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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>
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- | <p><span></span>1. Parameter range determination;
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- | <br/><span></span>2. Use local sensitivity method to analyze theoretically;
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- | <br/><span></span>3. Determine vital parameters for parameter sweep;
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- | <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.
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- | <br/>
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- | <br/>
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- | <h2>Parameters important</h2>
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- | <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/>
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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.
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- | | + | |
- | <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
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- | <a><img style="margin-left:210px;" src="https://static.igem.org/mediawiki/2012/1/1f/Ouc-modeling-math6.jpg" /></a>
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- | <br/><span></span>Mathematically, the sensitivity coefficients are the first-order derivatives of model outputs with respect to the model parameters:
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- | <br/>
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- | <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/>
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- | <br/>
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- | <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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- | <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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