Abstract
Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Here, we examine the behavior of a coupled feedback system, the Negative Autoregulated Frustrated bistability motif (NAF). This motif is a combination of two previously explored motifs, the frustrated bistability motif (FBM) and the negative auto regulation motif (NAR), which both can produce oscillations. The NAF motif was previously suggested to govern long term memory formation in animals, and was used as a synthetic oscillator in bacteria. We build a mathematical model to analyze the dynamics of the NAF motif. We show analytically that the NAF motif requires an asymmetry in the strengths of activation and repression links in order to produce oscillations. We show that the effect of time delays in eukaryotic cells, originating from mRNA export and protein import, are negligible in this system. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes.
Highlights
Oscillators and switches are important elements of regulation in biological systems
In these simulations the circuits could produce oscillatory expression of components at a wide range of parameters, and allowed engineering of the characteristics of oscillations. These minimal models assumed a homogeneous, single-compartment intracellular space and operated with a single step protein production process. These assumptions are generally used in models of prokaryotic transcriptional regulation, where transcription and translation occur in the same space and mRNA half-lives are typically short compared to cell division time[11]
When we compare the dynamics of the Negative Autoregulated Frustrated bistability motif (NAF) motif to the dynamics of the frustrated bistability motif (FBM), we find that the parameter space where the NAF motif oscillates is substantially smaller (Fig. 6B)
Summary
Oscillators and switches are important elements of regulation in biological systems. These are composed of coupling negative feedback loops, which cause oscillations when delayed, and positive feedback loops, which lead to memory formation. Based on the reported protein and mRNA half-lives in eukaryotic cells, we find that even though the NAF motif possesses the ability for oscillations, it mostly promotes constant protein expression at the biologically relevant parameter regimes Many cellular functions, such as regulation of metabolism, decision making, memory, biological rhythm, and homeostasis are emerging from combinations of feedback loops[1]. In order to understand the effect of the time delay and the long mRNA half life, we constructed a more detailed mathematical model for the NAF motif, a circuit composed of coupled positive and negative feedback loops (Fig. 1). The vast majority of transcription factors do not meet these requirements
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