2.1. Strigolactone-mediated BRC1 expression inhibits bud activation in 1-node explants

The dual action of strigolactone on BRC1 and PIN1 provides an opportunity to assess the relationship between these two modes of bud regulation. Strigolactone signaling leads to the degradation of SMXL678 proteins [12,13,15], such that the smxl678 triple mutant has constitutively active strigolactone signaling, with high levels of BRC1 expression and PIN1 removal from the plasma membrane [14] (Fig 2A).

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Fig 2. The inhibition of smxl678 buds is rescued by brc1brc2 in 1-node but not in 2-node explants.

(A) PIN1 removal and BRC1 expression phenotype in Col-0, brc1brc2, smxl678, and brc1brc2smxl678. (B) Bud length on 1-node explants measured daily for 10 days. Active buds (blue) are defined as those with a maximum growth rate > 2.5 mm/day, n = 41–72. (C) Number of lag days (number of days before growth rate > 2.5 mm/day) for active buds, n = 41–71 (D) Mitchison plots of top vs. bottom bud lengths on 2-node explants, measured daily for 10 days. The final length of buds is shown with a blue dot, n = 33–67. (E) Percentage of active explants (explants with at least one active bud) from three experimental repeats (where only one percentage is indicated, it is the same across the repeats). Below, relative growth index (RGI) of active explants at day 10. The RGI is defined as the length of the longest bud divided by the total length of both buds. The orange dot indicates the mean, n = 15–58). Letters represent statistically significant differences for p < 0.05 from a multi-level model of three experimental replicates with pairwise comparisons and Bonferroni correction. Data and analysis underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g002

To test the impact of BRC1 on bud outgrowth dynamics, we compared bud behaviors on 1-node explants of Col-0, brc1brc2, smxl678, and brc1brc2 smxl678. We use the brc1brc2 double mutant throughout our work because, although a substantial body of evidence suggests that BRC1 plays a dominant role, there is likely some redundancy between BRC1 and BRC2 [4,5,19]. Throughout, we refer to the effect of BRC1, but this may include an effect of BRC2. Buds were defined as active if their growth rate reached at least 2.5 mm/day. Unlike on Col-0 and brc1brc2 explants, smxl678 buds did not activate within the timeframe of our experiment (Fig 2B). However, their activation was fully restored in the brc1brc2smxl678 quintuple mutant, suggesting that the lack of growth of smxl678 buds in 1-node assays is due primarily to high levels of BRC1 expression. We calculated the duration of the initial slow-growing lag phase, defined as the number of days before bud growth rate exceeds 2.5 mm/day (Fig 2C). As previously reported, brc1brc2 mutants have a shorter lag phase than Col-0 [8], which was also the case for brc1brc2smxl678 (Fig 2C). Therefore with respect to early bud activation, brc1brc2 is fully epistatic to smxl678 in this assay. Interestingly, branches on brc1brc2smxl678 explants consistently stopped growing earlier than Col-0 or brc1brc2 branches (Fig 2B), suggesting that BRC1-independent strigolactone signaling influences sustained bud growth.

2.2. Strigolactone-mediated regulation of bud-bud competition in 2-node explants is due to BRC1-dependent and -independent effects

To explore the role of BRC1 in mediating competition between buds, we assessed the behavior of buds on 2-node explants of Col-0, brc1brc2, smxl678, and brc1brc2smxl678. The growth of buds on each explant is shown on Mitchison plots (introduced in Fig 1C) (Fig 2D). We use the relative growth index (RGI) of active explants (defined as explants with at least one active bud) to compare bud behavior between genotypes. The RGI is the length of the longest bud as a ratio of the total length of both buds. An RGI of 0.5 indicates both buds growing equally, while an RGI of 1 indicates one bud dominating the other.

Col-0 explants exhibited all three possible outcomes for active explants (introduced in Fig 1C), with either one or both buds activating in each explant (Fig 2D). In brc1brc2 explants, both buds activated on all explants (Fig 2D), resulting in a lower mean RGI than for Col-0, although here this difference is not statistically significant (Fig 2E). This is consistent with previous results [22,52], and with the high branching of brc1brc2 plants [4]. While smxl678 buds did not activate in 1-node explants, interestingly one bud did activate in a substantial number of 2-node explants (Fig 2D), resulting in very high RGIs (Fig 2E).

Importantly, unlike for 1-node explants (Fig 2B), brc1brc2 was not fully epistatic to smxl678 in 2-node explants, but rather in brc1brc2smxl678 explants, one bud often dominated the other, resulting in an RGI intermediate between that of brc1brc2 and smxl678 (Fig 2D and 2E). As in 1-node explants, brc1brc2smxl678 active apices stopped growing early. This was often followed by activation of the other bud, with this growth pattern clearly visible on the Mitchison plots (Fig 2D), consistent with the ability of one bud to inhibit the other in this genotype. Taken together, these results indicate that the high RGI of smxl678 is due to a combination of BRC1-dependent and -independent effects of strigolactone-mediated bud inhibition.

2.3. Incorporating BRC1 into a canalization-based model of bud-bud competition

Bud-bud competition is hypothesized to be based on competitive auxin transport canalization into the stem [25,32,45,53], and we previously hypothesized that the lag phase of bud growth corresponds to the time during which canalized auxin transport is established [8]. Given this, the impact of brc1brc2 on the length of the lag phase and on the growth outcomes of buds in 2-node explants suggests that BRC1 might influence auxin efflux from buds during the establishment of auxin transport canalization. The auxin transport network, and hence the developmental processes it regulates such as shoot branching, are heavily feedback-driven, making their dynamics difficult to intuit [54,55]. Mathematical modelling is a powerful tool to test which interactions can account for observed phenomena [56–58]. To test whether the hypothesis that BRC1 influences the dynamics of auxin transport canalization can account for the behaviors we observe, we built a mathematical model of canalization-based bud-bud competition in 2-node explants.

The model consists of two self-activating and mutually-inhibiting buds (Fig 3A). It preserves the most conceptually important aspects of the auxin transport canalization model for shoot branching from Prusinkiewicz and colleagues [25]. These include a hysteretic bistable switch in bud activation caused by flux-regulated polar PIN accumulation dictated by a Hill function, combined with linear PIN removal. We simplified the formulation of auxin flux by using a formulation for the ratio of auxin influx to efflux [59]. We also combine parameters referring to PINs, auxin concentration, and auxin diffusion, into one efflux term (Mathematical appendix). This was possible because we abstracted the stem section joining the two buds, and assumed that buds have an equal and constant auxin concentration over time, given evidence of homeostatic feedback on auxin synthesis [26]. We also abstracted the top and bottom bud positions, representing the explant as symmetrical. We obtain the following formulation for the efflux of auxin, E and F, out of the top and bottom bud, respectively (Fig 3B):

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Fig 3. Branching behaviors of 2-node explants can be captured by a model with self-activating and mutually-inhibiting buds.

