Abstract
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.
Highlights
The identification of motifs within biological networks and assignment of function to those motifs has been a key undertaking of Systems Biology [1,2]
The glycolytic [14,15] and cAMP oscillators have been alternatively attributed to a twocomponent negative feedback motif
We address the principles by which these positive feedback loops are beneficial in biochemical oscillations and unify several common mechanisms known to promote oscillations, such as Michaelis-Menten [17] degradation kinetics [18] and self-activation
Summary
The identification of motifs within biological networks and assignment of function to those motifs has been a key undertaking of Systems Biology [1,2]. The glycolytic [14,15] and cAMP oscillators have been alternatively attributed to a twocomponent negative feedback motif (the choice of motif length depends on the components and processes considered essential in the model). The core negative feedback motif is augmented with positive feedback loops in several of these systems [3]. This raises the question of the evolutionary purpose of these auxiliary positive feedback loops. We address the principles by which these positive feedback loops are beneficial in biochemical oscillations and unify several common mechanisms known to promote oscillations, such as Michaelis-Menten [17] degradation kinetics [18] and self-activation
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