Many organisms need to respond to complex, noisy environmental signals for developmental decision making. Here, we dissect how Arabidopsis plants integrate widely fluctuating field temperatures over month-long timescales to progressively upregulate VERNALIZATION INSENSITIVE3 (VIN3) and silence FLOWERING LOCUS C (FLC), aligning flowering with spring. We develop a mathematical model for vernalization that operates on multiple timescales—long term (month), short term (day), and current (hour)—and is constrained by experimental data. Our analysis demonstrates that temperature sensing is not localized to specific nodes within the FLC network. Instead, temperature sensing is broadly distributed, with each thermosensory process responding to specific features of the plants’ history of exposure to warm and cold. The model accurately predicts FLC silencing in new field data, allowing us to forecast FLC expression in changing climates. We suggest that distributed thermosensing may be a general property of thermoresponsive regulatory networks in complex natural environments.

Investigation of such a complex phenomenon requires interdisciplinary approaches, exploiting mathematical modeling as well as experiments (). This approach has been used to forecast flowering responses (). However, it is unclear how VIN3 and FLC expression are controlled by a plant’s history of warm and cold exposure (). Here, we systematically investigate the temperature dependencies for VIN3 and FLC dynamics, using a repeated cycle of hypothesis generation via mathematical modeling, followed by experiments under both controlled and natural field conditions (see Figure S1 A). This methodology identifies multiple thermosensing inputs into both VIN3 and FLC expression that respond to distinct features of the fluctuating temperature profile. The resulting mathematical model also successfully predicts VIN3/FLC expression dynamics for newly acquired field measurements. More broadly, our data, with numerous temperature-dependent steps for VIN3/FLC, support the general hypothesis that temperature sensitivity will be distributed throughout thermally responsive regulatory networks in biological systems, rather than being concentrated at particular steps with the rest of the network being temperature compensated. We emphasize that this distributed property of temperature sensing does not refer to a spatial distribution but rather to the distribution of the temperature response over many nodes of the network that regulates VIN3/FLC, a feature which is likely to be a general property of temperature sensing in biology. Overall, this work greatly extends our ability to understand and predict the thermal responses of biological systems to complex, real-world environmental conditions.

Previous work has shown that FLC downregulation during the cold is the result of at least two separate thermosensory pathways. The first pathway acts to downregulate FLC transcription and is responsive to transient low temperatures, such as autumn cold (). The second pathway enacts epigenetic silencing of FLC and requires the action of the conserved Polycomb Repressive Complex 2 (PRC2) combined with members of a PHD protein family, including VERNALIZATION INSENSITIVE3 (VIN3;). VIN3 is a key thermosensory component of the vernalization response, with VIN3 mRNA levels slowly rising with increasing weeks of cold exposure but rapidly decreasing in the warm (). These dynamics are consistent with control of VIN3 itself by (at least) two upstream thermosensitive inputs. VIN3 expression is very sensitive to spikes of warm temperature during the day, and so epigenetic silencing only occurs once winter temperatures prevail ().

Alignment of plant development to favorable environmental conditions requires mechanisms for sensing and integrating the environmental cues that indicate seasonal change. One of the key seasonal indicators is temperature, and many plant species need to experience winter chilling in order to flower (). In the Brassicaceae family, including Arabidopsis thaliana, the transcriptional regulator FLOWERING LOCUS C (FLC) represses the transition to flowering (). FLC is downregulated by prolonged cold and epigenetically silenced to maintain this state into the spring to allow the plant to be maximally responsive to floral-promoting long-day photoperiods (reviewed in). To accomplish this objective, the regulatory network controlling FLC must distinguish a clear seasonal signal over months, despite daily temperature fluctuations that can exceed average seasonal differences.

For both modifications to the temperature profile, we see an effect on simulated FLC shutdown. A 10-fold decrease in FLC mRNA concentration compared to its starting level is predicted to be reached on the 87 th day in Norwich for 2014–2015. In the ×2 treatment, this is reached with a 4-day delay, while in the +3 treatment a 22-day delay is predicted. For a 100-fold decrease in FLC level, which in Norwich 2014–2015 is predicted to be reached on the 126 th day, the delays have increased to 14 and 27 days, respectively. These results suggest that two potential effects of climate change, general warming and increased temperature fluctuations, will both negatively affect the efficiency of vernalization.

In comparison, stretching the field temperature profile T above and below the daily mean temperature (T) for each day, i.e., keeping the mean temperatures unchanged while increasing the fluctuations, had a smaller but still visible effect ( Figures 6 G, 6H, 6I, 6J, 6K, 6L, S11 C, and S11E). This effect was even smaller in the case of the vin3-4 mutant, where FLC decreased only due to the VIN3-independent pathway, for which the presence of cold was the driving mechanism. The stretch treatment did not increase the proportion of cold in the profile by much and therefore had little effect on the VIN3-independent pathway ( Figures 6 H and 6K). However, in Norwich, simulated VIN3 expression was lower in the stretch treatment, especially at later times due to the increase of the warm spikes, and this effect led to a slower simulated shutdown of FLC in the wild-type. The simulated epigenetic shutdown of FLC was even further impeded by the very low temperatures in the stretch treatment at those late times ( Figure S11 C).

