Publications about 'periodic inputs' |
Articles in journal or book chapters |
What complicated dynamics can arise in the simplest biochemical systems, in response to a periodic input? This paper discusses two models that commonly appear as components of larger sensing and signal transduction pathways in systems biology: a simple two-species negative feedback loop, and a prototype nonlinear integral feedback. These systems have globally attracting steady states when unforced, yet, when subject to a periodic excitation, subharmonic responses and strange attractors can arise via period-doubling cascades. These behaviors are similar to those exhibited by classical forced nonlinear oscillators such as those described by van der Pol or Duffing equations. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology. |
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 \emph{C.elegans} olfactory sensory neurons. |
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to fixed limit cycles. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. |
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