Hydration percolation model

Careri et al. (1986), using the framework of percolation theory, analyzed the explosive growth of the capacitance with increasing hydration above a critical water content (Fig. 14). The threshold for onset of the dielectric response was found to he 0.15 h for free lysozyme and 0.23 h for the lysozyme—substrate complex. In the percolation model the thresh-... 

The use of the percolation model to analyze the d.c. conductivity in hydrated lysozyme powders (Careri et al., 1986, 1988) and in purple membrane (Rupley et al, 1988) introduces a viewpoint from statistical physics that is relevant to a wide range of problems originating in disordered systems. Percolation theory is described in the appendix to this article, for readers unfamiliar with it. Here, we discuss the significance of percolation specihcally for protein hydration and function. 

Domain coalescence (Karplus and Weaver, 1976) is a possible mechanism for protein folding. Zientara et al. (1980) examined the dependence of the coalescence lifetime on the hydration shell. The lifetime depends on the activation barrier contributed by the shell and the extent of the shell. If domains resemble the native protein in hydration, then the minimal extent of the shell and its fluidity favor coalescence. In passing, one notes that the percolation model may apply to folding the coalescence of domains should be analogous to gelation or to diffusion on a partially filled lattice. 

In these expressions, p is the porosity of the SiC, i.e. the volume fraction of empty space. In the asymmetric MG model, we have chosen the coating to be the solution, since the opposite choice of SiC-encapsulated liquid spheres will not permit diffusion through the medium. With this choice, the SiC does not percolate and hence there is no structural support. The selectivity of the membrane is based in part on the size and shape of the protein molecules. The expressions for (pD)eff in the effective medium models [Equations (12.2) and (12.3)] do not contain a size scale, but it is necessary to introduce a scale in order to account for the size of a protein molecule. For simplicity, we assume that the proteins are spherical with effective (hydration) radius r. The excluded volume within the pores due to nonzero size is taken into account by replacing the porosity p with an effective porosity p. For the columnar... 

Below we show how the appearance of spanning water networks may be detected in computer simulations. In particular, a percolation transition of water upon hydration was studied by simulations in model lysozyme powders and on the surface of a single lysozyme molecule. In protein crystals, increase in hydration of a biomolecular surface may be achieved by applying pressure. In some hydration range, pressurization leads to the formation of spanning water networks enveloping the surface of each biomolecule. Finally, the formation of the spanning water network is shown for the DNA molecule at various conformations and for different forms of DNA. 

In low-humidity tetragonal crystal with the partial density of lysozyme of about 0.80 g/cm, approximately 120 water molecules are in the first hydration shell of lysozyme molecule. In order to explore a wide range of hydration level up to monolayer coverage (about 300 water molecules), partial density of lysozyme in powder should be < 0.80 g/cm. In Ref. [401], two models for protein powder were studied densely packed powder with the density of dry protein 0.66 g/cm and loosely packed powder with a density 0.44 g/cm. In loosely packed powder, the percolation transition of water was noticeably (by a factor of two) shifted to higher hydration levels compared with experiment. The fractal dimension of the water network at the percolation threshold as well as other properties evidenced that the percolation transition of water in this model was not two dimensional. The spanning water network consists of the 2D sheets at the protein surface as well as of the 3D water domains, formed due to the capiUaiy condensation of water in hydrophilic cavities. The latter effect causes essential distortion of various distribution functions of water clusters in loosely packed powder. Therefore, below we present an overview of the results obtained for the densely packed model powder. 

Spanning probability R, defined as a probability to observe a water cluster that crosses the model system at least in one dimension, shows sigmoid dependence on the mass fraction C of water (Fig. 98, upper panel). At ambient temperature (T = 300 K), the inflection point of this dependence corresponding to R = 50% is located at about C = 0.122. This hydration level is close to that where the mean cluster size Smean passes through a maximum (Fig. 98, middle panel). Fractal dimension of the largest water cluster achieves the value at C 0.155 (Fig. 98, lower panel). Summarizing, the percolation transition of water may be attributed to the hydration level C 0.155. The cluster size distribution ns supports this conclusion [401]. 

The detailed studies of the percolation transition of hydration water in model biosystems (Section 7.1) makes it possibile to consider various physical properties of these systems below and above the percolation threshold. The total MSD (( )) of water at the surfaces of rigid and flexible lysozyme molecules continuously increases upon hydration (Fig. 112). Similar behavior was observed in the simulation studies of water near the surface of differently hydrated plastocyanin [640, 641]. 

Note that a correct comparison of the absolute values of the temperatures of the percolation transitions of water in the hydration shells of ELP and Snase, obtained in simulations, with the real temperature scale needs special consideration, as the phase diagrams of the available water models differ noticeably from the phase diagram of real water (see [5, 6] for a comparative analysis of the phase diagrams of various water models). There are two main characteristic temperatures that can be used for estimating the temperature shift of the phase diagram of model water with the behavior of real water the critical temperature of the hquid-vapor phase transition and the temperature of the liquid density maximum. The latter temperature is the most important parameter for studies carried on close to ambient conditions. For example, the phase diagram of TIP3P water model is shifted downward by at least 35 K with respect to real water. 

P. M. Suherman, G. Smith, A percolation transition cluster model of the temperature dependent dielectric properties of hydrated proteins, J. Phys. D Appl. Phys. 36 (2003) 336-342. 

Based on the cluster network model, further studies propose an interpretation of the percolation properties of proton conductivity as a function of water content by using a random network model [102], which is a modification of the cluster network model. This model includes an intermediate region wherein the side chains ending with pendant sulfonic acid groups, which are bonded to the perfluorinated backbones, tend to form cluster within the overall structure of the material resulting in the formation of hydrated regions. Unlike the cluster network model, the... 

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