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Team Colombia @ 2012 iGEM

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Parameters of the equations

When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.

There are three possible ways to find this parameters:

i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed.

ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations.

iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a range where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.

How did we do it?

For our biological system we use options i) and iii). In the literature it was possible to find the parameters for the complete CI activation box and for the rest of values we found an aproximately range where they could be, so we proceeded to step iii).

Once the ranges of the parameters was set, we proceed to do the screening. We tried a lot of techniques and most of the failed, here we present the steps of the succesful one:

1.Sensitivity Analysis

Now we have an idea of which parameters affect the response the most. Although we still don't know what is the exact value of the parameter we know how the system is supose to response.With this two things we can proceed to step 2.

2. Optimization of parameters

A process of optimization takes a function and maximizes o minimizes changing the some variable of it. The changing variables are named optimization variables and function is called objective function. If we want to have some limitations or behaves with the variable we can add restrictions to the system, and the function will be optimized without breakinf this limitations.

In our case the objective function is a minimum difference of squares betweem the points of our expected behaviour and the behaviour of the equations with a set of optimization variable. When the distance between these points is minimun the parameters are found!!!

3.Screening

If we have a set of parameters why do we do a screening?

In the last step we found a set of parameters that give the expexted response of the system. But the optimization method does not know if these parameters are real