Kinetic analysis of sequential multistep reactions

Many processes in biology and chemistry involve multistep reactions or transitions. The kinetic data associated with these reactions are manifested by superpositions of exponential decays that are often difficult to dissect. Two major challenges have hampered the kinetic analysis of multistep chemical reactions: (1) reliable and unbiased determination of the number of reaction steps, and (2) stable reconstruction of the distribution of kinetic rate constants. Here, we introduce two numerically stable integral transformations to solve these two challenges. The first transformation enables us to deduce the number of rate-limiting steps from kinetic measurements, even when each step has arbitrarily distributed rate constants. The second transformation allows us to reconstruct the distribution of rate constants in the multistep reaction using the phase function approach, without fitting the data. We demonstrate the stability of the two integral transformations by both analytic proofs and numerical tests. These new methods will help provide robust and unbiased kinetic analysis for many complex chemical and biochemical reactions.