Gentle introduction to the modeling of chemical kinetics

1. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Modelling chemical kinetics
Nicolas Le Novère, The Babraham Institute
n.lenovere@gmail.com

2. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
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 reconfiured quickly by addini or removini a process
A
B
P
Q
R
a
b
p
q
substances
A and B
are
consumed
by
reaction R that
produces
substances
P and Q

3. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
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 4
5
6
7
8
9
10

4. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Chemical kinetics and fuxes
S1
S2
E
P

5. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Statistical physics and chemical reaction

6. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Statistical physics and chemical reaction
Probability to find an
object in a container
within an interval of time

7. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Statistical physics and chemical reaction
Probability to find an
object in a container
within an interval of time

8. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Law of Mass Action
Waaie and Guldberi (1864)
rate-constant
velocity
stoichiometry
activity

9. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Law of Mass Action
Waaie and Guldberi (1864)
activity
rate-constant
velocity
stoichiometry
ias
solution

10. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Evolution of a reactant
 Velocity multiplied by stoichiometry
 neiative if consumption, positive if production
 Example of a unimolecular reaction

11. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Evolution of a reactant
 Velocity multiplied by stoichiometry
 neiative if consumption, positive if production
 Example of a unimolecular reaction

12. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Evolution of a reactant
 Velocity multiplied by stoichiometry
 neiative if consumption, positive if production
 Example of a unimolecular reaction
[x]0
[x]0
/e
t
k
1/
ln k
2/
[x]0
/2

13. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Reversible reaction
is equivalent to

14. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Reversible reaction
is equivalent to

15. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Conformational equilibrium

16. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Binding equilibrium

17. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
How does a ligand activate its target?

18. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
How does a ligand activate its target?

19. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
How does a ligand activate its target?
hint: K1
>1

20. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7

21. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Example of an enzymatic reaction

22. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Example of an enzymatic reaction

23. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Example of an enzymatic reaction

24. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
t
[x]
Not feasible in ieneral
Numerical inteiration
Example of an enzymatic reaction

25. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Euler method:
Numerical integration
t
[x]
Dt
t
[x]
[x]t+Dt
– [x]t

26. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Euler method:
Numerical integration
t
[x]
Dt
t
[x]
[x]t+Dt
– [x]t

27. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Euler method:
Numerical integration
t
[x]
Dt
t
[x]
[x]t+Dt
– [x]t
t
[x]
Dt
4th
order Runie-Kutta:
with

28. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Choose the right formalism

29. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Choose the right formalism
irreversible catalysis

30. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Choose the right formalism
irreversible catalysis
product escapes before rebindini

31. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Choose the right formalism
irreversible catalysis
product escapes before rebindini
quasi-steady-state

32. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Enzyme kinetics
Leonor Michaelis, Maud Menten (1913).
Die Kinetik der Invertinwirkuni,
Biochem. Z. 49:333-369
Victor Henri (1903)
Lois Générales de l'Action des Diastases.
Paris, Hermann.
Georie Edward Briiis, John Burdon Sanderson
Haldane (1925)
A note on the kinetics of enzyme action,
Biochem. J., 19: 338-339

33. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Briggs-Haldane on Henri-Michaelis-Menten
[E]=[E0
]-[ES]

34. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Briggs-Haldane on Henri-Michaelis-Menten
[E]=[E0
]-[ES]
steady-state!!!

35. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Generalisation: activators
x y

36. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Generalisation: activators
a
x y
x y
(NB: You can derive that as the fraction
of target bound to the activator)

37. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Phenomenological ultrasensitivity

38. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Hill (1910) J Physiol 40: iv-vii.

39. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Hill (1910) J Physiol 40: iv-vii.

40. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Generalisation: inhibitors
x y
i
x y
(NB: You can derive that as the fraction
of target not bound to the inhibitor)

41. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Mathematics are beautiful

42. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Generalisation: activators and inhibitors
log [a]
log [i]
x y
a
x y
i

43. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
absolute Vs relative activators
a
x y

44. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
absolute Vs relative activators
a
x y
a
x y

45. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
Ø Ø
x

46. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
Ø Ø
x

47. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
Ø Ø
[x]
time
x

48. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
Ø Ø
[x]
time
0
x

49. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
Ø Ø
[x]
time
0
1
x

50. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Homeostasis
How can-we maintain
a stable level with a
dynamic system?
[x]
time
0
1
Ø Ø
x

51. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
1 compartment

52. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments

53. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments
A B
Per unit of time

54. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments … with diferent volumes
A
B

55. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments … with diferent volumes
A
B
Per unit of time

56. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments … with diferent volumes
A
B
Per unit of time

57. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments … with diferent volumes
A
B
Per unit of time

58. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
2 compartments … with diferent volumes
A
B
Per unit of time
Kinetic constants must
be scaled with volumes:

59. Bioinformatics for the neuroscientist, 28 September 2015
In Silico Systems Biology, EMBL-EBI, 03-08 June 2018
Questions?