Statistical Inference for Ergodic Algorithmic Model (EAM), Applied to Hydrophobic Hydration Processes.

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) RlnKdual = (-ΔG°dual/T) ={f(1/T)*g(T)} and ß) RTlnKdual = (-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 ±ξw, 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 <Δhfor>A = -22.7 ± 0.7 kJ·mol-1·ξw-1 sets with standard deviation σ = ±3.1% and <Δsfor>A = -445 ± 3J·K-1·mol-1·ξw-1J·K-1·mol-1·ξw-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.

Hydrophobic Hydration Processes: Intensity Entropy and Null Thermal Free Energy and Density Entropy and Motive Free Energy.

The processes at the molecule level, which are the source of the ergodic properties of thermodynamic systems, are analyzed with special reference to entropy. The entropy change produced by increasing the temperature T depends on the increase of velocity of the particles with a decrease of the squared mean sojourn time (τm 2) and gradual loss of instant energy intensity. The diminution, which is due to dilution, of the number of terms in the summation of cumulative sojourn time (τi 2)Σ produces loss of energy density, thus generating a gradual increase of density entropy, dS Dens. The ergodic property of thermodynamic systems consists of the equivalence of density entropy (dependent on dilution) with intensity entropy (dependent on temperature). This equivalence has been experimentally verified in every hydrophobic hydration process as thermal equivalent dilution. An ergodic dual-structure partition function {DS-PF} represents the state probability of every hydrophobic hydration process, corresponding to the biphasic composition of these systems. The dual-structure partition function {DS-PF} (K mot·Î¶th) is the product of a motive partition function {M-PF} (K mot) multiplied by a thermal partition function {T-PF} (ζth = 1). {M-PF} gives rise to changes of density entropy, whereas {T-PF} gives rise to changes of intensity entropy. {M-PF} is referred to a reacting mole ensemble (reacting solute) composed of few elements (moles), ruled by binomial distribution, whereas {T-PF} is referred to a nonreacting molecule ensemble (NoremE) (nonreacting solvent), which is composed of a very large population of elements (molecules), ruled by Boltzmann statistics. Statistical thermodynamic methods cannot be applied to {M-PF} that can be calculated by numerical methods from the experimental titration data. By development of the dual-structure partition function {DS-PF}, parabolic convoluted binding functions are obtained. The tangents to the binding functions represent the dual enthalpy, -ΔH dual = (-ΔH mot - ΔH th), and the dual entropy, ΔS dual = (ΔS mot + ΔS th). The connections between canonical and grand-canonical partition functions of statistical thermodynamics with thermal and motive partition functions of chemical thermodynamics, respectively, are discussed. Special attention has been devoted to the equality ΔH th/T + ΔS th = 0, typical of NoremEs, as an entropy-enthalpy compensation with ΔG th/T = 0. The thermodynamic potential change Δµ, as proposed by potential distribution theorem (PDT) for iceberg formation from {T-PF} of the solvent, is nonexistent because the excess solvent is at a constant potential (Δµsolv = 0). The information level offered by the ergodic algorithmic model (EAM) is more complete and correct than that offered by the potential distribution theorem (PDT): the stoichiometry of the water reaction in hydrophobic hydration processes is determined by the EAM as the function of the number ±ξw. Quasi-chemical approximation, renamed the chemical molecule/mole scaling function (Che. m/M. sF), is a fundamental breakthrough in the application of statistical thermodynamics to chemical reactions. Boltzmann statistical molecule distribution of the thermal partition function {T-PF} is scaled with binomial mole distribution of the motive partition function {M-PF}. For computer-assisted drug design, the alternative calculation procedure of Talhout, based on the previous experimental determination of binding functions, is recommended. The ergodic algorithmic model (EAM), applied to the experimental convoluted binding functions, can recover the distinct terms of intensity entropy (ΔH mot/T) and density entropy (ΔS mot), together with other essential information elements, lost by computer simulations.

Hydrophobic Hydration Processes. I: Dual-Structure Partition Function for Biphasic Aqueous Systems.

