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The kinetic behavior of dissociating enzyme system of the type: inactive monomer reversible active dimer where the dimeric form is stabilized by a specific ligand (in particular by substrate) which is bound in the region of the contact of monomers has been analysed. It is assumed that the dissociation of the dimer results in formation of the monomer, which retains the subsites for specific ligand binding. The shape of the dependences of enzyme reaction rate (v) on substrate concentration (S) is characterized using the order of enzyme reaction rate with respect to substrate concentration: ns = dlnv/dln[S]. When the substrate concentrations are low the dependences of v on [S] have S-shaped form (the maximum value of ns exceeds the unity) at the definite values of parameters of the enzyme system. The value of ns approaches -2 at sufficiently high substrate concentrations (in the region where the substrate reveals the inhibitory effect due to blocking the association of inactive monomers into active dimer). The methods of calculation of the parameters of the dissociating enzyme system under discussion have been elaborated on the basis of the analysis o the experimental dependences of specific enzyme activity on enzyme concentration obtained at various fixed substrate concentrations. It has been shown that depending on its concentration allosteric effector may act as an activator or an inhibitor.

The new method for Hill's coefficient (nH) calculation in the region of substrate concentrations where the latter acts as an inhibitor has been developed. The method does not need preliminary determination of maximum value of enzyme reaction rate (V) for ascending branch of the plot of enzyme reaction rate versus substrate concentration and allows to avoid over-estimation of value of nH when the magnitude of optimal reaction rate is less than value of V. The literature data for inhibition of phosphofructokinase by excess of ATP are used for illustration of applicability of the suggested method of Hill's coefficient calculation.

A theoretical analysis has been made of dependencies of specific enzymatic activity (a) on the concentration of the enzyme for associating enzyme systems, in which the association of protein molecules leads to the formation of linear associates of an unlimited length (M in equilibrium M2 in equilibrium M3 in equilibrium ...) and is accompanied by steric shielding of active centers, and also for systems of the type 2 M in equilibrium D in equilibrium D2 in equilibrium D3 in equilibrium ... (M is an inactive monomer and D is an active dimer), in which the specific enzymatic activity of the dimer does not depend on the degree of association. For both models an analysis has been made of the S-shape of the curves of the dependence of a on the concentration of the substrate. Experimental data for glutamate dehydrogenase from ox liver and phosphofructokinase from rabbit skeletal muscles have been used as illustrations.

A shape of the curves of a product accumulation in time (t) is analysed for the variant of Monod, Wyman and Changeux model which is characterized by comparable rates of equilibration between R and T enzyme forms on the one hand and the enzymatic process on the other hand. It is assumed that the complex of R and T forms with substrate are in rapid equilibrium with the free components. The character of the dependences of effective constant of R denoting T isomerization and the value of tau on substrate concentration are analysed (tau is the intercept of t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity). It is also shown that the low rate of R denoting T isomerization may be manifested by the shape of the plot of initial reaction rate versus substrate concentration unusual for the model of Monod et al. (the plots with intermediate plateau and ones with Hill's coefficient of cooperativity less than unity).

The rate constants and equilibrium constants for four stages of process of the abortive ternary complex lactate dehydrogenase (porcine isoenzyme H4)-NAD-pyruvate formation are determined. These stages are 1) the enolization of pyruvate, 2) the formation of binary complex enzyme-NAD, 3) the formation of "intermediate" ternary complex enzyme-NAD-enol and 4) the transformation of "intermediate" complex into "final" ternary one, accumulation of the latter being followed by spectrophotometric and fluorometric methods. The constants obtained were compared with the corresponding ones for porcine isoenzyme M4 determined in earlier work. It was shown that the greater stability of ternary complex and the greater initial rate of ternary complex formation in the case of H4 is due to greater affinity of isoenzyme H4 with respect to NAD, greater magnitude of reaction rate constant for transformation of "intermediate" ternary complex into "final" one and lesser magnitude of reaction rate constant for the reverse transition.

Interaction of muscle glycogen phosphorylase b (EC 2.4.1.1) with glycogen was studied by sedimentation, stopped-flow and temperature-jump methods. The equilibrium enzyme concentration was determined by sedimentation in an analytical ultracentrifuge equipped with absorption optics and a photoelectric scanning system. The maximum adsorption capacity of pig liver glycogen is 3.64 μmol dimeric glycogen phosphorylase b per g glycogen, which corresponds to 20 dimeric enzyme molecules per average glycogen molecule of M r 5.5 · 10 6 . Microscopic dissociation constants were determined for the enzyme-glycogen complex within the temperature range from 12.7 to 30.0°C. Enzyme-glycogen complexing is accompanied by increasing light scattering and its increment depends linearly on the concentration of the binding sites on a glycogen particle that are occupied by the enzyme. Complex formation and relaxation kinetics are in accordance with the proposed bimolecular reaction scheme. The monomolecular dissociation rate constant of the complex increases as the temperature increases from 12.7 to 30.0°C, whereas the bimolecular rate constant changes sligtly and is about 10 8 M −1 · s −1 . These data point to the possibility of diffusional control of the complex formation.

The shape of the plots of product accumulation versus time (t) has been analysed for slowly equilibrating association-dissociation enzyme systems of the types 2p in equilibrium P (P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) and M in equilibrium M2 in equilibrium M2 in equilibrium... (M is monomer which has two association sites overlapping with active sites). It is assumed that the rate of equilibration between oligomeric forms is comparable with the rate of over-all enzymatic reaction and that substrate-oligomer complexes are in rapid equilibrium with free components. It has been shown that characteristic feature of kinetic behavior of slowly equilibrating association-dissociation enzyme systems is that the value of tau depends on enzyme concentration (tau is the intercept on t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity).