12,951 research outputs found
Dynamical Consequences of Bandpass Feedback Loops in a Bacterial Phosphorelay
Under conditions of nutrient limitation, Bacillus subtilis cells terminally differentiate into a dormant spore state. Progression to sporulation is controlled by a genetic circuit consisting of a phosphorelay embedded in multiple transcriptional feedback loops, which is used to activate the master regulator Spo0A by phosphorylation. These transcriptional regulatory interactions are “bandpass”-like, in the sense that activation occurs within a limited band of Spo0A~P concentrations. Additionally, recent results show that the phosphorelay activation occurs in pulses, in a cell-cycle dependent fashion. However, the impact of these pulsed bandpass interactions on the circuit dynamics preceding sporulation remains unclear. In order to address this question, we measured key features of the bandpass interactions at the single-cell level and analyzed them in the context of a simple mathematical model. The model predicted the emergence of a delayed phase shift between the pulsing activity of the different sporulation genes, as well as the existence of a stable state, with elevated Spo0A activity but no sporulation, embedded within the dynamical structure of the system. To test the model, we used time-lapse fluorescence microscopy to measure dynamics of single cells initiating sporulation. We observed the delayed phase shift emerging during the progression to sporulation, while a re-engineering of the sporulation circuit revealed behavior resembling the predicted additional state. These results show that periodically-driven bandpass feedback loops can give rise to complex dynamics in the progression towards sporulation
Star Cluster Simulations: The State of the Art
This paper concentrates on four key tools for performing star cluster
simulations developed during the last decade which are sufficient to handle all
the relevant dynamical aspects. First we discuss briefly the Hermite
integration scheme which is simple to use and highly efficient for advancing
the single particles. The main numerical challenge is in dealing with weakly
and strongly perturbed hard binaries. A new treatment of the classical
Kustaanheimo-Stiefel two-body regularization has proved to be more accurate for
studying binaries than previous algorithms based on divided differences or
Hermite integration. This formulation employs a Taylor series expansion
combined with the Stumpff functions, still with one force evaluation per step,
which gives exact solutions for unperturbed motion and is at least comparable
to the polynomial methods for large perturbations. Strong interactions between
hard binaries and single stars or other binaries are studied by chain
regularization which ensures a non-biased outcome for chaotic motions. A new
semi-analytical stability criterion for hierarchical systems has been adopted
and the long-term effects on the inner binary are now treated by averaging
techniques for cases of interest. These modifications describe consistent
changes of the orbital variables due to large Kozai cycles and tidal
dissipation. The range of astrophysical processes which can now be considered
by N-body simulations include tidal capture, circularization, mass transfer by
Roche-lobe overflow as well as physical collisions, where the masses and radii
of individual stars are modelled by synthetic stellar evolution.Comment: Accepted by Cel. Mech. Dyn. Astron., 12 pages including figur
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