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Revision as of 12:03, 7 August 2009
University of Aberdeen - Pico Plumber
Contents |
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 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:
Where koff and kon are the on and off rates in the equation
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:
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*,†,§
