The Effect of Accessibility of Insoluble Substrate on the Overall Kinetics of Enzymatic Degradation

The enzymatic reaction kinetics on cellulose and other solid substrates is limited by the access of the enzyme to the reactive substrate sites. We introduce a general model in which the reaction rate is determined by the active surface area, and the resulting kinetics consequently reflects the evolving relationship between the exposed substrate surface and the remaining substrate volume. Two factors influencing the overall surface-to-volume ratio are considered: the shape of the substrate particles, characterized by a single numerical parameter related to its dimensionality, and the distribution of the particle sizes. The model is formulated in a form of simple analytical equations, enabling fast and efficient application to experimental data, and facilitating its incorporation into more detailed and complex models. The application of the introduced formalism exploring its potential to account for the observed reaction rate is demonstrated on two examples: the derivation of particle size distribution from experimentally determined reaction kinetics, and the prediction of reaction slowdown from experimental particle size distribution.