1. Modelling A Cookbook to Success:
4 easy steps to modelling your system today !

2. Overview Framework not a method
Pathway
Derive Equation (inc. Assumptions)
Think Menten or Hill Kenetics
Normalisation
Simulation
We will work through 2 examples using this framework

3. Oscillator from last year
Complex system
Today focus is on using a ‘take-away’ framework to model a part from last year
1st Example : General Promoter Activator
2nd Example : Part Specific

4. General Derivation Pathway : Derivation: Think Michaelis-Menten = 0
1st assumption: Steady-state of complex:
Rearranging yields Michaelis Constant:

5. General Derivation Therefore: …2nd assumption:
Using conservation of mass: where total concentration of promoter is constant:
Subs. into steady-state equation and rearranging gives:

6. General Derivation Rate of reaction is given by protein (Z) formation:
…but
Substitution yields:
…but
…Generic Equation
…THEREFORE

7. Pathway : T9002 Component ‘Prey Sensing’
Derivation
Normalisation
Simulation
How to use?
Pathway : T9002 Component ‘Prey Sensing’
AHL & LuxR form a Complex
Complex activates pLuxR promoter
GFP synthesis
GFP degradation

8. Derivation Want to Reuse General Derivation for : Can We ?
Pathway
Derivation
Normalisation
Simulation
How to use?
Derivation
Want to Reuse General Derivation for :
Can We ?
P : Promoter pLuxR
A : AHL / LuxR complex
PA : pLuxR/AHL/LuxR complex
Z : GFP
What about ?
Degradation of GFP
Formation of complex

9. Formation of Complex Want to Reuse General Derivation for :
Pathway
Derivation
Normalisation
Simulation
How to use?
Formation of Complex
Want to Reuse General Derivation for :
Want an expression for [A]
Pathway:
Steady State Assumption
Assume LuxR is constant:
Together:

10. Degradation of GFP Want to Reuse General Derivation for :
Pathway
Derivation
Normalisation
Simulation
How to use?
Degradation of GFP
Want to Reuse General Derivation for :
Want degradation expression
Pathway :
Assume Natural degradation

11. Substitution into General Equ
Pathway
Derivation
Normalisation
Simulation
How to use?
Substitution into General Equ
Want to Reuse General Derivation for :

12. Anyone for Dessert? Normalisation Pathway Derivation Normalisation
Simulation
How to use?
Normalisation
Anyone for Dessert?

13. Normalisation Initially… Pathway Derivation Normalisation Simulation
How to use?
Normalisation
…(1)
…(2)
Initially…

14. OR Normalisation Pathway Derivation Normalisation Simulation
How to use?
Normalisation OR

15. Normalisation …POST-Normalization Pathway Derivation Normalisation
Simulation
How to use?
Normalisation
…(1)
…(2)
…POST-Normalization

16. Normalisation WHY? = Happy Simulation Easier analysis & manipulation
Pathway
Derivation
Normalisation
Simulation
How to use?
Normalisation
WHY?
Easier analysis & manipulation
Easier/better readability & comprehension
= Happy Simulation

17. Normalisation HOW? (1st rename variables)
Pathway
Derivation
Normalisation
Simulation
How to use?
Normalisation
HOW?
(1st rename variables)
Select reversible, continuous mapping of the variables (time and vector X) into a different set of variables (α and vector U)
State the transformed variables
Perform parameter clumping and rescaling

18. Normalisation Voilà 1 1 2,3,4 Pathway Derivation Normalisation
Simulation
How to use?
Normalisation
Voilà 1 1
2,3,4

19. Normalisation Voilà 2 1 2,3,4 Pathway Derivation Normalisation
Simulation
How to use?
Normalisation
Voilà 2 1
2,3,4

20. Normalisation …where… Rescaled Spatial Variables are
Pathway
Derivation
Normalisation
Simulation
How to use?
Normalisation
…where…
Rescaled Spatial Variables are
U=X/a0 , V = a0Y/c0 & s = at/a0

21. Pathway
Derivation
Normalisation
Simulation
How to use?
Simulations
Modelling (mathematical description of a system's behaviour) and simulation (instantiation of a model over time) go hand-in-hand.
Simulation attempts to represent certain features of the behaviour of a physical system by the behaviour of another system: our dimensionless model.
In other words, simulation allows the user to role-play a system scenario – range of variables, parameter variation, etc.
Tools: Matlab, Cell Designer, COPASI, E Cell

22. Pathway
Derivation
Normalisation
Simulation
How to use?
Cell Designer

23. Take Home Message Framework not a method
Pathway
Derivation
Normalisation
Simulation
How to use?
Take Home Message
Framework not a method
Pathway
Derive Equation (inc. Assumptions)
Think Menten or Hill Kenetics
Assumptions : Steady State & Mass Conservation
Normalisation
Simulation
A model stands on its Assumptions