by Aalt-Jan van Dijk
Wageningen University, The Netherlands
In one of my previous commentaries (see ‘A hitchhiker guide to modelling’), I discussed some issues related to the development of computational models for the molecular regulation of flowering. One aspect that I did not mention was how the different timescales at which biological processes take place have repercussions for the models built to represent these processes, and vice versa, how different models deal with time in different ways. One example is that in some modelling approaches (e.g. Boolean Networks) time is represented as a discrete variable. In other modelling approaches, time is continuous. Ordinary differential equations (ODEs) are the most prominent example of such models. ODEs can model processes that take place ‘fast’ as well as ‘slow’. This is encoded in the model either by the structure of the equations or by the value of specific parameters in the equations. One example from my own work is transport of FT which can be included in an ODE model using a so-called delay term in the equations (Leal Valentim et al., 2015).
Different time scale are clearly present during vernalization. As it is well-known, FLC is downregulated by prolonged cold and epigenetically silenced to allow the plant to be maximally responsive to floral-promoting long-day photoperiods in spring. The regulatory network controlling FLC must distinguish a seasonal signal over months, despite daily temperature fluctuations that can exceed average seasonal differences. A recent publication by Antoniou-Kourounioti et al. 2018 analyse the regulation of FLC by temperature using a mathematical model for vernalization that operates on multiple timescales: long term (month), short term (day), and ‘immediate’ response. Here, I describe how this model was built and how it describes fast and slow response of plants to temperature.
The model contains two main modules: one consisting of a model for VIN3 regulation, and the other for FLC regulation. In both models, temperature sensing itself is not directly modelled; rather, heuristic functions are defined which reflect how temperature changes would affect VIN3 and FLC. In addition, temperature-induced changes in VIN3 also affect FLC because of the regulation of FLC by VIN3.
For VIN3 regulation, two thermoregulatory processes were already known experimentally, and both of these were included in the model. (i) One temperature-sensitive pathway holds the memory of the duration of the cold. This process was described by a component that would be 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. (ii) For a second temperature-sensitive pathway a component was used which measures current temperature and has fast-acting dynamics. This component is responsible for the rapid reduction in VIN3 levels observed at high temperatures. In addition to these two temperature-dependent pathways, a temperature-independent function was used to represent the circadian clock.
After performing experiments with temperature spikes which I do not describe here, a vernalization model was constructed, representing the dynamics of FLC, incorporating both VIN3-dependent (derived from the VIN3 model above) and VIN3-independent pathways. The FLC model consists of three states of the FLC gene, together with transitions between these states. One of the states is transcriptionally active. Gene copies in this state can switch to a transcriptionally inactive state through a VIN3-independent pathway. From the inactive state, there is an irreversible switch to an epigenetically stable off state. The rate at which this switch takes place depends on the cold-induced VIN3 level. An additional VIN3-dependent transition directly from the active stage to the off state allows epigenetic silencing of FLC in the absence of VIN3-independent FLC downregulation. In addition to the temperature dependence of VIN3 dynamics, the transitions to the off state are also directly temperature dependent in this model.
To build the model described above, experimental data were used for model construction and for parameter fitting. The fact that the model can reproduce these data does not tell us whether it is capable of predicting anything. To test this, the authors used additional field experiments: measured temperature profiles from these experiments were used as input to predict VIN3 and FLC, and these predictions were compared with measurements. Such comparison is less straightforward than one might think. For example, the time of the day at which sampling takes place could clearly have an influence. It is mentioned that the diurnal pattern of VIN3 was shifted by several hours between different experimental conditions. This change meant that the peak of VIN3 expression was much later than the sampling time in some conditions, and therefore, compared to the model, the experiments had much lower amplitude for these samples. To me this demonstrates one key reason why models can be useful: not only when they are ‘correct’ but in particular when there is a mismatch between model predictions and experimental data, which helps to make knowledge gaps very explicit.
Having established that the VIN3/FLC combined model can predict responses to field conditions, it was examined to which features of the field temperature profile the model was most sensitive. First, the full temperature profile was replaced by the mean temperature of each day. According to the model, because of lower activation of the VIN3-independent pathway, the absence of cold temperatures in the day-mean profile initially lead to slower FLC downregulation. However, later in winter, the absence of daily warm spikes caused simulated VIN3 levels to be higher, leading to lower simulated FLC levels. In subsequent simulations, a higher mean temperature as well as the same mean temperature with more fluctuations were tested.
One main conclusion from the paper is that temperature sensing is broadly distributed, with various thermosensory processes responding to specific features of the plants’ history of exposure to warm and cold. Less strongly stated, the paper presents a model describing distributed thermosensing, which is in accordance with the available experimental data. Apart from what these results mean for our understanding of thermosensing, I found it particularly interesting that the paper demonstrates how a computational model can be used to improve our understanding of fast and slow response during vernalization.
Antoniou-Kourounioti RL, Hepworth J, Heckmann A, Duncan S, Qüesta J, Rosa S, Säll T, Holm S, Dean C, Howard M. 2018. Temperature sensing is distributed throughout the regulatory network that controls FLC epigenetic silencing in vernalization. Cell 7, 643-655.e9. https://doi.org/10.1016/j.cels.2018.10.011
Espinosa-Soto C, Padilla-Longoria P, Alvarez-Buylla ER. 2004. A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. The Plant Cell, (16) 2923–2939. DOI: https://doi.org/10.1105/tpc.104.021725
Leal Valentim F, van Mourik S, Posé D, Kim MC, Schmid M, van Ham RCHJ, Busscher M, Sanchez-Perez GF, Molenaar J, Angenent GC, Immink RGH, van Dijk ADJ. 2015. A quantitative and dynamic model of the Arabidopsis flowering time gene regulatory network. PLoS ONE 2015 doi: 10.1371/journal.pone.0116973. https://doi.org/10.1371/journal.pone.0116973