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

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.

Given stoichiometric matrix S and a vector of rates f , collecting terms in the system size expansion gives us describing the deterministic rate equations for the system, and a Fokker-Planck equation describing the time evolution of the distribution Π(ξ, t) of the fluctuating components. For the symmetric system, the ODEs governing mean behaviour, arising from Eqn. 1, are: The steady-state solution of these equations then gives our predicted mean values. Multiplying Eqn. 2 through by the appropriate powers of our variables and integrating, we obtain ODEs governing variances and covariances for the symmetric system: Again, the steady-state solution of these equations gives our predictions for the variances and covariances, where ξ 2 A is of particular interest.
The expression for ξ 2 A in the single-pathway model, and for ξ 2 A in the two-pathway model when β s = β d , both have the form For the two-pathway case, γ ≡ β; for the one-pathway case, γ ≡ (β − 4).
Theory-simulation comparison. Fig. S1 shows the agreement between theory and stochastic simulation for parameterisations and models used throughout this study.

Germination propensities.
The experimental data from Ref. [4] takes two forms. First, several replicates of the following experiment were performed. Two sets of 30 seeds of wildtype plants and two sets of 30 seeds of pTaEM:SbNCED mutant plants (increasing ABA levels) are plated. The germination proportion in each set of 30 seeds is recorded after 5 days, obtaining proportions p W T,1 , p W T,2 , p M U,1 , p M U,2 respectively for the two wildtype (WT) and two mutant (MU) sets. We report the (untransformed) mean germination proportion for WT (µ W T = p W T,1 + p W T,2 and MU (µ M U = p M U,1 + p M U,2 ). Next we logit transform the individual germination proportions p •,• using p •,• = log(p •,• /(1 − p •,• )). We then take the (transformed) standard deviation of WT and MU (σ 2 . The statistics we plot are (µ W T , σ W T ), (µ M U , σ M U ). Second, several replicates of the following experiment were performed. ABA levels are measured in 3 sets of 50 wildtype seeds and 3 sets of 50 pTaEM:SbNCED mutant seeds. The mean µ and standard deviation σ of ABA mass per seed are reported. The statistics we plot are µ and the coefficient of variation η = σ/µ.

Dependence on degradation parameters.
In the main text we set δ s = δ d = 1 to allow an intuitive exploration of the system's behaviour. Fig. S2 shows some sampled effects of relaxing this assumption and allowing δ s and δ d to vary independently over orders of magnitude. While a quantitatively diverse range of behaviours is exhibited, an intuitive general trend is seen. Decreasing δ d increases the influence of the ABA degradation pathway, lowering mean ABA levels and increasing noise. Decreasing δ s has the opposite effect, increasing the influence of the synthesis pathway, increasing mean ABA levels and decreasing noise. Increasing δ d or δ s has a comparatively limited effect in many cases; as the other parameter values are constrained to lie on [0, 1], excess degradation of one pathway has limited influence once this pathway provides only a weak contribution to the overall dynamics.