title: The role of time delay in adaptive cellular negative feedback systems.
abstract: Adaptation in cellular systems is often mediated by negative feedbacks, which usually come with certain time delays causing several characteristic response patterns including an overdamped response, damped or sustained oscillations. Here, we analyse generic two-dimensional delay differential equations with delayed negative feedback describing the dynamics of biochemical adaptive signal-response networks. We derive explicit thresholds and boundaries showing how time delay determines characteristic response patterns of these networks. Applying our theoretical analyses to concrete data we show that adaptation to osmotic stress in yeast is optimal in the sense of minimizing adaptation time without causing oscillatory behaviour, i.e., a critically damped response. In addition, our framework demonstrates that a slight increase of time delay in the NF-κB system might induce a switch from damped to sustained oscillatory behaviour. Thus, we demonstrate how delay differential equations can be used to explicitly study the delay in biochemical negative feedback systems. Our analysis also provides insight into how time delay may tune biological signal-response patterns and control the systems behaviour.
authors.affiliation: Institute for Experimental Internal Medicine, Medical Faculty, Otto-von-Guericke University, Pfälzer Platz 2, Magdeburg 39106, Germany.
authors.forename: Anastasiya
authors.initials: A
authors.lastname: Lapytsko
authors.affiliation: Institute for Experimental Internal Medicine, Medical Faculty, Otto-von-Guericke University, Pfälzer Platz 2, Magdeburg 39106, Germany. Electronic address: j.schaber@web.de.
authors.forename: Jörg
authors.initials: J
authors.lastname: Schaber
mesh_terms: D000222:Adaptation, Physiological; D003198:Computer Simulation; D025461:Feedback, Physiological; D005990:Glycerol / Q000378:metabolism; D008954:Models, Biological; D016328:NF-kappa B / Q000378:metabolism; D009994:Osmolar Concentration; D013997:Time Factors
chemical_list: D016328:NF-kappa B; D005990:Glycerol
keywords: Adaptation; Characteristic response pattern; Hog1; Hopf bifurcation; NF-κB