Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics

By N. Mangan, Steven L. Brunton, Joshua L. Proctor, J. Nathan Kutz. 2016

429 citations recorded by the source corpus.

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 data-driven method to infer networked nonlinear dynamical systems by using sparsity-promoting optimization to select a subset of nonlinear interactions representing dynamics on a network. In contrast to standard model selection methods-based upon information content for a finite number of heuristic models (order 10 or less), our model selection procedure discovers a parsimonious model from a combinatorially large set of models, without an exhaustive search. Our particular innovation is appropriate for many biological networks, where the governing dynamical systems have rational function nonlinearities with cross terms, thus requiring an implicit formulation and the equations to be identified in the null-space of a library of mixed nonlinearities, including the state and derivative terms. This method, implicit-SINDy, succeeds in inferring three canonical biological models: 1) Michaelis-Menten enzyme kinetics; 2) the regulatory network for competence in bacteria; and 3) the metabolic network for yeast glycolysis.

Subfields: Computational Theory and Mathematics, Molecular Biology

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Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “More recently, sparsity [23] has been used to determine the governing dynamical system [24, 25, 26, 27, 28, 29, 30, 31, 32, 33].”
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics (2020, methodology): “We use the same parameters as in [47], with jx = 0.”
Universal Differential Equations for Scientific Machine Learning (2020, methodology): “The SINDy algorithm [10, 11, 12] enables data-driven discovery of governing equations from data.”
Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences (2019, background): “Examples: Inferring operators that form ordinary [Mangan et al., 2016] and partial differential equations [Wang et al., 2019].”
Sparse identification of nonlinear dynamics for model predictive control in the low-data limit (2017, background): “It is also possible to extend the SINDy algorithm to identify models in libraries that encode richer dynamics, such as rational function nonlinearities [43].”
Constrained sparse Galerkin regression (2016, background): “However, the extensions of SINDy to identify partial differential equations (Rudy et al. 2017; Schaeffer 2017) and biological regulatory networks (Mangan et al. 2016) highlight the flexibility of this simple regression framework.”
Data-driven discovery of coordinates and governing equations (2019, background): “…a number of theoretical extensions to the SINDy framework, including for identifying partial differential equations [11, 57], multiscale physics [58], parametrically dependent dynamical models [59], hybrid (switching) dynamical systems [60], and models with rational function nonlinearities [61].”
Model selection for dynamical systems via sparse regression and information criteria (2017, methodology): “Since the original SINDy method, there have been numerous innovations and extensions to handle rational function nonlinearities [4], PDEs [2] and highly corrupted data [33], and to build Galerkin regression models in fluids [34].”
Data-Driven Sparse Sensor Placement for Reconstruction: Demonstrating the Benefits of Exploiting Known Patterns (2017, background): “june 2018 « IEEE CONTROL SYSTEMS MAGAZINE 85 [43] N.”