BDC-Decomposition for Global Influence Analysis

In biochemical networks, the steady-state input-output influence is the sign of the output steady-state variation due to a persistent positive input perturbation; if the sign does not depend on the value of the strictly positive system parameters, the influence is structural. As recently shown for small perturbations, when the linearized system approximation is valid, steady-state input-output influences can be structurally assessed, for biochemical networks with <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> unknown parameters, by means of a vertex algorithm with complexity <inline-formula> <tex-math notation="LaTeX">$2^{m}$ </tex-math></inline-formula>. This letter shows that the structural input-output influence of a biochemical network is a global property, which does not require any small-perturbation assumption. It also shows that, using a new algorithm, the complexity can be reduced down to <inline-formula> <tex-math notation="LaTeX">$2^{m-n}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the system order, thus drastically reducing the computation time. Finally, when the uncertain parameters belong to known intervals, non-conservative bounds are given for the steady-state ratio between output and input, allowing for sensitivity analysis.

[1]  Hiroaki Kitano,et al.  Biological robustness , 2008, Nature Reviews Genetics.

[2]  Franco Blanchini,et al.  Computing the structural influence matrix for biological systems , 2016, Journal of mathematical biology.

[3]  Andrei Zinovyev,et al.  Inferring hidden causal relations between pathway members using reduced Google matrix of directed biological networks , 2017 .

[4]  Jeffrey M. Dambacher,et al.  RELEVANCE OF COMMUNITY STRUCTURE IN ASSESSING INDETERMINACY OF ECOLOGICAL PREDICTIONS , 2002 .

[5]  M. Elowitz,et al.  Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[6]  A. Oudenaarden,et al.  A Systems-Level Analysis of Perfect Adaptation in Yeast Osmoregulation , 2009, Cell.

[7]  Eduardo Sontag,et al.  Fold-change detection and scalar symmetry of sensory input fields , 2010, Proceedings of the National Academy of Sciences.

[8]  Jeffrey M Dambacher,et al.  UNDERSTANDING AND PREDICTING EFFECTS OF MODIFIED INTERACTIONS THROUGH A QUALITATIVE ANALYSIS OF COMMUNITY STRUCTURE , 2007, The Quarterly Review of Biology.

[9]  Franco Blanchini,et al.  Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular , 2017, Autom..

[10]  Franco Blanchini,et al.  Structurally robust biological networks , 2011, BMC Systems Biology.

[11]  Eduardo Sontag.  A technique for determining the signs of sensitivities of steady states in chemical reaction networks. , 2013, IET systems biology.

[12]  David Angeli,et al.  Remarks on the invalidation of biological models using monotone systems theory , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Ankit Gupta,et al.  Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. , 2014, Cell systems.

[14]  Claudio Altafini,et al.  Qualitative and quantitative responses to press perturbations in ecological networks , 2017, Scientific Reports.

[15]  M. Feinberg,et al.  Structural Sources of Robustness in Biochemical Reaction Networks , 2010, Science.

[16]  Claudio Altafini,et al.  Interaction sign patterns in biological networks: From qualitative to quantitative criteria , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[17]  Franco Blanchini,et al.  Piecewise-linear Lyapunov functions for structural stability of biochemical networks , 2014, Autom..

[18]  Franco Blanchini,et al.  Determining the structural properties of a class of biological models , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[19]  Giulia Giordano,et al.  Structural Analysis and Control of Dynamical Networks , 2016 .

[20]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[21]  J. Doyle,et al.  Robust perfect adaptation in bacterial chemotaxis through integral feedback control. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[22]  B. Fiedler,et al.  Sensitivity of chemical reaction networks: a structural approach. 2. Regular monomolecular systems , 2015, 1606.00279.

[23]  U. Alon.  An introduction to systems biology : design principles of biological circuits , 2019 .

[24]  David Koslicki,et al.  Exact probabilities for the indeterminacy of complex networks as perceived through press perturbations , 2016, bioRxiv.

[25]  M. Khammash,et al.  Calcium homeostasis and parturient hypocalcemia: an integral feedback perspective. , 2002, Journal of theoretical biology.

[26]  Kazuyuki Aihara,et al.  Modeling Biomolecular Networks in Cells , 2010 .

[27]  Giulia Giordano,et al.  Negative feedback enables structurally signed steady-state influences in artificial biomolecular networks , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[28]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .