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# define repressilator model

repressilator = function(times, x, p){

with(as.list(c(state,parameters)),{

# Extract the state variables

mlacI = x[1]

mtetR = x[2]

mcI = x[3]

placI = x[4]

ptetR = x[5]

pcI = x[6]

# Extract the parameter values

alpha0 = p[1]

alpha = p[2]

beta = p[3]

n = p[4]

# Evaluate the differential equations (at time t)

dmlacIdt = -mlacI + alpha/(1+(pcI)^n) + alpha0

dmtetRdt = -mtetR + alpha/(1+(placI)^n) + alpha0

dmcIdt = -mcI + alpha/(1+(ptetR)^n) + alpha0

dplacIdt = -beta*(placI-mlacI)

dptetRdt = -beta*(ptetR-mtetR)

dpcIdt = -beta*(pcI-mcI)

# Combine into a single vector

dxdt = c(dmlacIdt,dmtetRdt,dmcIdt,dplacIdt,dptetRdt,dpcIdt)

```
list(c(dxdt))
```

})

}

#Begin Code for Setup and Execution of Function

# Set up time vector

time = seq(0,250,10)

# Set up vector of parameter values

alpha0 = 0

alpha = 50

beta = 0.2

n = 2

params = c(alpha0,alpha,beta,n) # Parameter Vector

# Set initial values for state variables

mlacI0 = 0.2

mtetR0 = 0.1

mcI0 = 0.3

placI0 = 0.1

ptetR0 = 0.4

pcI0 = 0.5

states0 = c(mlacI0,mtetR0,mcI0,placI0,ptetR0,pcI0) # State Variable Vector

# Now, Find Numerical Solutions to the ODE!

# Function ode() takes in, in this order:

# state variables, times vector, your ODE function name,

# and parameters

numSolutions = ode(states0,time,repressilator,params)

# Note that the ode() function returns a matrix with

# the number of rows defined by the length of the time vector

# and the number of columns equal to the number of state variables

# plus one. The first column is the time points at which the function

# is evaluated. The remaining columns are the solutions for each

# state variable in the order defined by your ODE function.

# Next, Plot Output from Model

matplot(numSolutions[,1], numSolutions[,2:3], type=c("l","l","l","l","l","l"),

lty=c(1,2), lwd=c(4,4), xlab="",ylab="",col=c("purple","pink","red","blue","green","orange"))

# Add a legend in the top right corner with legend labels

legend('topleft',legend=c("mlacI0","mtetR0","mcI0","placI0","ptetR0","pcI0"), col=c("purple","pink","red","blue","green","orange"),

lty=c(1,2), lwd=c(4,4), cex=0.75)

# Add a title and axes labels

title("Repressilator Model",xlab="time",ylab="Expression")