Nonparametric Analysis of Nonlinear Distortions for Biomolecular Systems

Abstract System identification of biomolecular circuits is a challenging problem, including due to the nonlinearities that are often present in them. The extent to which these nonlinearities contribute to the overall behaviour of the biomolecular circuit is unclear. Here, we address this issue for simple biomolecular circuit models by exploiting the properties of broadband random phase multisine excitations. We analysed the classical models of a two-state signaling system, an enzymatic signaling system, and of a transcriptional feedback circuit for the presence of nonlinear distortions at certain parametric settings and studied their dependence on the input parameters. These results should help the modeller in quantifying the effect of nonlinearities and assessing the validity of the linear models at a particular operating condition.

[1]  James E. Ferrell,et al.  Bistability in cell signaling: How to make continuous processes discontinuous, and reversible processes irreversible. , 2001, Chaos.

[2]  Xin Liu,et al.  State and parameter estimation of the heat shock response system using Kalman and particle filters , 2012, Bioinform..

[3]  Rik Pintelon,et al.  Advantages of Odd Random Phase Multisine Electrochemical Impedance Measurements , 2009 .

[4]  D. Koshland,et al.  An amplified sensitivity arising from covalent modification in biological systems. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[5]  R. Bourret,et al.  Two-component signal transduction. , 2010, Current opinion in microbiology.

[6]  D. Vecchio,et al.  Biomolecular Feedback Systems , 2014 .

[7]  Chi-Ying F. Huang,et al.  Ultrasensitivity in the mitogen-activated protein kinase cascade. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[9]  J. Schoukens,et al.  Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach , 1998, IEEE Trans. Autom. Control..

[10]  Rik Pintelon,et al.  Linear System Identification in a Nonlinear Setting: Nonparametric Analysis of the Nonlinear Distortions and Their Impact on the Best Linear Approximation , 2016, IEEE Control Systems.

[11]  Yves Rolain,et al.  Analysis of windowing/leakage effects in frequency response function measurements , 2006, Autom..

[12]  David T. Westwick,et al.  Identification of nonlinear physiological systems , 2003 .

[13]  Douglas B. Kell,et al.  Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation , 1998, Bioinform..

[14]  R. de Figueiredo.  The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

[15]  Ramon Bragós,et al.  Fast Electrical Impedance Spectroscopy for Moving Tissue Characterization Using Bilateral QuasiLogarithmic Multisine Bursts Signals , 2009 .

[16]  Darren J. Wilkinson,et al.  Bayesian methods in bioinformatics and computational systems biology , 2006, Briefings Bioinform..

[17]  Wendy Van Moer,et al.  Measurement and characterization of glucose in NaCl aqueous solutions by electrochemical impedance spectroscopy , 2014, Biomed. Signal Process. Control..

[18]  Abhishek Dey,et al.  Describing function-based approximations of biomolecular signalling systems , 2015, 2015 European Control Conference (ECC).

[19]  Johan Schoukens,et al.  Data-Driven Nonlinear Identification of Li-Ion Battery Based on a Frequency Domain Nonparametric Analysis , 2017, IEEE Transactions on Control Systems Technology.