Scaling limit inhomogeneous models

Besides issues related to the accuracy of force fields in spatially inhomogeneous systems comprising many chemically distinct components, the basic restriction related to the chemically detailed models is the rather small length and time scales that they can access. This limitation imposes severe restrictions for considering collective phenomena in amphiphilic vesicles, i.e., processes that involve large particle numbers. Typical examples include vesicle assembly, vesicle fusion, phase separation and shape transformations of multicomponent amphiphilic vesicles. For many of these processes, it is expected that the underlying atomistic details of the molecular constituents can be captured by a small number of relevant characteristics and universality classes, comprised of systems with a rather different atomistic structure, can be identified. These phenomena can be successfully investigated via minimal... 

Continuum electrostatic models [72,108-113] are presently most developed and commonly nsed for the evaluation of the solvation energies in proteins however, they carry a nnmber of limitations and uncertainties, which cannot be avoided unless the microscopic interactions of the quantum subsystem and the protein are taken into account [114], For example, it is not clear which dielectric constant of the polarizable water cavities one should use in such calculations even the usually assumed dielectric constant of a dry protein (typically assumed as 4 [99,115,116]) is not that well defined—many studies indicate that the effective dielectric of the protein is much higher [114,117-119]— primarily due to internal water [120], and partially due to protein (nonlinear) charge relaxation. Proteins are also inhomogeneous media. It is understood that only microscopic simulations should eventually provide a correct picture and remove the inherent uncertainty of phenomenological approach [71,114,115,121-132]. Despite the drawbacks, the continuum models provide most computationally efficient approach for the treatment of the protein electrostatics, which make possible large-scale investigation of the enzyme properties, such as CcO. 

The re-establishment of a direct link between capillary phenomena and the intermolecular forces had to await the development of the statistical mechanics of systems that are hig hly inhomogeneous on the scale of length of the range of these forces. This topic is the subject of our long fourth chapter, the results of which provide a justification f< and show the limitations of the earlier quasi-thermodynamk dieories. The statistical results are applied in mean-field approximation to some tractable but ardficial model systems in Chapter 5. M< e realistic models are treated both by computer simulation (Chapter 6) and by approximating the exact statistical equations (Chapter 7). 

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