Fig. 3. Mechanochemical analysis of allosteric acceleration.

a Strain energies of the substrate (solid lines) and the coupled compressive potential with compliance of 2 Å/nN (dashed lines) for the reactant (red) and the transition state (blue) as the function of the ensemble-average compressive force on E-SS, 〈f_E〉. b the minimum energy needed to reduce the isomerization barrier by ΔΔG^ǂ_isom = ΔG^ǂ_allost−ΔG^ǂ_free, where ΔG^ǂ_X is the activation free energy of isomerization of free E-SS (X = free) or E-SS in an effector-bound allosteric substrate (e.g., macrocycles in Fig. 1, X = allost). For each ΔΔG^ǂ_isom, all combinations of the two 〈f_E〉 values corresponding to effector-free and effector-bound reactant were considered to identify the minimum necessary increase in the total reactant strain energy, ΔE_strain. For macrocycles (blue dots), ΔΔG^ǂ_bind describes the reaction free energy of PtCl₂ transfer between free and SS-coupled BiPHEP (eq. 1). c 〈f_E〉 of E-SS prior to effector binding giving the highest achievable ΔΔG^ǂ_isom/ΔE_strain ratio (see Supplementary Table 3 for the definition of all parameters of the mechanochemical model). The plotted data is tabulated in Supplementary Tables 7–9.