Data-Driven Identification of Rational Nonlinear Dynamics in Biochemical Networks via an Implicit Singular Value Decomposition Based Framework.

Using rational functions to describe the dynamics of the biological network is common in the field of biology. Estimating such dynamics from data is challenging owing to the complex nonlinearities. Although sparse identification of nonlinear dynamics (SINDy) approach works for many systems, it struggles with rational functions because constructing separate basis libraries for numerators and denominators is computationally prohibitive. Hence, this study proposes an effective method to identify the rational form dynamics of complex biological networks. The method applies singular value decomposition (SVD) to a library of observational functions that mix state and derivative terms, capturing the implicit form of the rational functions. The null space obtained from this SVD analysis is then used for model identification. The data information was condensed into the observable space through the SVD approach. The computational cost to obtain the null space depends on the size of the observable space. Therefore, it can easily handle large-scale data. The proposed method was successfully applied to four biological models: (1) Michaelis-Menten kinetics, (2) Bacillus subtilis competence network, (3) penicillin production kinetics and (4) the yeast glycolytic metabolic network, demonstrating its effectiveness and generalisability across different biological systems.