Percolation transition of water in low-hydrated biosystems

Formation of the hydrogen-bonded water networks may affect conductivity of a system in a drastic way, as these networks provide the paths for the conduction of protons, ions, or other charges in the system. So, the qualitative changes in the conductivity may be expected at hydrations, close to the percolation transition of water. Surface conductivity of quartz increases relatively slowly with increasing hydration level until the completion of the adsorbed water monolayer, but much faster at higher hydrations [582]. The hydration dependence of the dielectric losses of hydrated collagen 

The conductivity exponent of about 1.23 indicates 2D character of the percolation transition. Similar values of the conductivity exponent were obtained for the hydration dependence of the conductivity of embryo and endosperm of maize seeds [595, 596], where the percolation threshold is /t = 0.082 and 0.127 g/g, respectively. In hydrated bakers yeast, protonic conductivity evidences 2D percolation transition of water at h = 0.163 g/g, and the value of the conductivity exponent is about 1.08 [597]. In this system, increase in conductivity due to 3D water percolation is observed at essentially higher hydration level h= 1.47 g/g, where conductivity exponent is about 1.94, i.e., close to the 3D value t = 2.0. Conductivity measurements of Anemia cysts at various hydrations show strong increase in conductivity starting from the threshold hydration h = 0.35 g/g [598] (see Fig. 97). The conductivity exponent in this system is 1.635, which is in between the values expected for 2D and 3D systems. DC conductivity of lichens, evaluated from the dielectric studies at frequencies between 100 Hz and 1 MHz [599], shows strong enhancement at some hydration level. Fit of the conductance-hydration dependence to equation (24) gave the following parameters he = 0.0990 g/g, t = 1.46 for Himantormia lugubris and he = 0.0926 g/g, t = 1.18 for Cladonia 

Low-frequency dielectric measurements (0.1 Hz-1 MHz) of hydrated lysozyme, ovalbumin, and pepsin were used to estimate the fractal dimension for the random walk of protons through the hydrogen-bonded network of water molecules by fitting the shape of the dielectric loss peak [600, 601]. In all three systems, a crossover from 2D to 3D water network occurs within the interval of hydration from 0.05 to 0.10 g/g. For lysozyme, these values are noticeably below the value of about 0.17 g/g, reported in [592]. This difference may be attributed to the presence of about 0.07 g/g of strongly bound water, which presumably was not taken into account in [601]. When hydration exceeds the threshold value, dielectric losses increase almost Unearly with temperature. With approaching T 310 to 330 K, this increase slows down and dielectric losses turn to decrease with temperature. This behavior may reflect thermal break of the spanning hydrogen-bonded water network, which wdl be considered in Section 8.1. 

At low temperatures, radiation-induced conductivity critically depends on the water content and appears only above the critical hydration levels 0.41 and 0.79 g/g for collagen and DNA, respectively [602, 603]. The critical hydration level for DNA corresponds to about 15 water molecules per phosphate group (F = 15). The effects of various additives on the conductivity evidence charge migration in the hydration shell of DNA [604]. At much lower hydrations (0.12 to 0.22g/g), conductivity of hydrated DNA shows exponential dependence on h [605], which may be attributed to the intrinsic semiconductivity of the DNA backbone. More detailed experimental studies of DNA hydration [606] show that radiation-induced conductivity starts not strictly atP =15 [602, 603] but via a sigmoid-like increase within hydration range from r = lltoF = 16 with subsequent stepwise increase at F 24. 

The above experimental studies of the conductivity of hydrated biosystems directly evidence the formation of a spanning network of hydration water via percolation transition. The charge transfer itself may play a crucial role in biofunction [607]. In most of the cases, described above, the percolation transition of water occurs at the hydration level, where various forms of biological activity develop in a stepwise manner (see Section 6). In particular, the following biological processes starts close 

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