Team:Brown/Modeling/ODEs

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ODE Modeling of the Quad-State circuit

We formulated a system of differential equations which we used to model our system. As we have many players in our system and thus many equations, we chose to combine transcription and translation into single equations representing protein synthesis.

In all cases the equations represent the change in concentration in nanomoles/minute. Most equations make use of the Hill equation, which is used to model the cooperative binding of a ligand to a molecule. This is accomplished by describing the fraction of bound macromolecule as a function of ligand concentration.

We model induction by ligand X as: Ligand induction.png

We model repression by ligand X as: Ligand repression.png

Where rho is the fraction of occupied ligand binding sites, [X] is the ligand concentration, n is the hill coefficient, and K_d is the equilibrium constant for dissociation.

We chose to simplify our model by expressing simultaneous repression/induction as the product of the corresponding hill equations. This is a simplification because it allows both the repressor and inducer to bind simultaneously, while in reality they are competing for available space.


Contents


Production of LovTAP

Production of LovTAP*

Production of tetR

Production of Mnt

Production of AraC

Production of LacI

Production of CI

Production of CI434

Production of SupD

Production of T7ptag

Production of T7 Polymerase

Production of GAL4

Production of S1

Production of S2

Production of S3

Production of S4