Yildirim2003_Lac_Operon
Ontology highlight
ABSTRACT:
SUBMITTER: 
Nicolas Le Novère
PROVIDER: BIOMD0000000065 | BioModels | 2006-06-21
REPOSITORIES: BioModels
Publications
Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.
Yildirim Necmettin N Mackey Michael C MC
Biophysical journal 20030501 5
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 ...[more]
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Project description:This SBML file is a translation of a MatLab model utilized in
the following paper. It describes the interplay of IkB and P100 negative feedback to
control the cellular localization of the NFkB transcription factor in response to
activation of IkB Kinase 1 (IKK1) and IkB Kinase 2 (IKK2).
Soumen Basak, Ha Na Kim, Jeffrey D. Kearns, Vinay Tergaonkar,
Ellen O'Dea, Shannon L. Werner, Chris A. Benedict, Carl F. Ware, Gourishankar
Ghosh, Inder M. Verma, Alexander Hoffmann. "A Fourth IkB Protein in the NFkB
Signaling Module." Cell (2007)
Questions concerning the paper should be addressed to the
corresponding author. Alexander Hoffmann (ahoffmann@ucsd.edu)
Technical questions concerning the implementation of the model
within SBML should be addressed to Jeff Kearns (jkearns@ucsd.edu)
-
Introduction:
The original model was written and simulated within MathWorks
MatLab 2006a using the ode15s (stiff/NDF) solver. It is highly recommended
that those wanting to model this system use the MatLab version which we will
freely provide upon request. As always, simulation results vary according to
the numerical solver used. In addition, there are also shortcomings in the
Stimulation Phase of the model (listed below) that maybe resolved with future
versions of SBML.
-
SBML Generation :
Translation to SBML Level 2.1 was performed via reconstruction
of the model within MathWorks SimBiology Desktop (version 2.1)
followed by an Export to SBML.
-
Running the model :
Simulations require two sequential runs of the model. It is
recommended that you generate a script to pass the final component
concentrations from the first run into the initial concentrations of the
second.
1. Equilibrium Phase.- In both phases, total NFkB (0.125 micromole), IKK1 (0.1 micromole), and IKK2
(0.1 micromole) protein remains constant. These exist in free and bound forms.- Synthesis and degradation reactions are included for IkBa,
IkBb, IkBe, and P100 mRNA and protein.- Equilibrium state nuclear NFkB (NFkBn) levels for
combinations of IkB and P100 protein knockouts are included in the Cell
paper. Use these to validate whether your simulation time is long enough and
whether your solver is behaving properly.
2. Stimulation Phase.- The simulations of this phase have known shortcomings due to insufficient support by the SBML framework. These include
not being able to utilize an interpolation function and lack of delay functions (resolved in SBML 2.2, but not yet in the MathWorks SimBiology tool).
Resolution of these should enable recapitulation of the Stimulation Phase results shown in the Cell paper.- The model input signal is defined as activity profiles for
IKK1 and IKK2 (measured via biochemical assays). Profiles are included below
for Lympotoxin-Beta (LTB) activation of IKK1 and for Tumor Necrosis Factor
(TNF) and Lipopolysaccharide (LPS) activation of IKK2.
- Combinations of IKK1 and IKK2 inputs are possible. In the
paper, a pulse stimulation with TNF (IKK2) followed later by LTB (IKK1)
stimulation was used.
