Synbio course

From CSBLwiki

Contents 1 2010 Fall LMB904 2 Practices in R 2.1 Practice #1 2.2 Practice #2 2.3 Practice #3

2010 Fall LMB904

• What is Synthetic Biology? - Introduction to Synthetic Biology
  • check readings (recent special issue of various journals) in above link

• We will use R package for simulating several biological processes
  • check bioconductor for more applications in bioinformatics
  • tutorials and course materials in CSBL's R page (some collections)

Practices in R

• We will practice some materials in MIT open courseware (department of physics)

Practice #1

• Simulating Michaelis–Menten kinetics in R
  • underlying assumption: quasi-equilibrium state (pseudosteady state) of enzyme-catalyzed reaction
  • OCW Matlab code will be ported in R
  • using R
    • install a specific package (e.g. 'odesolve') in R (there are several ways to do this)

# execute 'R' & run a command
# you should have an internet connection

>install.package("odesolve")

• R-code

library(odesolve)
# Michaelis-menten equation
# E + S <-> ES -> E + P
#      k1,k2   k3
# rate equations
# dE = -k1*E*S+k2*ES, dS = -k1*E*S+k2*ES+k3*ES, dES = k1*E*S-k2*ES-k3*ES
# quasi-equilibrium; E0 = E + ES; dES = 0
# dE = -k1*E0*S+(k1*S+k2)*ES, dES = k1*E0*S-(k1*S+k2+k3)*ES, dP = k2*ES

### define ode functions
michaelis = function(t,y,p) {
  # t, y, p: vector
  # t: a time scale
  # y: S = y[1]; ES = y[2]; P = y[3]
  # p: k1 = p[1]; k2 = p[2]; k3=p[3]; E0=p[4]
  dS = -p[1]*p[4]*y[1]+(p[1]*y[1]+p[2])*y[2]
  dES = p[1]*p[4]*y[1]-(p[1]*y[1]+p[2]+p[3])*y[2]
  dP = p[2]*y[2]
  list(c(dS,dES,dP))
}

#### initial parameters
k1 = 1e3
k2 = 1
k3 = 5e-2
E0 = 5e-4

p = c(k1,k2,k3,E0)  # <-- parameters (initial values)
t = seq(0,100,1)    # <-- a time scale (0 to 100 sec.)

y = c(1e-3,0,0)     # <-- initial values of [S], [ES] and [P]

#### solving equations
res = lsoda(y,t,michaelis,p)    # store result (101 x 4 matrix)  


#### plotting results
time = res[,1]    # time range - column 1
S = res[,2]       # [S] changes - column 2
ES = res[,3]      # [ES]
E = p[4]-res[,3]  # [E] free enzyme
P = res[,4]       # [P] product

plot(time,S,type="l",col="red",ylim=c(0,0.001))
points(time,ES,type="l",col="blue")
points(time,E,type="l",col="cyan")
points(time,P,type="l",col="green")

• Result (above script is working but the result will not be correct; you may have to find an error in the code)

Michaelis-Menten simulation result (correct one)

Practice #2

• A Genetic Switch in Lamba Phage in R

library(odesolve)
# Lambda phage lysogeny
# ODE
# dx/dt = alpha*x^2/(1+(1+sigma1)*x^2+sigma2*x^4)-gamma*x+1
#
# define ODE function
hastyfunc = function(t,y,p) {
   # p[1:4] = c(alpha,gamma,sigma1,sigma2)
   dy = p[1]*y^2/(1+(1+p[3])*y^2+p[4]*y^4)-p[2]*y+1
   list(dy)
}
#
# initial parameters
#
# p[1:4] = c(alpha,gamma,sigma1,sigma2)
p = c(50,20,1,5)
t = seq(0,10,1)
y0 = 0; y1 = 1
res0 = lsoda(y0,t,hastyfunc,p)
res1 = lsoda(y1,t,hastyfunc,p)
plot(t,res0[,2],type="l",col="blue",main="Hasty function",
     xlab="Time",ylim=c(0,1))
points(t,res1[,2],type="l",col="red")

1. Error fetching PMID 10681449: [LAM]

Practice #3

• A Genetic Toggle Switch in R

2. Error fetching PMID 10659857: [TOG]