- ▪S. J. Rahi, J. Larsch, K. Pecani, N. Mansouri, A. Y. Katsov, K. Tsaneva-Atanasova, E. D. Sontag, F. R. Cross, "Oscillatory stimuli differentiate adapting circuit topologies", Nature Methods, vol. 14, pp. 1010-1016, 2017. pdfentrainment · systems biology · periodic inputs · subharmonic responses · biochemical systems · forced oscillations · reaction networks · periodic behaviors · monotone systems · oscillations · incoherent feedforward loop · feedforward · IFFL · systems biology
Abstract
Elucidating the structure of biological intracellular networks from experimental data remains a major challenge. This paper studies two types of ``response signatures'' to identify specific circuit motifs, from the observed response to periodic inputs. In particular, the objective is to distinguish negative feedback loops (NFLs) from incoherent feedforward loops (IFFLs), which are two types of circuits capable of producing exact adaptation. The theory of monotone systems with inputs is used to show that ``period skipping'' (non-harmonic responses) is ruled out in IFFL's, and a notion called ``refractory period stabilization'' is also analyzed. The approach is then applied to identify a circuit dominating cell cycle timing in yeast, and to uncover a calcium-mediated NFL circuit in C.elegans olfactory sensory neurons.
- ▪D. Angeli, E.D. Sontag, "Oscillations in I/O monotone systems", IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology, vol. 55, pp. 166-176, 2008. pdfPreprint version in arXiv q-bio.QM/0701018, 14 Jan 2007monotone systems · hopf bifurcations · circadian rhythms · tridiagonal systems · nonlinear dynamics · systems biology · reaction networks · oscillations · periodic behavior · delay-differential systems
Abstract
In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory establishes global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, based on the application of a tight small gain condition. This stability persists even under arbitrary delays in the feedback loop. On the other hand, when the condition is violated a Poincare'-Bendixson result allows to conclude existence of oscillations, for sufficiently high delays.
- ▪D. Angeli, E.D. Sontag, "An analysis of a circadian model using the small-gain approach to monotone systems", In Proc.\ IEEE Conf.\ Decision and Control, Paradise Island, Bahamas, Dec.\ 2004, IEEE Publications, pp. 575–578, 2004. pdfcircadian rhythms · tridiagonal systems · nonlinear dynamics · systems biology · reaction networks · oscillations · periodic behavior · monotone systems · delay-differential systems
Abstract
We show how certain properties of Goldbeter's original 1995 model for circadian oscillations can be proved mathematically. We establish global asymptotic stability, and in particular no oscillations, if the rate of transcription is somewhat smaller than that assumed by Goldbeter, but, on the other hand, this stability persists even under arbitrary delays in the feedback loop. We are mainly interested in illustrating certain mathematical techniques, including the use of theorems concerning tridiagonal cooperative systems and the recently developed theory of monotone systems with inputs and outputs.