Model Documentation

Documentation Preface

The documentation of the model consists of the derivations of all the equations used to create the model. Each equation contributes a piece of the picture which ultimately results in the calculations of important cell characteristics. These equations live in the matlab model that can be found here.

Experimental Data Analysis

Let fluorescent mRNA and protein concentration be represented by [Rf] and [Pf] respectively. They are related directly to the fluorescence level, which we will label Fr and Fp. The mRNA and protein concentration levels can be measured by just the fluorescence. To do this, we will abide by the assumptions that

Where Sr and Sp are scaling factors for mRNA and protein respectively and kr and kp are constants that transform fluorescence to mRNA and protein concentrations.

In the experiment, one uses a plate reader with varying concentration of the dyes in rows and varying time measurements in columns. The following image represents this.

We will also have another row for in vitro measurements. From this row we will graph the fluorescence versus the dye concentration, and the fluorescence will level off at some saturation point. Because the saturation point in vitro will be greater than the saturation point in vivo, we must scale all the fluorescence measurements we find in vivo, which is the importance of Sr and Sp.

At this point we will find out the scaling factors Sr and Sp. Step 1 is to put samples into the plate reader and take more samples of the same concentration and measure them in vitro. Then, we will measure all the wells at the same time point, and find the saturation fluorescence of the in vitro and the in vivo wells. Dividing the two gives us the Sr and Sp.

At each time point we will graph the in vivo fluorescence vs dye concentrations and find the first dye concentration where saturation occurs. This dye concentration is thus the mRNA/protein total concentration, as we will assume that there will be a 1-1 correspon- dence of dye and mRNA/protein. We then multiply each by the scaling factor Sr or Sp to get the actual mRNA.

Equilibrium Constants

To check, we can find the fluorescent mRNA concentrations from the mRNA values we obtained in vivo. General first order chemical reactions begin (theoretically):