Difference between revisions of "Team:Toronto/Analysis"
| Line 29: | Line 29: | ||
<div id="subsection-Introduction" class="subsection"> | <div id="subsection-Introduction" class="subsection"> | ||
<h2 class="text-yellow">Introduction</h2> | <h2 class="text-yellow">Introduction</h2> | ||
| − | <p>Using the previously derived expressions from our ODEs, we use the Mathworks Simulink package to derive solutions to 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> | ||
<div class="figures"> | <div class="figures"> | ||
<div class="image"><img src="https://static.igem.org/mediawiki/2017/7/7b/T--Toronto--2017_CI.png" alt="data"></div> | <div class="image"><img src="https://static.igem.org/mediawiki/2017/7/7b/T--Toronto--2017_CI.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)</figcaption> | ||
<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/c/c3/T--Toronto--2017_sgRNA.png" alt="data"></div> | ||
| + | <figcaption>Figure 1.b: <b>sgRNA Simulation</b> Lower sgRNA protein concentrations in the dark (LacILOV is bound, Eq. 2)</figcaption> | ||
<div class="image"><img src="https://static.igem.org/mediawiki/2017/5/54/T--Toronto--2017_anti_crispr.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"></div> | ||
| + | <figcaption>Figure 1.c: <b>anti-CRISPR Simulation</b> Anti-CRISPR expression inversely proportional to LacILOV activation, Eq. 3</figcaption> | ||
<div class="image"><img src="https://static.igem.org/mediawiki/2017/2/23/T--Toronto--2017_ci_anti.png" alt="data"></div> | <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.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 01:50, 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 repository for 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:
