Team:Aberdeen Scotland/parameters/invest 1

Dissociation Constants

Introduction

Our model uses hill kinetics; we have three repression hill functions of the form:

It also has one activation hill function of the form:

And one repression / induction hill function of the form

Where β is the maximal transcription rate, [X] is the concentration of protein X and K_d is the dissociation constant for molecule X to the operator in question, [S] is the concentration of the inducer, S and K_s is the dissociation constant for the inducer to the repressor, X. K_d is defined as follows:

Where k_off and k_on are the on and off rates in the equation

K_d has a more biologically meaningful definition however, it is the concentration of X at which the operator will be repressed 50% of the time.

The issue

The units of K_d are usually given in M, the molarity, or moles per litre. Our model works with the exact number of molecules so we convert our K_d values into molecules per cell. This is achieved as follows:

Molecules per cell=Molarity ×Avogadro's number ×volume of the cytoplasm (litres)

Where the volume of the cytoplasm of the cell is 6.7×〖10〗^(-16) litres

This conversion constant of Avogadro’s number multiplied by the cytoplasm volume is ~ 402000000 (402 million).