title: How time delay and network design shape response patterns in biochemical negative feedback systems.
abstract: Negative 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.
  
  
  
  We 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.
  
  
  
  Our 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.
authors: Institute for Experimental Internal Medicine, Medical Faculty, Otto-von-Guericke University, Pfälzer Platz 2, Magdeburg, 39106, Germany.|Biozentrum, University of Basel and Swiss Institute of Bioinformatics, Klingelbergstrasse 50-70, Basel, 4056, Switzerland.
authors: Anastasiya
authors: A
authors: Börsch
authors: Institute for Experimental Internal Medicine, Medical Faculty, Otto-von-Guericke University, Pfälzer Platz 2, Magdeburg, 39106, Germany. j.schaber@web.de.
authors: Jörg
authors: J
authors: Schaber
mesh_terms: D025461:Feedback, Physiological; D008954:Models, Biological; D013997:Time Factors; D016159:Tumor Suppressor Protein p53 / Q000378:metabolism
chemical_list: D016159:Tumor Suppressor Protein p53
keywords: Auto-inhibiton; Bifurcation; Mass conservation; Stability; p53