Abstract
An epigenetic regulatory network that influences transgenerational inheritance of a heat-altered phenotype was recently discovered in Arabidopsis. Our analysis shows that transgenerational inheritance of the heat-altered phenotype operates in a switch-like manner and can be turned on or off as a function of heat. We also show that trans-acting small interfering RNAs act as an “inverse amplifier” of HTT5, the protein that controls the heat-altered phenotype by a currently unknown mechanism. Our analysis uses the resultant to find an analytic expression for a cusp curve in parameter space and to find a parameter bound on switch-like behavior.
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This work was supported by NSF DMS # 1515130 and the BioFire Diagnostics Fellowship.
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Appendix A
Appendix A
1.1 A.1 Software Used
Figure 2 is plotted using MATLAB 2020a. Figures 3, 4, 5, 6 and 7 are created using XPP AUTO (version 8.1) and plotted using Ting-Hao Hsu’s MATLAB interface (available at http://www.math.pitt.edu/~bard/xpp/xpp.html) using MATLAB 2017b.
1.2 A.2 Nondimensionalization Details
1.3 A.3 Figures
See Fig. 7.
The HSFA2 and SGIP1 steady-state solutions of system (22)–(26) as a function of \(p_{\text {heat}}\), the dimensionless heat-dependent production rate of nondimensional HSFA2. Red and black curves represent stable and unstable solutions, respectively. The nondimensional concentration of HSFA2 and SGIP1 exhibits bistable switch-like behavior as a function of \(p_{\text {heat}}\). All other parameter values used can be found in Table 2. (Color figure online)
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FitzGerald, C., Keener, J. . Bifurcation Analysis of a Heat-Sensitive Epigenetic Regulatory Network. Bull Math Biol 84, 14 (2022). https://doi.org/10.1007/s11538-021-00960-x
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DOI: https://doi.org/10.1007/s11538-021-00960-x