Team:ETH Zurich/Modeling/UVR8

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Contents

UVR8-TetRDBD

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. However, we employ it differently, as described here. In the following, we analyse the theoretical requirements for our system that employs UVR8's dimerisation ability to work. It involves some manual parameter optimisation in order to determine the optimal concentration regimes for the receptors and enzymes in the cell.

Circuit

The following scheme illustrates the system:

ETH UVR8.png

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-TetRDBD is conserved. This translates to a model not explicitly accounting for UVR8-TetRDBD expression/degradation, as this will be the case for most systems in steady state anyway.
  • The photoconversion process upon UV exposure of UVR8-TetRDBD is modelled as a 2-state process. While fundamentally it is highly likely that the conversion process involves a number of (meta-stable) intermediates, 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, PABA overexpression can be achieved without upregulating pabC (aminodeoxychorismate lyase). Hence, this step is not rate-determining 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 a production term of PABA depending on the produced PabAB concentration and the assumed intracellular [Chorismate]cell concentrations and a first-order outflux term with kout.
  • Lastly, PabAB is constitutively degraded with kdeg.
  • We are interested in the effect of PABA on the dissociation of UVR8. As PABA can be regarded as a competitor for UVB in the cell, we model this negative feedback loop with a hill-like term in the dissociation step.

ODEs

With the aforementioned assumptions, the coupled systems boil down to:

Fig. 1: ODEs for the no-inhibition model.
Fig. 2: ODEs for the inhibition model. Notice the hill-like inhibition term highlighted in red.

The parameter khv and kdecay have been determined from gel assays with approximative half-lives. The promoter strength has been optimised such that we get the required enzyme concentrations. Degradation rates have been assumed from a mean half-life of 5 hours. The enzyme kinetical parameters can be found in the literature [Roux1992]. Lastly, the outflux term kout has been selected such that PABA steady-state values are comparatively large - this would involve certain metabolic optimisations in-vivo. n in the hill kinetic term with [PABA] accounts for a more or less sigmoidal behaviour of PABA inhibition.
Find the parameters we used on our parameter page.

Results

ETH UVR8-noInhib.png

Simulations have first been run for 4 hours in the dark ("inside condition"), with another 4 hours under sunny conditions. Notice the time span between first sun exposure and half-maximum of PABA production, the second sigmoidal step: This time is around 1 hour, a satisfactory time scale for the production of protective PABA for the average european caucasian after sun exposure.

Considerations

Using half-lives from in-vitro gels gives a rough figure of the timescale on which UVR8-TetRDBD dissociates. Calculating reaction parameters for UVR8 from first principles proved to be harder than expected: there are a number of consecutive chemical reactions involved in leading to a dissociated monomer, all of which we believe tend to occur on the same timescale. This clearly conflicts with an assumed 2-state model. As such, this would require an extensive photoinduction model, which is not possible at the moment, due to the exact number of reactions required not entirely known.

Another future 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 more knowledge about how PABA UVB-absorption interferes with the receptor (UVR8) UV absorption. This might require a diffusion model of PABA when considering a layer model.


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