Team:ETH Zurich/Modeling/Construct1

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Contents

UVR8-TetRDBD/LovTAP

In order to account for varying light intensity ratios, we employ a second photoreceptor to "calibrate" for light intensity. This prevents spurious activation of the downstream protection system. As UVR8-TetRDBD is our engineered protein that we wish to employ for UVB detection, we combine it with LovTAP in the form of a decoder. For this, we define a set of conditions beforehand and devise a model to differentiate between these light sources. The designed circuit includes a number of reporter genes for debugging. Once the circuit has been shown to work as a whole, pabAB is placed under control of the central operon regulated by UVR8 and LacI, as is depicted here.

Boolean logic

Boolean response
UV-Lightinput Blue-Lightinput OutputGreen OutputRed OutputViolet/pabAB Situation
0 0 0 0 0 darkness
0 1 1 0 0 modern interior light source e.g. [http://en.wikipedia.org/wiki/Cold_cathode CCFL]
1 0 0 1 0 tanning bed - known carcinogen!
1 1 0 0 1 sun exposure

Circuit

The following scheme illustrates the system:

ETH Construct1 Circuit.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 and LovTAP are conserved. This translates to a model not explicitly accounting for photoreceptor expression/degradation, as this will be the case for most systems in steady state anyway. Biological optimisation will instead focus on choosing the optimal ratio of promoter strength kP to degradation rate kdeg of the photoreceptors that effectively equal the steady state concentration of UVR8-TetRDBD.
  • All photoconversion processes are modelled as 2-state processes.
  • Degradation rates are identical for all proteins. While this obviously does not resemble biological reality, setting a degradation rate for every protein species individually is practically impossible, as such rate parameters are not ubiquitous in literature.
  • The negative feedback has not been modelled explicitly here, as it has been accounted for in the previous simpler UVR8-TetRDBD model. As no oscillations are possible, the negative feedback loop merely reduces the dynamic range of the switching.
  • Basal expression as fraction of complete induction is the same for all promoters (= 15% in our case).

ODEs

With the previous assumptions, the coupled system boils down to:

ETH Construct1 ODEs.png


Find the parameters we used on our parameter page.

Results

ETH Construct1 Plots.png

Notice the vertical dashed bars at 4 h, these indicate a switch of conditions from beginning in darkness to a physical situation highlighted by the black light sources in each row. The horizontal dotted lines indicate the response threshold, where values above such threshold indicate a positive (1) response and values below indicate a negative (0) response. Note that only the values in steady-state have a meaning - dynamics of the system might temporarily lift some pigment concentrations above the threshold that will drop below it in steady state again (as is the case for the red pigment in situation [no UV, no Blue] and [UV, Blue]). The separation between conditions is comparatively small - this is due to the intrinsic basal expression that we have modelled.

Biological implications

The system has been tuned manually to maximise the dynamic range between conditions. This has resulted in promoter expression parameters that constrain the model:

ETH Construct1 Constraints.png

This in effect requires the same promoter strengths to be employed in-vivo. While most promoters have a rough notion of expression strength attached to them, this will eventually boil down to a trial-and-error inspection of the correct promoter. From a informatics-heuristical point of view, we suggest working in a binary-logarithmic "divide-and-conquer" fashion, always choosing a new candidate promoter that is between 2 promoters having expressions levels too low and too high.

Outlook

For the constraints here we have optimised the parameters by hand using some intuition. In line with the general trend of computational optimisation of biological systems, we aim to optimise the dynamic range by mathematical optimisation of certain free parameters (such as the promoter strengths). This procedure is non-trivial and rather demanding, involving non-linear optimisation. This could increase the dynamic range further.


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