Team:Toronto/Analysis
Analysis
Introduction
Using the previously derived expressions from the ODE team we use the Mathworks Simulink package to derive solutions to our system for a range of parameters.
ODE Solution
Solving:
Integrating Factor:
Multiplying both sides by our integrating factor:
R plots
// #reading data
table <- read_excel("C:/Users/Ali/Desktop/igem/Wiki Files/table2.xlsx")
#Vectorizing Data
time <- table$`RFU/OD600`[c(3:15)]
time <- as.numeric(time)
x1 <-table$X__1[c(3:15)]
x1 <- as.numeric(x1)
x2 <- table$X__2[c(3:15)]
x2 <- as.numeric(x2)
x3 <- table$X__3[c(3:15)]
x3 <- as.numeric(x3)
x <- c(x1,x2,x3)
time_ <- c(time,time,time)
#plotting data vs time
#plot(c(time,time,time), c(x1,x2,x3), xlab = 'Time', ylab = 'RFU/OD600')
#Transforming variable
log_x = log(x)
plot(c(time,time,time), log_x, xlab = 'Time', ylab = 'log(RFu/OD600)')
#regression model
fit <- lm(log(x) ~ c(time,time,time))
#regression information
summary(fit)
#graphing best fit line
abline(fit, col='red')
#orginal data points
plot(c(time,time,time), x, xlab='Time', ylab='RFu/OD600')
#transformed prediction line
time_val <- seq(min(time),max(time), by = 13/38)
#prediction
lm2 <- exp(predict(fit,list(time=time_val)))
#plotting prediction
lines(time_val, lm2[c(1:39)], col="red")
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:
