JWS Online

yildirim1

yildirim1

 Detail
 Download

Reactions

r_a1

Basal_Allolactose_Degradation

A > ∅

r_a2

Betagalactosidase_mediated_Allolactose_Degradation

A > ∅

r_a3_l1

Beta_galactosidase_reaction

L > A

r_b1

Beta_galactosidase_Degradation

B > ∅

r_b2_i2

Beta_galactosidase_synthesis

I2 > B

r_i1

allolactose_controlled_partial_mRNA_synthesis

∅ > I1

r_i2

Partial_Beta_galactosidase_synthesis

∅ > I2

r_i3

partial_permease_synthesis

∅ > I3

r_l2

lactose_degradation

L > ∅

r_l3

Lactose_transport_out

L > ∅

r_l4

Lactose_transport_in

∅ > L

r_m1

Basal_mRNA_Synthesis

∅ > M

r_m2

mRNA_Degradation

M > ∅

r_m3_i1

allolactose_controlled_mRNA_synthesis

I1 > M

r_p1

permease_degradation

P > ∅

r_p2_i3

permease_synthesis

I3 > P

Parameters

Global parameters

Fixed species

Initial values

Functions and Rules

Events

Constraints

Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.


Species:

Reactions:

Middle-click: pin/unpin nodes
Shift-click: pool/unpool species
Right-click: context menu
Apply alternate model layout to overlapping elements in current model:

log scales

y-axis min/max

x-axis min/max

Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.

  • Necmettin Yildirim
  • Michael C Mackey
Biophys. J. 2003; 84 (5): 2841-2851
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 SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000065). Biomodels notes: "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" JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.