Identification of a bet-hedging network motif generating noise in hormone concentrations and germination propensity in Arabidopsis

Abstract

Plants have evolved to exploit stochasticity to hedge bets and ensure robustness to varying environments between generations. In agriculture, environments are more controlled, and this evolved variability decreases potential yields, posing agronomic and food security challenges. Understanding how plant cells generate and harness noise thus presents options for engineering more uniform crop performance. Here, we use stochastic chemical kinetic modelling to analyse a hormone feedback signalling motif in Arabidopsis thaliana seeds that can generate tunable levels of noise in the hormone ABA, governing germination propensity. The key feature of the motif is simultaneous positive feedback regulation of both ABA production and degradation pathways, allowing tunable noise while retaining a constant mean level. We uncover surprisingly rich behaviour underlying the control of levels of, and noise in, ABA abundance. We obtain approximate analytic solutions for steady-state hormone level means and variances under general conditions, showing that antagonistic self-promoting and self-repressing interactions can together be tuned to induce noise while preserving mean hormone levels. We compare different potential architectures for this 'random output generator' with the motif found in Arabidopsis, and report the requirements for tunable control of noise in each case. We identify interventions that may facilitate large decreases in variability in germination propensity, in particular, the turnover of signalling intermediates and the sensitivity of synthesis and degradation machinery, as potentially valuable crop engineering targets.

Keywords: bet-hedging; cell noise; food security; germination; plant hormones; stochastic processes.

Figure 1.

An antagonistic pair of feedback loops governs hormone levels in Arabidopsis. (a) Synthesis and degradation of the hormone ABA (species A) are modulated by two pathways (involving S and D, respectively) that themselves respond to ABA levels. Throughout this work, we will use parameters β_i to correspond to the strengths of these responses, and Λ_i to correspond to the sensitivity of ABA to these signals. (b) A, S and D are produced and degraded, with levels modulating the rates of these processes. (c) Fluorescence microscopy following Topham et al. [37] identifies cellular localization of members of the S and D pathways in Arabidopsis embryos, showing that they are both present (scaled reflectance >0) in a range of cells (highlighted) at the same developmental stage. The antagonistic feedback loops thus together modulate ABA levels in these cells.

Figure 2.

Hormone levels over time as a function of feedback responses and sensitivities. Behaviour of hormone level A over time, in five stochastic simulations in each panel, as (top) sensitivity Λ and (bottom) response β change. Increasing Λ increases noise monotonically while preserving the mean hormone level; increasing β drives noise levels through a peak before decreasing. (Online version in colour.)

Figure 3.

Noise in hormone levels as a function of β and Λ. Noise η in hormone levels predicted by equation (2.9) as sensitivity Λ and response β change over orders of magnitude. As suggested by figure 2 and shown by equation (2.9), increasing Λ monotonically increases η for a given β (saturating according to equation (2.10), and increasing β drives η through a peak (equation (2.11)). Mean hormone levels are constant at λ/ν throughout this phase plane. (Online version in colour.)

Figure 4.

A general solution for noise under asymmetric interactions provides a roadmap for artificial interventions. (a) Phase portraits for the asymmetric model: behaviour of (i) noise η, (ii) scaled noise η′ and (iii) logarithm of mean level ϕ_A as pairs of parameters are varied. For ϕ_A, colours denote increases (blue) and decreases (red) from the usual λ/ν value. (b) Predicted response of mean hormone level ϕ_A and noise η for a variety of interventions. Each arrow shows the resultant motion in the (ϕ_A, η) plane when, starting from the default initial parametrization (corresponding to the grey ellipse), some parameters are increased or decreased according to the legend. The black line shows .

Figure 5.

Experimental results of increasing β_s. Arrows denote the change in behaviour from wild-type Arabidopsis to a mutant line where a transgenically introduced positive feedback circuit enhances the hormone synthesis pathway via β_s. (a) Absolute ABA levels are generally both increased and harmonized with β_s. (b) Germination propensity (inversely linked to ABA) generally decreases with β_s, with noise in germination propensity also decreasing with β_s, in line with higher, more harmonized ABA levels. (Online version in colour.)

Figure 6.

Behaviour of alternative regulatory motifs with similar structure. (a) The ‘direct feedback’ model, where levels of A directly regulate the production and degradation of A. (b) The ‘single-pathway’ model, where a single species X responds to A levels and influences both synthesis and degradation of A. (c–e) Two pathways are required for noise induction through symmetric regulation. Traces of hormone levels in five stochastic simulations, as in figure 2, for increasing Λ. The two-pathway system (c) allows increasing Λ to induce noise as above; the single-pathway (d) and direct feedback (e) systems show no increased noise with Λ. (f,g) Behaviour of hormone levels under alternative regulatory models. (f) Noise η, scaled noise η′ and logarithm of mean level ϕ_A as Λ_s and Λ_d vary in the ‘direct feedback’ model. Negative feedback alone can drive noise below its usual λ/ν level. (g) Noise, scaled noise and mean level for parameter changes in the ‘single-pathway’ model.