Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics

Abstract

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental data enable statistical approaches based on information theory for model selection and goodness-of-fit metrics. We propose an alternative method to infer networked nonlinear dynamical systems by using sparsity-promoting 1 optimization to select a subset of nonlinear interactions representing dynamics on a fully connected network. Our method generalizes the sparse identification of nonlinear dynamics (SINDy) algorithm to dynamical systems with rational function nonlinearities, such as biological networks. We show that dynamical systems with rational nonlinearities may be cast in an implicit form, where the equations may be identified in the null-space of a library of mixed nonlinearities including the state and derivative terms; this approach applies more generally to implicit dynamical systems beyond those containing rational nonlinearities. This method, implicit-SINDy, succeeds in inferring three canonical biological models: Michaelis-Menten enzyme kinetics, the regulatory network for competence in bacteria, and the metabolic network for yeast glycolysis.

Methods for data-driven multiscale model discovery for materials

“…For actuated systems, SINDy has been generalized to include inputs and control [52], and these models are highly effective for model predictive control [53]. It is also possible to extend SINDy to identify dynamics with rational function nonlinearities [54], integral terms [55], and based on highly corrupt and incomplete data [56]. SINDy was also recently extended to incorporate information criteria for objective model selection [57], and to identify models with hidden variables using delay coordinates [35].…”

Accelerated reference frames (ARFs) reveal networks from time series data

“…n N 0 i  -. Whereas exactly synchronous or phase-locked dynamics in principle can generally not reveal the complete network topology, inferring from transient dynamics towards synchrony or locking was so far restricted to driving-response settings with known signals [16] or to general model-free approaches using a large repertoire of functions [11,12,14,15]. While the former strategy allows to create linear mappings from recorded dynamics to network topology, the latter allows to infer links from transient dynamics following an unknown driving or perturbation.…”

“…Researchers routinely resort to indirect methods to infer the physical interactions from the networks' collective dynamics [9]. State-of-the-art approaches infer physical interactions via ODE modeling using large repertoire of functions [10][11][12][13][14]. Such approaches require the entire dynamics to admit a sparse representation in the chosen repertoire, which is difficult to satisfy if no prior information is provided.…”

Reverse-engineering biological networks from large data sets

“…Nonlinear reverse-engineering schemes based on massaction kinetic laws like Michaelis-Menten or Hill equations [21] are also used in reconstruction [234,235].…”