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Team:Aberdeen Scotland/parameters/invest 1
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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: | 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: | ||
| - | + | [[Image:Dissociation_Constants_Eq_6.gif|center]] | |
Where the volume of the cytoplasm of the cell is 6.7×〖10〗^(-16) 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). | This conversion constant of Avogadro’s number multiplied by the cytoplasm volume is ~ 402000000 (402 million). | ||
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| + | 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. | ||
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| + | 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. | ||
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</table> | </table> | ||
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| + | And here are the other parameters we found in the literature | ||
<table width="80%" margin="0" cellpadding="5px" cellspacing="0" border="1px" bordercolor="#AAAAAA" font color="#000000" background="#E4E9EE" align="center"> | <table width="80%" margin="0" cellpadding="5px" cellspacing="0" border="1px" bordercolor="#AAAAAA" font color="#000000" background="#E4E9EE" align="center"> | ||
Revision as of 11:37, 7 August 2009
University of Aberdeen - Pico Plumber
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 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:
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 |
| 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] |
