Discriminating between Concerted and Sequential Allosteric Mechanisms by Comparing Equilibrium and Kinetic Hill Coefficients.

Amnon Horovitz,Tridib Mondal

doi:10.1021/acs.jpcb.0c09351

Amnon Horovitz, Tridib Mondal

Open Access

https://doi.org/10.1021/acs.jpcb.0c09351

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Abstract

Hill coefficients, which provide a measure of cooperativity in ligand binding, can be determined for equilibrium (or steady-state) data by measuring fractional saturation (or initial reaction velocities) as a function of ligand concentration. Hill coefficients can also be determined for transient kinetic data from plots of the observed rate constant of the ligand-promoted conformational change as a function of ligand concentration. Here, it is shown that the ratio of the values of these two Hill coefficients can provide insight into the allosteric mechanism. Cases when the value of the kinetic Hill coefficient is equal to or greater than the value of the equilibrium coefficient indicate concerted transitions whereas ratios smaller than one indicate a sequential transition. The derivations in this work are for symmetric dimers but are expected to have general applicability for homo-oligomers.

Highlights

Insights into reaction mechanisms are often obtained through identifying and characterizing reaction intermediates
Examples include a calorimetric criterion for two-state folding according to which the measured calorimetric enthalpy change upon unfolding should be equal to the van’t Hoff enthalpy change calculated assuming a twostate transition.[1−3] Another criterion is that the m-value for equilibrium denaturation should be equal to the sum of m-values for folding and unfolding obtained from transient kinetic data.[4]
We explored whether the ratio of the Hill coefficients for transient and equilibrium data

Summary

■ INTRODUCTION

Insights into reaction mechanisms are often obtained through identifying and characterizing reaction intermediates. In the case of the concerted model,[5] the forward rate constant, k, of the conformational change of a symmetric dimer, as a function of the ligand concentration, can be expressed, as follows (Figure 1): k k0 + 2k1K1[S] + k2K1K2[S]2 1 + 2K1[S] + K1K2[S]2. The MWC model is applied to the transition state, ‡, and reverse reactions from R to T are ignored as before (eq 9) In such a case, the rate constants for the conformational changes promoted by i bound ligand molecules can be expressed as follows: ki = k0xi (14). In the case of the sequential model for a symmetric dimer, the rate constant of the conformational change, k, as a function of the ligand concentration can, be expressed, as follows:. The value of nk,0.5 approaches one when kb ≫ ka as expected

■ CONCLUDING REMARKS

■ REFERENCES

■ ACKNOWLEDGMENTS