association constants for both ML and HL. Also, in generalized computer programs dealing with equilibrium constants it is general practice to use cumulative constants rather than stepwise constants and to omit ionic charges from equilibrium expressions. For example, if NTA, nitrilotriacetic acid, N(CH2CO2H)3 is designated as H3L and forms complexes ML and MHL with a metal ion M, the following expressions would apply for the dissociation constants. The cumulative association constants can be expressed as Note how the subscripts define the stoichiometry of the equilibrium product. Micro-constants When two or more sites in an asymmetrical molecule may be involved in an equilibrium reaction there are more than one possible equilibrium constants. For example, the molecule -DOPA has two non-equivalent hydroxyl groups which may be deprotonated. Denoting -DOPA as LH2, the following diagram shows all the species that may be formed (X = ). The concentration of the species LH is equal to the sum of the concentrations of the two micro-species with the same chemical formula, labelled L1H and L2H. The constant K2 is for a reaction with these two micro-species as products, so that [LH] = [L1H] + [L2H] appears in the numerator, and it follows that this macro-constant is equal to the sum of the two micro-constants for the component reactions. K2 = k21 + k22 However, the constant K1 is for a reaction with these two micro-species as reactants, and [LH] = [L1H] + [L2H] in the denominator, so that in this case 1/K1 =1/ k11 + 1/k12, and therefore K1 =k11 k12 / (k11 + k12). Thus, in this example there are four micro-constants whose values are subject to two constraints; in consequence, only the two macro-constant values, for K1 and K2 can be derived from experimental data. Micro-constant values can, in principle, be determined using a spectroscopic technique, such as infrared spectroscopy, where each micro-species gives a different signal. Methods which have been used to estimate micro-constant values include Chemical: blocking one of the sites, for example by methylation of a hydroxyl group, followed by determination of the equilibrium constant of the related molecule, from which the micro-constant value for the "parent" molecule may be estimated. Mathematical: applying numerical procedures to 13C NMR data. Although the value of a micro-constant cannot be determined from experimental data, site occupancy, which is proportional to the micro-constant value, can be very important for biological activity. Therefore, various methods