The Arabidopsis dormancy–germination transition is known to be environmentally cued and controlled by the competing hormones abscisic acid (ABA) and gibberellin (GA) produced by the seed. Recently, new molecular details have emerged concerning the propagation of red light through a complex gene regulatory network involving PhyB, PIF1, and RVE1. This network influences the formation of the PIF1-RVE1 complex [1,2]. The PIF1-RVE1 complex is a transcription factor that regulates the production of ABA and GA and helps shift the balance to high concentration of ABA and low concentration of GA, which corresponds to a dormant seed state. This newly discovered gene regulatory network has not been analyzed mathematically. Our analysis shows that this gene regulatory network exhibits switch-like bistability as a function of the red light input and makes a suite of biologically testable predictions concerning seed dormancy and germination in response to the amplitude and periodicity of an oscillatory red light input.
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This work was supported by NSF Grant DMS-1515130.
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A Note on Parameter Values
Many of the dimensional parameters in this model have not been reported in the biological literature, and are for now unknown. However, the nondimensionalized model described by system (5)–(8) has only six parameters that change the steady-state analysis (\(p_2\), \(p_3\), \(p_5\), \(p_6\), \(p_8\), and \(p_9\)). \(p_5\) and \(p_8\) are chosen small relative to the other parameter because they represent leak terms that allow for small amounts of protein to be translated. The parameter set used in the analysis was chosen arbitrarily, as the system exhibits switch-like bistability over large parameter swaths, which can be seen through two-parameter bifurcation diagrams. Figure 3 displays a cusp bifurcation in \(p_2\)-\(p_6\) space. An analogous diagram can be found for \(p_2\) and any other parameter that influences the steady-state analysis. The two-parameter bifurcation in \(p_2\)-\(p_9\) space is shown in Fig. 10.
A Note on Multistability
Given the interlocked nature of the system’s two feedback loops, it is natural to consider the existence of tristability or other more exotic multistable behaviors. However, tristability or other exotic multistability behaviors are not possible in this system. To show this conclusively, consider steady-state equations (9)–(12), which be reduced to a single fourth-degree polynomial in p. A necessary condition for switch-like tristability is the existence of 5 positive roots for some positive parameter regime. However, the steady-state polynomial is only degree 4, which at most can have four positive roots. Therefore, switch-like tristability and other multistable behaviors are not possible.
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FitzGerald, C., Keener, J. Red Light and the Dormancy–Germination Decision in Arabidopsis Seeds. Bull Math Biol 83, 17 (2021). https://doi.org/10.1007/s11538-020-00849-1
- Bifurcation analysis
- Arabidopsis seeds
- Switch-like behavior
- Seed dormancy