Quantitative analysis of structure–activity relationships in engineered proteins by linear free-energy relationships

Abstract

Protein engineering is being used increasingly to study the fine details of the structure and activity of enzymes. How can small effects of mutation on activity be reliably quantified and systematized, and artefacts be recognized? A traditional means of doing this in organic chemistry is the use of linear free-energy relationships that link changes in rate constant for a reaction to changes in its equilibrium constant as the structure of the reagents is altered—Brønsted or Hammett plots¹. We now find that the same type of plot may be applied to enzymatic reactions for variation of the structure of an enzyme with mutation. The activities of many mutant tyrosyl-transfer RNA synthetases fit structure-activity relationships which relate the rate constant for the formation of enzyme-bound tyrosyl adenylate (E.Tyr–AMP) to its equilibrium constant with enzyme-bound tyrosine and ATP (E.Tyr. ATP). This reaction results in an increase in binding energy between certain side chains of the enzyme and the side chain of tyrosine and the ribose ring of ATP. Plots of rate against equilibrium constant for a series of enzymes mutated in the relevant positions indicate that 71% of the binding energy change occurs on formation of the transition state for the chemical reaction and 90% occurs on formation of the E.Tyr–AMP.PP_i complex. Other mutations show a different behaviour which is diagnostic of residues that specifically bind the transition state. Linear free-energy plots show trends and allow exceptions to be readily noted. That the activities of a large number of mutants conform to linear free-energy equations is the best evidence yet that mutation of an enzyme can probe general properties and trends in the relationship between structure and activity.