(306b) Dynamical Pathway Sensitivity Analysis for Biological Systems

The normal functioning of biological systems relies on the coordinated actions of a multitude of components (i.e., from genes to proteins to metabolites and small molecules). The complexity that is often associated with cellular response to a particular stimulus, limits human intuition in understanding their functional dynamics and emergent behaviors. This has motivated the use of quantitative dynamical models to represent the underlying behavior of biological systems¹. To this end, various modeling paradigms and their associated systems analysis tools, such as the one presented here and elsewhere^2,3, have been developed to elucidate the underlying mechanistic details that are responsible for giving the observed behavior. Existing model analysis tools, based on perturbations on system dynamics, include structured singular values⁴, bifurcation analysis⁵, and parametric sensitivity analysis⁶ and its variants, such as dynamic Green’s Function Matrix³ and impulse parametric sensitivity Analysis². Most of these analyses introduce static or dynamic perturbations to system states or parameters one at a time, and quantify the resulting change in system behavior, based on which mechanistic details of system dynamics are inferred.

On the other hand, there is increasing evidence that the structure of biological networks is closely related to their functions⁷. Hence, qualitative structural analysis of biological networks is an alternative tool used to understand system functionality and dynamics⁸. Existing structure analysis methods, mainly borrowed from graph theory concepts, range from simple degree centrality⁹ to spectral¹⁰ and communicability measures to SigFlux method¹¹. Given the network topology, these methods identify how important a particular molecule or a reaction is to the networks connectivity and system functionality.

But as said earlier, cells often rely not on a single molecule or reaction, rather on a group of molecules and reactions that gives rise to the observed behavior¹². Hence it is equally important to analyse pathways, comprising multiple molecules and reactions. To this end, we have created a new pathway sensitivity analysis tool that combines both the above said, structural and dynamic information of the network. The analysis presented here consists of two steps: (1) identification of elementary signaling modes⁸ (structure) and (2) introduction of impulse perturbations on the parameters associated with each individual modes (dynamics).

The efficacy of the present method is demonstrated using two biological applications for: (i) understanding the competing mechanisms of type-I/II apoptosis in Jurkat cell lines, which gives raise to the caspase-3 cleavage¹³, and (ii) identifying the robustness causing mechanism of central carbon metabolism in E. coli¹⁴. The pathway sensitivity analysis of Fas-induced apoptosis in Jurkat cell lines showed that the initial activation of caspase-3 is due to mitochondrial independent pathway, which is later taken over by mitochondrial dependent pathway. On the other hand, the pathway sensitivity to E. coli central carbon metabolism revealed the 6pg-ribu5p pathway, including the Tkb conversion of xyl5p to f6p, as the responsible mechanism that promotes the robustness in pyruvate production against external perturbations.

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2.         Perumal TM, Gunawan R. Understanding dynamics using sensitivity analysis: caveat and solution. BMC Syst Biol. Mar 15 2011;5(1):41.

3.         Perumal TM, Wu Y, Gunawan R. Dynamical analysis of cellular networks based on the Green's function matrix. J Theor Biol. Nov 21 2009;261(2):248-259.

4.         Shoemaker JE, Doyle III FJ. Identifying Fragilities in Biochemical Networks: Robust Performance Analysis of Fas Signaling-Induced Apoptosis. Biophys J. 2008.

5.         Battogtokh D, Tyson JJ. Bifurcation analysis of a model of the budding yeast cell cycle. Chaos. Sep 2004;14(3):653-661.

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7.         Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED. Metabolic network structure determines key aspects of functionality and regulation. Nature. Nov 14 2002;420(6912):190-193.

 8.        Wang RS, Albert R. Elementary signaling modes predict the essentiality of signal transduction network components. BMC Syst Biol. 2011;5:44.

9.         Wasserman S, Faust K. Social network analysis : methods and applications. Cambridge ; New York: : Cambridge University Press; 1994.

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11.       Liu W, Li D, Zhang J, Zhu Y, He F. SigFlux: a novel network feature to evaluate the importance of proteins in signal transduction networks. BMC Bioinformatics. 2006;7:515.

12.       Bhalla US, Iyengar R. Emergent properties of networks of biological signaling pathways. Science. 1999;283(5400):381--387.

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