Abstract
BackgroundNegative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. Here, we study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks.ResultsWe investigate the influence of several design features on the stability of the model equilibrium, i.e., presence of auto-inhibition and/or mass conservation and the kind and/or strength of the delayed negative feedback. We show that auto-inhibition and mass conservation have a stabilizing effect, whereas increasing abruptness and decreasing feedback threshold have a de-stabilizing effect on the model equilibrium. Moreover, applying our theoretical analysis to the mammalian p53 system we show that an auto-inhibitory feedback can decouple period and amplitude of an oscillatory response, whereas the delayed feedback can not.ConclusionsOur theoretical framework provides insight into how time delay and design features of biochemical networks act together to elicit specific characteristic response patterns. Such insight is useful for constructing synthetic networks and controlling their behaviour in response to external stimulation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0325-9) contains supplementary material, which is available to authorized users.
Highlights
Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks
Recent studies [22, 35] demonstrated that nested negative feedbacks may suppress oscillations of biochemical species involved in delayed negative feedback (DNF)
Model formulation We investigated four different two-dimensional models containing DNF that describe generic signal-response networks (Fig. 1)
Summary
Negative feedback in combination with time delay can bring about both sustained oscillations and adaptive behaviour in cellular networks. We study which design features of systems with delayed negative feedback shape characteristic response patterns with special emphasis on the role of time delay. To this end, we analyse generic two-dimensional delay differential equations describing the dynamics of biochemical signal-response networks. Recent studies [22, 35] demonstrated that nested negative feedbacks may suppress oscillations of biochemical species involved in DNF These studies provided no insight into how time delay influences the dynamics of Börsch and Schaber BMC Systems Biology (2016) 10:82
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