We then modified the temperatures measured in the field to test what type of future climate changes might have the most significant effects on FLC expression. We first changed the mean temperatures while keeping the absolute size of the temperature fluctuations the same by adding 3°C to the entire field temperature profile (with the exception of temperatures around 0°C, when the plants are mainly covered by snow; STAR Methods ). Such a change is within the predicted range of temperature increases for the end of this century (). In Norwich, this intervention strongly impeded simulated upregulation of VIN3 and downregulation of FLC expression, as expected ( Figures 6 G, 6H, 6I and S11 B) since both the frequency and magnitude of high temperature spikes were increased ( Figure 6 G), while the frequency and magnitude of low temperature dips were reduced ( Figure 6 H). On the other hand, in North Sweden ( Figure S11 D), there was very little difference in the presence of cold ( Figure 6 J) or warm ( Figure 6 K) following this modification. As a result, simulated VIN3 and FLC both behaved similarly in the modified and original temperature profiles (Figure 6L). Interestingly, in the late phase of vernalization in Sweden (after ∼100 days), slightly faster simulated FLC shutdown could be observed in the case of added 3°C. This effect arose because temperatures close to 0°C and lower hinder vernalization (). Therefore, the increased but still low temperatures of the modified profile for Sweden are closer to the optimal range for FLC downregulation.

To more clearly distinguish these differing effects of the VIN3-dependent and -independent pathways, we also simulated the behavior of a vin3 null mutant ( Figures 6 E and 6F). In this case, as expected, we observed a significant impediment in the later simulated downregulation of FLC, as this mutant was blocked in epigenetic silencing. Once again, the day-mean treatment gave slower simulated downregulation in early winter ( Figure 6 F), confirming that this was due to the VIN3-independent pathway. Furthermore, a decrease in the frequency of low temperatures in the late period ( Figure 6 D) led to simulated reactivation of FLC in the vin3-4 mutant much earlier under the day-mean treatment ( Figure 6 E).

Having established that the VIN3/FLC combined model can predict responses to field conditions, we next examined which features of the field temperature profile it is most sensitive to by altering the temperature input. We first compared the results from the full temperature profile for Norwich 2014–2015 with that under a simplified treatment (day-mean) where the temperature profile each day is replaced by the mean value of that day ( Figures 6 A, 6B, 6C, 6D, 6E, 6F and S11 A) for ColFRI(the wild-type line, “ColFRI”). We find that, over an early period ( Figure 6 F), the absence of cold temperatures in the day-mean profile ( Figure 6 D) leads to slower simulated FLC downregulation, partly due to the VIN3-independent pathway being less activated. However, later in winter, the absence of daily warm spikes in the day-mean treatment ( Figure 6 A) causes simulated VIN3 levels to be higher ( Figure 6 C), leading to lower simulated FLC levels ( Figure 6 E).

(L) FLC and VIN3 mRNA predictions based on North Sweden 2014–2015 temperature (orange) compared to the modified profiles as in (J) and (K). Dashed lines are for vin3-4 mutant.

(J) “Presence of warm” features in three temperature profiles, North Sweden 2014–2015 (orange), the North Sweden profile modified by adding 3°C (“+3,” blue) or by stretching the temperatures around the daily mean (“x2,” pink).

(I) FLC and VIN3 mRNA predictions based on Norwich 2014–2015 temperature (orange) compared to the modified profiles as in (G) and (H). Dashed lines are for vin3-4 mutant.

(G) “Presence of warm” features in three temperature profiles, Norwich 2014–2015 (orange), the Norwich profile modified by adding 3°C (“+3,” blue) or by stretching the temperatures around the daily mean (“x2,” pink).

(A–F) Norwich 2014–2015 prediction for ColFRI Sf2 (ColFRI, green) compared to the prediction where the temperature at each time point is replaced by the 24-hr average temperature of that day (ColFRI day-mean, blue). The same is shown also for the vin3-4 mutant (pink and orange, respectively). (A) shows “presence of warm” features in the two temperature profiles, green for measured temperature, and blue for day-mean temperature. Presence of color stripe corresponds to a high temperature spike on that day (day maximum above 15°C). (B) Figure legend for (A)–(F). (C) VIN3 mRNA prediction, for ColFRI. (D) shows “presence of cold” features in the two temperature profiles, green for measured temperature and blue for day-mean temperature. Presence of color stripe corresponds to a low temperature dip on that day (day minimum below 10°C). (E and F) FLC mRNA prediction, for ColFRI and vin3-4 mutant. (F) shows the same predictions as (E) but only for the first 60 days, as indicated by dashed line square in (E).

In summary, we found substantive agreement between the model and our experiments, with the model showing significant predictive skill despite the intricate, fluctuating nature of the field temperature signal. Naturally, we cannot exclude the existence of other mechanisms that could explain this behavior. Nevertheless, the fact that our model can reproduce data collected from a wide range of conditions (including from field and various controlled-temperature profiles, from this paper, and from the literature) demonstrates that the model can be a powerful predictive tool.

The results of the temperature fluctuations in the field are visible in the VIN3 profile (e.g., Figure 5 A), where short-term temperature dynamics feed through to influence VIN3 expression. However, the slow, digital switching dynamics of FLC loci lead to noise filtering and to a smooth overall FLC expression profile, where sustained fluctuations affect the overall long-term rate of downregulation, but without a significant response of FLC to any specific temperature fluctuation event. Initially, VIN3 levels are low, and therefore the VIN3-independent pathway dominates the FLC dynamics. In a later phase, where VIN3 levels increase significantly, the rate of shut-down of FLC also tends to increase. Both years in Norwich and in North Sweden 2016–2017, the temperature conditions are such that an increase from low to high VIN3 levels happens abruptly, leading to a clear separation of the two phases ( Figures 3 C, 4 C, and 5 ). In 2014–2015 in Sweden, levels of VIN3 increase quickly right from the start of measurement ( Figures 3 D, 3E, 4 D, 4E, S6 A, and S6B). Small changes to the rate of FLC repression do subsequently occur in Sweden due to further increase of VIN3 levels. However, at the same time, lower temperatures directly reduce the efficiency of the transition to an epigenetically silenced state. These two effects substantially cancel out, effectively leading to a single, approximately exponential, FLC mRNA decay profile in the field ( Figures 4 D, 4E, and S6 B).

Nevertheless, there were still aspects of these new datasets that could not be accounted for, in particular for VIN3 ( Figure 5 C, late time points). Every day, VIN3 levels start very low and peak in the afternoon. Therefore, the sampling time relative to this diurnal pattern is critical to correctly estimate the amplitude of the oscillations. In North Sweden 2016–2017, we found that the diurnal pattern of VIN3 was shifted by several hours from that observed in controlled conditions or in Norwich 2016–2017 ( Figures S10 B, S10E, and S10H). This change meant that the peak of VIN3 expression was much later than our sampling time, and therefore we were greatly underestimating its amplitude. This effect could, in part, explain the difference between our data and the model prediction after ∼60 days in North Sweden ( Figure 5 C). The amplitude of the circadian clock gene EARLY FLOWERING3 (ELF3) and both the amplitudes and phases of LATE ELONGATED HYPOCOTYL (LHY) and especially CIRCADIAN CLOCK ASSOCIATED1 (CCA1) show differences between experimental sites and over time ( Figure S10 ), which could be related to the cold () and which may explain this shift. However, due to the uncertainties regarding the behavior of the circadian clock under these fluctuating field conditions, we did not attempt to explain this changed behavior with a more complex model for D. Overall, despite some discrepancies, we conclude that the model could predict VIN3 behavior, even in extremely challenging heterogeneous field conditions.

To fully test our parameterized model, we challenged it with a second set of field data from winter 2016–2017. Experiments were repeated in North and South Sweden, as well as Norwich, UK but brought forward by 2 weeks to ensure that warmer field temperatures would fully test our predictions on temperature sensitivity. The effectiveness of the model was demonstrated by our ability to predict the behavior of VIN3 and FLC in Norwich ( Figures 5 A and 5B ), North Sweden ( Figures 5 C and 5D), and South Sweden ( Figures S6 C and S6D), without reparameterization.

(C and D) As for (A) and (B) for new field conditions in North Sweden 2016–2017. n = 3–6; average > 4.6. For data, squares and bars show mean and standard error, respectively, while for the model, circles show the mean of the predicted values of VIN3 mRNA in the sampling time window and bars show the maximum and minimum values during that time window.

The overall mathematical model ( Figure 4 B; full description in STAR Methods ) was successfully fitted to experimental FLC data for mutants ( Figure S8 ) and wild-type plants (ColFRI) from the first field experiment ( Figures 4 C, 4D, 4E and S6 B), as well as laboratory experiments ( Figures 4 F and S9 ). As in the VIN3 model, temperature sensitivities enter in multiple places in the FLC model, supporting a hypothesis of distributed thermosensing, with routes to silenced FLC requiring temperature responsiveness at almost every step.

In addition to the temperature dependence of VIN3 dynamics, the I to E and H to E transitions are also directly temperature dependent. This feature is necessary to explain the absence of silencing in the warm in lines overexpressing VIN3 (), suggesting cold is necessary for the nucleation of epigenetic silencing. We also observed a difference in the rate of FLC downregulation at the different field sites, with the Swedish sites having slower downregulation despite higher levels of VIN3 compared to Norwich (). Consistently, vernalization has previously been found to be hindered by temperatures around 0°C or less (). The model therefore incorporated direct temperature dependency in the I to E and H to E transitions, with an optimal temperature for epigenetic silencing and no silencing either above 18°C or below −1°C.

The FLC model was parameterized using a wide variety of data from the literature ( Figures 4 C, 4D, 4E, 4F, S6 B, and S8 ), including 2014–2015 field data and the data presented in this paper ( Figures 2 S4 , and S9 ). The VIN3-independent part of the model was parameterized based on data from the vin3-4, vrn5-8, and vrn2-1 mutants ( Figures S4 and S8 ), where the PRC2-based switches to E are blocked. The VIN3-independent transition from H to I is reversible, since in the absence of epigenetic silencing, FLC levels reactivate in the warm (). Additionally, as shown above in Figures 2 and S4 , VIN3 levels are the same in the case of the midday and night spike treatments, but FLC levels are lower if the spike occurs during the day. The temperature-sensitive VIN3-independent dynamics of FLC (shown in the STAR Methods to be the I to H transition, r) are therefore taken to be controlled by night-time temperatures, defined as the 6 hr either side of subjective midnight. The rate of r is positively correlated with temperature in the range of “cool” temperatures ( Figure 4 B and STAR Methods ), as can be inferred from the faster rate of shutdown at colder temperatures in Figure S8

We next constructed a more extensive vernalization model, representing the dynamics of FLC, incorporating both VIN3-dependent (derived from the VIN3 model above) and VIN3-independent pathways. A conceptual outline of the FLC module is shown in Figure 4 A, based on previous experimental results (). Unlike the LSCD model, which represents the action of inferred thermosensory processes on VIN3 transcription, the FLC model consists of a series of digital states of the FLC gene that define its transcriptional state (), together with various transitions between the states. Only the first state (H, high transcription) is transcriptionally active. Gene copies in the H state can switch to a transcriptionally inactive state I, inactive) through a VIN3-independent pathway (). The mechanistic basis of the VIN3-independent pathway is still to be fully resolved but is likely to involve the functionality of non-coding COOLAIR antisense transcription or of the resulting transcripts (). Gene copies in the I state can then switch irreversibly to an epigenetically stable OFF state (E, epigenetically silenced) with a rate that depends on the cold-induced VIN3 level (). We also included an additional VIN3-dependent transition directly from H to E to allow epigenetic silencing of FLC in the absence of VIN3-independent FLC downregulation, but at a much slower rate than for the I to E transition (). Ordinary differential equations were used to capture the dynamics of the relative proportions of gene copies in each state over the whole plant ( Figure 4 B). Each gene copy switches states independently of other copies within the same cell or in surrounding cells ().

