The theory of diffusion-controlled reaction was originally utilized by R.A. Alberty, Gordon Hammes, and Manfred Eigen to estimate the upper limit of enzyme-substrate reaction. According to their estimation, the upper limit of enzyme-substrate reaction was 10 M s.
In 1972, it was observed that in the dehydration of HCO catalyzed by carbonic anhydrase, the second-order rate constant obtained experimentally was about 1.5 × 10 M s, which was one order of magnitude higher than the upper limit estimated  by Alberty, Hammes, and Eigen based on a simplified model.
To address such a paradox, Kuo-Chen Chou and his co-workers proposed a model by taking into account the spatial factor and force field factor between the enzyme and its substrate and found that the upper limit could reach 10 M s, and can be used to explain some surprisingly high reaction rates in molecular biology.
The new upper limit found by Chou et al. for enzyme-substrate reaction was further discussed and analyzed by a series of follow-up studies.
A detailed comparison between the simplified Alberty-Hammes-Eigens model (a) and the Chous model (b) in calculating the diffusion-controlled reaction rate of enzyme with its substrate, or the upper limit of enzyme-substrate reaction, was elaborated in the paper.