Team:Aberdeen Scotland/parameters/invest 1

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<td><b>Parameter</b></td>
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<td><b>Value</b></td>
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<td><b>Value (molecules per cell)</b></td>
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<td><b>Description</b></td>
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<td><b>Reference</b></td>
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<td>K<sub>LacI</sub></td>
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<td> ~1*10 -12 M OR ~1.8*10-12 M </td>
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<td>0.0004 molecules OR 0.00072 molecules</td>
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<td>Dissociation constant for LacI to LacO DNA site</td>
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<td>[1][2]</td>
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<td>K<sub>IPTG</sub></td>
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<td>1*10-6 M</td>
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<td>402 molecules</td>
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<td>Dissociation constant for IPTG to LacI</td>
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<td>[3]</td>
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<td>K<sub>tetR</sub></td>
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<td>(5.6 ± 2) × 10-9 M OR 1.53*10-8 M</td>
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<td>2.25 molecules OR 6.1506 molecules</td>
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<td>Dissociation constant for TetR to TetO</td>
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<td>[4][5]</td>
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<td>K<sub>CI</sub></td>
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<td>50 * 10-9 M</td>
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<td>20 molecules</td>
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<td>Dissocitation constant for cI to DNA site</td>
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<td>[6]</td>
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Revision as of 10:50, 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
Parameter Value Value (molecules per cell) Description Reference
KLacI ~1*10 -12 M OR ~1.8*10-12 M 0.0004 molecules OR 0.00072 molecules Dissociation constant for LacI to LacO DNA site [1][2]
KIPTG 1*10-6 M 402 molecules Dissociation constant for IPTG to LacI [3]
KtetR (5.6 ± 2) × 10-9 M OR 1.53*10-8 M 2.25 molecules OR 6.1506 molecules Dissociation constant for TetR to TetO [4][5]
KCI 50 * 10-9 M 20 molecules Dissocitation constant for cI to DNA site [6]


 

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