Team:Colombia/Modeling/Paramterers

From 2012.igem.org

(Difference between revisions)
(→Parameters of the equations)
(→Parameters of the equations)
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::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.  
::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.  
::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.  
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::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.
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::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank 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?'''
'''How did we do it?'''
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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).
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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 rank 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:
+
Once the ranks of the parameters were 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'''
:'''1.Sensitivity Analysis'''
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:'''2. Optimization of parameters'''
:'''2. Optimization of parameters'''
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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.  
+
A process of optimization takes a function and maximizes o minimizes changing 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!!!   
+
In our case the objective function is a minimum difference of squares between 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!!!   
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::''If we have a set of parameters why do we do a screening?''
::''If we have a set of parameters why do we do a screening?''
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In the last step we found a set of parameters that give the expected response of the system. But this is only a point.....What if are there more points? Does the optimization method know if these parameters are real or have biological sense?.. We only take one expected response, are there similar behaviours of the system with the desired response?
+
In the last step we found a set of parameters that give the expected response of the system. But this is only a point.....What if are there more points? Does the optimization method know if these parameters are real or have biological sense?.. We only take into account one expected response, are there similar behaviours of the system with the desired response?
-
To answer this questions we perfom a sceening of the parameters. Taking the optimal point as a start
+
To answer this questions we perfom a sceening of the parameters. This method tries different combinations of parameters and see if some conditions are accomplished. The ranks we use to make this screeining is not the original one!!!!

Revision as of 20:54, 21 September 2012

Team Colombia @ 2012 iGEM

Template:Https://2012.igem.org/User:Tabima


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 rank 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 rank where they could be, so we proceeded to step iii).


Once the ranks of the parameters were 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 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 between 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 expected response of the system. But this is only a point.....What if are there more points? Does the optimization method know if these parameters are real or have biological sense?.. We only take into account one expected response, are there similar behaviours of the system with the desired response?

To answer this questions we perfom a sceening of the parameters. This method tries different combinations of parameters and see if some conditions are accomplished. The ranks we use to make this screeining is not the original one!!!!

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