(A) and (B) Model conceptualization and mathematical formulation. The interaction between two buds in a 2-node explant can be considered as a set of self-activating and mutually-inhibiting feedbacks on auxin efflux. Each bud promotes its own auxin efflux and inhibits efflux from the other bud. The auxin efflux E and F from the top and bottom bud, respectively, is influenced by three components (i) a basal rate of auxin efflux v0, (ii) a Hill function which creates a positive feedback on auxin efflux, where v sets the maximum rate of auxin efflux, S the strength of auxin efflux, K the Hill saturation coefficient, n the degree of non-linearity of the Hill function, D the strength of the mutual inhibition between the auxin efflux of the two buds, and (iii) a linear decrease in auxin efflux, the strength of which is set by µ. E and F influence bud lengths N and M, respectively. The relationship between auxin efflux and growth rate is a Hill function, where m influences the degree of nonlinearity, and Q is the saturation coefficient. (C) Steady state growth rate as a function of the steady state of auxin efflux, for different values of Q and m. Three grey vertical lines mark three steady states of auxin efflux at 0.25, 0.5, and 0.75. (D) and (E) Three stochastic simulations illustrating the model behaviors. Each set of simulations is represented with a different color. (F) Deterministic simulation showing the change in auxin efflux E over time for 5 different values of v0: 0.01, 0.03, 0.05, 0.07, and 0.09. Scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g003

The change in auxin efflux is described by: (i) v0, a basal rate of efflux, which corresponds to non-polar auxin efflux of auxin out of the bud and depends on auxin levels, auxin transport activity, and auxin diffusion; (ii) a Hill function that represents the positive feedback of auxin efflux on itself, mirroring previous models of canalization, with v as the maximum rate of efflux for the Hill function, S the efficiency of feedback-driven auxin efflux, n the Hill exponent that influences the degree of nonlinearity in the feedback, and K a threshold parameter, and (iii) µ, a linear decrease in efflux, which relates to both the removal of PINs from the plasma membrane and the degradation of auxin. The auxin efflux from one bud, conceptually contributing to the auxin concentration in the stem, dampens its own auxin efflux and that of the other bud at a strength that is proportional to D and proportional to the sink strength of the main stem, which is determined by the sum of auxin efflux E and F from each bud. This captures the source/sink dynamics between the buds and the main stem.

To model bud growth rate, we postulate a relationship between growth and bud auxin efflux, captured by another Hill function:

N and M are the length of the top and bottom bud, respectively. Q is the Hill saturation coefficient and m is the Hill exponent that influences the degree of non-linearity between auxin efflux and growth rate (Fig 3B). This relationship is informed by our previous analysis which suggested a positive relationship between auxin transport and growth rate in 1-node explants [8], though in some cases buds can grow rapidly with low steady state levels of auxin transport, for example in brc1brc2smxl678 buds [22; Fig 2]. We therefore chose a parameter range where changes in steady state auxin efflux did not consistently cause a large change in growth rate (Fig 3C, dark blue).

To represent the initial dormancy of buds in 2-node explants, simulated buds were assigned equal very low starting values of auxin efflux. For simulations with relevant parameters, the positive feedback on auxin efflux increases the auxin efflux out of both buds. Without stochasticity, both buds switch to high auxin export in all simulations. However, if the positive feedback on auxin efflux exhibits some stochasticity, both buds initially increase their efflux, but one bud may gain a small advantage in its auxin efflux, which is amplified by the positive feedback, enabling one bud to establish canalized auxin export first, and to inhibit the canalization of the other bud (Fig 3D and 3E). Given the known correlation between auxin transport and sustained bud activity [25,30,31,33–35], and our previous hypothesis that the slow-growing lag phase corresponds to the time when buds establish canalized auxin transport [8], we chose parameters where the switch from slow to rapid growth coincides with an increase in auxin efflux (Fig 3D). This also entailed that inhibited buds, which export low auxin, exhibit little to no growth, consistent with experimental observations (Fig 3D and 3E) [45,8,60].

We next considered how to represent, in the model, the action of strigolactone on both PIN1 removal from the plasma membrane and BRC1 expression. For the former, we postulated in a previous model that the parameter μ can be conceptualized as PIN1 removal (Fig 3A and 3B), such that an increase in μ models strigolactone-mediated PIN1 removal from the plasma membrane [25,49,51]. To represent BRC1, we considered that BRC1 influences the length of the lag phase, which we hypothesize corresponds to the time of canalization establishment [8], and does not influence levels of bulk auxin transport through stem sections [61]. Given this, we assessed which parameters affect the timing of the switch to high auxin efflux during canalization, but not the steady state levels of auxin efflux. Both parameters v0 and K meet these criteria (Figs 3F and S1). We chose to focus on v0, influenced by our previous observations that mutation in the ABCB19 auxin efflux protein can partially suppress branching in brc1brc2 mutants, and ABCB19 plausibly contributes to v0 [52]. In addition, BRC1 may affect auxin homeostasis by transcriptional regulation of GH3 activity [18]. This could reduce auxin efflux in buds with high BRC1 expression, making it harder for them to establish canalized auxin transport. Taken together, we hypothesize that the dual action of strigolactone via PIN1 removal and BRC1 up-regulation can be represented by a simultaneous increase in μ and decrease in v0.

We identified a region of parameter space where the range of bud activation behaviors in the model match those in our experimental data, and where the dynamics of bud activation capture the basic properties described above. A range of (v0, µ) slices deliver these core behaviors (S2A and S2B Fig). After systematically exploring parameter space (S2 and S3 Figs), we chose one (v0, µ) slice for detailed analysis.

2.4. The model captures bud growth outcomes for a wide range of strigolactone-related genotypes and treatments

Strigolactone triggers PIN1 removal from the plasma membrane and promotes BRC1 transcription, represented in the model by parameters µ and v0, respectively. To determine whether appropriate changes in v0 and µ were sufficient to capture the effects of relevant strigolactone mutations and treatments, we compared the behavior of buds on 2-node explants with cognate changes in v0 and/or µ in the selected (v0, µ) slice, with all other parameters held constant.

Mitchison plots of bud measurements from experiments show that genotypes and treatments with variation in PIN1 removal and/or BRC1 expression, exhibit variation in the relative proportion of explants where two versus only one bud activates (Fig 4A). In the strigolactone receptor mutant, d14, and in the brc1brc2 mutant, both buds activate on all explants (Fig 4A, [52]). In Col-0 explants, either one or both buds grow (Fig 4A). Basal supply of the synthetic strigolactone rac-GR24 (hereafter GR24) or the smxl678 background, a constitutive strigolactone signaling triple mutant, increases the level of competition between buds, increasing the frequency with which only one bud activates [51]. A qualitatively similar effect is seen with GR24 application and smxl678 mutation in a brc1brc2 mutant background, in which strigolactone is predicted to affect PIN1 removal from the plasma membrane and not BRC1 expression (Fig 4A).

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Fig 4. Variation in two model parameters, representing BRC1 expression and PIN1 removal, captures variation in bud growth outcomes in 2-node explants for a range of genotypes and treatments.

