Synbio course

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==2010 Fall LMB904==
==2010 Fall LMB904==
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*[[Synthetic_Biology|Introduction to Synthetic Biology]]
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*What is Synthetic Biology? - [[Synthetic_Biology|Introduction to Synthetic Biology]]
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**check readings in above link
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**check readings (recent special issue of various journals) in above link
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*[[R|R package]] - [http://bioconductor.org bioconductor]
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**using R
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*We will use [[R|R package]] for simulating several biological processes
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**tutorials and course materials in [[R|R page]]
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**check [http://bioconductor.org bioconductor] for more applications in bioinformatics
 +
**tutorials and course materials in CSBL's [[R|R page]] (some collections)
 +
 
==Practices in R==
==Practices in R==
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*We will practice the materials in [http://ocw.mit.edu/courses/physics/8-591j-systems-biology-fall-2004/readings/ MIT open courseware]
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*We will practice some materials in [http://ocw.mit.edu/courses/physics/8-591j-systems-biology-fall-2004/readings/ MIT open courseware] (department of physics)
===Practice #1===
===Practice #1===
*Simulating [[w:Michaelis-Menten kinetics|Michaelis–Menten kinetics]] in R
*Simulating [[w:Michaelis-Menten kinetics|Michaelis–Menten kinetics]] in R
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**[http://ocw.mit.edu/courses/physics/8-591j-systems-biology-fall-2004/readings/CodeI1_v2.m Matlab code] will be ported in R
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**underlying assumption: quasi-equilibrium state (pseudosteady state) of enzyme-catalyzed reaction
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**R-code
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**[http://ocw.mit.edu/courses/physics/8-591j-systems-biology-fall-2004/readings/CodeI1_v2.m OCW Matlab code] will be ported in R
 +
**using R
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***install a specific package (e.g. 'odesolve') in R (there are several ways to do this)
<pre>
<pre>
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# execute 'R' & run a command
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# you should have an internet connection
 +
 +
>install.package("odesolve")
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</pre>
</pre>
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 +
*R-code
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<pre>
 +
library(odesolve)
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# Michaelis-menten equation
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# E + S <-> ES -> E + P
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#      k1,k2  k3
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# rate equations
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# 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]
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  dP = p[2]*y[2]
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  list(c(dS,dES,dP))
 +
}
 +
 +
#### initial parameters
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k1 = 1e3
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k2 = 1
 +
k3 = 5e-2
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E0 = 5e-4
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p = c(k1,k2,k3,E0)  # <-- parameters (initial values)
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t = seq(0,100,1)    # <-- a time scale (0 to 100 sec.)
 +
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y = c(1e-3,0,0)    # <-- initial values of [S], [ES] and [P]
 +
 +
#### solving equations
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res = lsoda(y,t,michaelis,p)    # store result (101 x 4 matrix) 
 +
 +
 +
#### plotting results
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time = res[,1]    # time range - column 1
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S = res[,2]      # [S] changes - column 2
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ES = res[,3]      # [ES]
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E = p[4]-res[,3]  # [E] free enzyme
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P = res[,4]      # [P] product
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 +
plot(time,S,type="l",col="red",ylim=c(0,0.001))
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points(time,ES,type="l",col="blue")
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points(time,E,type="l",col="cyan")
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points(time,P,type="l",col="green")
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</pre>
 +
 +
*Result (above script is working but the result will not be correct; you may have to find an error in the code)
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{| align=center
 +
|-
 +
|[[image:Michaelis-menten.png|thumb|left|Michaelis-Menten simulation result (correct one)]]
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|}
===Practice #2===
===Practice #2===
*A Genetic Switch in Lamba Phage in R
*A Genetic Switch in Lamba Phage in R
 +
<pre>
 +
library(odesolve)
 +
# Lambda phage lysogeny
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# ODE
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# dx/dt = alpha*x^2/(1+(1+sigma1)*x^2+sigma2*x^4)-gamma*x+1
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#
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# define ODE function
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hastyfunc = function(t,y,p) {
 +
  # p[1:4] = c(alpha,gamma,sigma1,sigma2)
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  dy = p[1]*y^2/(1+(1+p[3])*y^2+p[4]*y^4)-p[2]*y+1
 +
  list(dy)
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}
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#
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# initial parameters
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#
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# p[1:4] = c(alpha,gamma,sigma1,sigma2)
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p = c(50,20,1,5)
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t = seq(0,10,1)
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y0 = 0; y1 = 1
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res0 = lsoda(y0,t,hastyfunc,p)
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res1 = lsoda(y1,t,hastyfunc,p)
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plot(t,res0[,2],type="l",col="blue",main="Hasty function",
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    xlab="Time",ylim=c(0,1))
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points(t,res1[,2],type="l",col="red")
 +
</pre>
<biblio>LAM pmid=10681449</biblio>
<biblio>LAM pmid=10681449</biblio>
 +
===Practice #3===
===Practice #3===
*A Genetic Toggle Switch in R
*A Genetic Toggle Switch in R
<biblio>TOG pmid=10659857</biblio>
<biblio>TOG pmid=10659857</biblio>
<!-- <pubmed>10659857</pubmed> -->
<!-- <pubmed>10659857</pubmed> -->

Latest revision as of 14:47, 18 November 2010

Contents

2010 Fall LMB904

Practices in R

Practice #1

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

>install.package("odesolve")


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")
Michaelis-Menten simulation result (correct one)

Practice #2

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")
Error fetching PMID 10681449:
  1. Error fetching PMID 10681449: [LAM]

Practice #3

Error fetching PMID 10659857:
  1. Error fetching PMID 10659857: [TOG]
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