of metal ions and solvent molecules, was taken as the crystallographic radius of the metal ions, Rc. Inside the metal, and out to dl9 the relative dielectric constant was taken as unity. (It may be noted that these calculations, and subsequent ones83 which couple this model for the metal with a model for the interface, take the position of the outer layer of metal ion cores to be on the jellium edge, which is at variance with the usual interpretation in terms of Wigner-Seitz... 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

The effects of electric fields on monolayer domains graphically illustrates the repulsion between neighboring domains [236,237]. A model by Stone and McConnell for the hydrodynamic coupling between the monolayer and the subphase produces predictions of the rate of shape transitions [115,238]. 

Given the low permeability of the antioxidant across MDCK cell monolayers and its large membrane partition coefficient, efflux kinetic studies using drug-loaded cell monolayers cultured on plastic dishes could yield useful information when coupled with the following biophysical model. The steady-state flux of drug from the cell monolayer is equal to the appearance rate in the receiver solution ... 

One of the main in vitro permeability assays used in the pharmaceutical industry has been for many years the Caco-2 monolayer. Therefore, most of the in silica models developed to predict permeability were based on Caco-2 data. Hou and Johnson produced a couple of reviews that comprehensibly summarizes the recent efforts using Caco-2 permeability data [92, 94]. All those models are designed to predict the influx or apparent permeability of drugs in the same direction as intestinal absorption occurs, that is, from the apical to the basal side of the cell line, regardless of the extent of active transport involved in the permeation process. 

There exists a substantial history of interest in flow and deformation properties of monolayers. Perhaps, the first is the theoretical formulation of hydrodynamic coupling between the monolayer and subphase by Harkins and Kirkwook in 1938 [129], in determination of steady shear viscosity of mono-layers, which has since been augmented by Hansen [130] and Goodrich [131]. A variation of the method based on the Maxwell model was proposed by Mannheimher and Schechter [132] in an oscillatory mode in a canal. Experimentally, the method was implemented by joint efforts in our laboratories for determinations of steady shear viscosity of monolayers through the canal... 

The microscopic model, however, cannot take into account net coupling of dynamic dipoles oriented parallel to the surface for the thin (microscopic) film. Such coupling in adsorbed monolayers has been shown [57] by probing an otherwise disallowed transition on a metal through a combination band, to result in a red shift from the singleton frequency. This effect of parallel and normal dipole components can be best exemplified by comparison of the RAIRS spectrum of an isotropic physisorbed molecule with a very strong dipole oscillator, v(C-O) in Mo(CO)6, with the gas phase value (singleton frequency) [58]... 

The tilt angle derived from a detailed analysis of the peaks as a function of pressure is given in Fig. 11. In the absence of polymer one observes the reduction of t to zero whereas for PDADMAC t>25° even at the highest pressure. For comparison we also include the tilt angle measured for PAH in the subphase. The binding of this cationic polyelectrolyte apparently has only a minor influence on monolayer structure. The polyelectrolyte coupling may be best understood looking at the model of Fig. 12 which should hold specif-... 

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