(A) Mitchison plots with traces colored by growth outcome (yellow-both bud active, blue-one bud active), across genotypes and treatments with known effects on BRC1 expression and/or PIN1 removal. Buds were measured daily for 10−12 days, except smxl678 which was measured for 19 days due to its slow bud activation, n = 33–94. (B) (i) stochastic color map showing the change in growth outcomes across one (v0, μ) slice of parameter space, made from a grid of 159 × 159 (v0, μ) parameter combinations. The values of the other parameters remain constant. Each pixel represents the bud growth outcome for a combination of (v0, µ) values. Black boundaries distinguish regions with a different number and/or value of stable steady states. In regions with two possible behaviors (both buds growing (yellow) or only one bud growing (blue) in region 2; only one bud growing or neither bud growing (red) in region 4), the pixel intensity is calculated based on the relative occurrence of each outcome, obtained from 50 stochastic simulations. (ii) First step of the data-fitting process for 2-node data from seven known lines with variations in PIN1 removal and/or BRC1 expression, mapped as variations in μ and/or v0, respectively. For each genotype/treatment, there is a distribution of points in region 2 (tristable region) where the frequency of bud growth outcomes in the data matches the model. This distribution is superimposed onto the color map from panel (i). The distribution for each genotype/treatment is plotted in a different color, indicated next to the label for each genotype/treatment, and these colors do not relate to the ones used to categorize the bud growth outcome in (i). (iii) Superimposed dark grey horizontal and vertical bars were positioned based on experimental evidence for BRC1 expression and PIN1 removal in each genetic background/treatment, which constrained the position of each genotype/treatment in parameter space. A colored dot was placed at the intersection of these parameter-constraining bars to assign parameters to each mutant/treatment. (iv) Same color map as in panel (i), now with these locations of the genotypes and treatments of interest across the (v0, μ) slice. (C) Simulated Mitchison plots of genotypes and treatments with variation in v0 and µ, the values of which were assigned in panel B, n = 50. Traces are colored according to their growth outcome. Simulations were run for 120 time steps for smxl678 parameters and 80 for the others. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g004

To test whether our experimental data in Fig 4A can be reproduced in the model via changes in v0 and μ only, we mapped our experimental data onto the selected (v0, μ) slice of parameter space (Fig 4B (i)). Each pixel in the figure represents the modelled bud growth outcome at a given combination of v0 and μ parameter values. Buds are described as active if they achieve canalized auxin export. The pixel color quantitatively represents the outcomes: (i) both buds growing (yellow), (ii) one bud growing (blue), and (iii) neither bud growing (red). The black lines describe the boundaries between areas of parameter space that have a different number of possible outcomes (i.e. a different number of stable steady states). In zone 1 both buds always grow. Zone 2 has two possible behaviors, with either one bud growing or both. The proportion of simulations with both buds growing versus one bud growing varies within zone 2. To reflect this shifting probability distribution, the pixel intensity is assigned as the ratio of outcomes from 50 stochastic simulations at each point in parameter space. The only behavior in zone 3 is one bud growing. In zone 4, either one bud grows, neither bud grows, or both buds grow, though for the starting values and timeframe of our simulations, the most common outcome is no buds growing, with occasionally one bud activating. The resulting (v0, μ) map of parameter space shows that v0 and μ have similar effects but with opposite polarities, with increasing values of μ and reducing values of v0 shifting the outcome from both buds growing, through to only one bud, and eventually fully inhibited explants.

We calculated the relative frequency of the various bud growth outcomes in the data. On the color map, there is a distribution of points, broadly across the tristable region (zone 2), where the frequency of bud growth outcomes in the data is the same as in the model. We plotted this distribution for each genotype/treatment (Fig 4B (ii)). Given we represent PIN1 removal as μ and hypothesize that BRC1 expression can be represented as v0, we could constrain the placement of each genotype/treatment by considering their known phenotypes in terms of PIN1 accumulation and BRC1 expression levels: (i) Under our hypothesis that v0, the basal rate of auxin efflux, is negatively regulated by BRC1, the brc1brc2 mutant must have a higher value of v0 than Col-0, and this high value will be common to all brc1brc2 lines. (ii) PIN1:GFP membrane accumulation is the same in Col-0 and brc1brc2 [11], and therefore their value of μ is likely also the same. (iii) Applying the synthetic strigolactone GR24 triggers the removal of PIN1 from the membrane and increases BRC1 expression [4,10,11,49], so Col-0 + GR24 must have lower v0 and higher μ than Col-0. (iv) Applying GR24 is assumed to increase μ by the same amount in Col-0 and brc1brc2, so Col-0 + GR24 and brc1brc2 + GR24 are assumed to be on the same vertical line. (v) smxl678 and brc1brc2smxl678 have the same high PIN1 removal, such that they should be located on the same vertical line at a higher μ value than Col-0. (vi) Given its constitutive active strigolactone signaling, smxl678 is modelled as more effective than GR24 treatment at increasing μ and decreasing v0.

These relationships create three vertical bars determining a value of μ for (i) Col-0 and brc1brc2, (ii) GR24 treatments, and (iii) smxl678 backgrounds. In addition, three horizontal bars represent (i) the value of v0 in brc1brc2 mutant backgrounds, (ii) in Col-0, and (iii) after GR24 application, with smxl678 plotted at an even lower v0 value. Given these relationships, the values of v0 and μ that best fit the pixel distribution are shown by the dark grey bars in Fig 4B (iii). The genotypes and treatments were placed at the intersection of these bars, each shown with a colored dot. The strigolactone receptor mutant, d14, has very low BRC1 expression and low PIN1 removal [11], so was placed at the same low v0 value as the brc1brc2 mutants, with a lower μ value than Col-0 (Fig 4B (iii)).

Overall, the location of each genotype/treatment is on or near the distribution of points where the bud growth outcomes in the experimental data match those of the model. The resulting color map in Fig 4B (iv) shows the narrowed-down regions of the genotypes and treatments in parameter space. The simulations that generate these bud growth outcomes give similar Mitchison plots (Fig 4C) to the experimental data (Fig 4A), and produce associated bud growth dynamics, which we next compared to our experimental data.

2.5. The model captures the effects of strigolactone on the duration of the lag phase during bud activation

We previously characterized bud activation as occurring in two phases: a slow-growing lag phase followed by a period of rapid outgrowth [8] (Fig 1C). The parameters chosen to simulate our genotypes and treatments based on bud growth outcomes (Fig 4B) provide predictions about the length of the lag phase and the maximum growth rate of active buds in each genotype/treatment for these parameters.

To test these predictions, we produced a heatmap for the duration of the lag phase in the same (v0, μ) slice of parameter space used to map the genotypes/treatments in Fig 4B (Fig 5A). The genotypes and treatments in our experimental dataset were assigned the same v0 and μ values as in Fig 4B. The number of lag days for each set of (v0, µ) values are plotted in Fig 5B. In our model, a combined increase in µ and decrease in v0 progressively increase the length of the lag phase across d14, Col-0, Col-0 + GR24, and smxl678, which spans increasing strength in strigolactone signaling (Fig 5A and 5B, blue data points). This successfully captures the changes in our experimental dataset, where increasing BRC1 expression and PIN1 removal together progressively delay bud activation (Fig 5C, blue data points).

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Fig 5. Variation in two model parameters, representing BRC1 expression and PIN1 removal, captures variation in the duration of the bud activation lag phase on 2-node explants for a range of genotypes and treatments.