In all cases, squares and bars show mean and standard error, respectively. See also Figures S5, S6, S8 , and S9

To distinguish between these possibilities, we designed further temperature spike regimes with spikes in the morning, just before subjective day, or in the evening, just after the onset of subjective night (both in the dark). While these spikes again affected VIN3 similarly, they had different effects on FLC ( Figure S4 ): the morning spike and midday spike conditions were as effective for FLC downregulation as constant 12°C, despite the former treatments having higher average temperatures (12.75°C). However, the evening spike conditions were less repressive, and the night spike conditions repressed significantly less than the morning and midday spikes ( Figures S4 C–S4F; Kruskal-Wallis with Dunn’s post-hoc test, p < 0.05). The similar effects on FLC expression of the morning (in the dark) and midday (in the light) spikes suggest that light is not the gating factor. Overall, these results support a role for diurnal or circadian dynamics in the VIN3-independent pathway, with FLC repression being particularly sensitive to night-time temperatures.

We next turned to investigate the effect of temperature on FLC expression, mediated either through VIN3-dependent or -independent pathways. Above, we found that VIN3 expression was reduced by a spike of high temperature regardless of when that spike was applied, provided the spike occurred since the previous afternoon. We therefore examined the response of FLC to such spikes. In a previous study, we found that FLC is downregulated more in fluctuating 14.2°C conditions than constant 14.2°C, despite fluctuating 14.2°C conditions having lower VIN3 levels. This is due to the effect of the VIN3-independent pathway, which represses FLC at low temperatures, with lower temperatures being more repressive ( Figure 2 E;). Consistently, we found that fluctuating 14.2°C conditions had a similar level of downregulation as both constant 12°C and midday spike conditions ( Figure 2 E). However, despite having the same mean temperature and similar VIN3 expression profile as the midday spike (and also spike memory, which is treated identically to the midday spike for the 4 weeks prior to the day of sampling), the shift of the spike by 12 hr in the night spike impeded FLC repression ( Figure 2 E; Kruskal-Wallis with Dunn’s post hoc test p < 0.05) Furthermore, in the vin3-4 mutant, the night spike treatment also impeded repression ( Figure S4 D). These results suggest that the pathway controlling VIN3-independent transcriptional downregulation of FLC is gated in a diurnal, light-dependent, or circadian manner.

The model predicted large fluctuations from day to day in the “model daily” VIN3 levels in the spring ( Figures 3 C–3E). However, we do not have samples at high enough resolution to test if this was indeed the case in the field. Nevertheless, our predictions are consistent with the spring field samples we do have, as well as with results from our controlled experiments, such as for single days without a spike (spike memory) ( Figure 2 B), and also when a spike is introduced for the first time on the day of sampling (5°C with single spike) ( Figure S7 E and S7F).

However, the field experiments also exhibited phenomena not seen in the controlled environment data that the model was unable to capture, including variable VIN3 levels in the later stages of the 2014–2015 South Sweden data ( Figure 3 E). Field notes subsequently revealed that these plants had been buried under a mudslide during this time ( Figure 3 F), likely accounting for the divergence, since both hypoxia and light (indirectly, via circadian dynamics) regulate VIN3 (). We were also unable to reproduce an apparent age effect between the two plantings in North Sweden 2014–2015 ( Figures 3 D and S6 A), which we could not account for by temperature sensing alone since the plants were experiencing the same temperature conditions. Furthermore, the older plants ( Figure 3 D), which had experienced cold for longer, showed lower VIN3. Stress due to extreme cold conditions may have affected the younger plants more strongly than their older counterparts, leading to the observed effect.

The model could substantially reproduce the observed VIN3 behavior in constant and complex temperature conditions, both in controlled and field conditions ( Figures 3 C, 3D, 3E, S6 A, and S7 ). In particular, the model could recapitulate the VIN3 behavior observed in the warm spike experiments ( Figures S3 D–S3F; relative likelihood of LCD compared to LSCD based on Akaike’s information criterion: 5 × 10 Figures S7 E and S7F). In addition, the model also captured the substantial delay of VIN3 upregulation in Norwich due to warm autumn days ( Figure 3 C), as well as a subtler delay in the first North Sweden planting ( Figure 3 D).

(E) Comparison of model and experimental data from South Sweden in 2014–2015, as described for Norwich in (C). The late time points of the South Swedish data (brown bar) could not be fitted by our model, likely due to a mudslide (time given by start of brown bar) that damaged the plants and affected their VIN3 expression.

(D) Comparison of model and experimental data from North Sweden (early planting) in 2014–2015, as described for Norwich in (C).

(C) Comparison of LSCD model and fitted experimental VIN3 mRNA data for Norwich in 2014–2015. Data from, bars show mean and standard error, respectively. Model at sampling shows the mean of the predicted values of VIN3 mRNA in the sampling time window, which is defined as the period from 2 hr before the recorded sampling time to 2 hr after due to the long duration of sampling. The error bars show the maximum and minimum values of VIN3 mRNA during that time window. Model daily shows the predicted value for VIN3 mRNA at the same time every day (chosen as the time of the final sampling) to demonstrate the changes in amplitude of the VIN3 daily peak.

(A) Diagram of the LSCD model showing the primary signals registered by each component, their temperature dependence, and how they affect VIN3 transcription. Element L increases slowly in the cold (<17°C) and decreases slowly in the warm. Element S remembers the presence of a high temperature spike until the evening and, during that time, remains decreased. Element C is high at low temperatures and low at high temperatures, changing linearly with temperature between 8°C and 15.4°C. Element D cycles each day, peaking in the afternoon.

