Robust and Tunable Toggle Switches with Interlocked Positive Feedback Loops
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Robust and Tunable Toggle Switches with Interlocked Positive Feedback Loops Cuong Nguyen Physics Department, Chungbuk National University, Cheongju, Chungbuk 361-763, Korea and Vinmec Hightech Center, Vinmec Healthcare System, Hanoi 10000, Vietnam
Jae Kyoung Kim Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 34131, Korea
Seung Kee Han∗ Physics Department, Chungbuk National University, Cheongju, Chungbuk 361-763, Korea (Received 30 June 2020; revised 12 July 2020; accepted 20 July 2020) Toggle switches are widely used to make critical all-or-none decisions such as cell differentiation or apoptosis. While the toggle switch can be generated by using a single-type positive feedback loop (PFL), a natural toggle switch frequently emerges from interlocked PFLs composed of two different types of PFLs: one with two mutually activated units and the other with two mutually inhibiting units. To investigate the advantage of the interlocked PFL over the single type of PFL, here, we carefully analyze how the interlocked PFLs generate bistability and thus the toggle switch. We find that in the interlocked PFLs, mutual activation and mutual inhibition cooperate to generate a robust merged bistability. Interestingly, we also find that turning-on and turning-off of the merged bistability can be flexibly controlled by using the balance between the strengths of two competing PFLs. We illustrate the role of such robust and tunable joint toggle switches of the interlocked PFLs in the DNA damage checkpoint control of G2/M transition. Our work describes how natural toggle switches achieve two critical properties, robustness and tunability, simultaneously by merging opposite types of PFLs. Keywords: Feedback loops, Toggle switch, Interlocking, Bistability DOI: 10.3938/jkps.77.323
I. INTRODUCTION
Positive feedback loops (PFLs) composed of genes, proteins, and metabolites are an ubiquitous network motif in various regulation networks of biological systems: the transcriptional regulation network [1], the signal transduction pathway [2], and the cell cycle regulatory networks [3–6]. The PFLs with strong nonlinearity are responsible for bistability, creating a discontinuous output response from a continuous input [7]. They are used as toggle switches for making an all-or-none decision [8, 9] in various situations, including the lambda phage lysis-lysogeny switch [10], the cell-cycle transitions in eukaryotic cells [3–6], and cell differentiation [11]. PFLs can be divided into two groups [2,8,12]: a selfenhancing PFL (ePFL) composed of two mutually activating units and a self-recovering PFL (rPFL) containing two mutually inactivating units. They produce different ∗ E-mail:
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pISSN:0374-4884/eISSN:1976-8524
types of bistability: self-enhancement and self-recovery. Specifically, in the ePFL, the enhancement of the low state via mutual activation leads to a stiff transition from the lower OFF state to the upper ON state. On the other hand, the rPFL generates such a stiff transition by re
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