BioModels Database logo

BioModels Database

spacer

BIOMD0000000065 - Yildirim2003_Lac_Operon

 

 |   |   |  Send feedback
Reference Publication
Publication ID: 12719218
Yildirim N, Mackey MC.
Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.
Biophys. J. 2003 May; 84(5): 2841-2851
Centre for Nonlinear Dynamics, McGill University, Montreal, Quebec, Canada H4X 2C1.  [more]
Model
Original Model: BIOMD0000000065.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6624248569
Submission Date: 25 Aug 2006 12:48:14 UTC
Last Modification Date: 12 Feb 2014 16:36:21 UTC
Creation Date: 21 Jun 2006 14:47:26 UTC
Encoders:  Harish Dharuri
   Adam Halasz
   Vijayalakshmi Chelliah
set #1
bqmodel:isDerivedFrom PubMed 9104037
set #2
bqbiol:occursIn Taxonomy Escherichia coli
bqbiol:isVersionOf Gene Ontology carbon catabolite regulation of transcription
Notes

This a model from the article:
Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.
Yildirim N, Mackey MC Biophys. J. 2003 12719218 ,
Abstract:
A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

The model reproduces the time profile of beta-galactosidase activity as shown in Fig 3 of the paper. The delay functions for transcription (M) and translation (B and P) have been implemented by introducing intermediates ( I1, I2 and I3) in the reaction scheme which then give their respective products (I1-> M, I2 ->B and I3 ->P) after an appropriate length of time. The steady state values, attained upon simulation of model equations, for Allolactose (A), mRNA (M), beta-galactosidase (B), Lactose (L), and Permease (P) match with those predicted by the paper. The model was successfully tested on Jarnac, MathSBML and COPASI

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Model
Publication ID: 12719218 Submission Date: 25 Aug 2006 12:48:14 UTC Last Modification Date: 12 Feb 2014 16:36:21 UTC Creation Date: 21 Jun 2006 14:47:26 UTC
Mathematical expressions
Reactions
Basal_mRNA_Synthesis mRNA_Degradation allolactose_controlled_mRNA_synthesis allolactose_controlled_partial_mRNA_synthesis
Beta_galactosidase_Degradation Beta_galactosidase_synthesis Partial_Beta_galactosidase_synthesis Basal_Allolactose_Degradation
Betagalactosidase_mediated_Allolactose_Degradation Beta_galactosidase_reaction lactose_degradation Lactose_transport_out
Lactose_transport_in permease_degradation permease_synthesis partial_permease_synthesis
Physical entities
Compartments Species
cell mRNA Betagalactosidase allolactose
lactose_internal permease PartialmRNA
PartialBetagalactosidase PartialPermease External_Lactose
Global parameters
mu gamma_M gamma_B gamma_A
gamma_0 K alpha_M tau_B
alpha_A K_L1 alpha_B K_A
beta_A tau_M K_L gamma_L
gamma_P alpha_L alpha_P tau_P
beta_L1 K_Le K_1  
Reactions (16)
 
 Basal_mRNA_Synthesis  → [mRNA];  
 
 mRNA_Degradation [mRNA] → ;  
 
 allolactose_controlled_mRNA_synthesis [PartialmRNA] → [mRNA];  
 
 allolactose_controlled_partial_mRNA_synthesis  → [PartialmRNA];   {allolactose}
 
 Beta_galactosidase_Degradation [Betagalactosidase] → ;  
 
 Beta_galactosidase_synthesis [PartialBetagalactosidase] → [Betagalactosidase];  
 
 Partial_Beta_galactosidase_synthesis  → [PartialBetagalactosidase];   {mRNA}
 
 Basal_Allolactose_Degradation [allolactose] → ;  
 
 Betagalactosidase_mediated_Allolactose_Degradation [allolactose] → ;   {Betagalactosidase}
 
 Beta_galactosidase_reaction [lactose_internal] → [allolactose];   {Betagalactosidase}
 
 lactose_degradation [lactose_internal] → ;  
 
 Lactose_transport_out [lactose_internal] → ;   {permease}
 
 Lactose_transport_in  → [lactose_internal];   {permease} , {External_Lactose}
 
 permease_degradation [permease] → ;  
 
 permease_synthesis [PartialPermease] → [permease];  
 
 partial_permease_synthesis  → [PartialPermease];   {mRNA}
 
  Spatial dimensions: 3.0  Compartment size: 1.0
 
 mRNA
Compartment: cell
Initial concentration: 6.26E-4
 
 Betagalactosidase
Compartment: cell
Initial concentration: 0.0
 
 allolactose
Compartment: cell
Initial concentration: 0.038
 
 lactose_internal
Compartment: cell
Initial concentration: 0.372
 
 permease
Compartment: cell
Initial concentration: 0.0149
 
   PartialmRNA
Compartment: cell
Initial concentration: 0.0
 
   PartialBetagalactosidase
Compartment: cell
Initial concentration: 0.0
 
   PartialPermease
Compartment: cell
Initial concentration: 0.0
 
 External_Lactose
Compartment: cell
Initial concentration: 0.08
Constant
 
Global Parameters (23)
 
   mu
Value: 0.0226
Constant
 
   gamma_M
Value: 0.411
Constant
 
   gamma_B
Value: 8.33E-4
Constant
 
   gamma_A
Value: 0.52
Constant
 
   gamma_0
Value: 7.25E-7
Constant
 
   K
Value: 7200.0
Constant
 
   alpha_M
Value: 9.97E-4
Constant
 
   tau_B
Value: 2.0
Constant
 
   alpha_A
Value: 17600.0
Constant
 
   K_L1
Value: 1.81
Constant
 
   alpha_B
Value: 0.0166
Constant
 
   K_A
Value: 1.95
Constant
 
   beta_A
Value: 21500.0
Constant
 
   tau_M
Value: 0.1
Constant
 
   K_L
Value: 0.97
Constant
 
   gamma_L
Constant
 
   gamma_P
Value: 0.65
Constant
 
   alpha_L
Value: 2880.0
Constant
 
   alpha_P
Value: 10.0
Constant
 
   tau_P
Value: 0.83
Constant
 
   beta_L1
Value: 2650.0
Constant
 
   K_Le
Value: 0.26
Constant
 
   K_1
Value: 25200.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000065

Curator's comment: (updated: 24 Jun 2010 16:32:10 BST)

Figure 3 of the reference publication is reproduced. The model was integrated and simulated using Copasi v-4.5.31.

spacer
spacer