Team:ETH Zurich/Modeling/UVR8

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UVR8

UVR8 (UV Resistance Locus 8) acts as a UVB photoreceptor in plants. It regulates the transcription factor COP and indirectly affects the expression of a myriad of genes. Here we analyse the theoretical requirements for our system to work. It involves some mild mathematical optimisation in order to determine the optimal concentration regimes for the receptors in the cell.

Circuit

The following schematics illustrate the system:

Modelling assumptions

In order to analyse a number of properties of the system, the model needs to be tractable. For this, a number of assumptions and approximations have been made:

  • UVR8 is conserved. This translates to a model not explicitly accounting for UVR8 expression/degradation, as this will be the case for most systems in steady state anyway.
  • The photoconversion process is modelled as a 2-state process. While fundamentally it is highly likely that the conversion process involves a number of (meta-stable) intermediaries, there is usually one rate-determining step. All other steps are then assumed to be in quasi-stationary state, thus simplifying to a 2-state system.
  • Those parts of the metabolic pathway that have been cloned into our E.coli have been incorporated into our model. For this we assume the intracellular [Chorismate]cell concentrations to be constant.
  • Furthermore, as it is known that pABA overexpression can be achieved without upregulating pabC (aminodeoxychorismate lyase), this step is not the rate-determining step in PABA formation. Thus pabC has kinetics on a smaller timescale than PabAB such that 4-amino-4-deoxychorismate (ADC) concentrations are never high - justifying another quasi-stationary-assumption.
    • This leads to production term of pABA depending on the produced PabAB concentration and the assumed intracellular [Chorismate]cell concentrations and a first-order outflux term.
  • UVR8 dissociation has been modelled with an additional inhibitory Hill-like term. As pABA absorbs in a similar range as UVR8, this will evidently cause less UVR8 to dissociate, effectively inhibiting the repression of PabAB. We analyse whether this system exhibits oscillations.
  • Lastly, PabAB is constitutively degarded.

ODEs

With these assumptions, the coupled system boils down to:

Figure 1: List of ODEs for the UVR8 system.

Performing linear stability analysis on this system yields:

Results

Plots

Outlook

As most cellular proteins containing tryptophan and tyrosine absorb in the UVB range, the theoretical calculations for the rate parameters are a first approximation. Taking this general background absorption into account will refine and provide for a more realistic model.

Another improvement to be included will focus on improving the negative feedback part of the model. Currently this negative feedback from pABA is modelled with a Hill-like inhibition - in future this should be from first principles which will require an effective absorbance cross-section (?!).


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