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<h1 style="border-bottom:none;">Parameter sensitivity analysis</h1>
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<p><strong>Aim:</strong> To figure out the sensitive parameters in this ternary system.
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<br/>
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<br/>
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<p><strong>Steps:</strong>
 +
<p><span></span>1. Parameter range determination;
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<br/><span></span>2. Use local sensitivity method to analyze theoretically;
 +
<br/><span></span>3. Determine vital parameters for parameter sweep;
 +
<br/>
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<br/>
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<p><strong>Brief results:</strong><span></span>sRNA::mRNA binding rate(km) and mRNA degradation rate(βm) are both sensitive parameters.
 +
<br/>
 +
<br/>
 +
<h2>Parameters important</h2>
 +
<p><span></span>We need to figure out which parameter is playing significant role in this ternary system,then we will try to further our optimization of our parameter set we found in ODE equations.
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<br/>
 +
<br/>
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<a><img style="margin-left:175px;" src="https://static.igem.org/mediawiki/2012/1/15/Ouc-project-designmaking-design3.JPG" /></a>
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<h2>How the sensitivity coefficient is calculated?</h2>
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<p><span></span>Local sensitivity analysis is a common approach that the sensitivity of a model output is performed by computing the first-order partial derivatives of the system output with respect to the input parameters, which can be viewed as the gradients around the multidimensional reference parameter space.
 +
 
 +
<br/><span></span>The systems biology models discussed here is a system of ODE that is dependent on a certain parameter set p and initial conditions yi(0), which is
 +
<a><img style="margin-left:210px;" src="https://static.igem.org/mediawiki/2012/1/1f/Ouc-modeling-math6.jpg" /></a>
 +
<br/><span></span>Mathematically, the sensitivity coefficients are the first-order derivatives of model outputs with respect to the model parameters:
 +
<br/>
 +
<a><img style="margin-left:195px;" src="https://static.igem.org/mediawiki/2012/3/30/Ouc-modeling-math7.jpg" /></a>
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<br/>
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<span></span>Here we adopt finite difference approximation:
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<br/>
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<a><img style="margin-left:210px;" src="https://static.igem.org/mediawiki/2012/5/59/Ouc-modeling-math8.jpg" /></a>
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<br/>
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<h2>Result</h2>
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<p><strong>Comparator</strong><span></span>Parameter sensitivity for comparator: βm> km>βs>αm
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<br/>
 +
<br/>
 +
<a><img style="margin-left:65px;" src="https://static.igem.org/mediawiki/2012/6/6a/Ouc-modeling-math9.jpg" /></a>
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<br/>
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<br/>
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<p><span></span>The 2~4 columns are the indicator of sensitivity coefficient
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<br/>
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<br/>
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<a><img src="https://static.igem.org/mediawiki/2012/3/34/Ouc-modeling-math10.jpg" /></a>
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<br/>
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<br/>
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<p><strong>Ratio Sensor:</strong><span></span>Apparently, km and βm both are sensitive parameters for ratio sensor.
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<br/>
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<br/>
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<a><img style="margin-left:40px;" src="https://static.igem.org/mediawiki/2012/f/fa/Ouc-modeling-math11.jpg" /></a>
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<br/>
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<br/>
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<p>NOTE: The 2~4 columns are the indicator of sensitivity coefficient for different indicators.
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<br/>
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<br/>
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<a><img  src="https://static.igem.org/mediawiki/2012/b/bf/Math12.jpg" /></a>
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<p><strong>References:</strong><span></span>[1] Z. Zi, Sensitivity analysis approaches applied to systems biology models, IET Syst. Biol., 2011, Vol. 5, Iss. 6, pp. 336–346
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Latest revision as of 02:22, 25 October 2012

Parameter sensitivity analysis

Aim: To figure out the sensitive parameters in this ternary system.

Steps:

1. Parameter range determination;
2. Use local sensitivity method to analyze theoretically;
3. Determine vital parameters for parameter sweep;

Brief results:sRNA::mRNA binding rate(km) and mRNA degradation rate(βm) are both sensitive parameters.

Parameters important

We need to figure out which parameter is playing significant role in this ternary system,then we will try to further our optimization of our parameter set we found in ODE equations.







How the sensitivity coefficient is calculated?

Local sensitivity analysis is a common approach that the sensitivity of a model output is performed by computing the first-order partial derivatives of the system output with respect to the input parameters, which can be viewed as the gradients around the multidimensional reference parameter space.
The systems biology models discussed here is a system of ODE that is dependent on a certain parameter set p and initial conditions yi(0), which is
Mathematically, the sensitivity coefficients are the first-order derivatives of model outputs with respect to the model parameters:

Here we adopt finite difference approximation:

Result

ComparatorParameter sensitivity for comparator: βm> km>βs>αm



The 2~4 columns are the indicator of sensitivity coefficient



Ratio Sensor:Apparently, km and βm both are sensitive parameters for ratio sensor.



NOTE: The 2~4 columns are the indicator of sensitivity coefficient for different indicators.



References:[1] Z. Zi, Sensitivity analysis approaches applied to systems biology models, IET Syst. Biol., 2011, Vol. 5, Iss. 6, pp. 336–346

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