Team:Aberdeen Scotland/parameters/invest 1

From 2009.igem.org

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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.
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 ===
=== The issue ===
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=== References ===
=== References ===
[1] Mitchel Lewis (2005) The Lac repressor. C. R. Biologies 328 (2005) 521–548
[1] Mitchel Lewis (2005) The Lac repressor. C. R. Biologies 328 (2005) 521–548
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[2] Falcon C.M and Matthews K.S. (2000) Operator DNA sequence Variation Enhances High Affinity Binding by Hinge Helix Mutants of Lactose Repressor Protein. Biochemistry. 39, 11074-11084
[2] Falcon C.M and Matthews K.S. (2000) Operator DNA sequence Variation Enhances High Affinity Binding by Hinge Helix Mutants of Lactose Repressor Protein. Biochemistry. 39, 11074-11084
 +
[3] Uri Alon, An introduction to systems Biology, p244
[3] Uri Alon, An introduction to systems Biology, p244
 +
[4] Nucleic Acids Res. 2004; 32(2): 842–847.
[4] Nucleic Acids Res. 2004; 32(2): 842–847.
Two mutations in the tetracycline repressor change the inducer anhydrotetracycline to a corepressor
Two mutations in the tetracycline repressor change the inducer anhydrotetracycline to a corepressor
Annette Kamionka, Joanna Bogdanska-Urbaniak, Oliver Scholz, and Wolfgang Hillen*
Annette Kamionka, Joanna Bogdanska-Urbaniak, Oliver Scholz, and Wolfgang Hillen*
 +
[5] Volume 272, Number 11, Issue of March 14, 1997 pp. 6936-6942, The Role of the Variable Region in Tet Repressor for Inducibility by Tetracycline, Christian Berens , Dirk Schnappinger and Wolfgang Hillen
[5] Volume 272, Number 11, Issue of March 14, 1997 pp. 6936-6942, The Role of the Variable Region in Tet Repressor for Inducibility by Tetracycline, Christian Berens , Dirk Schnappinger and Wolfgang Hillen
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[6] http://parts.mit.edu/igem07/index.php?title=ETHZ/Parameters
[6] http://parts.mit.edu/igem07/index.php?title=ETHZ/Parameters
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[7] Detailed map of a cis-regulatory input function – Y. Setty*,†, A. E. Mayo*,†, M. G. Surette‡, and U. Alon*,†,§  
[7] Detailed map of a cis-regulatory input function – Y. Setty*,†, A. E. Mayo*,†, M. G. Surette‡, and U. Alon*,†,§  

Revision as of 11:43, 7 August 2009

University of Aberdeen iGEM 2009


Contents

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

Dissociation Constants Eq 6.gif

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).

The problem with this is that most dissociation constants found in the literature equate to a value of molecules per cell that is less than 1. Clearly in a cell with 10 plasmids and therefore 10 operators 1 molecule could not repress all of them.

Below is a table of the conflicting information we found. This is an extract from the EHTZ wiki [6] with the new column of the value in molecules per cell added.


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

And here are the other parameters we found in the literature

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]

References

[1] Mitchel Lewis (2005) The Lac repressor. C. R. Biologies 328 (2005) 521–548

[2] Falcon C.M and Matthews K.S. (2000) Operator DNA sequence Variation Enhances High Affinity Binding by Hinge Helix Mutants of Lactose Repressor Protein. Biochemistry. 39, 11074-11084

[3] Uri Alon, An introduction to systems Biology, p244

[4] Nucleic Acids Res. 2004; 32(2): 842–847. Two mutations in the tetracycline repressor change the inducer anhydrotetracycline to a corepressor Annette Kamionka, Joanna Bogdanska-Urbaniak, Oliver Scholz, and Wolfgang Hillen*

[5] Volume 272, Number 11, Issue of March 14, 1997 pp. 6936-6942, The Role of the Variable Region in Tet Repressor for Inducibility by Tetracycline, Christian Berens , Dirk Schnappinger and Wolfgang Hillen

[6] http://parts.mit.edu/igem07/index.php?title=ETHZ/Parameters

[7] Detailed map of a cis-regulatory input function – Y. Setty*,†, A. E. Mayo*,†, M. G. Surette‡, and U. Alon*,†,§



 

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