Thermodynamic and kinetic cooperativity in ligand binding to multiple sites on a protein: Ca2+ activation of an ATP-driven Ca pump.

Abstract

Contrary to common belief, theoretical analysis does not predict-any necessary relationship between cooperativity in the equilibrium binding of an ion to multiple binding sites on a protein and cooperativity in the kinetic activation of a reaction for which such binding is prerequisite. The (5). Under these conditions, the conventional allosteric mechanism for generation of cooperativity can come into play, as illustrated by the cooperative association of oxygen with the four virtually identical and inherently independent binding sites of hemoglobin (6, 7).Binding of Ca2' to the same two sites in the E1 state of the pump protein is essential for activation of ATP hydrolysis. Although there is some diversity in the available experimental data (see Discussion), the hydrolysis rate is usually also reported to be a highly cooperative function of Ca2' concentration (1, 2), and this result is sometimes accompanied by the assertion that such similarity between equilibrium and kinetic manifestations of cooperativity is theoretically expected. This paper addresses itself to this latter assertion. We report a theoretical analysis of the problem, which demonstrates that different parameters determine cooperativity in the two situations, so that no general correspondence between equilibrium and kinetic cooperativities can exist.Kinetic equations for any protein-catalyzed reaction are directly related to the catalytic reaction cycle, and it is therefore necessary to assume an explicit model for the Ca pump reaction cycle if kinetic cooperativity is to be quantitatively discussed. We here assume a mechanism for the Ca pump cycle that was suggested in the first paragraph of this paper, namely one involving equivalence and independence of the two Ca2' binding sites in the E1 state of the protein and allosteric generation of cooperativity in equilibrium binding. Our conclusions therefore apply directly only to this simple model, but this is sufficient to demonstrate the lack of a general relationship between the two kinds of cooperativity. Model for the Pump CycleFor detailed analysis, we use the reaction cycle for the Ca pump shown in Fig. 1, essentially the same as the cycle originally introduced by de Meis and Vianna (5). The transport protein alternates in the course of the cycle between conformational states E1 and E2. E1 has two Ca2' binding sites (of high affinity, as already noted), which in vivo face the cytoplasmic side of the membrane; it also has a nucleotide binding site with high affinity for ATP. E2 has two Ca2+ binding sites (with low binding affinity), which in vivo face the sarcoplasmic reticulum lumen; it also has a binding site for inorganic phosphate, to which ATP presumably can bind with low affinity, as discussed in a previous paper (8). The cycle as here drawn allows the binding of Cae+ and ATP to E1 to occur in random order, a feature implicit in the de Meis mod-2 C T P ,

An investigation of functional similarities between the sarcoplasmic reticulum and platelet calcium-dependent adenosinetriphosphatases with the inhibitors quercetin and calmidazolium

“…In Figure 1, substrate ligation occurs in a random order, with the preferred pathway (or combination of pathways) being de-termined by the concentration of ATP and calcium. This type of ligation scheme has been proposed (Inesi et al, 1980;Tanford et al, 1985;Reynolds et al, 1985;Gould et al, 1986) to account for transient and steady-state kinetic measurements (Neet & Green, 1977;Inesi et al, 1980;Moller et al, 1980;Gould et al, 1986) involving substrate activation of the sarcoplasmic reticulum Ca 2+ -ATPase. The scheme in Figure 1 includes only steps that can be probed by varying calcium and ATP concentration on a steady-state time scale.…”

“…The hydrolytic cycle of the sarcoplasmic reticulum Ca 2+ -ATPase has been characterized as abbreviated in Figure 1 (De Meis & Vianna, 1979;Inesi et al, 1980;Tanford et al, 1985). Upon exposure to calcium and ATP, ligation of two calcium ions and ATP occurs in a random manner with the most favorable ligation sequence determined by the concentration of ligands.…”

Parameter estimation for mathematical models of a nongastric H+(Na+)-K+(NH4+)-ATPase

“…For the 1:1-per-ATP and 2:2-per-ATP models, the rate constants corresponding to the on and off binding of ATP, ADP, and P i are fixed and assumed equal to those reported by Tanford et al (37), as Brzezinski et al (6) and Weinstein (43) …”

Variable stoichiometry in active ion transport: theoretical analysis of physiological consequences.

“…Previously used rate and equilibrium constants, listed in the fourth column ofTable 1 in ref. 7, have been retained for the present analysis. These parameters quantitatively account for equilibrium Ca2+ binding to the pump protein at pH 7 and for kinetic activation of the pump reaction in leaky SR vesicles by ATP and cytoplasmic Ca2+, deviating from experimental data only in that the degree of cooperativity ofkinetic activation by Ca2+ is somewhat lower than most (but not all) investigators have reported.…”

“…7, have been retained for the present analysis. These parameters quantitatively account for equilibrium Ca2+ binding to the pump protein at pH 7 and for kinetic activation of the pump reaction in leaky SR vesicles by ATP and cytoplasmic Ca2+, deviating from experimental data only in that the degree of cooperativity ofkinetic activation by Ca2+ is somewhat lower than most (but not all) investigators have reported. The second (loop f3), created by reaction step 1, permits the uncoupled leak of Ca2+ from high concentration in the SR into the cytoplasm, doing so by removing the restriction that the E2= E1 transition requires unoccupied Ca2+ binding sites.…”