(A) Heatmap of the number of lag time steps for 25,281 combinations of parameters v0 and μ (159 × 159 grid). The pixel color intensity reflects the mean number of lag days from 50 simulations run for 120 time steps. The genotypes/treatments are assigned the same parameter values as in Fig 4B (iii and iv). (B) Boxplot of the simulated number of lag time steps calculated for each of the genotypes indicated in panel A. The number of lag times steps was calculated from 100 simulations run for 120 time steps. (C) Number of lag days calculated as the number of days before growth rate > 2.5 mm/day for the same dataset as Fig 4A. In the left hand plot, buds were measured for 12 days, except smxl678 which was measured for 19 days. In the right hand plot, all buds were measured for 10 days, n = 12–72. Below, the percentage of active explants, defined as explants with at least one active bud, n = 43–74. The series of genotypes/treatment with a gradual increase in BRC1/v0 and PIN1 removal/µ are shown in light blue. Data and simulations are shown for the longest bud of active explants. Letters represent statistically significant differences for p < 0.05 from a multi-level model with pairwise comparisons and Bonferroni correction. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g005

In the model, an increase in μ alone causes only a small delay in bud activation (Fig 5B, black data points). This matches our experimental observation that increasing PIN1 removal in a brc1brc2 mutant background, either through application of GR24, or in a smxl678 background, has respectively no or a small significant effect on the number of lag days (Fig 5C, black data points). Overall, the model captures qualitatively the observed trends in number of lag days between genotypes and treatments. It is notable that we observe significant within and between-experiment variation in the timing of bud activation in smxl678 lines (if bud activation is even observed within the timeframe of our experiment) (Figs 2E and 5C). Interestingly, simulated lag days at very low v0, representing smxl678, are sensitive to small changes in parameter values (S4A and S4B Fig). Trends across our other genotypes/treatments are robust to such changes (S4A and S4B Fig).

2.6. The model captures the effects of strigolactone on bud maximum growth rate

After the lag phase, buds switch into a period of rapid outgrowth [8] (Fig 1C), which can be quantified by measuring the maximum growth rate. We generated a heatmap of the maximum growth rate across the previously used (v0, μ) slice (Fig 6A). The parameter μ has a stronger influence on the maximum growth rate than v0, because it has a stronger influence on the steady state levels of auxin efflux (S1 Fig), which in the model, determines the growth rate of active buds (Fig 3C). The plots of maximum growth rate for each simulated genotype/treatment show the expected decrease in maximum growth rate with increasing µ with or without simultaneous changes in v0 (Fig 6B). These trends are robust to small changes in parameter values (S4B and S4C Fig).

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Fig 6. Variation in two model parameters, representing BRC1 expression and PIN1 removal, captures variation in the maximum growth rate of buds on 2-node explants for a range of genotypes and treatments.

(A) Heatmap of the maximum growth rate for 25,281 combinations of parameters v0 and μ (159 × 159 grid). The pixel color intensity reflects the mean maximum growth rate from 50 simulations run over 120 time steps. The genotypes/treatments are assigned the same parameter values as in Fig 4B (iii and iv). (B) Simulated maximum growth rate for each of the genotypes indicated in panel A. The maximum growth rate was calculated from 100 simulations run for 120 time steps. (C) maximum growth rate calculated from the same dataset as Fig 4A. In the left-hand plot, buds were measured for 12 days, except smxl678 which was measured for 19 days. In the right-hand plot, all buds were measured for 10 days, n = 12–72. The series of genotypes/treatment with a gradual increase in BRC1/v0 and PIN1 removal/µ are shown in light blue. Data and simulations are shown for the longest bud of active explants. Letters represent statistically significant differences for p < 0.05 from a multi-level model with pairwise comparisons and Bonferroni correction. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g006

To test whether this reflects the experimentally observed changes in maximum growth rate, we calculated the maximum growth rate across the same group of genotypes and treatments used previously (Fig 6C). Simultaneously increasing BRC1 expression and PIN1 removal lowers the maximum growth rate, as can be seen across the d14, Col-0, Col-0 + GR24 strigolactone signaling gradient (Fig 6C, blue data points). One discrepancy between the model and our experiments is that brc1brc2smxl678 had the same maximum growth rate as Col-0 in the experimental data, while the model predicts a lower maximum growth rate (Fig 6B and 6C). The lower maximum growth rate was observed when brc1brc2 2-node explants are treated with GR24 (Fig 6B and 6C), indicating the model better captures the maximum growth rate of GR24 treatment than that of a smxl678 background.

2.7. The middle region of the hydrophilic loop is key for strigolactone-mediated effects on PIN1 but not on BRC1

We have shown that changes in v0 and μ can capture a wide range of experimentally observed bud growth characteristics across different genotypes and treatments with altered levels of BRC1 expression and/or PIN1 accumulation. While we can use the brc1brc2 mutant to test the BRC1-independent effects of strigolactone on shoot branching, testing the PIN1-independent effects has so far not been possible, due to the pleiotropy of the pin1 mutant phenotype, which includes failure to form lateral organs and axillary meristems. To overcome this limitation, we sought to generate a strigolactone-insensitive PIN1 by identifying the region of PIN1 responsible for its strigolactone sensitivity and replacing it with the cognate region from a strigolactone-insensitive PIN family member. Canonical PIN proteins consist of 10 helices functioning as 2 groups of 5 transmembrane domains, separated by a hydrophilic loop exposed to the cytosolic environment. The hydrophilic loop contains several phosphosites which are targeted by kinases to regulate PIN recycling, transport activity, and polarization [62,63], thereby influencing the properties of the auxin transport network. We hypothesized that the hydrophilic loop was a likely target for strigolactone-mediated PIN1 endocytosis.

To test this hypothesis, we performed domain swaps between sections of the PIN1 hydrophilic loop and equivalent regions of PIN3, which is insensitive to strigolactone (Fig 7A, [52]). In particular, we swapped the middle region of the loop, which we termed L2, spanning residues 253–364 of PIN1. To assess the strigolactone sensitivity of the domain-swap constructs, we quantified the effect of GR24 on the accumulation of the chimeric PINs at the plasma membrane of xylem parenchyma cells. Transverse stem sections were incubated in 5 μM GR24 or mock treatment for 6 h before imaging. As expected, GR24 treatment reduced the accumulation of PIN1:GFP at the plasma membrane but did not affect that of PIN3. The fluorescence intensity of the PIN1::PIN3-PIN1_L2:GFP construct, i.e., GFP-tagged PIN3 with the middle region of PIN1 driven from the PIN1 promoter, was lower in the GR24 treatment than in mock treated stems, indicating that it is strigolactone sensitive. We named this construct STRIGOLACTONE SENSITIVE PIN3 (SSP3). Conversely, the fluorescence intensity of PIN1::PIN1-PIN3_L2:GFP, i.e. GFP-tagged PIN1 with the middle region of the PIN3 loop, was the same in mock and GR24 treatments, indicating that this construct has reduced strigolactone sensitivity compared to native PIN1 (Fig 7A and 7B). We named it STRIGOLACTONE INSENSITIVE PIN1 (SIP1). Overall, these results suggest that the L2 region of the PIN1 loop is necessary and sufficient for sensitivity to strigolactone-mediated removal from the plasma membrane.

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Fig 7. The middle region of the PIN1 hydrophilic loop confers strigolactone sensitivity.