We chose forms for the temperature sensitivity that fitted our data and were simple to implement, but these are not unique, and indeed other forms could have been chosen, provided they had a similar shape in the ranges we investigated. More constraining were the timescales at which each pathway responded. Any plausible model must have temperature sensing at three timescales (long—month; short—day; current—hour), as well as diurnal variation, in order to explain our experimental observations. These three timescales are not tightly defined, with the exception of S, which appears to be tied to the 24-hr diurnal cycle. A 20% change in the timescale of L resulted in only a modest change in the agreement between the model and data (<5% change in relative error; see STAR Methods ). Furthermore, C is here modeled as instantaneous, but the splicing rate of VIN3 constrains the observed timescale of the current response, giving only an upper bound for the timescale of C. Therefore, a wide range of “Long” and “Current” timescales may be tolerated, but the two must be very well separated, being much longer and much shorter than a day, respectively.

We next added the short-term memory of warm spikes (S) process to our mathematical model for VIN3 dynamics. The functional forms we chose to represent L, S, C, and D in our LSCD model are defined in Figures 3 A, 3B, and S5 and STAR Methods . These functional forms and other parameters were fitted based on existing data from the literature ( Figures 3 C, 3D, 3E and S6 A), as well as the data from Figures 2 and S7 STAR Methods ). This overall dataset includes both controlled and field experiments.

Our results reveal distributed thermosensory inputs into VIN3 expression, involving slow (L), intermediate (S), and fast (C) dynamics, as well as inputs from the circadian clock (D). The overall effect of the LSCD regulation of VIN3 is a long-term memory of the length of cold, through L, which controls the amplitude of the diurnal VIN3 peak (D) and which is further adjusted by daily temperature values, either immediate (C) or since the previous afternoon (S).

Our experiments also allowed us to derive further understanding about L and C. After a fixed period of constant temperature, levels of VIN3 are anticorrelated with temperature (the graded response mentioned in the previous section; Figures 2 A–2D, “before”;). Conceptually, this effect could arise from either L building up more slowly at higher temperatures with a similar C or from C differentially affecting the transcription rate of VIN3 at different temperatures but with the underlying L dynamics being similar (provided the temperature is sufficiently low). To distinguish between these possibilities, we studied plants treated with different cold temperature regimes but then brought together for a final day at a common temperature. We found that VIN3 levels were different in the initial cold treatment ( Figure 2 D, “before”), as expected, but became similar on the final day ( Figure 2 D, “after”). This result clearly favors similar L dynamics but with fast-acting C responsible for higher VIN3 transcription rates at lower temperatures.

S must act on VIN3 transcription, since similar effects are seen for both spliced and unspliced VIN3 ( Figures 2 B and 2C). Moreover, since unspliced VIN3 levels respond immediately during and after the spike ( Figure 2 C, 12:30 data point in midday spike versus constant 12°C), this result still requires the presence of an immediate response (C) in addition to the short-term memory response of S. These two temperature-sensitive processes together combine to give the “absence of warmth response” that plants exhibit in vernalization thermosensing.

This deficiency suggests the need for a further thermosensitive process: a short-term memory (S) of the temperature experienced by the plant. S reduces VIN3 levels if warm temperatures have been experienced since the previous afternoon, consistent with the spike memory experiment and with the fact that a spike instead given the previous evening is still remembered the next day ( Figures S4 A and S4B). A more complicated alternative thermosensing structure might also be able to explain these data, for example, if C, as well as directly affecting VIN3 transcription, also feeds into D (thus indirectly introducing temperature sensing at a third timescale, through D). However, here we define a more general case by introducing S, as described above.

It is important to note that, in our reasoning above, although we referred to L and C, we did not use any of the specific properties assigned to them in the model presented in Figure S2 A, other than the timescales that we knew they must satisfy from experimental data. Therefore, we found that an LCD model with temperature input at two timescales cannot reproduce the effect of the temperature spikes. To further demonstrate this point, we used the specific model of Figure S2 A as an example and showed where it fails ( Figures S3 A–S3C).

We found that 2 hr of warm temperatures were sufficient to reduce VIN3 expression levels, as expected given the known fast response of VIN3 to warmth ( Figures 2 A–2C, midday spike versus constant 12°C). However, the timing of the temperature spike was not important for its effect on expression: the night spike had a similar effect on the following day’s VIN3 profile as a midday spike during the day of sampling ( Figures 2 A–2C, night spike versus midday spike). Immediate temperature sensing (C) is insufficient to explain this phenomenon, as the night spike occurred 10 hr before VIN3 reduction is greatest. Potentially, the temperature spikes could have caused a reduction in the long-term response. However, the influence of the spikes did not continue for longer than 24 hr: when plants were moved from 4 weeks in spike conditions back to constant 12°C, these plants behaved similarly to those with 12°C constant treatment without spikes ( Figures 2 A–2C, spike memory versus constant 12°C), indicating that L is unaltered.

We dissected this absence of warmth response by testing if a short spike of high temperature, applied daily in controlled conditions, would be sufficient to reproduce this behavior. We used a spike of 2 hr since we had observed that, post-cold, in constant warm conditions (above 20°C), VIN3 levels were significantly reduced after this time period (). We additionally tested whether the spike would produce different responses if it was received during the day or night. We therefore designed conditions in which plants remained at constant 12°C except for 2 hr at 21°C, with the spike in temperature during the day (midday spike, 2 hr after dawn) when VIN3 levels were high, but also during the night (night spike, 6 hr after dusk) when VIN3 levels were low ( Figure 2 A). We compared these conditions with constant 12°C, as well as with the constant and fluctuating temperature conditions (both with average 14.2°C) used previously ().

