Synbio course

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Revision as of 12:39, 29 October 2010 (view source) Igchoi (Talk | contribs) (→Practice #1) ← Older edit		Revision as of 12:50, 29 October 2010 (view source) Igchoi (Talk | contribs) (→Practice #1) Newer edit →
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	# quasi-equilibrium; E0 = E + ES; dES = 0		# 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		# dE = -k1*E0*S+(k1*S+k2)*ES, dES = k1*E0*S-(k1*S+k2+k3)*ES, dP = k2*ES
-	# ode functions	+
		+	### define ode functions
	michaelis = function(t,y,p) {		michaelis = function(t,y,p) {
-	# S = y[1]; ES = y[2]; P = y[3]	+	# t, y, p: vector
-	# k1 = p[1]; k2 = p[2]; k3=p[3]; E0=p[4]	+	# 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]		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]		dES = p[1]*p[4]*y[1]-(p[1]*y[1]+p[2]+p[3])*y[2]
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	list(c(dS,dES,dP))		list(c(dS,dES,dP))
	}		}
-	#### initial parameter	+
-	k1 = 1000; k2 = 1; k3 = 0.05; E0 = 0.0005	+	#### initial parameters
-	p = c(k1,k2,k3,E0)	+	k1 = 1e3
-	t = seq(0,100,1) # time scale	+	k2 = 1
-	#t = 1	+	k3 = 5e-2
-	y = c(0.001,0,0) # initial values of S, ES and P	+	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		#### solving equations
-	res = lsoda(y,t,michaelis,p)	+	res = lsoda(y,t,michaelis,p)   # store result (101 x 4 matrix)
		+
	#### plotting results		#### plotting results
-	plot(res[,1],res[,2],type="l",col="red",ylim=c(0,0.001))	+	time = res[,1]   # time range - column 1
-	points(res[,1],res[,3],type="l",col="blue")	+	S = res[,2]       # [S] changes - column 2
-	E = p[4]-res[,3]	+	ES = res[,3]      # [ES]
-	points(res[,1],E,type="l",col="cyan")	+	E = p[4]-res[,3]  # [E] free enzyme
-	points(res[,1],res[,4],type="l",col="green")	+	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")
	</pre>		</pre>
		+
	*Result (above script is working but the result is not correct; you may find an error in the code)		*Result (above script is working but the result is not correct; you may find an error in the code)
	[[image:Michaelis-menten.png|thumb|left|Michaelis-Menten simulation result]]		[[image:Michaelis-menten.png|thumb|left|Michaelis-Menten simulation result]]

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Revision as of 12:50, 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

• 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 is not correct; you may find an error in the code)

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]