Regulation of oscillation dynamics in biochemical systems with dual negative feedback loops

Abstract

Feedback controls are central to cellular regulation. Negative-feedback mechanisms are well known to underline oscillatory dynamics. However, the presence of multiple negativefeedback mechanisms is common in oscillatory cellular systems, raising intriguing questions of how they cooperate to regulate oscillations. In this work, we studied the dynamical properties of a set of general biochemical motifs with dual, nested negative-feedback structures. We showed analytically and then confirmed numerically that, in these motifs, each negativefeedback loop exhibits distinctly different oscillation-controlling functions. The longer, outer feedback loop was found to promote oscillations, whereas the short, inner loop suppresses and can even eliminate oscillations. We found that the position of the inner loop within the coupled motifs affects its repression strength towards oscillatory dynamics. Bifurcation analysis indicated that emergence of oscillations may be a strict parametric requirement and thus evolutionarily tricky. Investigation of the quantitative features of oscillations (i.e. frequency, amplitude and mean value) revealed that coupling negative feedback provides robust tuning of the oscillation dynamics. Finally, we demonstrated that the mitogen-activated protein kinase (MAPK) cascades also display properties seen in the general nested feedback motifs. The findings and implications in this study provide novel understanding of biochemical negative-feedback regulation in a mixed wiring context.

Anatomy of a negative feedback loop: the case of I κ B α

“…Indeed, these properties are not required for the NFkB dimer stabilization/chaperone function recently ascribed to IkBb [28]. Our results illustrate the more general point: that negative feedback regulation in cells is a complex process that depends on multiple molecular properties beyond activator-induced expression [29,30]. These findings may well extend to other transcriptional networks as nuclear transport is a defining feature of many gene regulatory networks.…”

How time delay and network design shape response patterns in biochemical negative feedback systems

“…This observation confirms previous results [21, 35] showing that nested auto-inhibitory feedbacks repress oscillatory dynamics in networks containing DNF.…”

Understanding complexity in the HIF signaling pathway using systems biology and mathematical modeling

“…While a primary function of negative feedback regulation is to enable signal adaptation, it is well known to underlie oscillatory behaviours [50,51]. Under concurrent control of multiple negative feedbacks, it is expected that HIF-1 may oscillate in specific cellular contexts [51].…”

“…Under concurrent control of multiple negative feedbacks, it is expected that HIF-1 may oscillate in specific cellular contexts [51].…”