Team:Aberdeen Scotland/parameters/invest 1

From 2009.igem.org

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[[Image:Dissociation_Constants_Eq_3.gif|center]]
[[Image:Dissociation_Constants_Eq_3.gif|center]]
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Where β is the maximal transcription rate, [X] is the concentration of protein X and K<sub>d</sub> is the dissociation constant for molecule X to the operator in question, [S] is the concentration of the inducer, S and K<sub>s</sub> is the dissociation constant for the inducer to the repressor, X. K<sub>d</sub> is defined as follows.
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Where β is the maximal transcription rate, [X] is the concentration of protein X and K<sub>d</sub> is the dissociation constant for molecule X to the operator in question, [S] is the concentration of the inducer, S and K<sub>s</sub> is the dissociation constant for the inducer to the repressor, X. K<sub>d</sub> is defined as follows:
[[Image:Dissociation_Constants_Eq_4.gif|center]]
[[Image:Dissociation_Constants_Eq_4.gif|center]]
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Where k<sub>off</sub> and k<sub>on</sub> are the on and off rates in the equation
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[[Image:Dissociation_Constants_Eq_5.gif|center]]
[[Image:Dissociation_Constants_Eq_5.gif|center]]
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K<sub>d</sub> has a more biologically meaningful definition however, it is the concentration of X at which the operator will be repressed 50% of the time.
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=== The issue ===
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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:
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Molecules per cell=Molarity ×Avogadro's number ×volume of the cytoplasm (litres)
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Where the volume of the cytoplasm of the cell is 6.7×〖10〗^(-16) litres
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This conversion constant of Avogadro’s number multiplied by the cytoplasm volume is ~ 402000000 (402 million).

Revision as of 10:49, 7 August 2009

University of Aberdeen iGEM 2009


Dissociation Constants

Introduction

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

Dissociation Constants Eq 1.gif

It also has one activation hill function of the form:

Dissociation Constants Eq 2.gif

And one repression / induction hill function of the form

Dissociation Constants Eq 3.gif

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

Dissociation Constants Eq 4.gif

Where koff and kon are the on and off rates in the equation

Dissociation Constants Eq 5.gif

Kd 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).


Parameter Value Value (molecules per cell) Description
KLacI 0.1 - 1 [pM] OR 800 [nM] 0.00004-0.0004 molecules OR 322 molecules LacI repressor dissociation constant
KIPTG 1.3 [µM] 522 molecules IPTG-LacI repressor dissociation constant
KtetR 179 [pM] 0.07 molecules TetR repressor dissociation constant
KCI 8 [pM] OR 50 [nM] 0.003 molecules OR 20 molecules CI repressor dissociation constant
KAHL 0.09 - 1 [µM] 402 molecules AHL-LuxR activator dissociation constant


 

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