Arabidopsis cell expansion is controlled by a photothermal switch

In Arabidopsis, the seedling hypocotyl has emerged as an exemplar model system to study light and temperature control of cell expansion. Light sensitivity of this organ is epitomized in the fluence rate response where suppression of hypocotyl elongation increases incrementally with light intensity. This finely calibrated response is controlled by the photoreceptor, phytochrome B, through the deactivation and proteolytic destruction of phytochrome-interacting factors (PIFs). Here we show that this classical light response is strictly temperature dependent: a shift in temperature induces a dramatic reversal of response from inhibition to promotion of hypocotyl elongation by light. Applying an integrated experimental and mathematical modelling approach, we show how light and temperature coaction in the circuitry drives a molecular switch in PIF activity and control of cell expansion. This work provides a paradigm to understand the importance of signal convergence in evoking different or non-intuitive alterations in molecular signalling.


Parameter Optimization
All experimental data were collected from seedlings grown in constant red light (660nm) conditions for 7 days, therefore the concentrations of Pr, Pfr and PIF were at equilibrium for each light intensity recorded. This supports our use of a steady-state model; hence the ODEs were solved explicitly using parameter values constrained to available hypocotyl and protein data. All experimental data have been normalized to the dark values, i.e. dark grown hypocotyls have length 1. The parameter values were estimated within valid biological ranges by various methods: k 1 and k 2 are the rate of photoconversion between Pr and Pfr forms of phyB in red and far-red light respectively. These parameters were calculated explicitly by k 1 =N λ σ r and k 2 =N λ σ fr where N λ denotes the photon flux at wavelength λ (660nm) and σ r/fr represents the photoconversion cross-sections of red/far-red pigment 7 . Parameters m 1 (P r c degradation), m 2 (P fr c degradation), p 1 (rate of dark reversion), p 2 (translocation from P fr c to P fr n ), p 3 (translocation from P r s to P r n ), p 4 (translocation from P fr s to P fr n ) and p 5 (translocation from P fr n to P fr

Details of Model II
We observed that at 17°C Model I provided a good fit to the wild type experimental data up to However our experimental data (Fig. 1a) illustrate that further hypocotyl inhibition occurs above the 1.4 μmol m -2 s -1 threshold. In Model I the fluence response of hypocotyl growth is directly linked to PIF levels (Eq. 8); which, in turn, are dependent on the levels of active phyB (Eq. 7).
Therefore one possibility was that increased hypocotyl inhibition could be achieved through increased phyB levels promoting further PIF degradation. However, our experimental data clearly indicate the decrease in total phyB levels stabilizes to low levels of phyB at around 1.4 µmol m -2 s -1 , regardless of further fluence rate increases ( Supplementary Fig. 3a). This plateauing of phyB levels implies there could be no further reduction of PIF levels after 1.4 µmol m -2 s -1 . This hypothesis was supported by western blots of the PIF3 protein, which is acutely sensitive to phyB Pfr levels 8 . Like phyB, PIF3 depletes to a low stable level that is maintained at high fluence rates ( Supplementary Fig. 1c). However, PIF4-HA and PIF4-LUC show a continued depletion as fluence rate increases (Fig. 2a, b). This implies that PIF quantity does not correlate with the hypocotyl response, which in turn indicates that Model I is incapable of achieving further hypocotyl inhibition at high fluence rates. To test this we ran the model through 200,000 parameters sets selected using Latin Hypercube Sampling (LHS). None of these parameter sets matched the data, suggesting that an additional component(s) was required to deliver the requisite behaviour at high fluence rates.
As phyB and PIF levels did not correlate with hypocotyl length at higher fluence rates, we surmised that altered PIF activity could be an important contributory factor. Reinforcing this proposition, PIFs are known to be regulated post-translationally [9][10][11] . In accordance Model I was extended to incorporate component X, which elicits fluence rate-dependent inhibition of PIF activity, to create Model II (Supplementary Fig. 2c).