(A) Fluorescence intensity of basal plasma membranes of xylem parenchyma cells of stems expressing GFP-tagged PIN variants after 6 h mock treatment or treatment with 5 µM GR24. For each stem, the mean fluorescence intensity represents the mean of the 5 brightest membranes for that stem, n = 14−24. (B) Fluorescence intensity of basal plasma membranes of xylem parenchyma cells for stems expressing GFP-tagged PIN variants of each genotype. For each stem, the mean fluorescence intensity represents the mean of the 5 brightest membranes for that stem, n = 28−37. (C) Representative images for dataset presented in panel B. PIN1:GFP visible in green and chlorophyll autofluorescence in magenta. (D) Bulk stem auxin transport in basal inflorescence stem internodes of plants at terminal flowering for the genotypes indicated. Transport was determined as accumulation of radiolabeled auxin in the basal 5 mm of 15 mm stem segments after 16 h incubation with apical 22 nM 3H-IAA, n = 56−68. (E) Relative expression of BRC1 as measured by qRT-PCR in Col-0, SIP1pin1, smxl678, and SIP1pin1smxl678 in small buds (>2.5 mm, presumed inactive) and big buds (<5 mm, presumed active). Buds were harvested from cauline nodes of whole Arabidopsis plants. Each point represents a biological replicate, with the larger point and bar, representing the mean and associated standard error. Each biological replicate corresponds to the expression level measured in at least 10 pooled buds. Statistical comparisons were made on log transformed data, using two-way ANOVA with Bonferroni correction. In all panels, stars or different letters indicate statistically significant differences at p < 0.05 from custom contrasts or pairwise comparison, respectively. Unless otherwise stated, statistical analysis involved a multi-level model with Bonferroni corrections. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g007

Crossing SIP1 into the pin1 mutant background rescued the formation of leaves, axillary buds and flowers (S5A Fig). To assess the shoot branching phenotype conferred by SIP1pin1, we quantified branching in plants grown to terminal flowering in long day conditions (S5B and S5C Fig). SIP1 confers a modest increase in branching in both the pin1 and smxl678pin1 backgrounds, consistent with its strigolactone resistance. However, branching was not significantly increased in the brc1brc2 background, such that the combination of brc1brc2 with SIP1 was unable to phenocopy the full branching phenotype of the d14 strigolactone receptor mutant.

To assess further the effect of substituting PIN1 L2 for PIN3 L2, we quantified its accumulation on the plasma membrane of xylem parenchyma cells in transverse stem sections in several genetic backgrounds. The fluorescence intensity of SIP1 on SIP1pin1 membranes was higher than that of PIN1:GFP in a pin1 background, and its accumulation was not significantly reduced in the pin1smxl678 background, which has very low accumulation of PIN1:GFP, even with the inclusion of max2, to which smxl678 fully epistatic (Fig 7B and 7C) [14]. These results are consistent with strigolactone insensitivity of SIP1. However, accumulation of SIP1 in a wild-type background was not as high as that of PIN1:GFP in the d14 background. It is therefore possible that SIP1 retains some strigolactone response.

To test the influence of SIP1 on auxin transport, we performed bulk auxin transport assays through SIP1pin1 and SIP1pin1smxl678 stem segments (Fig 7D). SIP1pin1 stems have significantly lower levels of bulk auxin transport than Col-0, despite the higher fluorescence intensity on the plasma membrane, and therefore presumably higher membrane accumulation of the protein (Fig 7B). Similarly, high SIP1 accumulation on the plasma membrane did not correlate with high bulk auxin transport activity in the smxl678 background, with auxin transport levels as low in SIP1pin1smxl678 as in smxl678.

Overall, these results confirm that strigolactone sensitivity of SIP1 is severely compromised, but also suggest that swapping the middle region of the PIN1 loop with that of PIN3 has other impacts beyond changes in strigolactone sensitivity, including impacts on the efficiency of auxin transport. This means that any effects of SIP1 could be due to its strigolactone resistant accumulation, or to these other changes. Furthermore, it is possible that some sensitivity to strigolactone is retained in SIP1.

To test whether SIP1 has any effect on BRC1 expression, we performed qRT-PCR on RNA extracted from pools of small (presumed dormant) and big (presumed active) buds of Col-0, SIP1pin1, smxl678, and SIP1pin1smxl678. Consistent with previous results and its role suppressing bud growth, BRC1 expression in Col-0 was higher in small than large buds (Fig 7E). This trend was observed in all lines tested. In addition, as previously reported [11], smxl678 mutant buds had higher BRC1 expression than Col-0. The expression level of BRC1 in SIP1pin1 and SIP1pin1smxl678 was not consistently different to that in the cognate native PIN1 backgrounds (Figs 7E and S6). This suggests that SIP1 does not affect BRC1 expression, consistent with a model where strigolactone-mediated effects on BRC1 expression and PIN1 removal are independent.

2.8. The effect of strigolactone in SIP1pin1 backgrounds can be predicted by changes in the parameter v0

We sought to predict the 2-node bud growth phenotypes conferred by SIP1pin1. We account for the lower bulk auxin transport in SIP1pin1 lines (Fig 7D), by assigning a lower value of S, a parameter corresponding to the efficiency of feedback-driven auxin efflux. This places the SIP1pin1 mutants on a different (v0, μ) slice than that used in the previously described simulations (Fig 8A). Predicting the location of SIP1pin1 lines on this slice (and hence their phenotype) required estimating their values of v0 and μ. Given no evidence of an effect of SIP1 on BRC1 expression (Figs 7E and S6), we assigned the v0 value previously used for each genetic background and treatment. The second parameter μ, which corresponds to PIN1 removal from the plasma membrane, is not measured directly. Given that the strigolactone response of SIP1 is reduced compared to PIN1, and the steady state level of GFP accumulation on the plasma membrane is high, we assigned to the SIP1pin1 lines the same value of μ as d14, which has no strigolactone-mediated removal of PIN1 (Fig 8A). If in SIP1 strigolactone acts only via BRC1, and not via PIN1 removal, we predicted that SIP1pin1, SIP1pin1 + GR24, and SIP1pin1smxl678 should have the same low value of μ, but progressively lower values of v0.

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Fig 8. Model predictions for SIPpin1 bud growth outcomes largely match experimental data.

(A) Stochastic color map of the bud growth outcomes for the (v0, µ) slice used previously (Fig 4), with parameter values for genotypes and treatments in black (as in Fig 5A); and (v0, µ) slice at a 20% lower value of the parameter S, to account for the lower bulk auxin transport in SIP1pin1 lines, with the predicted location in parameter space of each SIP1 line shown with a green dot. (B) Mitchison plots of predicted (top) and (C) empirical (bottom) bud growth phenotypes. Predictions show 50 stochastic simulations per genotype/treatment run for 80 time steps, and those of smxl678 run for 120 time steps. For the experimental data, SIP1pin1smxl678 buds were measured for 19 days and the other genotypes were measured for 12 days. (D) Predicted and (E) empirical relative growth index (RGI) for the genotypes/treatments indicated. Data and simulations of Col-0, Col-0 + GR24, and smxl678 are the same as those from Fig 4A and 4C. The RGI is obtained by calculating the length of the longest bud divided by the combined length of both buds, and is shown only for active explants (those with at least one active bud), n = 50 for predictions and 12–80 for experimental data. Letters indicate statistically significant differences at p < 0.05 obtained from multi-level model with Bonferroni corrections. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g008

Looking at bud growth outcomes, the model predicts a gradual increase in the proportion of explants with only one active bud across the SIP1pin1, SIP1pin1 + GR24, SIP1pin1smxl678 strigolactone signaling gradient (Fig 8A and 8B), and thus an increasing RGI (Fig 8D). To test this prediction, we performed 2-node assays on these genotypes, including Col-0, Col-0 + GR24 and d14 as controls. From the Mitchison plots, we indeed found a gradual increase in explants with only one active bud across SIP1pin1, SIP1pin1 + GR24, and SIP1pin1smxl678 (Fig 8C), which was reflected in the increased RGI (Fig 8E). In SIP1pin1smxl678, one bud often dominated then stopped growing, followed by the activation of the second bud (Fig 8C), leading to a low RGI despite strong mutual inhibition in this genotype (Fig 8E). Like smxl678, SIP1pin1smxl678 buds activated very slowly, so to track their growth we measured bud length for 19 days, while the other genotypes were measured for 12 days.

