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− | + | <div class="image"><img src="https://static.igem.org/mediawiki/2017/c/c3/T--Toronto--2017_sgRNA.png" alt="data" width="200px"></div> | |
− | <div class="image"><img src="https://static.igem.org/mediawiki/2017/c/c3/T--Toronto--2017_sgRNA.png" alt="data"></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/2017/5/54/T--Toronto--2017_anti_crispr.png" alt="data"></div | + | <figcaption>Figure 1: A) <b>cI Protein Simulation</b> Lower cI protein concentrations in the dark (LacILOV is bound, Eq. 1), B)<b>sgRNA Simulation</b> Lower sgRNA protein concentrations in the dark (LacILOV is bound, Eq. 2), C)<b>anti-CRISPR Simulation</b> Anti-CRISPR expression inversely proportional to LacILOV activation, Eq. 3), D) <b>anti-CRISPR vs cI Protein</b>Anti-CRISPR protein concentration increases in lower cI concentration</figcaption> |
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− | <div class="image"><img src="https://static.igem.org/mediawiki/2017/2/23/T--Toronto--2017_ci_anti.png" alt="data"></div> | + | |
− | <figcaption>Figure 1. | + | |
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<h2 class="text-yellow">R plots</h2> | <h2 class="text-yellow">R plots</h2> | ||
− | <p>Visit our <a href="https://github.com/igemuoftATG/drylab-matlab">GitHub repository</a> for our code.</p> | + | <p>Visit our <a href="https://github.com/igemuoftATG/drylab-matlab">GitHub repository</a>for our code.</p> |
<figure> | <figure> | ||
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<div class="image"><img src="https://static.igem.org/mediawiki/2017/6/66/T--Toronto--2017_mcherr_reg_log.png" alt="data"></div> | <div class="image"><img src="https://static.igem.org/mediawiki/2017/6/66/T--Toronto--2017_mcherr_reg_log.png" alt="data"></div> | ||
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− | <figcaption>Figure | + | <figcaption>Figure 2.a: Log Linear transformation of RFU/OD600 vs Time, Regression Line (red) fitted to data</figcaption> |
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</div> | </div> | ||
− | <figcaption>Figure | + | <figcaption>Figure 2.b: RFU/OD600 vs Time with Transformed Regression Line (red)</figcaption> |
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Revision as of 02:00, 16 December 2017
Analysis
Introduction
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.
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: