Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression

By Bryan C. Daniels, Ilya Nemenman. 2014

102 citations recorded by the source corpus.

The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the S-system formalism, which is a sensible representation of nonlinear mass-action kinetics typically found in cellular dynamics, maintains the efficiency of linear regression. We combine this approach with adaptive model selection to obtain efficient and parsimonious representations of cellular dynamics. The approach is tested by inferring the dynamics of yeast glycolysis from simulated data. With little computing time, it produces dynamical models with high predictive power and with structural complexity adapted to the difficulty of the inference problem.

Subfields: Genetics, Molecular Biology, Optimization & Training, Numerical Methods & Scientific Computing

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Citations in the corpus

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations (2018, methodology): “…behavior [11], automated inference of dynamics [12, 13, 14], normal form identiﬁcation in climate [15], nonlinear Laplacian spectral analysis [16], modeling emergent behavior [11], Koopman analysis [17, 18, 19, 20], automated inference of dynamics [12, 13, 14], and symbolic regression [21, 22].”
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems (2018, methodology): “To illustrate the ability of our method to identify parameterized dynamics, let us consider the Hopf normal form ˙ x = µx + y − x ( x 2 + y 2 ) , ˙ y = − x + µy − y ( x 2 + y 2 ) . of 7 biochemical species; i.e., The parameters of the model are chosen according to table 1 of [29].”
Discovering governing equations from data by sparse identification of nonlinear dynamical systems (2015, methodology): “Daniels BC, Nemenman I (2015) Efficient inference of parsimonious phenomenolog- ical models of cellular dynamics using S-systems and alternating regression.”
Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics (2016, methodology): “functional forms including: sparse Bayesian inference on a library of Hill functions [42], [43], Bayesian inference on the chemical reaction graph and kinetic parameters using a library of Hill functions [44], [45], an alternating regression using the compact S-system representation [2], [46], and a”
Systems biology informed deep learning for inferring parameters and hidden dynamics (2019, background): “[33, 35] and S3 Fig), and the inferred dynamics shown in S2 Fig and Fig 3 show that the learned dynamics match very well with the exact dynamics, the inferred parameters are valid.”
Data Driven Governing Equations Approximation Using Deep Neural Networks (2018, methodology): “Earlier efforts include methods using symbolic regression ([5, 43]), equation-free modeling [24], heterogeneous multiscale method (HMM) ([15]), artificial neural networks ([19]), nonlinear regression ([50]), empirical dynamic modeling ([46, 53]), nonlinear Laplacian spectral analysis ([18]), automat”
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control (2021, background): “…exist, including equation-free modeling [1], normal form identiﬁcation [2–4], nonlinear Laplacian spectral analysis [5], Koop-man analysis [6, 7] and dynamic mode decomposition (DMD) [8–10], symbolic regression [11–15], sparse regression [16, 17], Gaussian processes [18], and deep learning [19–24].”
Automated adaptive inference of phenomenological dynamical models (2015, methodology): “A more complicated test of the method is to reproduce nonlinear oscillatory dynamics, such as that describing yeast glycolysis, for which there has been recent interest in automated inference 14,24 .”
Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems (2017, methodology): “We use the standard model introduced in [23], a seven state nonlinear model with Michaelis-Menten dynamics.”