(E) FLC expression averaged over all the time points of sampling day after 4 weeks cold. Kruskal-Wallis with Dunn’s post hoc test between midday spike, night spike and spike memory (conditions with similar VIN3 expression for the 4 weeks of the treatment to test for VIN3-independent effect only) gives p < 0.05 significant difference ( ∗ in plot) between night spike and midday spike and between night spike and spike memory (no significant difference between midday spike and spike memory). Boxplots show median and 25 th and 75 th percentiles of the samples. Ends of whiskers show maximum and minimum values. n = 12–38; average > 30. In all cases, circle and bars show mean and standard error, respectively. RNA levels normalized to UBC, PP2A.

(D) VIN3 expression after 4 weeks cold in indicated conditions. “Before” refers to samples taken at 18:30 on sampling day, in the conditions indicated. “After” refers to samples that after 4 weeks cold in indicated conditions were further treated with, first, a further 4 days in the conditions indicated and then transferred in the afternoon (before dark) to constant 8°C conditions for approximately 24 hr before sampling at 18:30. n = 2–8; average = 4.4.

(B) VIN3 spliced expression during the day of sampling, sampled every 3 hr over a 12-hr period as shown. The green background indicates the time of the high temperature spike in the midday spike conditions. n = 1–9; average > 6.

(A) Temperature conditions given daily for 4 weeks (left) and then on day of sampling (right). Plants were grown in 20°C (night) or 22°C (day) 16-hr photoperiod for 1 week and then transferred to the conditions shown on the left. Dark background indicates nighttime (8-hr photoperiod).

To understand temperature sensing in natural conditions, we carried out experiments in field sites in three different climatic locations: North Sweden field (two plantings, 2 weeks apart), South Sweden field, and an unheated, unlit greenhouse in Norwich, UK ( Figure 1 A;). We sampled plants at regular intervals ( Figure 1 B), giving a high-resolution time series dataset for FLC and VIN3 RNA (). In field experiments, temperatures often spiked to high levels during the day in the autumn ( Figure 1 B), while, at the same time, the plants showed low VIN3 levels, despite low average temperatures (). High VIN3 levels instead occurred later in the season when high temperature spikes were absent.

(B) Example of sowing and sampling setup in the field experiments, showing the Norwich site 2014–2015. The temperature profile is shown together with the dates of sampling. Above the temperature plot, the approximate plant size throughout the experiment is shown, together with the tissues that were collected in the samples depending on the plants’ size (outlined in red), and the number of plants collected for each replicate. In Norwich, when plants were larger, only the youngest tissues were harvested, as indicated. 6 replicate samples were taken per time point, though some were lost in processing or unusable due to environmental factors, e.g., mudslides.

(A) Field sites in North Sweden (Ramsta), South Sweden (Ullstorp), and UK (Norwich). At the Swedish sites, plants were grown in trays bedded in the soil in the field. In Norwich, the plants were grown inside an unlit, unheated greenhouse with air-inlets, in trays bedded in vermiculite, ensuring the containment of transgenic lines while the plants still experienced natural conditions.

We combined these observations to generate a simple ordinary differential equation model for temperature-dependent VIN3 expression ( Figure S2 A). The three pathways operate such that the rate of “production” of VIN3 in the model is proportional to the product of L, C, and D ( STAR Methods ). This model was fitted to previously published data from controlled conditions (). We found that the data could in all cases be successfully described by the LCD model ( Figures S2 B–S2G). To further test our understanding, we then designed further experiments and tried to interpret the results using this model, as described in the next section.

In principle, these pathways could act on VIN3 transcription initiation, splicing, or degradation. However, we previously found similar expression patterns for both spliced and unspliced VIN3 RNA (). To explain this result, if splicing and degradation were modulated, these two processes would need to be altered in exactly the same way in response to temperature. In addition, the degradation rate of VIN3 mRNA is observed to be fast in both the warm and the cold, with an estimated timescale of hours (), arguing against temperature regulation of degradation. In the model, we therefore assume the simpler hypothesis that only transcription initiation is altered by temperature, which naturally generates the same response for both spliced and unspliced VIN3 levels.

Additionally, transcription of VIN3 is regulated by the circadian clock, with a peak of transcription in the afternoon in constant temperature conditions (). For this aspect, we require an additional component of VIN3 regulation, which we term diurnal (D), which we assume within this model to be temperature independent. We use a simplified function to represent the circadian clock ( Figure S2 A) as a mechanistic representation of this complex system is beyond the scope of this study and has been investigated in detail elsewhere (). Both C and D must act directly on VIN3 rather than on L due to the very different timescales of C and D (fast) as compared to L (slow) ().

The second thermosensitive pathway, which here we term current (C), measures current temperature and has fast-acting dynamics. C is responsible for the rapid reduction in VIN3 levels observed at high temperatures (), so that it can reproduce the “absence of warm” response seen in. However, there is also a graded response to cold in an intermediate temperature range, taking higher values at lower temperatures (). For simplicity, we modeled both these behaviors here as part of C ( Figure S2 A, equation for C), such that above this intermediate temperature range, it has a very low value, regardless of the temperature, and below this range, it takes its maximal value.

We modeled L such that it is produced only in the cold and degrades very slowly in both the cold and the warm, thereby integrating over the period of cold that the plant has experienced. To test this property, plants were grown in warm conditions for different lengths of time. When these plants were transferred to the cold for 1 day, they showed no evidence of increased L, since very low levels of VIN3 expression were observed regardless of the duration of the growth time ( Figure S1 F). L does not, therefore, accumulate at high (∼20°C) temperatures.

