Effect of temperature and pressure on the protonation of glycine.

Flow calorimetry has been used to study the interaction of glycine with protons in water at temperatures of 298.15, 323.15, and 348.15 K and pressures up to 12.50 MPa. By combining the measured heat for glycine solutions titrated with NaOH with the heat of ionization for water, the enthalpy of protonation of glycine is obtained. The reaction is exothermic at all temperatures and pressures studied. The effect of pressure on the enthalpy of reaction is very small. The experimental heat data are analyzed to yield equilibrium constant (K), enthalpy change (DeltaH), and entropy change (DeltaS) values for the protonation reaction as a function of temperature. These values are compared with those reported previously at 298.15 K. The DeltaH and DeltaS values increase (become more positive), whereas log K values decrease, as temperature increases. The trends for DeltaH and DeltaS with temperature are opposite to those reported previously for the protonation of several alkanolamines. However, log K values for proton interaction with both glycine and the alkanolamines decrease with increasing temperature. The effect of the nitrogen atom substituent on log K for protonation of glycine and alkanolamines is discussed in terms of changes in long-range and short-range solvent effects. These effects are used to explain the difference in DeltaH and DeltaS trends between glycine protonation and those found earlier for alkanolamine protonation.

Calculation of site affinity constants and cooperativity coefficients for binding of ligands and/or protons to macromolecules. I. Generation of partition functions and mass balance equations.

The thermodynamics of binding of a ligand A and/or proton H to a macromolecule M is treated by the partition function method. In complex systems, the representation of the equilibria by means of cumulative constants beta PQR used as coefficients in partition functions ZM, ZA, and ZH is ill-suited to least-squares refinement procedures because the cumulative constants are interrelated by common cooperativity functions gamma j(i) and common site affinity constants kappa j. There is therefore the need to express ZM, ZA, ZH as functions of site constants kappa j and cooperativity coefficients bj. This is done by developing an algebra of partition functions based on the following concepts: (i) factorability of partition functions; (ii) binary generating function Jj = (1 + kappa j[Y])i tau for each class j of sites, represented by column (Jj) and row (Jj) vectors; (iii) cooperativity between sites of one class described by functions gamma j(i), represented by diagonal matrices gamma j; (iv) probability of finding microspecies represented by elements of tensor product matrix Ll = (J1)[J2]; (v) statistical factors mij obtained from Newton polynomials, Jj; (vi) power operators Oi', O(i-l)', and O(i tau-l)', transforming vectors Jj; and (vii) operators Oi or O(i-l) indicating tensor products of i or (i-l) vectors Jj. Vectors Jj combined in tensors Ll give rise to both an affinity/cooperativity space and a parallel index space. The partition functions ZM, ZA, and ZH and the total amounts TM, TA, and TH can be obtained as an appropriate sum of elements of matrices Ll, each of which is represented in an index space by a combination p1, p2,...q1, q2,...r1, r2,... of indices ij. From these indices the contribution of that element to partition function ZM, ZA, or ZH and to total amount TM, TA, or TH is calculated in the affinity/cooperativity space as product of factors: [i tau !/i !(i tau-i)!]kappa ij(exp[bj (i-1)i])[X]i, i being any index p, q, r and X any component M, A, or H. Future applications of this algorithm to practical problems of macromolecule-ligand-proton equilibria are outlined.

Calculation of site affinity constants and cooperativity coefficients for binding of ligands and/or protons to macromolecules. II. Relationships between chemical model and partition function algorithm.

The relationships between the chemical properties of a system and the partition function algorithm as applied to the description of multiple equilibria in solution are explained. The partition functions ZM, ZA, and ZH are obtained from powers of the binary generating functions Jj = (1 + kappa j gamma j,i[Y])i tau j, where i tau j = p tau j, q tau j, or r tau j represent the maximum number of sites in sites in class j, for Y = M, A, or H, respectively. Each term of the generating function can be considered an element (ij) of a vector Jj and each power of the cooperativity factor gamma ij,i can be considered an element of a diagonal cooperativity matrix gamma j. The vectors Jj are combined in tensor product matrices L tau = (J1) [J2]...[Jj]..., thus representing different receptor-ligand combinations. The partition functions are obtained by summing elements of the tensor matrices. The relationship of the partition functions with the total chemical amounts TM, TA, and TH has been found. The aim is to describe the total chemical amounts TM, TA, and TH as functions of the site affinity constants kappa j and cooperativity coefficients bj. The total amounts are calculated from the sum of elements of tensor matrices Ll. Each set of indices (pj..., qj..., rj...) represents one element of a tensor matrix L tau and defines each term of the summation. Each term corresponds to the concentration of a chemical microspecies. The distinction between microspecies MpjAqjHrj with ligands bound on specific sites and macrospecies MpAqHR corresponding to a chemical stoichiometric composition is shown. The translation of the properties of chemical model schemes into the algorithms for the generation of partition functions is illustrated with reference to a series of examples of gradually increasing complexity. The equilibria examined concern: (1) a unique class of sites; (2) the protonation of a base with two classes of sites; (3) the simultaneous binding of ligand A and proton H to a macromolecule or receptor M with four classes of sites; and (4) the binding to a macromolecule M of ligand A which is in turn a receptor for proton H. With reference to a specific example, it is shown how a computer program for least-squares refinement of variables kappa j and bj can be organized. The chemical model from the free components M, A, and H to the saturated macrospecies MpAQHR, with possible complex macrospecies MpAq and AHR, is defined first.(ABSTRACT TRUNCATED AT 250 WORDS)