Evaluation of the degree of rate control via automatic differentiation

The degree of rate control (DRC) quantitatively identifies the kinetically relevant (sometimes known as rate-limiting) steps of a complex reaction network. This concept relies on derivatives which are commonly implemented numerically, for example, with finite differences (FDs). Numerical derivatives are tedious to implement, and can be problematic, and unstable or unreliable. In this study, we demonstrate the use of automatic differentiation (AD) in the evaluation of the DRC. AD libraries are increasingly available through modern machine learning frameworks. Compared with the FDs, AD provides solutions with higher accuracy with lower computational cost. We demonstrate applications in steady-state and transient kinetics. Furthermore, we illustrate a hybrid local-global sensitivity analysis method, the distributed evaluation of local sensitivity analysis, to assess the importance of kinetic parameters over an uncertain space. This method also benefits from AD to obtain high-quality results efficiently.