The fluence rate component of X regulation can be achieved either through phyB dependent (Eq. 10) or independent (Eq. 11) processes. In both cases the rate of production of X is made directly proportional to the light intensity. For a phyB dependent process, this is achieved by making the production rate proportional to Pr, i.e., to the flux from Pr to Pfr. A simple biochemical mechanism by which such a flux counter can be implemented would involve the creation of a molecule of X each time that a molecule of Pr changes to Pfr; this is explicitly modelled by the first term on the right hand side of Eq. 10. For a phyB independent mechanism, X is assumed to depend on a factor involved, for example, in photosynthesis; in the absence of information about which factor this is and of the specific pathway/s involved, this case can only be modelled by making the production rate of X directly proportional to the light intensity (see first term on the right hand side of Eq. 11). In both cases a light-independent decay of X is introduced such that X is in steady-state. Note that assuming the production rate of X to be directly proportional to Pfr does not lead to the same case as above since Pfr levels are not directly proportional to the light intensity but rather saturate at low light intensities. The steady-state hypocotyl length for Model II and the two possible type of kinetic equations for X can be described by In order to distinguish between the two possible model inputs for X we initially estimated b 1 (inhibition constant of X) and m 6 (X degradation) using simultaneous simulated annealing leastsquare fitting to hypocotyl growth data and the underlying PIF and phyB levels of Columbia wild type (Col WT) at 17°C (Fig. 1a and Supplementary Fig. 1c, 3a). Both equations for the concentration of X have the same number of unknown parameters and as they are being compared to the same data the standard method for model selection, Bayesian Information Criterion (BIC), can be reduced to χ 2 values. The χ 2 values are 0.020 and 0.018 for phyBdependent and independent X respectively ( Supplementary Fig. 7a, b), showing that we cannot differentiate between these two possible methods for regulating X. Purely as a point of reference, hereafter X was modelled as phyB-dependent. Supplementary Figure 2c, d. Figure 2b and 2d we show that X affects hypocotyl elongation at high fluence rates, through suppression of PIF activity. Most importantly inclusion of X leads to a model which agrees with the experimental data over the whole range of fluence rates tested.

Including Temperature Effects in Model II
Our next aim was to integrate the temperature and light signals affecting hypocotyl elongation into one model, which necessitated the extension of Model II to describe the fluence dependent hypocotyl elongation seen at 27°C. A possible hypothesis was that this switch from inhibition to promotion of hypocotyl elongation was primarily due to dark reversion (dr); the light-independent conformational change from Pfr to Pr. Earlier model analysis showed that the light driven photochemical reactions that establish Pr:Pfr ratio fail to deliver the characteristic fluence response curve over a large fluence range 3 . Inclusion of dr corrected this deficiency, highlighting the importance of dr in light intensity sensing. Dark reversion is known to be temperature dependent 12 ; hence it is possible that changes in dr kinetics could drive the thermal switch in the fluence rate response. Countering this suggestion, dr is only thought to be influential at the low fluence rate range 13 , while the temperature induced changes are observed at higher fluence rates.
Nonetheless we tested whether dark reversion was required for the switch to address this uncertainty. Here we examined the phyB-401 mutant that carries a G-E amino acid substitution at position 564. This substitution increases the spectral range of activity and blocks dr 14 .
Concurring with previous results, the phyB-401 mutation led to extreme hypersensitivity to red light, evidenced by the exaggerated response to very low fluence rate light (Supplementary Fig.   3b). This was observed at both 17°C and 27°C. phyB-401 exhibited a clear switch response, as at 27°C hypocotyl elongation was driven by fluence rate. These results eliminate dr as a principal regulatory factor in the photothermal switch.
All reactions are affected by temperature to some extent, we therefore postulated that the inclusion of temperature sensitivity to multiple parameters within Model II could illicit the required switch in hypocotyl behaviour. Hence we assigned each parameter a Q 10 value. A Q 10 value measures the change in a rate constant due to an increase from an initial temperature, T 1 , to the final temperature, T 2 : In all of our models the temperature increase was 10°C. Hence a Q 10 value of 1 implies no temperature sensitivity in the rate of reaction whereas a Q 10 value of 5 infers a fivefold increase in reaction rate over a 10°C temperature increase 15,16 . Biologically relevant Q 10 values are thought to be in the range of 1-5 15 , the most commonly found is Q 10 = 2 which is the familiar doubling of the rate constant for every 10°C increase in the temperature 17 . Using this measure of temperature sensitivity we aimed to identify the reactions where a change in temperature dependence has a noticeable effect on the overall hypocotyl growth.
