title: Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations.
abstract: Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.
authors.affiliation: Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
authors.forename: Katharina
authors.initials: K
authors.lastname: Baum
authors.affiliation: Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
authors.forename: Antonio Z
authors.identifier: http://orcid.org/0000-0003-4788-0933
authors.initials: AZ
authors.lastname: Politi
authors.affiliation: Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
authors.forename: Bente
authors.initials: B
authors.lastname: Kofahl
authors.affiliation: Institute for Theoretical Biology, Humboldt University of Berlin, Berlin, Germany.
authors.forename: Ralf
authors.initials: R
authors.lastname: Steuer
authors.affiliation: Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
authors.forename: Jana
authors.initials: J
authors.lastname: Wolf
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D020013:Calcium Signaling / Q000502:physiology*; D002468:Cell Physiological Phenomena; D002940:Circadian Rhythm / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D009991:Oscillometry / Q000379:methods*