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For many years, we have devoted our research to the study of the thermodynamic properties of hydrophobic hydration processes in water, and we have proposed the Ergodic Algorithmic Model (EAM) for maintaining the thermodynamic properties of any hydrophobic hydration reaction at a constant pressure from the experimental determination of an equilibrium constant (or other potential functions) as a function of temperature. The model has been successfully validated by the statistical analysis of the information elements provided by the EAM model for about fifty compounds. The binding functions are convoluted functions, RlnK_eq = {f(1/T)* g(T)} and RTlnK_eq = {f(T)* g(lnT)}, where the primary linear functions f(1/T) and f(T) are modified and transformed into parabolic curves by the secondary functions g(T) and g(lnT), respectively. Convoluted functions are consistent with biphasic dual-structure partition function, {DS-PF} = {M-PF} ∙ {T-PF} ∙ {ζ_w}, composed by ({M-PF} (Density Entropy), {T-PF}) (Intensity Entropy), and {ζ_w} (implicit solvent). In the present paper, after recalling the essential aspects of the model, we outline the importance of considering the solvent as “implicit” in chemical and biochemical reactions. Moreover, we compare the information obtained by computer simulations using the models till now proposed with “explicit” solvent, showing the mess of information lost without considering the experimental approach of the EAM model. Full article

The thermodynamic properties of hydrophobic hydration processes can be represented in probability space by a Dual-Structure Partition Function {DS-PF} = {M-PF} · {T-PF}, which is the product of a Motive Partition Function {M-PF} multiplied by a Thermal Partition Function {T-PF}. By development of {DS-PF}, parabolic binding potential functions α) RlnK_dual = (−ΔG°_dual/T) ={f(1/T)*g(T)} and β) RTlnK_dual = (−ΔG°_dual) = {f(T)*g(lnT)} have been calculated. The resulting binding functions are “convoluted” functions dependent on the reciprocal interactions between the primary function f(1/T) or f(T) with the secondary function g(T) or g(lnT), respectively. The binding potential functions carry the essential thermodynamic information elements of each system. The analysis of the binding potential functions experimentally determined at different temperatures by means of the Thermal Equivalent Dilution (TED) principle has made possible the evaluation, for each compound, of the pseudo-stoichiometric coefficient ±ξ_w, from the curvature of the binding potential functions. The positive value indicates convex binding functions (Class A), whereas the negative value indicates concave binding function (Class B). All the information elements concern sets of compounds that are very different from one set to another, in molecular dimension, in chemical function, and in aggregation state. Notwithstanding the differences between, surprising equal unitary values of niche (cavity) formation in Class A <Δh_for>_A = −22.7 ± 0.7 kJ·mol⁻¹·ξ_w⁻¹ sets with standard deviation σ = ±3.1% and <Δs_for>_A = −445 ± 3J·K⁻¹·mol⁻¹·ξ_w⁻¹J·K⁻¹·mol⁻¹·ξ_w⁻¹ with standard deviation σ = ±0.7%. Other surprising similarities have been found, demonstrating that all the data analyzed belong to the same normal statistical population. The Ergodic Algorithmic Model (EAM) has been applied to the analysis of important classes of reactions, such as thermal and chemical denaturation, denaturation of proteins, iceberg formation or reduction, hydrophobic bonding, and null thermal free energy. The statistical analysis of errors has shown that EAM has a general validity, well beyond the limits of our experiments. Specifically, the properties of hydrophobic hydration processes as biphasic systems generating convoluted binding potential functions, with water as the implicit solvent, hold for all biochemical and biological solutions, on the ground that they also are necessarily diluted solutions, statistically validated. Full article