To assess bud activation dynamics, we produced a heatmap (Fig 9A) and boxplot (Fig 9B) of the number of lag days from model simulations using the parameters assigned for each genotype, with associated sensitivity analysis (Fig 5E and 5F). The simulations show that modelling SIP1 with low μ, wild-type lag days are expected. Gradually increasing v0 across the SIP1pin1, SIP1pin1 + GR24, SIP1pin1smxl678 series, predicts that bud activation is increasingly delayed. The experimentally observed number of lag days calculated from the data validates these predictions (Fig 9C), with a longer delay in bud activation of SIP1pinsmxl678 than predicted. For the maximum growth rate, the simulations with low μ, produce a wild-type maximum growth rate, and gradually increasing v0 across the SIP1pin1, SIP1pin1 + GR24, and SIP1pin1smxl678 series predicts no effect on maximum growth rate (Fig 9D and 9E). While the comparisons of SIP1pin1 with SIP1pin1 + GR24, and SIP1pin1 + GR24 with SIP1pin1smxl678, are consistent with these predictions, we observe a statistically significant decrease in maximum growth rate between Col-0 and SIP1pin1smxl678 (Fig 9F).

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Fig 9. Model predictions for SIPpin1 bud activation dynamics largely match experimental data.

(A) and (D) Heatmaps of the number of lag days and maximum growth rate from the (v0, µ) slice used previously (Fig 4), with parameter values for genotypes and treatments from Fig 5A and 6A in black (left); and (v0, µ) slice at a 20% lower value of parameter S to account for the lower bulk auxin transport in SIP1pin1 lines, with the predicted parameter values for SIP1pin1 lines shown in green. Heatmaps are obtained by calculating the number of lag time steps or maximum growth rate for 25,281 combinations of parameters v0 and μ (159 × 159 grid). (B) and (E) Predictions for the lag time steps and maximum growth rate for genotypes and treatments using the parameter values in A and D, each obtained from 100 simulations run for 120 time steps. (C) and (F) Experimentally determined number of lag days and maximum growth rate calculated from 2-node explants in Fig 8B, where bud length was measured over 12 days, or 19 days for smxl678 and SIP1pin1smxl678, n = 12–80. The percentage of active explants is calculated as the percentage of explants with at least one active bud, n = 43–96. Letters indicate statistically significant differences at p < 0.05 obtained from multi-level models with Bonferroni corrections. Data and scripts of simulations underlying this figure can be found at https://doi.org/10.17863/CAM.120831.

https://doi.org/10.1371/journal.pbio.3003395.g009

Overall, we find that changes in v0 only were largely sufficient to capture the phenotypes we observed across three SIP1pin1 backgrounds with increasingly strong strigolactone signaling. This is consistent with our hypothesis that PIN1-independent strigolactone action occurs via v0, with variation in v0 corresponding to BRC1-mediated strigolactone signaling.

2.9. Strigolactone acting independently of PIN1 L2 and BRC1 can affect bud growth outcomes and maximum growth rate but cannot delay bud activation

If SIP1pin1 is fully strigolactone resistant and strigolactone acts only via PIN1 L2 and BRC1, we would predict that SIP1pin1brc1brc2 should have no strigolactone response. To test this prediction, we generated the SIP1pin1brc1brc2 mutant. The brc1brc2 mutant background did not affect SIP1 membrane accumulation or bulk auxin transport as compared to SIP1pin1 (S7 Fig).

We performed a 2-node assay to compare the effect of GR24 on SIP1pin1brc1brc2 to that on SIP1pin1 and brc1brc2 (S8 Fig). With respect to the lag phase, GR24 extends the number of lag days in both the brc1brc2 and SIP1pin1 backgrounds. However, there was no significant effect of GR24 on the lag phase in the SIP1pin1brc1brc2 background.

In contrast, we found that SIP1pin1brc1brc2 buds retain a GR24 response with respect to RGI and maximum growth rate, with a small but significant increase observed in both measures (S8A, S8B, and S8D Fig). These results are consistent with SIP1 retaining some strigolactone sensitivity, or with a PIN1-, BRC1-independent mode of action for strigolactone. To assess whether this could be due to the presence of functional PIN7, which is also likely to be strigolactone responsive [52], we made SIP1pin1pin7. We observed the same branching phenotype in SIP1pin1pin7 as for SIP1pin1 (S5B and S5C Fig). Buds in 2-node explants showed no difference in the responses to strigolactone in the SIP1pin1pin7 background (S8 Fig). Therefore, the remaining strigolactone responsiveness is unlikely to be mediated by PIN7, but analysis of the SIP1pin1pin7brc1brc2 would be required to rule this out definitively.

3.1. Multi-scale signal integration in the regulation of bud activity

Plants continuously integrate local and systemic inputs to tune shoot branching. Two regulatory hubs have been identified as central to this process, with the BRC1 transcription factor acting locally in the bud to repress outgrowth, and the auxin transport network systemically mediating competition between apices.

The competition between apices is hypothesized to occur via an autocatalytic feedback between auxin transport and its upregulation and polarization in the prevailing transport direction. This creates competition for access to auxin transport in the main stem, with reinforcement through the autocatalytic feedback. Competition with reinforcement is a classical regulatory architecture for a self-organizing system [64,65]. Systemic modulation of the feedbacks in the auxin transport network allows the number of active apices across the shoot system to be tuned, for example according to nutrient availability [66–68], while exactly which buds activate can be influenced by local bud-acting factors such as light quality.

Local bud competitiveness is likely mediated in part by the BRC1 regulatory hub [5,18,22]. How these local and systemic factors are integrated is not well understood. The analysis of the impacts of strigolactone signaling on shoot branching has provided important insights. Strigolactone acts on both hubs, through upregulating BRC1 transcription in buds [4,9,10], and through triggering rapid depletion of PIN1 from the plasma membrane in a transcription-independent manner [51], which makes auxin transport canalization more difficult for buds to achieve. This is consistent with the high branching of strigolactone receptor or biosynthesis mutants [69–71].

Further insights into the regulation of bud activity come from considering the impacts of mutations and treatments on the slow-growing lag and rapid growth phase in isolated 1-node explants [46,60,72]. For example, strigolactone extends the lag phase during bud activation and reduces the maximum growth rate of active branches, and brc1brc2 mutant buds are relatively strigolactone-resistant to effects on the former but not on the latter [8]. This approach has enabled the dissection of the shoot branching regulatory network. It has provided evidence to support the ideas that (i) the establishment of auxin transport canalization occurs during the slow-growing lag phase of bud activation, with the transition to rapid growth corresponding to fully canalized export, which is hard to reverse, (ii) BRC1 influences the length of the lag phase, and (iii) the rate of rapid growth is influenced by the level of auxin efflux from the bud.

