Modeling Goals

The purpose of the model in the scope of the project is to provide an acceptable estimate of desired parameters within the biological system. These parameters often cannot be measured or calculated directly, which highlights the importance of modeling. The advancements in measurement capabilities have allowed us to develop a suitable model of these processes.

The focus of our model is to help characterize promoters, by computing translational efficiency and Polymerases Per Second (PoPS). These parameters are notoriously difficult to measure consistently in vivo. In addition to these main output values, the model also calculates other characteristics of the cell, such as degradation constants for mRNA and protein, and transcriptional strength. By identifying these parameters, the model will help better characterization of promoters that are to be used in experiments.

The black-box representation of our model, with its inputs and outputs is shown on the right, and the details of the model are described here.

Inputs to the model constitute measurements taken from the actual biological system. Dyes mixed with solutions of the cells bind to mRNA and protein complexes to cause the cells to fluoresce over time. These fluorescent measurements form the basis of the inputs to the model. Using a gradient of concentrations of dye vs. time applied to cells, one can obtain estimates about the amount of bound mRNA and protein. More formally, inputs to our model include: time steps and RNA fluorescence measured at those time steps, (t, R(t)); time steps and protein fluorescence measured at those time steps, (t, P(t)).

The outputs of the model represent estimated system parameters that fit experimental measurements: transcriptional strength (Ts), RNA degradation rate (α), translational efficiency (Tl), protein degradation rate (β), and PoPS.

The model is composed in Matlab. It incorporates file input/output to retrieve experimental measurement data. The inputs to the model are time dependent and dye-dependent fluorescence measurements of mRNA and protein. Several time dependent measurements can be included in input files: mRNA fluorescence during synthesis, mRNA fluorescence during degradation (with or without mRNA production), protein fluorescence during synthesis, and protein fluorescence during degradation (with or without protein production). Other constants are approximated as needed.

Using the total mRNA and protein measurements, along with either estimates or measurements of the degradation of mRNA and protein, one can determine the transcriptional and translational efficiency using general differential equations. Finally, PoPS can be determined using translational efficiency, as we describe in detail here.