Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations

PLoS Comput Biol. 2016 Dec 27;12(12):e1005298. doi: 10.1371/journal.pcbi.1005298. eCollection 2016 Dec.


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.

MeSH terms

  • Animals
  • Biological Clocks / physiology*
  • Calcium Signaling / physiology*
  • Cell Physiological Phenomena*
  • Circadian Rhythm / physiology*
  • Computer Simulation
  • Humans
  • Kinetics
  • Models, Biological*
  • Oscillometry / methods*

Grant support

KB was funded by a PhD fellowship from Max Delbrück Center for Molecular Medicine in the Helmholtz Association (MDC). AZP, BK, JW were funded by the ForSys program of the German Ministry of Education and Research (BMBF, grant 0315289). KB, RS, BK, and JW acknowledge funding by the graduate school Computational Systems Biology (CSB) of the German Research Foundation (DFG – Graduiertenkolleg 1772). RS is supported by the German Federal Ministry of Education and Research as part of the “e:Bio – Innovationswettbewerb Systembiologie” [e:Bio – systems biology innovation competition] initiative (reference: FKZ 0316192). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.