User:Tom Adie/CS2: Difference between revisions

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{{Imperial/Box1|R Exercise 2 (ODE Solver)|
{{Imperial/Box1|R Exercise 2 (ODE Solver)|


* RK4 solver:
RK4 solver:
#[http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/odesolve/html/rk4.html RK4 documentation]
#[http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/odesolve/html/rk4.html RK4 documentation]
#Interface: rk4(y, times, func, parms, ...)  
#Interface: rk4(y, times, func, parms, ...)  


* Model: Constitutive gene expression
Model: Constitutive gene expression
#ODE System:
#ODE System:
** d[mRNA]/dt {{Equals}} k_1 - d_1*[mRNA]
** d[mRNA]/dt {{Equals}} k_1 - d_1*[mRNA]
** d[protein]/dt {{Equals}} k_2[mRNA] -d_2*[protein]  
** d[protein]/dt {{Equals}} k_2[mRNA] -d_2*[protein]  


* Questions:
Questions:
#Considering that the half-life for the mRNA and the protein is respectively 3min and 1h. Workout the values of (k_1, d_1, k_2, d_2) so that, at steady state, [mRNA] {{Equals}} 3 and [protein] {{Equals}} 500.
*1. Considering that the half-life for the mRNA and the protein is respectively 3min and 1h. Workout the values of (k_1, d_1, k_2, d_2) so that, at steady state, [mRNA] {{Equals}} 3 and [protein] {{Equals}} 500.
#Using the previously found parameter values, plot on the same graph [mRNA](t) and [protein](t) for t{{Equals}}[0, 5h].
''Using the relationship '''degradation rate {{Equals}} ln2 / half-life''' we get values of '''d1 {{Equals}} 0.23''' and '''d2 {{Equals}} 0.012'''. At steady state, '''d[mRNA]/dt''' and '''d[Protein]/dt''' are set to 0. Rearranging gives''
#Parameter scanning: Consider parameter d_2 to vary [-20%, 20%] of its nominal value (10 uniformly spread values). Generate on the same graph the 10 [protein](t) trajectories (t{{Equals}}[0, 5h]).
<center>[mRNA]{{Equals}}k1/d1 <br>
k2/d2{{Equals}}[Protein]/[mRNA] </center><br>
 
''substituting in values of d1, d2 [mRNA] and [Protein] we find '''k1 {{Equals}} 3*0.23 {{Equals}} 0.69''' and '''k2 {{Equals}} 0.012*500/3 {{Equals}} 2'''''
 
*2. Using the previously found parameter values, plot on the same graph [mRNA](t) and [protein](t) for t{{Equals}}[0, 5h].
*3. Parameter scanning: Consider parameter d_2 to vary [-20%, 20%] of its nominal value (10 uniformly spread values). Generate on the same graph the 10 [protein](t) trajectories (t{{Equals}}[0, 5h]).
|}}
|}}


Revision as of 07:00, 9 December 2008

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MRes Case Study 2

R Exercise 2 (ODE Solver)


RK4 solver:

  1. RK4 documentation
  2. Interface: rk4(y, times, func, parms, ...)

Model: Constitutive gene expression

  1. ODE System:
    • d[mRNA]/dt = k_1 - d_1*[mRNA]
    • d[protein]/dt = k_2[mRNA] -d_2*[protein]

Questions:

  • 1. Considering that the half-life for the mRNA and the protein is respectively 3min and 1h. Workout the values of (k_1, d_1, k_2, d_2) so that, at steady state, [mRNA] = 3 and [protein] = 500.

Using the relationship degradation rate = ln2 / half-life we get values of d1 = 0.23 and d2 = 0.012. At steady state, d[mRNA]/dt and d[Protein]/dt are set to 0. Rearranging gives

[mRNA]=k1/d1
k2/d2=[Protein]/[mRNA]

substituting in values of d1, d2 [mRNA] and [Protein] we find k1 = 3*0.23 = 0.69 and k2 = 0.012*500/3 = 2

  • 2. Using the previously found parameter values, plot on the same graph [mRNA](t) and [protein](t) for t=[0, 5h].
  • 3. Parameter scanning: Consider parameter d_2 to vary [-20%, 20%] of its nominal value (10 uniformly spread values). Generate on the same graph the 10 [protein](t) trajectories (t=[0, 5h]).

Intro

Links:

Inputs:

  • Wavelength
  • Intensity
  • Stimulation time (pulse length)

Outputs:

  • Viability of cells (bearing in mind YtvA pathway triggers stress response)
  • PoPs
References
  1. One
  2. Two
  3. Three
  4. Four
  5. Five

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