nicolas le novère, babraham institute, embl-ebi n ......nicolas le novère, babraham institute,...
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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
n.lenovere@gmail.com
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
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
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Statistical physics and chemical reaction
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
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
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
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
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
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
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Reversible reaction
is equivalent to
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Reversible reaction
is equivalent to
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Example of an enzymatic reaction
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
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
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
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Choose the right formalism
irreversible catalysis
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
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
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
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]
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)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Generalisation: activators
x y
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
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
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)
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
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.
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
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)
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Mathematics are beautiful
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
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
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
1 compartment
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
2 compartments … with different volumes
AB
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
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
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
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:
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
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
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
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
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
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
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Questions?
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Conformational equilibrium
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
Binding equilibrium
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
How does a ligand activate its target?
Bioinformatics for the neuroscientist, 28 September 2015
Introduction to modelling in biology, Babraham Institute, 24 November 2016
How does a ligand activate its target?
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
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
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