- The activity profile encodes what fraction of the IKK is able
to mediate IkB and P100 protein degradation by acting as a rate constant
multiplier. Specifically....
ikk1_multiplier = IKK1(t) =
IKK1 active at time 't', where 1=
100%
pd_c_2pq
=
pd_c_2pq
* ikk1_multiplier;
pd_c_3pqn
=
pd_c_3pqn
* ikk1_multiplier;
ikk2_multiplier = IKK2(t) =
IKK2 active at time 't', where 1 =
100%
pd_c_2ai
=
pd_c_2ai
* ikk2_multiplier;
pd_c_2bi
=
pd_c_2bi
* ikk2_multiplier;
pd_c_2ei
=
pd_c_2ei
* ikk2_multiplier;
pd_c_3ain
=
pd_c_3ain
* ikk2_multiplier;
pd_c_3bin
=
pd_c_3bin
* ikk2_multiplier;
pd_c_3ein
=
pd_c_3ein
* ikk2_multiplier;
In the equilibrium phase, the ikk1_multiplier is 0.01 and
ikk2_multiplier is 0.001.
- IKK1 activation also regulates the translation rate of P100
and the nuclear IkB/NFkB association rates by unknown mechanisms. We include
this in the Stimulation Phase via a fold IKK1 activation multiplier.ikk1_multipler_tsl_asn = IKK1(t) / IKK1(t=0)
ps_c_p = ps_c_p *
ikk1_multiplier_tsl_asn
a_n_an = a_n_an *
ikk1_multiplier_tsl_asn
a_n_bn = a_n_bn *
ikk1_multiplier_tsl_asn
a_n_en = a_n_en *
ikk1_multiplier_tsl_asn
- The IKK profile interpolation does NOT work in the SBML
version.
Any ideas on how to
make it work are appreciated (contact Jeff Kearns). - In brief, the MatLab version takes in two arrays-- IKK
profile versus time -- to create a time-dependent IKK input function via
piecewise cubic interpolation. As this creates N-1 polynomials for arrays
with N datapoints, it is difficult to incorporate this into SBML via Rules or
Events.
It might be possible to
construct the interpolation function using the tools present in MathML.
The MatLab code is included below to
help anyone attempt this.
%==========================================================
% GENERATE_IKK_INPUTS
%==========================================================
function ikk1_curve =
interpolate_ikk1 (stimulus)
global SIM_TIME;
if (strcmp(stimulus, 'LTB'))
values
= [1 1.2 1.4 1.9 2.4 2.6 2.6 2.6] /
100;
time
= [0 180 300 480 600 900 1200
2400]; %minutes
elseif (strcmp(stimulus, 'LTB_20hr'))
values
= [1 1 1.2 1.4 1.9 2.4 2.6 2.6] /
100;
time
= [0 1200 1380 1500 1680 1800 2100
2400];
elseif (strcmp(stimulus, 'basal_1'))
values
= [1 1 1 1 1] / 100;
time
= [0 360 600 1200 2400];
else
error('Incorrect IKK1 input');
end
ikk1_curve
= interp1(time, values,
0:SIM_TIME);
-------------
function ikk2_curve =
interpolate_ikk2(stimulus)
global SIM_TIME;
if (strcmp(stimulus, 'TNF_p15'))
values
= [0.1 60 100 65 50 36 21 16 10 .1 .1
.1 .1] / 100;
time
= [0 5 10 15 20 25 30 45 59 60 360
1200 2400];
elseif (strcmp(stimulus, 'LPS_p45'))
values
= [0.1 3 8 24 25 15 8 5 0.1 0.1] /
100;
time
= [0 15 30 45 60 120 240 360 600
2400];
elseif (strcmp(stimulus, 'basal_1'))
values
= [.1 .1 .1 .1 .1] / 100;
time
= [0 360 600 1200 2400];
else
error('Incorrect IKK2 input name');
end
ikk2_curve
= interp1(time, values,
0:SIM_TIME);
- mRNA synthesis (transcription) is comprised of a constitutive
process and an inducible process. This inducible process is dependent upon
the concentration of nuclear NFkB (NFkBn). We know from biochemical assays
that the inducible transcription of three of the components (IkBbt,
IkBet, and P100t) are delayed and we
included this delay strictly within the Stimulation Phase of the MatLab mocel
(not in the equilibrium phase).
This requires the value of NFkBn at a previous time point.