Complementing results from isolated 1-node explants, 2-node explants are a powerful minimal system to study the impact of another bud on growth dynamics, thereby revealing some of the systemic properties of shoot branching regulation [30,32,45,53]. After excision from the plant, typically both buds on 2-node explants enter the slow-growing lag phase. If both buds have strong self-activation and/or low mutual-inhibition, then both activate. Alternatively, if one bud establishes rapid growth quickly and inhibits the growth of the other, then the second bud will stop growing. This phenomenon can be quantified using the relative growth index (RGI). Even when both buds activate, the presence of another bud extends the lag phase of both buds, and reduces their maximum growth rate [8]. Strigolactone has the same effects on the lag and rapid growth phases as in 1-node explants (Figs 5 and 6), and additionally increases the RGI, typically resulting in one bud dominating the other [51]. Hence analyzing the effect of strigolactone at the scale of 2- rather than 1-node explants casts strigolactone as systemically tuning the level of bud-bud competition rather than simply inhibiting bud activity [49,51]. The RGI in brc1brc2 is also increased by strigolactone, though to a lesser extent than in wild-type [22].

Combining brc1brc2 with the smxl678 constitutive strigolactone response mutant further elucidated the interplay between the two hubs in the strigolactone-mediated regulation of bud-bud competition (Fig 2). In 1-node explants, smxl678 buds are inhibited, while brc1brc2 and brc1brc2smxl678 buds have the same rapid bud activation (Fig 2B). However, brc1brc2 and brc1brc2smxl678 do not exhibit the same phenotype in 2-node explants, where the level of bud-bud competition is higher in brc1brc2smxl678 than brc1brc2 (Fig 2D and 2E). These observations can be explained within a canalization-based model, where high PIN1 removal in smxl678 and brc1brc2smxl678 makes canalization harder to establish [14]. Bud activation may be possible despite high PIN1 removal only in more permissive contexts, as seen in 1-node explants of brc1brc2smxl678 but not smxl678. In 2-node explants, high bud-bud competition in brc1brc2smxl678 may emerge from a combination of low BRC1 expression, creating a locally permissive environment in each bud, combined with a systemic canalization-inhibitory environment from high PIN1 removal.

Taken together, the suite of assays, metrics, mutants and treatments presented above provide a powerful toolkit to understand the properties of the bud regulatory network, and to explore the relationship between systemic and local regulation, and the two known bud regulatory hubs.

3.2. Computational models for understanding bud regulation

In addition to experimental work, computational modelling has been key to providing evidence that the proposed regulatory architecture is capable of delivering the wide range of behaviors and properties we observe. In particular, our previous model has demonstrated that many non-intuitive bud growth phenomena can be explained under the auxin transport canalization-based model for bud activation, with strigolactone promoting PIN1 removal from the plasma membrane [25,49].

Here we describe an extension of this previous work. We incorporate the key features of the auxin transport canalization-based model for bud activation into a simplified model representing the 2-node branching assay (Fig 3). The model includes two new features based on the advances in our understanding of bud growth dynamics outlined above. First, we explicitly model bud growth rate, expressing it as a function of bud auxin export. Second, we model BRC1 as affecting basal levels of auxin efflux. This latter hypothesis was motivated by the characteristic short lag phase for bud activation observed in brc1brc2 mutant backgrounds, suggesting rapid auxin transport canalization, along with the ability of the abcb19 mutant to suppress many of the bud growth phenotypes of brc1brc2 mutants [8,52]. The ABCB19 auxin efflux carrier is plausibly a major contributor to basal levels of auxin efflux.

Using this simple model, with strigolactone acting through both PIN1 removal and BRC1-mediated reduction in basal levels of auxin efflux, we simulate a wide range of 2-node assay experimental results. We compare these simulations to empirical results, for corresponding mutant backgrounds and treatments. We focus on dissecting the dual activity of strigolactone, using brc1brc2 mutants and a PIN1 variant that has compromised strigolactone response.

3.3. Two biologically relevant model parameters capture multiple properties of bud behavior

Based on the above reasoning, we model BRC1 as influencing basal auxin efflux via v0, and PIN1 removal as μ. Tuning these parameters to match the effects of a range of relevant loss of function mutations and strigolactone treatments successfully captures much of the corresponding variation in bud behavior in 2-node assays, including effects on the number of lag days, maximum growth rate, and growth outcomes.

For example, at high v0 (low BRC1), changes in µ (PIN1 removal) modify 2-node growth outcomes without substantial effects on the number of lag days (Fig 5A). This captures our observation that increasing PIN1 removal through strigolactone treatment or smxl678 mutation in a brc1brc2 background leads to one bud more often dominating the other, while maintaining rapid bud activation (Fig 5C). Furthermore, an increase in µ creates a much greater delay in bud activation at low compared to high v0. The effect of one parameter therefore depends on the value of the other, matching the different impacts on the time of bud activation of smxl678 mutation in brc1brc2 and wild-type backgrounds.

The effectiveness of this simple model in capturing so many of the behaviors of buds on 2 node explants provides evidence that the hypotheses underlying the model are correct. In particular, the concordance between modelled and observed behaviors provides further evidence to support the canalization-based model of bud activation, with buds competing to establish canalized auxin transport into the stem, and the lag phase corresponding to the canalization period. Furthermore, the results support the two new hypotheses we propose here, namely that BRC1 downregulates the basal rate of auxin efflux, and that bud growth rate is influenced by the level of auxin efflux.

The model used here replicates key features from the whole plant model set out in Prusinkiewicz and colleagues [25]. This model is able to reproduce the spatial and temporal patterns of bud activation in multiple plant architectures by simple parameter changes. Combining the novel features of the 2-node model presented here with the whole plant model described previously could provide further insights on how growth is balanced across the shoot system.

3.4. Mechanisms of BRC1 action

Basal auxin efflux (i.e., auxin efflux that is independent of canalization), occurs principally through the action of non-polar auxin transporters and diffusion, and depends on auxin levels. Hence for BRC1 to reduce basal auxin efflux, it could act in a number of ways.

First, BRC1 could down-regulate basal auxin efflux by downregulating the activity of non-polar auxin transporters, which are collectively expressed more broadly than PIN1. These transporters, namely PIN3, PIN4, PIN7 (collectively PIN347), and ABCB19 are thought to be important in the early stages of canalization, promoting auxin loading in the bud and background auxin flux between the bud and the stem. This enables the subsequent polarization of PIN1, which drives the high-capacity, highly polar auxin transport characteristic of canalized tissue [52,61,73]. This hypothesis is consistent with the observation that BRC1 influences the length of the lag phase and not the maximum growth rate, because BRC1-mediated regulation of ABCB19/PIN347 would mainly influence the dynamics of auxin flux before PIN1 polarization, regulating the timing of the transport switch but not the steady state levels of auxin transport, which are principally determined by PIN1.

Previous analyses of transcriptional changes downstream of BRC1 do not identify auxin transporters as BRC1 targets in Arabidopsis, although in cucumber, BRC1 has been shown to regulate PIN3 expression [74]. BRC1-dependent regulation of PIN347/ABCB19 could occur post-transcriptionally for example via phosphoregulation, an important mode of non-transcriptional regulation of PIN1 activity [63]. An effect could also occur via ABA. Three downstream targets of BRC1 are HD-ZIP transcription factors promoting ABA accumulation [18,20], and ABA influences PIN2 accumulation in roots [75,76].

Alternatively, BRC1 may down-regulate the basal rate of auxin efflux by tuning the available auxin concentration. BRC1 could lower auxin availability by promoting amino-acid conjugation of auxin via GH3.5, an IAA-amido synthetase involved in auxin homeostasis identified as a direct BRC1 target [18]. In the model, auxin concentration affects both the basal rate of auxin efflux via v0 and the maximum rate of the Hill function via v. For the parameters investigated, v0 is a bigger determinant of early efflux levels, while v acts in the positive feedback of canalization and so becomes increasingly important as auxin efflux increases. Given BRC1 expression is rapidly downregulated during bud activation [4], BRC1-mediated effects on auxin availability would be most prominent early in bud activation, modifying basal auxin efflux, v0, without affecting the positive feedback via v.

