Team:DTU-Denmark/Achievements/Modelling

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Modelling

The main objective of the experimental part of our project was to develop a method for determining promoter activities by measuring fluorescence from the Spinach RNA-fluorophore complex.

Fluorescence Signal is Linearly Dependent on the Concentration of Spinach-DFHBI Complex

When the fluorophore DFHBI is bound by Spinach, it fluoresces much more intensely than in its unbound form. The fluorescence of a sample can be assumed to increase linearly with the concentration of Spinach-DFHBI complex:

where the intercept b is the background fluorescence without any Spinach-DFHBI complex, and the slope a is the increase in fluorescence for each concentration unit of Spinach-DFHBI complex.

By adding known concentrations of DFHBI to an excess amount of Spinach RNA, it is possible to make a standard series describing the correlation between fluorescence and DFHBI concentration, and estimate the parameters a and b, if it is assumed that DFHBI is bound completely by the excess Spinach, i.e.:

This can be used to calculate the concentration of the Spinach-DFHBI complex given a fluorescence measurement:

If the fluorescence of a Spinach-expressing culture is measured, the standard series can thus be used to calculate the concentration of Spinach-DFHBI complex in the culture.

Calculating Total Spinach Concentration In the Culture

If the fluorescence is measured in the culture with a large excess of DFHBI it can be assumed that the concentration of Spinach-DFHBI is equal to the concentration of correctly folded Spinach, i.e.:

If it is assumed that the fraction of Spinach that is correctly folded is constant and known, the total concentration of Spinach can be calculated:

Quantification of Spinach Per Cell

The amount of Spinach per cell can be calculated if the cell density is measured:

The CFU count can also be approximated with an OD600 measurement:

The Spinach concentration should be in units molecules per liter. This can be calculated from μM by multiplying by Avogadros Constant and dividing by 10⁶.

Calculating Spinach Production Rate

During balanced growth, or steady state, there is an equilibrium between the production and degradation of Spinach. This means that the steady state concentration of Spinach is given by the relationship.

where β is the production rate of Spinach (molecules per second), μ is the growth rate of the cells (s^-1) and α_deg is the in vivo degradation rate of Spinach (s^-1).

Thus the Spinach production rate can be calculated by:

By combining the equations derived above, the Spinach RNA production rate β can be calculated from the Spinach concentration and cell density:

β is a measure of the total production rate of Spinach in the cell. If β is divided by the number of Spinach genes i.e. the plasmid copy number, the obtained production rate per gene copy is analogous to the promoter activity.

The degradation rate of Spinach must be measured. This is most easily done by growing a cell culture that expresses Spinach and stopping the transcription and thereby the production of new Spinach RNA by adding rifampicin. The degradation of Spinach can then be monitored by taking a time series of samples and measuring fluorescence on each one (see our protocol (link)).

The above derivations are equally valid for Spinach2 and Spinach2.1 as well as for the modified ligand DFHBI-1T. See our results section (LINK) for how this model was applied to our experimental data.