Frontiers in Microbiology (Nov 2016)
Time series analysis of the Bacillus subtilis sporulation network reveals low dimensional chaotic dynamics
Abstract
Chaotic behaviour refers to a behaviour which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behaviour 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 system’s components. In this case, indeed, embedding the major drivers of chaos in a system into the modelling approach allows us to improve predictability of the system’s dynamics. Here, we analysed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. The estimation of several indices reflecting the chaotic nature of a system indicates that this network’s dynamics is affected by deterministic chaos. The neat separation between the indices obtained from time series simulated from the model and those obtained from time series generated by Gaussian noise confirmed that the B. subtilis sporulation network dynamics is affected by chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the network’s chaotic dynamics in the sporulation initiation phosphotransferase B (Spo0B). We then analysed the parameter 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 assumed by Spo0B, and 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 the B. subtilis sporulation network by gathering evidence for the system’s chaotic behaviour, and by suggesting candidate molecules driving chaos in the system. The results from this chaos analysis could help to refine theoretical predictions of the behaviour of the system and to advance the control of the mechanisms underlying B. subtilis sporulation.
Keywords
