Synbio course

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Revision as of 07:54, 29 October 2010 (view source) Igchoi (Talk | contribs) (→Practice #1) ← Older edit		Revision as of 09:08, 29 October 2010 (view source) Igchoi (Talk | contribs) (→Practice #1) Newer edit →
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	#      k1,k2  k3		#      k1,k2  k3
	# rate equations		# rate equations
-	# dE = -k1*E*S+k2*ES	+	# dE = -k1*E*S+k2*ES, dS = -k1*E*S+k2*ES+k3*ES, dES = k1*E*S-k2*ES-k3*ES
-	# dS = -k1*E*S+k2*ES+k3*ES	+	# quasi-equilibrium; E0 = E + ES; dES = 0
-	# dES = k1*E*S-k2*ES-k3*ES	+	# dE = -k1*E0*S+(k1*S+k2)*ES, dES = k1*E0*S-(k1*S+k2+k3)*ES, dP = k2*ES
-	# v= dp/dt = k3*E0*S/(S+(k2+k3)/k1)	+	# ode functions
-	# E0 = E + ES	+	michaelis = function(t,y,p) {
-	# initial parameter	+	# S = y[1]; ES = y[2]; P = y[3]
-	k1 = 1e3	+	# k1 = p[1]; k2 = p[2]; k3=p[3]; E0=p[4]
-	k2 = 1	+	dS = -p[1]*p[4]*y[1]+(p[1]*y[1]+p[2])*y[2]
-	k3 = 0.05	+	dES = p[1]*p[4]*y[1]-(p[1]*y[1]+p[2]+p[3])*y[2]
-	E0 = 0.5e-3	+	dP = p[2]*y[2]
-	parms = c(k1,k2,k3)	+	list(c(dS,dES,dP))
-	# ode	+	}
		+	#### initial parameter
		+	k1 = 1000; k2 = 1; k3 = 0.05; E0 = 0.0005
		+	p = c(k1,k2,k3,E0)
		+	t = seq(0,100,1) # time scale
		+	#t = 1
		+	y = c(0.001,0,0) # initial values: S, ES, P
		+	# solving equations
		+	res = lsoda(y,t,michaelis,p)
		+	plot(res[,1],res[,2],type="l",col="red",ylim=c(0,0.001))
		+	points(res[,1],res[,3],type="l",col="blue")
		+	E = p[4]-res[,3]
		+	points(res[,1],E,type="l",col="cyan")
		+	points(res[,1],res[,4],type="l",col="green")
	</pre>		</pre>

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Revision as of 09:08, 29 October 2010

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

2010 Fall LMB904

• Introduction to Synthetic Biology
  • check readings in above link
• R package - bioconductor
  • using R
  • tutorials and course materials in R page

Practices in R

• We will practice the materials in MIT open courseware

Practice #1

• Simulating Michaelis–Menten kinetics in R
  • assumption: quasi-equilibrium state (pseudosteady state)
  • OCW Matlab code ported in R
  • 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
# ode functions
michaelis = function(t,y,p) {
  # S = y[1]; ES = y[2]; P = y[3]
  # 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 parameter
k1 = 1000; k2 = 1; k3 = 0.05; E0 = 0.0005
p = c(k1,k2,k3,E0)
t = seq(0,100,1) # time scale
#t = 1
y = c(0.001,0,0) # initial values: S, ES, P
# solving equations
res = lsoda(y,t,michaelis,p)
plot(res[,1],res[,2],type="l",col="red",ylim=c(0,0.001))
points(res[,1],res[,3],type="l",col="blue")
E = p[4]-res[,3]
points(res[,1],E,type="l",col="cyan")
points(res[,1],res[,4],type="l",col="green")

Practice #2

• A Genetic Switch in Lamba Phage in R

1. Error fetching PMID 10681449: [LAM]

Practice #3

• A Genetic Toggle Switch in R

2. Error fetching PMID 10659857: [TOG]