title: Time Series Analysis of theBacillus subtilisSporulation Network Reveals Low Dimensional Chaotic Dynamics.
abstract: Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation inBacillus subtilisto explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as theB. subtilissporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that theB. subtilissporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in theB. subtilissporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlyingB. subtilissporulation initiation control.
authors.affiliation: Department of Mathematics, University of Trento Trento, Italy.
authors.forename: Paola
authors.initials: P
authors.lastname: Lecca
authors.affiliation: Department of Industrial Engineering, Universidad de los Andes Bogotá, Colombia.
authors.forename: Ivan
authors.initials: I
authors.lastname: Mura
authors.affiliation: Laboratory of Translational Genomics, Centre for Integrative Biology, University of Trento Trento, Italy.
authors.forename: Angela
authors.initials: A
authors.lastname: Re
authors.affiliation: Gut Health and Food Safety, Institute of Food Research Norwich, UK.
authors.forename: Gary C
authors.initials: GC
authors.lastname: Barker
authors.affiliation: Gut Health and Food Safety, Institute of Food Research Norwich, UK.
authors.forename: Adaoha E C
authors.initials: AE
authors.lastname: Ihekwaba
keywords: Bacillus subtilis; computational modeling; low dimensional chaos; sensitivity analysis; signal transduction; sporulation; systems biology