Difference between revisions of "Team:Toronto/Analysis"
| Line 86: | Line 86: | ||
<p>Analyzed in R for this model, and got the following values with adjusted R-squared and p-value: </p> | <p>Analyzed in R for this model, and got the following values with adjusted R-squared and p-value: </p> | ||
<blockquote class="code"> | <blockquote class="code"> | ||
| − | Coefficients: | + | <pre>Coefficients: |
Estimate Std. Error t value Pr(>|t|) | Estimate Std. Error t value Pr(>|t|) | ||
(Intercept) 2.87199 0.21773 13.19 1.47e-15 *** | (Intercept) 2.87199 0.21773 13.19 1.47e-15 *** | ||
| Line 100: | Line 100: | ||
<p>Intercept represents the equilibrium value of LacILov, our intercept:</p> | <p>Intercept represents the equilibrium value of LacILov, our intercept:</p> | ||
\begin{eqnarray} | \begin{eqnarray} | ||
| − | 2.879199 \pm (0.21773)(2.026) \\ | + | 2.879199 &\pm (0.21773)(2.026) \\ |
| − | 2.879199 \pm 0.44112098 | + | 2.879199 &\pm 0.44112098 |
\end{eqnarray} | \end{eqnarray} | ||
</div> | </div> | ||
Revision as of 02:13, 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. We simulated our equations for cI Protein, sgRNA and anti-CRISPR, shown in Figure 1.
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
Analyzed in R for this model, and got the following values with adjusted R-squared and p-value:
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:
\begin{eqnarray} 2.879199 &\pm (0.21773)(2.026) \\ 2.879199 &\pm 0.44112098 \end{eqnarray}