Positive feedback promotes oscillations in negative feedback loops

PLoS One. 2014 Aug 15;9(8):e104761. doi: 10.1371/journal.pone.0104761. eCollection 2014.


A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically "unlikely." Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Biological Clocks*
  • Computer Simulation
  • Feedback, Physiological*
  • Humans
  • Models, Biological
  • Systems Biology

Grant support

BA was supported by a fellowship from the Alexander von Humboldt Foundation. The authors acknowledge support from BMBF (T-Sys, 0316164G), DFG (SPP InKomBio) and Bernstein Center for Computational Neuroscience Berlin (grant 01GQ1001C). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.