In darkness, when it is entirely in the Pr form and found only in the cytoplasm, phyB levels are slightly elevated at 27°C compared with 17°C, indicating either n 1 (formation) or m 1 (degradation) of Pr is temperature dependent. A moderate Q 10 value has therefore been assigned to Pr formation, reproducing the temperature dependent increase in phyB. Similarly PIF4 expression and protein levels have been shown to rise with temperature at all fluence rates and accordingly we have designated n 2 (PIF formation) and m 5 (PIF degradation) as potentially temperature dependent (Fig. 2a, b) [18][19][20] . Our data show m 3 (PIF-dependent degradation of Pfr) and m 4 (Pfr-dependent degradation of PIF) are also temperature sensitive. The gradient of reduction in phyB levels, a PIF-dependent process, is greater at 27°C (-1.04 μmol -1 m 2 s 1 ) than at 17°C (-0.68 μmol -1 m 2 s 1 ) (Supplementary Fig. 3a) indicating the PIF-dependent degradation of phyB (m 3 ) is effected by temperature. Likewise, fluence rate (and phyB Pfr-dependent) depletion of PIF protein (m 4 ) is temperature sensitive, with gradients of -0.038 μmol -1 m 2 s 1 at 27°C and -0.014 μmol -1 m 2 s 1 at 17°C (Fig. 2a, Supplementary Fig. 1c). In each case the gradients were measured between the dark value and the fluence rate at which phyB/PIF levels plateau. As dark reversion, p 1, known to be temperature dependent we assigned it a Q 10 value of 2; however due to dark reversion only affecting the hypocotyl length at very low light intensities, we anticipate that it will have little impact at the higher fluence rates (Supplementary Fig. 3b) 12,21 . The basal rate of cell expansion,  in the model is also reported to potentially be temperature dependent 17 and we will therefore assign it a Q 10 value. Finally our genetic data suggested that the activity of HY5 (X in Model II) may decrease with temperature; however HY5 protein levels do not. This would indicate that b 1 (the inhibition constant of X) is temperature dependent and therefore we included this as a possible temperature dependent parameter.
To identify other potential temperature parameters we performed a local sensitivity analysis on the effects of temperature within the system. For this analysis we recorded the extent of hypocotyl elongation at the three crucial fluence rates (dark, 1.4 μmol m -2 s -1 and 340 μmol m -2 s -1 ) in the absence of temperature dependence. Each separate parameter was doubled (Q 10 =2) and the simulated hypocotyl length was then recorded and normalized against hypocotyl length at 17°C. This analysis was used to identify those parameters where increasing temperature sensitivity generates a light dependent change in hypocotyl length ( Supplementary Fig. 6). As anticipated, in darkness, only parameters involved in determining PIF levels and activity, n 2 (PIF formation), m 5 (PIF degradation), β 1 (PIF activation rate) and α (basal growth rate), caused a change in hypocotyl length. However we do not observe significant temperature dependence in dark grown hypocotyls in the data (Fig. 1a).
Local temperature sensitivity analysis identified a small set of potentially interesting parameters which display a large light dependent temperature effect on hypocotyl length. At low fluence rates (1.4 μmol m -2 s -1 ) m 4 (Pfr-dependent degradation of PIF), n 1 (P r c formation), n 2 (PIF formation) and g 1 (Michaelis-Menten constant) have a significant effect. However in the data we observe a moderate reaction to temperature increase at this fluence rate, so this was taken into account when assigning Q 10 values to these parameters. At high fluence rates n 2 (PIF formation), m 3 (PIF-dependent degradation of Pfr) and α (basal growth rate) were identified as temperature sensitive parameters. Unexpectedly all other parameters were relatively insensitive to changes in temperature dependence. This sensitivity analysis supports the addition of temperature dependence to n 1 (formation rate of P r c ), n 2 (formation rate of PIF), p 1 (dark reversion rate), m 3 (PIF-dependent degradation of Pfr) and m 4 (Pfr-dependent degradation of PIF), m 5 (PIF degradation) and α (basal growth rate), parameters previously identified to potentially be temperature dependent. In addition the temperature sensitivity analysis indicated g 1 (Michaelis-Menten constant) may have a slight temperature effect on hypocotyl length. We are unable to validate this experimentally and therefore will include it as a potential temperature dependent parameter.
Based on this analysis and our biological constraints we introduced temperature sensitivity to the following parameters: n 1 (formation rate of P r c ), n 2 (formation rate of PIF), p 1 (dark reversion rate), m 3 (PIF-dependent degradation of Pfr), m 4 (Pfr-dependent degradation of PIF), m 5 (PIF degradation), α (basal growth rate), g 1 (Michaelis-Menten constant) and b 1 (inhibition constant of X). The exact value of Q 10 for each parameter was calculated using simultaneous least-square fitting to 1dp to our experimental data at 27°C (Fig. 1a) and is listed in Supplementary Table 1.
