To study the elementary steps (K₁, k₂, k_-2) surrounding the ATP binding step 1, the S=[ATP] is changed such as 0.1, 0.2, 0.5, 1, 2, 5, 10 mM, and the apparent rate constant 2πc is studied. The result is plotted in Fig. 5A.

Figure 5

2πc increases at 0.1-2 mM ATP, and then approaches saturation, exhibiting a typical hyperbolic curve. Such result can be explained by steps 1 and 2 of scheme 1. 

where K₁=ATP association constant (step 1), k₂=the rate constant of cross-bridge detachment (step 2) which ensue the ATP binding, and k_-2=the rate constant of its reversal step. For the ATP study, the step 0 is absent. Eq. 4 relates the kinetic constants (K₁, k₂, k_-2) and the ATP concentration (S) to the apparent rate constant 2πc:

By fitting the data to Eq. 4, one can deduce three kinetic constants K₁, k₂, and k_-2. Here D=[ADP] is assumed to be 0, because there is practically no ADP in the presence of the ATP regenerating system (phosphocreatine and creatine kinase with Lohman reaction). The data fits well as shown in the continuous curve in Fig. 5A, demonstrating the high credibility of the model shown in Scheme 1. Here it is important to note that we do not deduce unnecessarily many (>3) parameters from the data, and Scheme 1 with steps 1 and 2 is the minimal model to account for the data. If one deduces more parameters in an attempt to explain more complex model than Scheme 1, the credibility of the model becomes thin and its significance gets lost. K₂ is calculated as K₂=k₂/k_-2, hence this is not an independent parameter.

                To study the elementary step 0, ADP concentration (D) is changed such as 0, 1, 2, 4, 8 mM (in the absence of the ATP regenerating system), and the apparent rate constant 2πc is studied (Fig. 5B) at constant [ATP] (5 mM). The result is a decreasing hyperbolic function, and such curve is fitted to Eq. 4, where we use K₁ obtained from the ATP study and deduce only one parameter K₀, the ADP association constant. The data fits well as shown in the continuous curve in Fig. 5B.