Difference between revisions of "Team:Toronto/Analysis"
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<div id="subsection-Introduction" class="subsection"> | <div id="subsection-Introduction" class="subsection"> | ||
| − | <h2 class="text-yellow"> | + | <h2 class="text-yellow">MathWorks Simulations</h2> |
<p>Using the previously derived expressions from our ODEs, we use the Mathworks Simulink package to derive solutions to our system and model our system for a range of parameters. </p> | <p>Using the previously derived expressions from our ODEs, we use the Mathworks Simulink package to derive solutions to our system and model our system for a range of parameters. </p> | ||
<figure> | <figure> | ||
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<div class="image"><img src="https://static.igem.org/mediawiki/2017/5/54/T--Toronto--2017_anti_crispr.png" alt="data" width="200px"></div> | <div class="image"><img src="https://static.igem.org/mediawiki/2017/5/54/T--Toronto--2017_anti_crispr.png" alt="data" width="200px"></div> | ||
<div class="image"><img src="https://static.igem.org/mediawiki/2017/2/23/T--Toronto--2017_ci_anti.png" alt="data" width="200px"></div> | <div class="image"><img src="https://static.igem.org/mediawiki/2017/2/23/T--Toronto--2017_ci_anti.png" alt="data" width="200px"></div> | ||
| − | <figcaption>Figure 1: | + | <figcaption>Figure 1:<br> |
| − | + | A)<b>cI Protein Simulation</b> Lower cI protein concentrations in the dark (LacILOV is bound, Eq. 1)<br> | |
| − | + | B)<b>sgRNA Simulation</b> Lower sgRNA protein concentrations in the dark (LacILOV is bound, Eq. 2)<br> | |
| − | + | C)<b>anti-CRISPR Simulation</b> Anti-CRISPR expression inversely proportional to LacILOV activation, Eq. 3)<br> | |
| − | + | D) <b>anti-CRISPR vs cI Protein</b>Anti-CRISPR protein concentration increases in lower cI concentration</figcaption> | |
</div> | </div> | ||
</figure> | </figure> | ||
Revision as of 02:05, 16 December 2017
Analysis
MathWorks Simulations
Using the previously derived expressions from our ODEs, we use the Mathworks Simulink package to derive solutions to our system and model our system for a range of parameters.
A)cI Protein Simulation Lower cI protein concentrations in the dark (LacILOV is bound, Eq. 1)
B)sgRNA Simulation Lower sgRNA protein concentrations in the dark (LacILOV is bound, Eq. 2)
C)anti-CRISPR Simulation Anti-CRISPR expression inversely proportional to LacILOV activation, Eq. 3)
D) anti-CRISPR vs cI ProteinAnti-CRISPR protein concentration increases in lower cI concentration
ODE Solution
Solving:
\begin{eqnarray} \frac{x_2}{dt} = \alpha - \gamma x_2 \\ \frac{x_2}{dt} + \gamma x_2 = \alpha \end{eqnarray}Integrating Factor:
\begin{eqnarray} e^{\int \gamma dt} = e^{\gamma t} \end{eqnarray}Multiplying both sides by our integrating factor:
\begin{eqnarray} (\frac{x_2}{dt} + \gamma x_2)e^{\gamma t} = \alpha e^{\gamma t}\\ \int (\frac{x_2}{dt} + \gamma x_2)e^{\gamma t} = \int \alpha e^{\gamma t} \\ x_2 = \frac{\alpha}{\gamma} + ce^{-\gamma t} \end{eqnarray}R plots
Visit our GitHub repositoryfor our code.
R Analysis
R Analysis:
Call:
lm(formula = log(x) ~ c(time, time, time))
Residuals:
Min 1Q Median 3Q Max
-0.58853 -0.15536 0.01303 0.19867 0.44055
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.87199 0.21773 13.19 1.47e-15 ***
c(time, time, time) 0.15267 0.01142 13.37 9.74e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.2935 on 37 degrees of freedom
Multiple R-squared: 0.8285, Adjusted R-squared: 0.8238
F-statistic: 178.7 on 1 and 37 DF, p-value: 9.741e-16
Intercept represents the equilibrium value of LacILov, our intercept:
