Hydrophobic hydration processes thermal and chemical denaturation of proteins

Fabrication and characterization of a cannabidiol-loaded emulsion stabilized by a whey protein-maltodextrin conjugate and rosmarinic acid complex

A cannabidiol (CBD)-loaded oil-in-water emulsion stabilized by a whey protein (WP)-maltodextrin (MD) conjugate and rosmarinic acid (RA) complex was fabricated, and its stability characteristics were investigated under various environmental conditions. The WP-MD conjugates were formed via dry-heating. The interaction between WP and MD was assessed by browning intensity, reduced amount of free amino groups, the formation of high molecular weight components in sodium dodecyl sulfate-PAGE, and changes in secondary structure of whey proteins. The WP-MD-RA noncovalent complex was prepared and confirmed by fluorescence quenching and Fourier-transform infrared spectroscopy spectra. Emulsions stabilized by WP, WP-MD, and WP-RA were used as references to evaluate the effect of WP-MD-RA as a novel emulsifier. Results showed that WP-MD-RA was an effective emulsifier to produce fine droplets for a CBD-loaded emulsion and remarkably improved the pH and salt stabilities of emulsions in comparison with WP. An emulsion prepared with WP-MD-RA showed the highest protection of CBD against UV and heat-induced degradation among all emulsions. The ternary complex kept emulsions in small particle size during storage at 4°C. Data from the current study may offer useful information for designing emulsion-based delivery systems which can protect active substance against environmental stresses.

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) 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.

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 (τ_m 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 (τ_i 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·ζ_th) is the product of a motive partition function {M-PF} (K _mot) multiplied by a thermal partition function {T-PF} (ζ_th = 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 (Δμ_solv = 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 ±ξ_w. 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·ζ_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.