Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics...
Transcript of Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics...
![Page 1: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/1.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Modelling chemical kinetics
Nicolas Le Novère, Babraham Institute, EMBL-EBI
![Page 2: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/2.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Systems Biology models ODE models
→ Reconstruction of state variable evolution from process descriptions:
Processes can be combined in ODEs (for deterministic simulations); transformed in propensities (for stochastic simulations)
Systems can be reconfigured quickly by adding or removing a process
A
B
P
Q
R
a
b
p
q
substancesA and B
areconsumed
by
reaction R thatproduces
substancesP and Q
![Page 3: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/3.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
ATP is consumed by processes 1 and 3, and produced by processes 7 and 10(for 1 reactions 1 and 3, there are 2 reactions 7 and 10)
1 2 3 45
6
78910
![Page 4: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/4.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Chemical kinetics and fluxes
S1
S2
E
P
![Page 5: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/5.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Statistical physics and chemical reaction
![Page 6: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/6.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Statistical physics and chemical reaction
Probability to find anobject in a containerwithin an interval of time
![Page 7: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/7.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Statistical physics and chemical reaction
Probability to find anobject in a containerwithin an interval of time
![Page 8: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/8.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Law of Mass Action
Waage and Guldberg (1864)
rate-constant
velocity
stoichiometry
activity
![Page 9: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/9.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Law of Mass Action
Waage and Guldberg (1864)
activity
rate-constant
velocity
stoichiometry
gas
solution
![Page 10: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/10.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Evolution of a reactant
Velocity multiplied by stoichiometry
negative if consumption, positive if production
Example of a unimolecular reaction
![Page 11: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/11.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Evolution of a reactant
Velocity multiplied by stoichiometry
negative if consumption, positive if production
Example of a unimolecular reaction
![Page 12: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/12.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Evolution of a reactant
Velocity multiplied by stoichiometry
negative if consumption, positive if production
Example of a unimolecular reaction
[x]0
[x]0/e
t1/kln2/k
[x]0/2
![Page 13: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/13.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Reversible reaction
is equivalent to
![Page 14: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/14.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Reversible reaction
is equivalent to
![Page 15: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/15.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
![Page 16: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/16.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
![Page 17: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/17.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
![Page 18: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/18.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
t
[x]
Not feasible in general
Numerical integration
Example of an enzymatic reaction
![Page 19: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/19.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Euler method:
Numerical integration (only for info. Not needed)
t
[x]
Dt
t
[x][x]
t+Dt – [x]
t
![Page 20: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/20.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Euler method:
Numerical integration (only for info. Not needed)
t
[x]
Dt
t
[x][x]
t+Dt – [x]
t
![Page 21: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/21.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Euler method:
Numerical integration (only for info. Not needed)
t
[x]
Dt
t
[x][x]
t+Dt – [x]
t
t
[x]
Dt
4th order Runge-Kutta:
with
![Page 22: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/22.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
![Page 23: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/23.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
irreversible catalysis
![Page 24: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/24.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
irreversible catalysis
product escapes before rebinding
![Page 25: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/25.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
irreversible catalysis
product escapes before rebinding
quasi-steady-state
![Page 26: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/26.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Enzyme kinetics
Victor Henri (1903) Lois Générales de l'Action des Diastases. Paris, Hermann.
Leonor Michaelis, Maud Menten (1913). Die Kinetik der Invertinwirkung, Biochem. Z. 49:333-369
George Edward Briggs and John Burdon Sanderson Haldane (1925) A note on the kinetics of enzyme action, Biochem. J., 19: 338-339
![Page 27: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/27.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Briggs-Haldane on Henri-Michaelis-Menten (only for info. Not needed)
[E]=[E0]-[ES]
![Page 28: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/28.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
[E]=[E0]-[ES]
steady-state!!!
Briggs-Haldane on Henri-Michaelis-Menten (only for info. Not needed)
![Page 29: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/29.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators
x y
![Page 30: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/30.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators
a
x y
x y
d[y]/dt
[a]
v
50%v
Ka
![Page 31: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/31.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators
d[y]/dt
[a]
v
50%v
Ka
d[y]/dt
log[a]
v
50%v
Ka
a
x y
x y
![Page 32: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/32.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators
d[y]/dt
[a]
v
50%v
Ka
d[y]/dt
log[a]
v
50%v
Ka
a
x y
x y
(NB: You can derive that as the fraction of target bound to the activator)
![Page 33: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/33.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Phenomenological ultrasensitivity
d[y]/dt
log[a]
v
50%v
Kad[y]/dt
log[a]
v
50%v
Kad[y]/dt
log[a]
v
50%v
Ka
![Page 34: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/34.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
The Hill function
Hill (1910) J Physiol 40: iv-vii.
![Page 35: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/35.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Hill (1910) J Physiol 40: iv-vii.
1
0
Y
[x]1/K
The Hill function
![Page 36: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/36.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: inhibitors
d[y]/dt
log[i]
v
50%v
Ki
x y
i
x y
(NB: You can derive that as the fraction of target not bound to the inhibitor)
![Page 37: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/37.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Mathematics are beautiful
![Page 38: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/38.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators and inhibitors
log [a]log [i]
x y
a
x y
i
![Page 39: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/39.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
absolute Vs relative activators
d[x]/dt
log[a]
v
50%v
Ka
a
x y
![Page 40: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/40.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
absolute Vs relative activators
d[y]/dt
log[a]
v
50%v
Ka
d[y]/dt
log[a]
v(1+
v
Ka
a
x y
a
x y
![Page 41: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/41.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
1 compartment
![Page 42: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/42.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments
![Page 43: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/43.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments
A B
Per unit of time
![Page 44: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/44.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
![Page 45: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/45.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
Per unit of time
![Page 46: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/46.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
Per unit of time
![Page 47: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/47.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
Per unit of time
![Page 48: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/48.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
Per unit of time
Stoichiometries (concentration change per Reaction events) are in factscaling with volumes:
![Page 49: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/49.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
Ø Øx
![Page 50: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/50.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
Ø Øx
![Page 51: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/51.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
Ø Ø
[x]
time
x
![Page 52: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/52.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
Ø Ø
[x]
time
0
x
![Page 53: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/53.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
Ø Ø
[x]
time
0
1
x
![Page 54: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/54.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Homeostasis
How can-we maintain a stable level with a dynamic system?
[x]
time
0
1
Ø Øx
![Page 55: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/55.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Questions?
![Page 56: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/56.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Conformational equilibrium
![Page 57: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/57.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Binding equilibrium
![Page 58: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/58.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
How does a ligand activate its target?
![Page 59: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/59.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
How does a ligand activate its target?
![Page 60: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/60.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
How does a ligand activate its target?
hint: K1>1
![Page 61: Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere ... · Modelling chemical kinetics Nicolas Le Novère, Babraham Institute, EMBL-EBI n.lenovere@gmail.com. Bioinformatics](https://reader030.fdocuments.net/reader030/viewer/2022041004/5ea7947bbd34ce644a6dedd2/html5/thumbnails/61.jpg)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Add energies
Multiply constants
+1 quantum energy = constant divided by 10
Explore constants exponentially:
Parameter space
-2.3 -4.6 -6.9 -9.2 -11.5 -13.8 -16.1
...
10-1 10-2 10-3 10-4 10-5 10-6 10-7
0.10.2
0.30.4
0.50.6
0.7