Formalisms to relate the observed rates of amide hydrogen exchange to thermodynamic stabilization of proteins have been developed . Amide hydrogens of proteins in the native, folded state are proposed to exchange according to the following equation:
where kop is the rate at which amide hydrogen converts from closed state to open state. Conversely, kcl is the rate amide hydrogen converts from open state to closed state. For most proteins at or below neutral pH, amide H/D exchange occurs by an EX2 mechanism , where kcl » kch and Eq. (3) becomes:
The closing equilibrium constant at each amide (Kcl — kcl/kop) is equal to the protection factor (pf) and can be translated into the stabilization free energy of closed state (AGcl) by Eq. (5).
AGcl — -RT ln(Kcl) — -RT ln(pf) — -RT ln(kch/kex) (5)
The measured H/D exchange rates in the folded protein (kex) can be compared with the calculated "intrinsic" rates (kch) to probe the extent of tertiary structure and resulting dynamics. Frequently, the hydrogen exchange rates of two or more physical states of a protein, such as with and without ligand (here represented by kex2 and kex1), are measured to locate stabilization free energy changes upon the perturbation (AAG1—2):
Thus, the measurement of exchange rates of backbone amide hydrogen serves as a precise thermodynamic sensor of the local environment.
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