Date Published: May 2, 2019
Publisher: Public Library of Science
Author(s): Lana Descheemaeker, Eveline Peeters, Sophie de Buyl, Jordi Garcia-Ojalvo.
We theoretically study the effects of non-monotonic response curves in genetic auto-regulation by exploring the possible dynamical behaviors for such systems. Our motivation is twofold: we aim at conceiving the simplest genetic circuits for synthetic biology and at understanding the natural auto-regulation of the LrpB protein of the Sulfolobus solfataricus archaeon which exhibits non-monotonicity. We analyzed three toy models, based on mass-action kinetics, with increasing complexity and sought for oscillations and (fast) bistable switching. We performed large parameter scans and sensitivity analyses, and quantified the quality of the oscillators and switches by computing relative volumes in parameter space reproducing the sought dynamical behavior. All single gene systems need finely tuned parameters in order to oscillate, but bistable switches are more robust against parameter changes. We expected non-monotonic switches to be faster than monotonic ones, however solutions combining both auto-activation and repression in the physiological range to obtain fast switches are scarce. Our analysis shows that the Ss-LrpB system can not provide a bistable switch and that robust oscillations are unlikely. Gillespie simulations suggest that the function of the natural Ss-LrpB system is sensing via a spiking behavior, which is in line with the fact that this protein has a metabolic regulatory function and binds to a ligand.
Synthetic biology aims at building an extended toolbox of elementary genetic circuits and efficient designs for assembling them. These building blocks are inspired by electronics. The biological equivalent of many circuits have been built for timekeeping, electronic memory storage, toggle switches, oscillators, cascades, pulse generators, time-delayed circuits, spatial patterning and logic gate behavior [1–6]. In order to construct predictable complex circuits, each building block must itself be predictable. In this work, we searched for the simplest genetic networks consisting of a single gene that produce, at the deterministic level, a dynamical behavior other than a stable steady state, i.e. oscillations or bistable switching. We also assessed the importance of molecular noise by performing Gillespie simulations. Our motivation is twofold. First, conceiving the simplest building blocks with only one gene is of interest to synthetic biology as it can potentially reduce undesired interference with other modules and facilitate the construction of complex circuits based on orthogonal compounds. Second, we want to understand the possible functions that can be fulfilled by single gene circuits. We are in particular interested in the function of the protein Ss-LrpB in the archaeon Sulfolobus solfataricus, both in the natural context and for its potential utility to develop simple building blocks for synthetic biology with Archaea, a territory almost unexplored. The relevance of non-monotonic regulation is broader than the Ss-LrpB system and is of importance for instance for toxin-antitoxin systems [7, 8].
We conclude by a discussion on the possible dynamical behavior of the leucine responsive protein B of the archaeon Sulfolobus solfataricus (Ss-LrpB). This protein regulates itself in a unique way. The regulation site of this protein contains three binding sites to which the protein can bind in dimeric form. The outer sites of this regulation site have the highest affinity and will be occupied before the middle site . Experimental results suggest that transcription is activated when one or both outer sites are occupied. Due to cooperativity the middle site gets bound when the outer sites are occupied and subsequently, DNA undergoes a conformational change and loops on itself. In this configuration the transcription is repressed . The mechanism of unlooping is unknown. Possible manners include unlooping when the proteins in the loop are degraded  or via faster direct unlooping . Both paths are denoted by dashed arrows in Fig 7. The temporal evolution of this system has not yet been observed experimentally, and most parameters have not been measured. As mentioned above, one hypothesis is that the Ss-LrpB system is a (possibly bursty) oscillator.
The question we addressed is the function of non-monotonic auto-regulation. A system with such auto-regulation exists in nature and we therefore assume it should have an advantage over other gene regulatory networks. We seek whether the non-monotonicity could result in dynamics other than a stable steady state, in particular oscillations and bistability. We studied three different single gene networks with increasing complexity that can exhibit non-monotonicity.