The first two hydration layers of two spherical solutes of radii and at a distance between their centers. The surface of each particle is shown as a thick solid line. The circles of diameter represent water molecules. The dashed circle of radius represents a molecule of the solute particle.
A water molecule in the first hydration shell (1HS) of the planar substrate surface (shadowed area). The lower and upper boundaries of the 1HS are marked as the planes and and shown as long-dashed lines. The molecule, shown as a disk , is at the distance from the lower boundary (closest to the hydrophobic surface) of the 1HS. The four hb arms of the molecule are shown as short-dashed lines with the empty circles as the arm tips. Arms 1 and 2 are in the plane of the figure, arm 3 points to the reader, and arm 4 is behind the figure plane. Their tips are shown as empty circles. Arms 3 and 4 are located out of the figure plane (one of them under it, the other above it). The angle between any two hb arms is . The angle is the angle formed between the hb arm and its tangential projection (parallel to the lower boundary of the 1HS). In this figure, the origin of the Carthesian coordinate system coincides with molecule , the axis being normal to the surface. It is assumed that with if the coordinate of the hb-arm tip is negative and if that coordinate is negative.
The BHB networks contribution to the total interaction potential between two spherical solutes, one of which is a composite particle of radius (and of hydrophobic surface fraction ) and the other is either a hydrophobic (lower curve) or hydrophilic (upper curve) particle of radius (which corresponds to a single protein residue). The potential is plotted as vs , where . The solvent is water under such conditions that .
A piece of a heteropolymer chain around a spherical cluster consisting of hydrophobic and hydrophilic beads. Bead 1 is in the plane of the figure, whereas other beads may all lie in different planes. All bond angles are equal to and their lengths are equal to . The radius of the cluster is and the distance from the selected bead 1 to the cluster center is .
The potentials (lower dashed curve), (upper dashed curve), (dot-dashed curve), and (solid curve), for a hydrophobic bead around a cluster with and . The confining potential is shown as a solid vertical line at .
The temperature dependence of (a) and (b), the times of protein denaturation (via spinodal decomposition) upon cooling and heating, respectively, divided by their values at the corresponding threshold temperatures. In both (a) and (b), the large points (upper series) are for the improved model of protein denaturation (taking into account the hb ability of water molecules as presented in this paper), whereas the small points (lower series) represent the previously reported predictions (Ref. 19) of the original model of protein unfolding (without taking into account hb effects).
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