Team:Aberdeen Scotland/parameters/invest 1

Contents 1 Dissociation Constants 1.1 Introduction 1.2 The issue 1.3 References

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 K_d is the dissociation constant for molecule X to the operator in question, [S] is the concentration of the inducer, S and K_s is the dissociation constant for the inducer to the repressor, X. K_d is defined as follows:

Where k_off and k_on are the on and off rates in the equation

K_d 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

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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