Difference between revisions of "Team:Rice/Modeling"

Violacein is a fluorescent reporter with anticancer activity (Ref) that has been used in several other igem projects (Cambridge 2009, Slovenia 2010, Johns Hopkins 2011, UCSF 2012). Although it would be a good pigment candidate for our project, it has a complex synthetic pathway requiring five specialized enzymes, and oxygen (Fig 1.) (Michael E. Lee et al, 2013). It also presents multiple off-path reactions that can reduce the efficiency of the pathway. Before building constructs to use for violacein production, we needed to find a way to determine which promoters to use for the five genes involved in the pathway. Although there are studies focused on the optimization of the production of violacein, none of the studies gives a biochemical model of the rates of the reactions that take place in the bacteria (Ref).

Create a biochemical model of the violacein production based on the synthetic pathway and violacein production data from bacteria with different promoters for each of the five genes involved in the pathway.

1. The rate of dilution of the enzymes and the intermediaries is much greater than its degradation (for example by ubiquitination for the proteins or by conversion to products not included on the pathway)
2. There is no saturation of the enzymes and all the reactions will follow the law of mass action
3. Independence of external factors such as oxygen and NADH in the reactions
4. None of the reactions are reversible

We use the mass action kinetics because this type of equation only requires one parameter for reaction and is less susceptible to overdosing

Because a major goal of the model is to predict the effects of the selection of promoters on the final production of violacein, we decided to find a way to characterize promoters first. To simplify the computation, we used the promoter strength as a single standard to characterize the promoters. Moreover, we assumed the degradation rate of proteins only depends on the growth rate of E.coli. Then, every enzyme has the same degradation rate. The bacteriophage T7 promoter has been widely used for protein expression and purification (J. Andrew Jones et al., 2013), so we used data of five mutant T7 promoters to create a proof-of-concept model. If this model is functional, we can implement the same modeling technique to the promoters we are working with. The five mutant T7 promoters have distinct promoter strength over time after induction. The experimental data are shown in the figure below.



The first step of our model is to describe the rate of change of enzymes based on promoter strength. Here we assumed that the enzyme production rate is directly proportional to strength of the promoter. Therefore, we were able to use a mass-action kinetics equation of promoters to describe the enzyme concentration. The equation is shown below:



In this equation, Ai is the concentration of enzyme i, ki­ is the production rate of each enzyme i, kd is the degradation rate of all enzymes, and t is time. By solving this equation, we derived the equation of enzyme concentration against time.



Since we assumed that the promoter strength is proportional to the promoter concentration, we can use the equation to fit our data using least squares method. The regression lines are overlaid on the data.



In the plot, circles represent data from paper. (J. Andrew Jones et al., 2013). The solid lines are regression lines. In general the regression lines are able to capture the change of strength of each enzyme over time. In this way, the parameters are determined. The table below lists the parameter values.



In the table, ki­ (i = 1,2,3,4,5) are the production rate coefficients of promoter I (i = 1,2,3,4,5), and kd is the degradation rate coefficient of all promoters.