To produce the long-term, graded accumulation shown experimentally in Figures S1 B–S1E, L must have a very slow degradation timescale (weeks) in the cold (defined here as less than approximately 15°C;). We previously showed that the long-term thermosensitive process is able to accumulate in conditions where the temperature fluctuates above 20°C for 4 hr daily (). Therefore, the decay rate of L must also be relatively slow in warm temperatures, on a timescale of more than a few hours.

One temperature-sensitive pathway holds the memory of the duration of the cold. We termed this long term (L). For L to hold stable quantitative memory, an attractive hypothesis is a digital system similar to the one employed by FLC regulation (), in which individual cells show bimodal expression of FLC (either some or none). However, single molecule RNA fluorescence in situ hybridization (FISH) ( Figure S1 B) clearly showed an analog increase in the VIN3 RNA levels distributed evenly across different cells ( Figures S1 C–S1E). Hence, the effect of this thermosensitive process is graded, rather than all or nothing, at the level of VIN3 RNA.

To investigate the properties of these thermosensitive processes without knowledge of their biophysical identities, we developed a mathematical model of VIN3 dynamics. We were primarily constrained by the two very different timescales of the VIN3 response. We proceeded by fitting the temperature dependencies in the model at each timescale based on our and others’ previous experimental work ().

In order to fully understand how noisy field temperatures are integrated at FLC, we investigated the nature of the temperature inputs to the expression of the epigenetic regulator, VIN3. VIN3 expression is influenced by at least two separate thermosensitive processes (). One promotes expression while in the cold, providing the memory of cold duration with a long timescale of weeks, while a second reduces expression in the warm, with a fast-acting timescale of hours. The molecular basis of these processes is currently unknown but could include, for example, temperature-sensitive accumulation, depletion, conformational changes, or altered covalent modifications to proteins, RNA, or chromatin.

Discussion

In this work, we investigated the temperature sensitivity of the major regulators of vernalization, VIN3 and FLC, and then exploited this information to construct a modular mathematical model of the vernalization process. We used an experiment-driven approach, logically extracting from our data the features and timescales that an underlying model must include. We chose functional forms in the model that could reproduce our data and represent the observed varied temperature sensing. Our VIN3/FLC model could then in most circumstances accurately predict VIN3 and FLC response to temperature in the field, although we were not able to capture some aspects of age and diurnal response.

2 ,s 3 )) of the vernalization pathway had to be temperature sensitive. For the remaining steps, it was not necessary to include temperature sensitivity, but there was no evidence to suggest that such sensitivity could not exist. Multiple temperature sensitivities have also been found in the regulation of the gene FT ( Kinmonth-Schultz et al., 2018 Kinmonth-Schultz H.A.

MacEwen M.J.

Seaton D.D.

Millar A.J.

Imaizumi T.

Kim S.-H. Mechanistic model of temperature influence on flowering through whole-plant accumulation of FT. Quint et al., 2016 Quint M.

Delker C.

Franklin K.A.

Wigge P.A.

Halliday K.J.

van Zanten M. Molecular and genetic control of plant thermomorphogenesis. Wigge, 2013 Wigge P.A. Ambient temperature signalling in plants. In developing the model, we identified a need for multiple, distributed thermosensory inputs into VIN3 and FLC and progressed our understanding of which aspects of the temperature signal each step was sensitive to. In fact, we found that most steps (L, S, C, VIN3-independent (r), VIN3-dependent (s,s)) of the vernalization pathway had to be temperature sensitive. For the remaining steps, it was not necessary to include temperature sensitivity, but there was no evidence to suggest that such sensitivity could not exist. Multiple temperature sensitivities have also been found in the regulation of the gene FT (). Such distributed thermosensing is in contrast to an alternative hypothesis where thermal response is proposed to be governed by a small number of core thermosensors (). We find this latter hypothesis to be generally less likely due to the global temperature dependence of biochemistry. Furthermore, an isolated thermosensor would require the remainder of the network to be temperature compensated, a situation that would not be straightforward to achieve. For these reasons, we expect that temperature sensing will be fundamentally different from sensing other environmental signals such as light perception, where isolated, specialized sensors are certainly required.

Nagel et al., 2015 Nagel D.H.

Doherty C.J.

Pruneda-Paz J.L.

Schmitz R.J.

Ecker J.R.

Kay S.A. Genome-wide identification of CCA1 targets uncovers an expanded clock network in Arabidopsis. In our analysis, we identified a new thermosensing element: short-term memory of warm spikes (S). Its behavior is consistent with a response to warm temperatures that resets its short-term memory every evening. Indeed, in Figure 2 B, at the first time point after dusk, the levels of VIN3 in treatments with a temperature spike were reset to the levels of treatments with constant background temperature, suggesting that the circadian clock is involved. VIN3 is also regulated directly by the clock, through D, consistent with the known binding of the circadian regulator CCA1 to the VIN3 promoter ().

Bond et al., 2009a Bond D.M.

Dennis E.S.

Pogson B.J.

Finnegan E.J. Histone acetylation, VERNALIZATION INSENSITIVE 3, FLOWERING LOCUS C, and the vernalization response. Bond et al., 2009b Bond D.M.

Wilson I.W.

Dennis E.S.

Pogson B.J.

Jean Finnegan E. VERNALIZATION INSENSITIVE 3 (VIN3) is required for the response of Arabidopsis thaliana seedlings exposed to low oxygen conditions. Bond et al., 2011 Bond D.M.

Dennis E.S.

Finnegan E.J. The low temperature response pathways for cold acclimation and vernalization are independent. Finnegan et al., 2011 Finnegan E.J.

Bond D.M.

Buzas D.M.

Goodrich J.

Helliwell C.A.

Tamada Y.

Yun J.-Y.

Amasino R.M.

