Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops

Abstract

A simple negative feedback loop of interacting genes or proteins has the potential to generate sustained oscillations. However, many biological oscillators also have a positive feedback loop, raising the question of what advantages the extra loop imparts. Through computational studies, we show that it is generally difficult to adjust a negative feedback oscillator’s frequency without compromising its amplitude, whereas with positive-plus-negative feedback, one can achieve a widely tunable frequency and near-constant amplitude. This tunability makes the latter design suitable for biological rhythms like heartbeats and cell cycles that need to provide a constant output over a range of frequencies. Positive-plus-negative oscillators also appear to be more robust and easier to evolve, rationalizing why they are found in contexts where an adjustable frequency is unimportant.

Design principles for robust oscillatory behavior

“…On the contrary, negative autoregulation interactions are absent in robust topologies. Our result for positive autoregulation agrees with earlier studies which also demonstrated numerically (Tsai et al 2008) and experimentally Stricker et al 2008;Tigges et al 2009) the importance of positive autoregulation. In terms of having negative feedback loops in the network, at least one loop is required, with most robust topologies using at least two (Fig.…”

“…Not only can this shed light into which parameter configuration makes a topology oscillate, but also into how ''tunable'' a topology is, that is, how much the oscillatory response can be controlled by changing the parameters of the network. Tunability, as well as robustness, is a highly desirable feature in synthetic oscillators (Tsai et al 2008;Stricker et al 2008). We started our analysis by studying the distribution of the robustness among all three-component topologies.…”

“…Several studies have made contributions towards identifying some design principles for oscillatory behaviour. Network motifs-recurrent patterns of interactions believed to form the building blocks of any complex network (Milo et al 2002;Yeger-Lotem et al 2004;Barabasi and Oltvai 2004;Alon 2007;Kim et al 2010)-have also been highlighted to some extent for oscillators (Ferrell et al 2011;Wagner 2005;Novak and Tyson 2008;Tsai et al 2008;Burda et al 2011;Lomnitz and Savageau 2014;Noman et al 2015;Semenov et al 2015).…”

“…We do so by conducting extensive numerical simulations of every possible topological arrangement. Previous related work focused on exploring a limited number of topological variations of three-node oscillators (Tsai et al 2008;Ananthasubramaniam and Herzel 2014). Our approach, however, is not biased towards any specific architecture since we evaluate the robustness of every possible three-component network.…”

Thinking about flagellar oscillation

“…Some combination of curvature-based switching, with negative feedback, and sliding-based switching, with positive feedback, might be particularly advantageous [Tsai et al, 2008].…”