# Team:Northwestern/Modeling

### From 2013.igem.org

# Modeling

#### Objective

The primary motivation of this model is to use the information that we receive from the single-state promoter to inform our hypotheses on how the novel dual-state construct is behaving. Since a single promoter system is well characterized, we understand how the promoter and polymerase interacts to begin transcription. However, we are not sure whether the dual promoter system will interact in a way as to increase or decrease the polymerase’s binding affinity to the promoter. Our method of determining the gross effects of having two promoters is to compare total fluorescence level of the constructs to the single promoters. The interaction may range from a simple additive effect where two promoters simply work independently to a coupling effect where the binding of one promoter site by RNA polymerase affects binding on the other site.

Unfortunately, at the time of writing this website, the dual-state constructs, though cloned and sequenced, were not tested thoroughly. As a result, the rest of the page will describe the model for the single state. The dual-state model will be presented at the Jamboree.

#### Developing the Model

In order to develop this model, we considered the possible mechanisms and determined what was important. Since our ultimate goal is to understand how the dual-state promoter is functioning, the intricate, intracellular control mechanism is not important. The pH-responsive element can be included by making the binding affinity of the polymerase to the promoter a function of pH. The simplified model is demonstrated below. From there, a series of differential equations is devised and solved using Matlab ode45.

#### Constitutive Promoter

First, the model for the constitutive promoter is developed. Before, fitting the model to the data, the team tried to get the right general shape of the curves by making order of magnitude estimations. For instance, when the GFP levels were too high too quickly, the degradation constant was raised. The process is repeated for other constants until one empirical set of constants was found. This way, the model demonstrated the relationships between different processes. The following curve serves as the basis for both the pH-responsive element and the dual-state model.

#### pH Promoter

The pH promoter model is solved by making k1, the polymerase binding affinity constant, a function of pH. From the data, Asr-RBS proved to be the only pH-responsive promoter. As a result, the model tries to mimic the results of the Asr data set. Since the Asr results show no appreciable difference between 4.5 and 6.5 besides a basal level of fluorescence, we assumed that the tight regulation would symmetric about pH 5.5. To do this, we fitted a basic equation for the bell curve to the data, and we got the following equation.

We are successful in mimicking the data that we obtained from Asr. The graph shows a clear drop-off from pH = 5.5 to other pH ranges.