As SimBiology only supports SBML 2.1
(as of January 2007), the delay functions are NOT included in the SBML
model.
As tools include support
SBML 2.2, you can add these reactions.
IkBet = 45 minute delayIkBbt = 45 minute delayP100t = 90 minute delay
This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication
for more information. In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not..
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.
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An important transcription factor of B.subsilis is sigma B
. Liebal et al. (2012) have performed experiments in B.subtilis wild type and mutant straits to test and validate a mathematical model of the dynamics of sigma B
activity. The following three models were constructed and their ability to fit the experimental data were tested. 1) Transcription inhibition model (MODEL1212180000), 2) sigma B
proteolysis model (MODEL1302080000) and 3) Post-transcriptional instability model (MODEL1302080001). This model corresponds to the post-transcription instability model (MODEL1302080001).
This model is described in the article:
Proteolysis of beta-galactosidase following SigmaB activation in Bacillus subtilis.
Liebal UW, Sappa PK, Millat T, Steil L, Homuth G, Völker U, Wolkenhauer O.
2012 Jun;8(6):1806-14.
Abstract:
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Figure 3a of the reference article has been reproduced. beta-galactosidase (lacz in model) activity at different concentrations of IPTG (100M, 200M and 1000M) has been reproduced. SED-ML (Simulation Experiment Description Markup Language) file is available for this model (see curation tab).
This model is hosted on BioModels Database
and identified
by: MODEL1302080001
.
To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource
for published quantitative kinetic models
.
To the extent possible under law, all copyright and related or
neighbouring rights to this encoded model have been dedicated to the public
domain worldwide. Please refer to CC0 Public Domain
Dedication
for more information.
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Project description:Liebal2012 - B.subtilis transcription inhibition model
An important transcription factor of B.subsilis is sigma B
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activity. The following three models are constructed and their ability to fit the experimental data were tested. 1) Transcription inhibition model (MODEL1212180000), 2) sigma B
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This model is described in the article:
Proteolysis of beta-galactosidase following SigmaB activation in Bacillus subtilis.
Liebal UW, Sappa PK, Millat T, Steil L, Homuth G, Völker U, Wolkenhauer O.
2012 Jun;8(6):1806-14.
Abstract:
In Bacillus subtilis the σ(B) mediated general stress response provides protection against various environmental and energy related stress conditions. To better understand the general stress response, we need to explore the mechanism by which the components interact. Here, we performed experiments in B. subtilis wild type and mutant strains to test and validate a mathematical model of the dynamics of σ(B) activity. In the mutant strain BSA115, σ(B) transcription is inducible by the addition of IPTG and negative control of σ(B) activity by the anti-sigma factor RsbW is absent. In contrast to our expectations of a continuous β-galactosidase activity from a ctc::lacZ fusion, we observed a transient activity in the mutant. To explain this experimental finding, we constructed mathematical models reflecting different hypotheses regarding the regulation of σ(B) and β-galactosidase dynamics. Only the model assuming instability of either ctc::lacZ mRNA or β-galactosidase protein is able to reproduce the experiments in silico. Subsequent Northern blot experiments revealed stable high-level ctc::lacZ mRNA concentrations after the induction of the σ(B) response. Therefore, we conclude that protein instability following σ(B) activation is the most likely explanation for the experimental observations. Our results thus support the idea that B. subtilis increases the cytoplasmic proteolytic degradation to adapt the proteome in face of environmental challenges following activation of the general stress response. The findings also have practical implications for the analysis of stress response dynamics using lacZ reporter gene fusions, a frequently used strategy for the σ(B) response.
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This model is hosted on BioModels Database
and identified
by: MODEL1212180000
.
To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource
for published quantitative kinetic models
.
To the extent possible under law, all copyright and related or
neighbouring rights to this encoded model have been dedicated to the public
domain worldwide. Please refer to CC0 Public Domain
Dedication
for more information.
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