BRC1-mediated regulation of basal auxin efflux would provide a mechanism through which local environmental conditions in the bud, which influence BRC1 expression [19,20], can be integrated into the systemic canalization-based regulation of bud activation. Buds along a stem would exhibit variation in their basal rate of efflux, enabling those in more favorable conditions to establish canalized auxin transport into the stem, while the feedbacks between auxin sink and source strengths would balance the number of active apices across the whole plant.

3.5. PIN1-mediated action of strigolactone

Further tests of our model would benefit from the ability to prevent strigolactone action specifically via PINs. As a first step toward this, we identified the middle region of the PIN1 cytoplasmic hydrophilic loop as necessary and sufficient for strigolactone-mediated removal of PIN1 from the plasma membrane (Fig 7). This allowed us to create SIP1, a chimeric PIN1 in which the middle L2 region of the PIN1 loop has been swapped for that of PIN3. GFP-tagged SIP1 remains on the membrane in the presence of strigolactone and in a smxl678 background, confirming its strigolactone resistance at least with respect to accumulation at the plasma membrane.

It is important to note that SIP1 confers low bulk auxin transport levels (Figs 7D and S7), consistent with the hydrophilic loop being a dense regulatory environment with multiple phosphorylation sites important for PIN1 activity [63], which may have been affected in SIP1. This complicates the interpretation of SIP1 phenotypes. The low auxin transport efficiency of SIP1 might impact all the phenotypes of interest independently of strigolactone-mediated PIN1 removal. For example, the whole plant phenotypes conferred by SIP1 include a modest increase in branching, which contrasts to the highly branched phenotype of brc1brc2. This could indicate that strigolactone signaling via PIN1 has a relatively minor role in determining branching in whole plants. However, it is possible that in whole plants, the low transport efficiency of SIP1 masks the impact of its strigolactone resistance on shoot branching. Identification of the precise residues required for strigolactone-mediated PIN1 removal would further our understanding of strigolactone signaling and the role of strigolactone-mediated PIN1 removal in shoot branching.

Despite this complication, because the compromised auxin transport efficiency was common across all SIP1 lines, we could still investigate the PIN1 L2-independent effect of strigolactone by comparing phenotypes of SIP1pin1, SIP1pin1 + GR24, and SIP1pinsmxl678, which constitute a gradient of increased strigolactone signaling. After accounting for the lower auxin transport efficiency in our model, changes in v0 alone could accurately predict the effect of strigolactone in the SIP1 lines/treatment, further supporting our model. For example, the reduced effect of strigolactone on the maximum growth rate in the SIP1 background is consistent with our hypothesis that growth rate is influenced by the steady state level of auxin efflux, which in the model is not significantly affected when strigolactone acts via v0 (BRC1) and not via µ (PIN removal) (S1 Fig).

A second complication is that SIP1 does not over-accumulate to the same degree as PIN1 in the strigolactone receptor mutant background d14. Together with the residual strigolactone sensitivity of RGI and maximum growth rate in SIP1pin1brc1brc2, this leaves open the possibility that strigolactone acts through additional PIN regions, or through an entirely different mechanism in addition to its PIN1 and BRC1-mediated effects, such as via trehalose-6-phosphate [77]. Nonetheless, representing strigolactone action in our model solely via BRC1 and PIN1 removal was sufficient to capture multiple aspects of bud behavior observed in the range of mutant and transgenic backgrounds and treatments we tested. Importantly, the observation that SIP1pin1brc1brc2 was resistant to strigolactone-mediated effects on the number of lag days establishes PIN1 L2 and BRC1 as the two necessary strigolactone targets for its effects on the length of the lag phase.

3.6. Discrepancies between model and data in smxl678 mutant backgrounds

While there is generally a close match between the model predictions and empirical results, there are also some discrepancies. These occurred particularly in smxl678 backgrounds. The maximum growth rate of brc1brc2smxl678 and smxl678, and the number of lag days of SIP1pin1smxl678, were higher than predicted by the model; and the maximum growth rate of SIP1pin1smxl678 was lower than predicted by the model. There are several explanations for this. The smxl678 background may represent fully constitutive strigolactone signaling, and it is possible that the model simply does not adequately capture this extreme state. Alternatively, there may be some SMXL678-independent action of strigolactone, consistent with recent work showing D14 can be degraded independently of SMXL678 [78]. For example, these effects may occur via trehalose-6-phosphate [77,79].

The role of sugar in bud regulation may also account for the counterintuitive observation that smxl678 buds grow out less often on 1-node compared to 2-node explants, despite the mutual inhibition between buds in the latter case (Fig 2B and 2D). Sugar availability from leaves influences bud release in pea and rose [80,81], and sustained bud growth in Arabidopsis explants [72]. Sugars up-regulate auxin levels in several species and developmental contexts [82,83], including axillary buds of rose [84]. In our mathematical model, higher global auxin concentration increases the basal rate of auxin efflux v0 and the maximum rate of the Hill function v (mathematical appendix), thereby facilitating the activation of both buds (S2 Fig). Hence in smxl678 2-node explants, higher sugar from the presence of a second leaf might facilitate the establishment of auxin canalization, enabling some degree of bud outgrowth.

3.7. Conclusions

We propose a model that integrates BRC1 and auxin transport, two previously independent hubs in shoot branching regulation. Our model captures and predicts the phenotype of plants with defects in either one or both hubs, at the level of both bud growth dynamics and bud-bud interactions. This supports the model formulation, namely that buds compete to establish canalized auxin transport into the main stem, with the competitive strength of each bud locally tuned by BRC1. This regulatory system enables both the number and location of growing branches to be coordinated across the whole shoot system. Future experimental work should continue to investigate the detailed mechanisms underlying these hypotheses. Our model also guided our inquiry into the strigolactone-mediated regulation of shoot branching, leading us to identify a region of the PIN1 hydrophilic loop key for strigolactone responsiveness, which should be studied in more detail in the future. Experimental findings obtained from these lines of research could be iteratively incorporated back into our model, to continue exploring the multi-scale regulatory logic through which plants tune their shoot architecture.

4.1. Experiments

4.2. Statistical analysis

All statistical analysis was carried out in R v.4.1.31 and RStudio v.2022.02.1 + 461. Bud growth data was analyzed by fitting a growth model [93] to each bud growth trace in R, as specified in [8]. The number of lag days and maximum growth rate is only shown for active buds (maximum growth rate > 2.5 mm).

For statistical testing, multi-level models were fitted to the data to account for random variation between experiments. A linear multi-level model was used with either a normal or gamma distribution depending on the data. The model was fit using the R/lme4 package (v1.1.29; [94]) and contrasts of interest extracted using the R/emmeans package (v 1.8.2; [95]). Estimated marginal means and pairwise comparisons between genotypes were adjusted for multiple testing using Bonferroni correction. The box for all boxplots spans the first to the third quartile range with the middle line showing the median, and the superimposed black dot showing the mean. The minimum and maximum whisker values are calculated as Q1/Q3 (first or third quartile) ± 1.5*interquartile range. Adobe illustrator v29.5.1 was used to add the results of statistical tests to the plots and generate multi-panel figures.

4.3. Computational modelling