Given the importance of the circadian clock in regulating the timing of many processes within a plant, using systems biology to understand the mechanisms by which it is regulated becomes crucial. Whilst abstract models describing how major components interact to occur anti-phase is useful, it lacks the specificity needed to understand how the measured data is being produced in planta.
When a core component is altered in the plant, many effects occur because of it. Using an abstract model, it is often difficult to predict the effect on the other components, especially in a system like the clock where there are so many feedback loops. Using a mathematical model, however, the change to the physiology can be simulated and results hypothesized. This can help select which experiment is most likely to produce the desired results.
1.3.1
– Evolution of the Circadian Clock Model
The model of the plant circadian clock has gone through a number of iterations and developments in the last 8 years as more experimental data uncovered extra components and new connections. One of the earliest models was published in by(Locke et al. 2005). It consisted of two genes – LHY and TOC1 – and two hypothetical proteins – X and Y (Fig 1.4 A). Simulations of this model predicted a specific mRNA expression profile for gene Y. This included an acute peak at dawn as well as a more conventional peak around dusk. Using this information, an experiment was designed to look specifically for this expression profile by screening at a higher time resolution at dawn. Through this, GI was identified as a candidate for protein Y. This was then incorporated into the model, as well as an additional loop including the PRR’s that was discovered at the same time (Fig 1.4 B). This increased model had six genes – CCA1, LHY, PRR7, PRR9, GI, TOC1 – and two hypothetical proteins, X and Y. Although GI captured a large proportion of the hypothetical protein Y, it was not sufficient to fully explain the mutant data. This simplistic 3-loop model was capable of capturing the majority of the published data, generated under standard growth
Introduction
A)
C)
D)
Figure 1.4 Evolution of the Arabidopsis Circadian Clock Model. Visual depictions of the various incarnations of the circadian clock model from A) a 2-loop model (adapted from Locke et al. 2005), B) a 3-loop model (adapted from Locke et al. 2006), C) an expanded 3-loop model (adapted from Pokhilko et al. 2010) and D) the repressilator (adapted from Pokhilko et al. 2012).
Introduction
conditions. However, inclusion of hypothetical components suggested it was missing important information. Furthermore, light input to the clock was relatively simplistic in this model, with important nodes identified with lightning bolts. However, simulations using light regimes that were not 12 hour light:12 hour dark (12:12) did not match data as well as later models do.
This model was subsequently expanded by (Pokhilko et al. 2010) to better represent the morning loop, and to include ZTL within the evening loop. X was replaced with a modified form of TOC1 and a new unknown, NI, was included (Fig 1.4C). The split of PRR9 and 7 along with the addition of NI, of which PRR5 was thought to be a likely component, allowed the model to fit the data better, where there was a small but significant delay in the peak of these genes. This model was further developed by (Pokhilko et al. 2012) making use of new data on a multi protein complex referred to as the evening complex. This complex removed the need for component Y. Similarly the discovery that TOC1 binds to the promoters of LHY and CCA1 and represses their expression (Gendron et al. 2012) was incorporated into the model (Fig 1.4D). This model also included a more complex relationship between light and the circadian clock. Light interacts with the model at more points and in a more specific manner.
1.3.2
– Limitations of Models
Despite the improvements that have been made to the plant circadian clock models, they are still limited by the assumptions and data used to create them. Samples used to generate quantitative data are not only multicellular, but often contain several tissue types and even groups of plants. Thus, the model being produced is at best an average model. This leads to complications when fluorescent protein constructs under confocal imaging show that the clock in different tissues are often asynchronous. The problem with this is best shown by whether a plant is grown on sucrose or not. Plants grown in the dark without sucrose exhibit a rapidly dampening circadian rhythm when compared to plants on sucrose in the dark. However, single cell imaging studies show that the clock
Introduction
does not dampen, but rather individual cells become asynchronous with neighbouring cells, making the pooled sample arrhythmic as a whole (personal communication, Gould and Hall).
Furthermore, whilst light input is modelled in the clock, there is no mechanism by which other stimuli such as temperature may be considered. As such, current models may be good for looking at a whole plant grown on sucrose at 22˚C, but become increasingly misleading under other conditions are changed. Adding
Arrhenius functions to light inputs has been shown to produce a model that matches many of the gene period differences that are produced by growing
plants at different ambient temperatures (Gould et al. 2013). However, the
precise mechanism that allows themocycles to entrain the clock, as well as
maintain temperature insensitivity has not yet been modeled effectively.The
current best model also attempts to model CCA1 and LHY together as a single component. Considering these genes are known to perform partially redundant functions, this perhaps is not surprising. LHY has been shown to have a more critical role at high temperatures, whereas at low temperatures it was CCA1 that was dominant in controlling circadian rhythms (Gould et al. 2006).
1.3.3
– Simplifying the Clock for Modeling
In addition to the problems linked to the types of assumptions mentioned above, adapting the clock for various environmental conditions proves difficult due to the number of elements that need to be modelled. This then leads to a large number of parameters or connection strengths that need to be optimised or calculated. For many of the genes in the plant circadian network, we know values for the mRNA level, the cytoplasmic protein level and the nuclear protein level. These all have a basal rate of production and degradation as well the change in rates caused by interactions with other genes. Much of the research into expanding the plant clock model involves adding components rather than an option to simplify the number of interactions. However, previous models have successfully simulated data without the need for protein data. As such,
Introduction
only using mRNA abundance data to create a model, whilst simplistic, should be capable of capturing the major aspects of the network and provide a simpler skeleton to fit additional genes in (Akman et al. 2012). This will have parts missing, such as the evening complex, but just as X and Y have previously been used to explain a missing component or connection, so too can a representative variable (i.e. Z) be included to represent a protein complex, or complexes, should it/they be required to construct a viable model. Alternatively, a variable time delay between different genes can be used to model any additional protein step detected for some genes in the network.
Introduction