The thermodynamic properties of hydrophobic hydration processes have been analyzed and assessed. The thermodynamic binding functions result to be related to each other by the mathematical relationships of an ergodic algorithmic model (EAM). The active dilution d A of species A in solution is expressed as d A = 1/(Φ·x A) with thermal factor Φ = T -(C p,A/R) and (1/x A) = d id(A), where d id(A) = ideal dilution. Entropy function is set as S = f(d id(A),T). Thermal change of entropy (i.e., entropy intensity change) is represented by the equation (dS) d = C p dln T. Configuration change of entropy (i.e., entropy density change) is represented by the equation (dS)T = (-R dln x A)T = (R dln d id(A)) T . Because every logarithmic function in thermodynamic space corresponds to an exponential function in probability space, the sum functions ΔH dual = (ΔH mot + ΔH th) and ΔS dual = (ΔS mot + ΔS th) of the thermodynamic space give birth, in exponential probability space, to a dual-structure partition function { DS-PF }: exp(-ΔG dual/RT) = K dual = (K mot·Î¶th) = {(exp(-ΔH mot/RT))(exp(ΔS mot/R))}·{exp(-ΔH th/RT) exp(ΔS th/R)}. Every hydrophobic hydration process can be represented by { DS-PF } = { M-PF }·{ T-PF }, indicating biphasic systems. { M-PF } = f(T,d id(A)), concerning the solute, is monocentric and produces changes of entropy density, contributing to free energy -ΔG mot, whereas { T-PF } = g(T), concerning the solvent, produces changes of entropy intensity, not contributing to free energy. Entropy density and entropy intensity are equivalent and summed with each other (i.e., they are ergodic). From the dual-structure partition function { DS-PF }, the ergodic algorithmic model (EAM) can be developed. The model EAM consists of a set of mathematical relationships, generating parabolic convoluted binding functions R ln K dual = -ΔG dual/T = {f(1/T)*g(T)} and RT ln K dual = -ΔG dual = {f(T)*g(ln T)}. The first function in each convoluted couple f(1/T) or f(T) is generated by { M-PF }, whereas the second function, g(T) or g(ln T), respectively, is generated by { T-PF }. The mathematical properties of the thermodynamic functions of hydrophobic hydration processes, experimentally determined, correspond to the geometrical properties of parabolas, with constant curvature amplitude C ampl = 0.7071/ΔC p,hydr. The dual structure of the partition function conforms to the biphasic composition of every hydrophobic hydration solution, consisting of a diluted solution, with solvent in excess at constant potential.

Prospects of second generation artificial intelligence tools in calibration of chemical sensors.

Multivariate data driven calibration models with neural networks (NNs) are developed for binary (Cu++ and Ca++) and quaternary (K+, Ca++, NO3- and Cl-) ion-selective electrode (ISE) data. The response profiles of ISEs with concentrations are non-linear and sub-Nernstian. This task represents function approximation of multi-variate, multi-response, correlated, non-linear data with unknown noise structure i.e. multi-component calibration/prediction in chemometric parlance. Radial distribution function (RBF) and Fuzzy-ARTMAP-NN models implemented in the software packages, TRAJAN and Professional II, are employed for the calibration. The optimum NN models reported are based on residuals in concentration space. Being a data driven information technology, NN does not require a model, prior- or posterior- distribution of data or noise structure. Missing information, spikes or newer trends in different concentration ranges can be modeled through novelty detection. Two simulated data sets generated from mathematical functions are modeled as a function of number of data points and network parameters like number of neurons and nearest neighbors. The success of RBF and Fuzzy-ARTMAP-NNs to develop adequate calibration models for experimental data and function approximation models for more complex simulated data sets ensures AI2 (artificial intelligence, 2nd generation) as a promising technology in quantitation.

Data, knowledge and method bases in chemical sciences. Part IV. Current status in databases.

Computer readable databases have become an integral part of chemical research right from planning data acquisition to interpretation of the information generated. The databases available today are numerical, spectral and bibliographic. Data representation by different schemes--relational, hierarchical and objects--is demonstrated. Quality index (QI) throws light on the quality of data. The objective, prospects and impact of database activity on expert systems are discussed. The number and size of corporate databases available on international networks crossed manageable number leading to databases about their contents. Subsets of corporate or small databases have been developed by groups of chemists. The features and role of knowledge-based or intelligent databases are described.