Coupling between feedback loops in autoregulatory networks affects bistability range, open-loop gain and switching times

Abstract

Biochemical regulatory networks governing diverse cellular processes such as stress-response, differentiation and cell cycle often contain coupled feedback loops. We aim to understand how features of feedback architecture, such as the number of loops, the sign of the loops and the type of their coupling, affect network dynamical performance. Specifically, we investigate how bistability range, maximum open-loop gain and switching times of a network with transcriptional positive feedback are affected by additive or multiplicative coupling with another positive or negative feedback loop. We show that a network’s bistability range is positively correlated with its maximum open-loop gain and that both the quantities depend on the sign of the feedback loops and the type of feedback coupling. Moreover, we find that the addition of positive feedback could decrease the bistability range if we control the basal level in the signal-response curves of the two systems. Furthermore, the addition of negative feedback has the capacity to increase the bistability range if its dissociation constant is much lower than that of the positive feedback. We also find that addition of a positive feedback to a bistable network increases robustness of its bistability range, whereas addition of a negative feedback decreases it. Finally, we show that the switching time for a transition from a high to a low steady state increases with the effective fold change in gene regulation. In summary, we show that the effect of coupled feedback loops on the bistability range and switching times depends on the underlying mechanistic details.

Design of a bistable switch to control cellular uptake

“…The AR circuit corresponds to two positive feedback loops, where the internalized metabolite increases its own abundance by speeding up its import and slowing down its consumption. Interlinked positive feedback loops are known to improve the bistability properties in a number of natural networks [32][33][34] and there is evidence rsif.royalsocietypublishing.org J. R. Soc. Interface 12: 20150618 that nature favours bistability through interlinked regulation [2].…”

Importance of Feedback and Feedforward Loops to Adaptive Immune Response Modeling

“…13,14 A complex scenario arises when there is a presence of coupled feedback loops. 5,15 Kinetics in the presence of FFLs can also be drawn in a similar manner, Figure 1c, in which input signal X activates A, A activates B, and an activation or inhibition control of B from X in coherent or incoherent FFL, respectively. FFLs can be generated with different combinations of activation-inhibition pathways and are discussed in more details in refs.…”

“…A negative feedback can speed up the response and can cause overshoot whereas a positive feedback can slow down the response 13, 14. A complex scenario arises when there is a presence of coupled feedback loops 5, 15. Kinetics in the presence of FFLs can also be drawn in a similar manner, Figure 1 c , in which input signal X activates A, A activates B, and an activation or inhibition control of B from X in coherent or incoherent FFL, respectively.…”

What influences selection of native phosphorelay architectures?

“…Nevertheless, the amount of proteins of type SKRR, SKHpt, or SKRRHpt that are found without the remaining operon in genomes is much smaller than that of the same type of proteins that are assembled in operons with the remaining putative cognate proteins of the PR 4 , which indicates that any underestimation of these architectures is likely to be small. Second, the performance landscape of PR can be strongly affected by how its expression is regulated 45,[56][57][58] . Nevertheless, transcriptional regulation occurs on a timescale of tens to hundreds of minutes, while the regulation of phosphorylation levels of the PR occurs on a timescale of minutes and this timescale can also strongly influence the performance of the gene expression regulatory circuit 57,59 .…”