Dennis E.S. Polycomb proteins regulate the quantitative induction of VERNALIZATION INSENSITIVE 3 in response to low temperatures. From our analysis, we cannot exclude the possibility that there is cross-talk between the thermosensor pathways L, S, and C and indeed that some factors may be common between them. However, the key result is that they must be distinct in their response, as they sense temperature at different timescales. At present, there are no clear candidates for L, S, and C (). Instead, focused genetic screens in specific temperature regimes will need to be undertaken to identify these components. However, we expect that the detailed dissection of their properties carried out here should greatly facilitate their molecular identification.

Hepworth et al., 2018 Hepworth J.

Antoniou-Kourounioti R.L.

Bloomer R.H.

Selga C.

Berggren K.

Cox D.

Collier Harris B.R.

Irwin J.A.

Holm S.

Säll T.

et al. Absence of warmth permits epigenetic memory of winter in Arabidopsis. Aikawa et al., 2010 Aikawa S.

Kobayashi M.J.

Satake A.

Shimizu K.K.

Kudoh H. Robust control of the seasonal expression of the Arabidopsis FLC gene in a fluctuating environment. Chew et al., 2012 Chew Y.H.

Wilczek A.M.

Williams M.

Welch S.M.

Schmitt J.

Halliday K.J. An augmented Arabidopsis phenology model reveals seasonal temperature control of flowering time. Wang et al., 2002 Wang E.

Robertson M.J.

Hammer G.L.

Carberry P.S.

Holzworth D.

Meinke H.

Chapman S.C.

Hargreaves J.N.G.

Huth N.I.

McLean G. Development of a generic crop model template in the cropping system model APSIM. Wang et al., 2017 Wang E.

Martre P.

Zhao Z.

Ewert F.

Maiorano A.

Rötter R.P.

Kimball B.A.

Ottman M.J.

Wall G.W.

White J.W.

et al. The uncertainty of crop yield projections is reduced by improved temperature response functions. Weir et al., 1984 Weir A.H.

Bragg P.L.

Porter J.R.

Rayner J.H. A winter wheat crop simulation model without water or nutrient limitations. This work also confirms our earlier proposal () that the L element acts similarly to the “day-degree” element used in agricultural crop modeling, recording time within a temperature interval rather than the temperature itself (). Elements C and S then add information on current and recent temperatures to the VIN3 system, responding rapidly to current and recent conditions. This combination of long-term (L) and shorter-term (C and S) temperature monitoring provides a sophisticated mechanism to distinguish between autumn and winter, even in the presence of large seasonal temperature fluctuations. This ability is generated by multiplicative regulation of VIN3 by the thermosensing elements; if any are low, then the VIN3 levels are also low. Under normal conditions, in autumn, plants have not experienced cold for long enough to accumulate high levels of L. However, should L accumulate to high levels early due to inadvertent early germination, the fast response due to S and C will be sufficient to keep VIN3 levels low until temperatures stop spiking to high levels daily. On the other hand, in the case of an unusually cold autumn, when S and C may be high, low levels of the L thermosensor will act as a break early on, delaying the response of VIN3.

Chew et al., 2012 Chew Y.H.

Wilczek A.M.

Williams M.

Welch S.M.

Schmitt J.

Halliday K.J. An augmented Arabidopsis phenology model reveals seasonal temperature control of flowering time. Hepworth et al., 2018 Hepworth J.

Antoniou-Kourounioti R.L.

Bloomer R.H.

Selga C.

Berggren K.

Cox D.

Collier Harris B.R.

Irwin J.A.

Holm S.

Säll T.

et al. Absence of warmth permits epigenetic memory of winter in Arabidopsis. Sidaway-Lee et al., 2010 Sidaway-Lee K.

Josse E.M.

Brown A.

Gan Y.

Halliday K.J.

Graham I.A.

Penfield S. SPATULA links daytime temperature and plant growth rate. Topham et al., 2017 Topham A.T.

Taylor R.E.

Yan D.

Nambara E.

Johnston I.G.

Bassel G.W. Temperature variability is integrated by a spatially embedded decision-making center to break dormancy in Arabidopsis seeds. The importance of deepening our understanding of how fluctuations affect temperature responses has been widely recognized (). The slow dynamics of L and the digital nature of the epigenetic pathway of FLC shutdown combine to give a highly effective integration over the noisy temperature signal. However, we also find that the warm sensitivity of S and C combine to make the VIN3-dependent pathway particularly sensitive to warm spikes in temperature during the autumn in the field. In the present climate, this effect is largely compensated for by the VIN3-independent pathway, which responds to the cold nights of autumn and represses FLC transiently. In modeling future climates, we find that higher temperatures due to global warming are likely to lead to a decrease in repression provided by both the VIN3-dependent and VIN3-independent pathways in climates such as Norwich ( Figures 6 G–6I). However, the same temperature change in Sweden is not predicted to have as strong an effect on vernalization in the synthetic accession we analyzed in this study ( Figures 6 J–6L). In fact, the model shows that an increase of temperature would lead to less extreme cold temperatures, bringing the temperature profile closer to the vernalization optimum and therefore paradoxically accelerating FLC shutdown.

To make more realistic predictions of vernalization under future climates, it will be informative to utilize climate model projections. However, we find that warm temperature spikes of even a short duration can have dramatic effects on vernalization. It will therefore be necessary to use very high temporal resolution temperature profiles for the predictions. Furthermore, it will be important to consider the local microenvironment of the vernalizing plant tissues. For Arabidopsis, it will be the temperature at the soil surface that is most relevant and often in direct sunlight. Temperatures in such a microenvironment may be significantly different from the temperatures observed even 1 m above the soil or in the shade, particularly with reference to the absence of short-term warm spikes. Integrating models of the type described in this paper with appropriate climate projections will therefore be a significant challenge for future studies.