Kinetics of Hydrogen Exchange in Disordered Proteins

Examining the limits in (17.6), it appears that a disordered protein might undergo exchange within any of the three limits, EXX, EX2, or EX 1. However, it is likely that a disordered protein would only transiently occupy the closed state such that Under the EX2 limit, this would lead to 

The exact solution to the Linderstr0m-Lang scheme [46, 47] requires solving the system of two differential equations, (17.1) and (17.2), after invoking appropriate boundary conditions at f=0 and 

Solutions can be obtained by several different methods [44] that lead to the following results  

Equations 17.13-17.15 represent an exact, general solution of the Linderstr0m-Lang mechanism independent of any approximations. The observed exchange kinetics are biexponential with a fast process represented by and a slower process represented by [47]. Under the steady-state condition, k S k [44], the equations reduce to (17.4) and then can then be further reduced 

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