Analyzing the kinetic salt effect

The study of conditions that optimize the association of proteins in solution guides the design of protocols for the formation of large crystals that are amenable to analysis by the X-ray diffraction techniques discussed in Chapter 11. It is important to characterize protein dimerization because the process is considered to be the rate-determining step in the growth of crystals of many proteins. Consider the variation with ionic strength of the rate constant of dimerization in aqueous solution of a cationic protein P  

Strategy Although the dimer is not an activated complex in the same sense as in transition state theory, eqn 7.35 applies if we assume that the activated complex and the product (the dimer) are similar in the sense that two protein molecules associate to form the activated complex. Thus, the equilibrium constant for the dimerization is related to the rate constants for the formation of the dimer and its decomposition by ff = k /k c and K = K Ky. Hence k,=KcKyk c = Kyk°. It then follows, as in Justification 7.5, that 

Therefore, to infer the protein charge number z from the slope, 1.02z, we need to plot log (kjk j) against 

These points are plotted in Fig. 7.19. The slope of the straight line is 9.2, indicating that = 9. Because the protein is cationic, its charge number is -1-3. 

Equilibrium constant in terms of rate constants K=k,lk First order in each direction 

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