TABLE 1.

Values of the rate constants, equilibrium constants, and fluorescence parameters of the dimer model used for the simulations shown in Figs. 1 B and 2

Parameter	Reaction*	Value	Reference
k1	E1 + ATP → E1ATP	52 μM−1 s−1	(4,37,38)†
k−1	E1ATP → E1 + ATP	13 s−1	(38)
k2	E1ATP + ATP → (E1ATP)2	52 μM−1 s−1	this work‡
k−2	(E1ATP)2 → E1ATP + ATP	364 s−1	this work§
k3	E1ATP → E2P	15 s−1	this work¶
k−3	E2P → E1ATP	5 s−1	(11)‖
k4	(E1ATP)2 → (E2P)2	173 s−1	(10)**
	(E2P)2 → (E1ATP)2	5 s−1	(11)‖
	(E2P)2ATP → (E1ATP)2	75 s−1	this work††
KA1	E1ATP ↔ E1 + ATP	0.25 μM	(4,37,38)
KA2	(E1ATP)2 ↔ E1ATP + ATP	7.0 μM	(10)‡‡
KA	(E2P)2ATP ↔ (E2P)2 + ATP	143 μM	(10)§§
fE1	Fluorescence level of E1, E1ATP, and (E1ATP)2	1.0	this work¶¶
fE2P	Fluorescence level of E2P	1.57	this work‖‖
f(E2P)2	Fluorescence level of (E2P)2	2.14	this work***

^*For each reaction, Na⁺ ions have been omitted for simplicity, but in each case the rate constant refers to the value in the presence of 130 mM NaCl. Under such conditions all of the E1 states, with or without ATP, would be completely saturated with Na⁺ ions and would, thus, all have three bound Na⁺ ions. Also for simplicity, the dimeric nature of each enzyme species has been omitted. Thus, E1 actually represents a dimer E1:E1, where each E1 monomer can only bind a single ATP molecule.

^†The rate constant for ATP binding to the E1 state has been estimated by dividing the dissociation rate constant by the ATP dissociation constant, i.e., k₁ = k₋₁/K_A1.

^‡The rate constants for ATP binding to the E1ATP state has been taken to be equal that of binding to the E1 state. The differences in their ATP affinities are assumed to be due to different dissociation rate constants alone.

^§The rate constant for ATP dissociation from (E₁ATP)₂ has been estimated by multiplying the ATP dissociation constant by its ATP binding rate constant, i.e., k₋₂ = K_A2 × k₂.

^¶This value has been chosen so as to reproduce closely the observed experimental ATP dependence of the time course and the amplitudes of the fluorescence transients and to satisfy the condition (k₃ + k₋₃) = 20 s⁻¹, which is approximately the experimentally determined reciprocal relaxation time at an ATP concentration of 1 μM, which would be reasonably expected to saturate the first ATP binding site.

^‖The reverse reactions E2P → E1ATP and (E2P)₂ → (E1ATP)₂ are assumed to occur indirectly via the pathways E2P → E2 → E1 + ATP → E1ATP and (E2P)₂ → E2 → E1 + ATP → E1ATP + ATP → (E1ATP)₂ (see the Discussion for further explanation). In the absence of K⁺ ions the rate-determining step in these pathways would be expected to be the dephosphorylation, which has been experimentally determined to have a rate constant of ∼5 s⁻¹ under these conditions ((11); and references cited therein).

^**This value has been chosen to satisfy the condition () = 178 s⁻¹, the experimentally determined reciprocal relaxation time at saturating concentrations of ATP (10).

^††This value has been chosen to reproduce the experimentally determined drop in ΔF/F₀ at ATP concentrations >50 μM (see Fig. 2).

^‡‡This value has been derived from the concentration of ATP necessary to achieve half-saturation of the reciprocal relaxation time for the RH421 fluorescence change on mixing with ATP in the presence of Mg²⁺ ions.

^§§This value has been taken to equal the experimentally determined low affinity allosteric ATP dissociation constant of the E2 conformation of pig kidney enzyme (10).

^¶¶f_E1 has been arbitrarily been defined as 1.0 as a reference point for the fluorescence changes.

^‖‖This value has been chosen to be exactly midway between the values of f_E1 and f_(E2P)2.

^***This value has been chosen to give agreement with the experimentally observed ΔF/F₀ value at 500 μM ATP.