Interestingly changes in the temperature dependence of Model II parameters were insufficient to recreate the fluence rate dependent increase in hypocotyl elongation at high fluence rate shown at 27°C (Fig. 3e). This supports our conclusion that dr cannot drive the switch, and the new temperature component X also cannot elicit the switch. This implies Model II is unable to recreate the temperature and fluence rate dependent rise in hypocotyl elongation in its current form. To confirm this we used LHS to assign Q 10 values between 0-5 for each parameter then ran the model for 200,000 combinations of Q 10 values. None of the simulated model outcomes could recreate the 27°C increase in hypocotyl elongation at high fluence rates whilst ensuring the model was consistent with both WT data at low fluence rates and phyB and PIF protein levels ( Fig. 1a and Supplementary Fig. 1c, 3a). From this we can conclude that the existing components in Model II are not sufficient to elicit the photothermal switch. This led us to investigate possible methods by which a temperature dependent increase in hypocotyl elongation could be achieved through the development of Model III.

Details of Model III
Analysis of lines expressing 35S::PIF4 or 35S::PIF5 showed that while hypocotyl elongation was suppressed at higher fluence rates at 17C, it was promoted, particularly in the 35S::PIF5 line, at 27C (Fig. 4a,b). This provided support for the inclusion of X as a PIF suppressor at 17C.
Coupled with our data showing that PIF levels do not rise with fluence rate at 27C (Fig. 2a,   Supplementary Fig. 1c), these results also suggested the presence of a second component that activated PIF under warmer conditions. In accordance with these findings Model II was extended to include the component "Y" which activates PIFs in a temperature and fluence rate dependent manner, producing Model III. This was achieved as follows: where parameters are denoted as previously (Fig. 4d). As with component X, there are two plausible ways to incorporate a fluence response into component Y. In one, Y is dependent on phyB through the flux from Pr to Pfr conversion (Eq. 14). In the other, it is assumed that Y is independent of phytochrome, relying on a separate light input such as photosynthesis (Eq. 15).
As with component X, the formation of Y will be dependent on the wavelength and fluence rate of the light used and consequently can be modelled using the value of light intensity, N λ. , ) ( In order for Model III to emulate the photothermal switch, the concentration of Y must also be temperature dependent, i.e. the Q 10 of m 7 is high. We estimated the unknown parameters in Eq 13 using simultaneous simulated annealing least-square fitting to all WT data. Once again we use χ 2 -values to determine the best model input for Y. The χ 2 -values are 0.068 and 0.066 for phyB dependent and independent Y, respectively. Based on this method of model selection it is not possible to differentiate between the two hypotheses for Y input ( Supplementary Fig. 7c, d).
Purely for consistency with X, further analysis was conducted with Y as phyB-dependent. Using the Bayesian Information Criterion (BIC) we were able to directly compare Model III with the temperature dependent Model II. This analysis concluded that Model III is preferable (BIC of Model II minus the BIC of Model III is 5.78).
Strikingly, with the inclusion of Y, Model III matches the experimental data extremely well at both temperatures and at all fluence rates ( Supplementary Fig. 7c, d). We then tested the robustness of Model III by establishing whether the model simulations could match experimental mutant data. The phyB mutant has constitutively elongated hypocotyls across fluence rates ( Supplementary Fig. 8a), while pif mutants have short hypocotyls and reduced fluence rate dependency ( Supplementary Fig. 8b). To reproduce the null phyB mutant we decreased the rate of phyB synthesis to zero (Supplementary Fig. 8a). For pif mutants we decreased the formation rate of PIF by 25% for each PIF gene family knockout (e.g. PIF1, PIF3, PIF4 and PIF5) simulated. Only the pifq mutant (which lacks all four PIFs) is fluence rate independent. In all cases the model simulations matched the mutant data, which reinforces confidence in the model structure.
To further test the model we determined how Model III would react to light delivered continuously or in pulses. By replacing Eq. 13 in Model III with a time dependent equation for hypocotyl length (Eq. 16) we created a dynamical model of the whole system from which we were able to simulate hypocotyl length at 17°C and 27°C, under constant light compared to 5 or 15 minute pulses. The pulses delivered the same total fluence of light.