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

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

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

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

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

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

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

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

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:

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

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

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

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

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

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

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

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

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

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

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

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

Pathway Derivation Normalisation Simulation How to use? Cell Designer

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