FIGURE 1.

a, the proposed Mg²⁺-activation model. The forward AK reactions of the unactivated enzyme (E) and its Mg²⁺ activated counterpart (E*) each follow a random bi-bi model, illustrated by the diamond shapes and assumed to be in rapid equilibrium. The conversion between E and E* (vertical dashed lines) is treated with the steady-state approximation. In the activated form (the upper tier), the dissociation constants K_AMP and the catalytic rate k_cat are increased by a factor of α and β, respectively (E = AK enzyme, E* = AK·Mg²⁺, T = ATP·Mg²⁺, M = AMP, and D = ADP. T_f denotes ATP without Mg²⁺that has been bound to the enzyme). The blue arrows denote the second order correction to our proposed model. b, a reduction of the model in a according to the hybrid rapid equilibrium and steady-state assumption used to model the kinetic data.