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Modelling

Introduction

This project focuses on novel outputs, for example, for environmental sensors. However, there is a need for an 'adaptor'; a middle section to the machine that takes an input and processes it. Our initial work was based around the development of an amplifier that permits a large output that is clearly visible. The next planned stage was the creation of a system that allows switching on of output at different calibrated input signal levels. Creating a model allows the feasibility of the proposed systems to be tested. A basic model of the original amplifier system was put forward, building on both our data and the Cambridge 2007 data.

Modelling the phage activator system

This is the basic 'amplifier' system that consists of an input sensitive promoter system and a protein activator and sensitive promoter. It can therefore be divided into two boxes, the approach taken in putting forward an initial model.

The pBAD promoter

An arabinose input acts as an inducer, permitting transcription, by binding the AraC transcription factor. This is a dual transcription factor; when unbound to arabinose a dimer restricts access of polymersase to reduce basal levels of transcription, upon binding arabinose the conformation changes and the dimer permits binding of polymerase. [1]

To model this situation, araC is first assumed to take the role of a repressor that reversibly binds and unbinds a site on the DNA. If it binds arabinose, it is sequestered and cannot bind the DNA. Here, an input function is created, after Alon []. This gives the rate of transcription from the promoter dependent on the concentration of arabinose. Since mRNA is then ttranslated at a roughly constant rate, it is related within a multiplicative constant to the rate of protein production, in this case activator and RFP.

This gives the rate of transcription as a function of X^* which represents the concentration of active repressor, unbound to arabinose. B is the maximum rate of transcription, here this rate is when induced by arabinose at highest concentration. K_d is the dissociation constant (see modelling derivations). Parameters must be found by a parameter scan for sensible values or by comparing to already gathered data.