Membrane Model Development

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. 

The following steps describe the implementation of the membrane model developed in... 

Ion-selective bulk membranes are the electro-active component of ion-selective electrodes. They differ from biological membranes in many aspects, the most marked being their thickness which is normally more then 105 times greater, therefore electroneutrality exists in the interior. A further difference is given by the fact that ion-selective membranes are homogeneous and symmetric with respect to their functioning. However, because of certain similarities with biomembranes (e.g., ion-selectivity order, etc.) the more easily to handle ion-selective membranes were studied extensively also by many physiologists and biochemists as model membranes. For this reason research in the field of bio-membranes, and developments in the field of ion-selective electrodes have been of mutual benefit. 

The most likely way for pardaxin molecules to insert across the membrane in an antiparallel manner is for them to form antiparallel aggregates on the membrane surface that then insert across the membrane. We developed a "raft"model (data not shown) that is similar to the channel model except that adjacent dimers are related to each other by a linear translation instead of a 60 rotation about a channel axis. All of the large hydrophobic side chains of the C-helices are on one side of the "raft" and all hydrophilic side chains are on the other side. We postulate that these "rafts" displace the lipid molecules on one side of the bilayer. When two or more "rafts" meet they can insert across the membrane to form a channel in a way that never exposes the hydrophilic side chains to the lipid alkyl chains. The conformational change from the "raft" to the channel structure primarily involves a pivoting motion about the "ridge" of side chains formed by Thr-17, Ala-21, Ala-25, and Ser-29. These small side chains present few steric barriers for the postulated conformational change. 

The history of the development of the bilayer membrane model is fascinating, and spans at least 300 years, beginning with studies of soap bubbles and oil layers on water [517-519]. 

For acids, the membrane retention actually increases in the case of egg lecithin, compared to soy lecithin. This may be due to decreased repulsions between the negatively charged sample and negatively charged phospholipid, allowing H-bond-ing and hydrophobic forces to more fully realize in the less negatively charged egg lecithin membranes. The neutral molecules display about the same transport properties in soy and egg lecithin, in line with the absence of direct electrostatic effects. These differences between egg and soy lecithins make soy lecithin the preferred basis for further model development. 

Following the original simple concepts of Gorter and Grendel, a large number of membrane models have been developed over the subsequent half a century the two most contrasting are shown in Fig. 6.9. 

Here, we discuss a solid-state 19F-NMR approach that has been developed for structural studies of MAPs in lipid bilayers, and how this can be translated to measurements in native biomembranes. We review the essentials of the methodology and discuss key objectives in the practice of 19F-labelling of peptides. Furthermore, the preparation of macroscopically oriented biomembranes on solid supports is discussed in the context of other membrane models. Two native biomembrane systems are presented as examples human erythrocyte ghosts as representatives of eukaryotic cell membranes, and protoplasts from Micrococcus luteus as membranes... 

The studies on phospholipid bilayers with defined amounts of charged component are helpful to explain the partition characteristics in biological membranes. Liposome water partition data of propranolol in lipids from kidney epithelial cells (a common model system in pharmaceutical sciences for the uptake into the gastrointestinal tract) have been successfully described with partition models developed for pure bilayers or defined mixtures [159]. Since lipophilic cations and anions can be used as probes for the membrane potential, their interaction with microbial and mitochondrial membranes has been studied... 

In reality, this behavior is only observed in the limit of small jg. At currents o 1 A cm-2 that are relevant for fuel cell operation, the electro-osmotic coupling between proton and water fluxes causes nonuniform water distributions in PEMs, which lead to nonlinear effects in r/p M- These deviations result in a critical current density, p at which the increase in r/pp j causes the cell voltage to decrease dramatically. It is thus crucial to develop membrane models that can predicton the basis of experimental data on structure and transport properties. 

The phenomena of association colloids in which the limiting structure of a lamellar micelle may be pictured as composed of a bimolecular leaflet are well known. The isolated existence of such a limiting structure as black lipid membranes (BLM) of about two molecules in thickness has been established. The bifacial tension (yh) on several BLM has been measured. Typical values lie slightly above zero to about 6 dynes per cm. The growth of the concept of the bimolecular leaflet membrane model with adsorbed protein monolayers is traceable to the initial experiments at the cell-solution interface. The results of interfacial tension measurements which were essential to the development of the paucimolecular membrane model are discussed in the light of the present bifacial tension data on BLM. 

Several authors have already developed methodologies for the simulation of hybrid distillation-pervaporation processes. Short-cut methods were developed by Moganti et al. [95] and Stephan et al. [96]. Due to simplifications such as the use of constant relative volatility, one-phase sidestreams, perfect mixing on feed and permeate sides of the membrane, and simple membrane transport models, the results obtained should only be considered qualitative in nature. Verhoef et al. [97] used a quantitative approach for simulation, based on simplified calculations in Aspen Plus/Excel VBA. Hommerich and Rautenbach [98] describe the design and optimization of combined pervaporation-distillation processes, incorporating a user-written routine for pervaporation into the Aspen Plus simulation software. This is an improvement over most approaches with respect to accuracy, although the membrane model itself is still quite... 

Following on from this work two types of mathematical model were developed that do not rely on measuring the contact area. These models are the "liquid-drop" model (Yoneda, 1973) and the elastic membrane model (Cheng, 1987a Feng and Yang, 1973 Lardner and Pujara, 1980). 

An analytical elastic membrane model was developed by Feng and Yang (1973) to model the compression of an inflated, non-linear elastic, spherical membrane between two parallel surfaces where the internal contents of the cell were taken to be a gas. This model was extended by Lardner and Pujara (1980) to represent the interior of the cell as an incompressible liquid. This latter assumption obviously makes the model more representative of biological cells. Importantly, this model also does not assume that the cell wall tensions are isotropic. The model is based on a choice of cell wall material constitutive relationships (e.g., linear-elastic, Mooney-Rivlin) and governing equations, which link the constitutive equations to the geometry of the cell during compression. 

Note that the equations in Table I have a similar mathematical structure as the much simpler 2-state channel model developed earlier in this paper. One major difference should be emphasized namely, that the rate constants of the model depend on the physical movement of charge so are not instantaneous functions of membrane potential as assumed in the HH model. However, if the voltage sensing process is sufficiently faster than the dynamics of channel opening and closing, then the assumption of an instantaneous dependence of ex s and 3 s on V is reasonable (see Discussion). 

The conventional model developed to explain cell membrane characteristics influencing drug permeability is routinely referred to as the fluid-mosaic model (Figures 2.1 and 2.2). In this model the main components, for our purposes, are a phospholipid (e.g., sphingomyelin and phosphatidylcholine) bilayer (8 nm), with polar moieties at both the external and internal surfaces, and with proteins periodically traversing the phospholipid plane perpendicularly. 

Despite this last observation, for this type of simulation and modelling research, two main means of evolution remain the first consists in enlarging the library with new and newly coded models for unit operations or apparatuses (such as the unit processes mentioned above multiphase reactors, membrane processes, etc.) the second is specified by the sophistication of the models developed for the apparatus that characterizes the unit operations. With respect to this second means, we can develop a hierarchy dividing into three levels. The first level corresponds to connectionist models of equilibrium (frequently used in the past). The second level involves the models of transport phenomena with heat and mass transfer kinetics given by approximate solutions. And finally, in the third level, the real transport phenomena the flow, heat and mass transport are correctly described. In... 

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