Mathematical model in absolute units for the Arabidopsis circadian oscillator

The Earth’s oblique rotation results in changes in light and temperature across the day and time of year. Living organisms evolved rhythmic behaviours to anticipate these changes and execute appropriate responses at particular times. The current paradigm for the biological clocks in several branches of life is an underlying biochemical oscillator mainly composed by a network of repressive transcription factors. The slow decay in their activity is fundamental for generating anticipatory dynamics. Interestingly, these dynamics can be well appreciated when the biological system is left under constant environmental conditions, where oscillation of several physiological readouts persists with a period close to 24 hours, hence the term “circadian clocks”, circa=around dian=day. In plants the model species Arabidopsis thaliana has served as an invaluable tool for analysing the genetics, biochemical, developmental, and physiological effects of the oscillator. Many of these experimental results have been integrated in mechanistic and mathematical theories for the circadian oscillator. These models predict the timing of gene expression and protein presence in several genetic backgrounds and photoperiodic conditions. The aim of this work is the introduction of a correct mass scale for both the RNA transcript and protein variables of the clock models. The new mass scale is first introduced using published RNA data in absolute units, from qRT-PCR. This required reinterpreting several assumptions of an established clock model (P2011), resulting in an updated version named U2017. I evaluate the performance of the U2017 model in using data in absolute mass units, for the first time for this clock system. Introducing absolute units for the protein variables takes place by generating hypothetical protein data from the existing qRT-PCR data and comparing a data-driven model with western blot data from the literature. I explore the consequences of these predicted protein numbers for the model’s dynamics. The process required a meta-analysis of plant parameter values and genomic information, to interpret the biological relevance of the updated protein parameters. The predicted protein amounts justify, for example, the revised treatment of the Evening Complex in the U2017 model, compared to P2011. The difficulties of introducing absolute units for the protein components are discussed and components for experimental quantification are proposed. Validating the protein predictions required a new methodology for absolute quantification. The methodology is based on translational fusions with a luciferase reporter than has been little used in plants, NanoLUC. Firstly, the characterisation of NanoLUC as a new circadian reporter was explored using the clock gene BOA. The results show that this new system is a robust, sensitive and automatable approach for addressing quantitative biology questions. I selected five clock proteins CCA1, LHY, PRR7, TOC1 and LUX for absolute quantification using the new NanoLUC methodology. Functionality of translation fusions with NanoLUC was assessed by complementation experiments. The closest complementing line for each gene was selected to generate protein time series data. Absolute protein quantities were determined by generation of calibration curves using a recombinant NanoLUC standard. The developed methodology allows absolute quantification comparable to the calibrated qRT-PCR data. These experimental results test the predicted protein amounts and represent a technical resource to understand protein dynamics of Arabidopsis’ circadian oscillator quantitatively. The new experimental, meta-analysis and modelling results in absolute units allows future researchers to incorporate further, quantitative biochemical data

NOX effect on LL tau within the F2014 Arabidopsis Clock model

The model F2014 integrates new components into a more extensive clock model Fogelmark K. and Troein PLoS Comp. Bio. 2014. While exploring the effects of NOX in the framework I found two interesting problems. First, The effect of NOX in the eight reported parameter sets is inconsistent, some of them shorting the period and other lengthening it. The data for expressers of NOX using CaMV35S promoter present longer period from 25 hours wild type to 30 35S:BOA. Some of the parameter sets are not consistent with the data and can be discarded (short period as expression increases). Second, it is important to remark the high uncertainty in period predictions in this model. This is relevant for example if we try to relate the effect of multiple copies of BOA gene on the clock period. High variability in model predictions stop us from linking model results to experimental data. For example the experiment being super transformation of BOA in WT plants and quantifying the effects on period. From which we can attempt to infer amount of extra BOA and as a result total BOA amount in the extended system