veening1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000240) Biomodels notes: Figure 7A and 7B is reproduced here. We got the following useful information for curation from the authors. In the paper, the x-axis is mislabelled by a factor of 5, and also the values for 3 of the parameters are incorrect in the paper. The parameters and their correct values are 1) Kdim (K1 for aprE, in the paper)= 12, 2) kphos (kph, in the paper) = 0.004, and 3) kdephos (kdeph, in the paper) = 0.15. All these are implemented in the model. The model was simulated and integrated using Copasi JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Transient heterogeneity in extracellular protease production by Bacillus subtilis.

  • Jan-Willem Veening
  • Oleg A Igoshin
  • Robyn T Eijlander
  • Reindert Nijland
  • Leendert W Hamoen
  • Oscar P Kuipers
Mol. Syst. Biol. 2008; 4 : 184
Abstract
The most sophisticated survival strategy Bacillus subtilis employs is the differentiation of a subpopulation of cells into highly resistant endospores. To examine the expression patterns of non-sporulating cells within heterogeneous populations, we used buoyant density centrifugation to separate vegetative cells from endospore-containing cells and compared the transcriptome profiles of both subpopulations. This demonstrated the differential expression of various regulons. Subsequent single-cell analyses using promoter-gfp fusions confirmed our microarray results. Surprisingly, only part of the vegetative subpopulation highly and transiently expresses genes encoding the extracellular proteases Bpr (bacillopeptidase) and AprE (subtilisin), both of which are under the control of the DegU transcriptional regulator. As these proteases and their degradation products freely diffuse within the liquid growth medium, all cells within the clonal population are expected to benefit from their activities, suggesting that B. subtilis employs cooperative or even altruistic behavior. To unravel the mechanisms by which protease production heterogeneity within the non-sporulating subpopulation is established, we performed a series of genetic experiments combined with mathematical modeling. Simulations with our model yield valuable insights into how population heterogeneity may arise by the relatively long and variable response times within the DegU autoactivating pathway.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1e-15 litre
1.0 item
Id Name Spatial dimensions Size
univ 3.0 1.0
Id Name Initial quantity Compartment Fixed
AprE 0.0 univ
DegU 0.0 univ
DegUP 0.0 univ
Dim 0.0 univ
mAprE 0.0 univ
mDegU 0.0 univ

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
AprEdeg AprE > ∅

kdeg * AprE
AprEsyn ∅ > AprE

ksyn * mAprE * univ
DimerAss {2.0}DegUP > Dim

ka * pow(DegUP, 2)
DimerDis Dim > {2.0}DegUP

kd * Dim
degradation1 DegU > ∅

kdeg * DegU * univ
degradation2 DegUP > ∅

kdeg * DegUP * univ
degradation3 Dim > ∅

kdeg * Dim * univ
degradationmRNA mDegU > ∅

kdegm * mDegU
dephosphorylation DegUP > DegU

kdephos * DegUP
mRNAAprEdeg mAprE > ∅

kdegm * mAprE
mRNAAprEsyn ∅ > mAprE

Kr1 / (R + Kr1) * (Iro * (Dim * univ / Kdim + 1) / (1 + Dim * univ / Kdim + pow(Dim * univ, 2) / pow(Kdim, 2) + R / Kr) + Irmax * pow(Dim * univ, 2) / (pow(Kdim, 2) * (1 + Dim * univ / Kdim + pow(Dim * univ, 2) / pow(Kdim, 2) + R / Kr)))
phosphorylation DegU > DegUP

kphos * DegU
synthesisDegU ∅ > DegU

ksyn1 * mDegU * univ
synthesismRNA ∅ > mDegU

Io * K / (Dim * univ + K) + Imax * Dim * univ / (Dim * univ + K)

Global parameters

Id Value
DegU_Total 0.0
Imax 0.048
Io 0.004
Irmax 0.4
Iro 0.02
K 7.0
Kdim 12.0
Kr 7.0
Kr1 7.0
R 7.0
V 1.0
ka 0.025
kd 0.1
kdeg 0.0004
kdegA 0.0001
kdegm 0.01
kdephos 0.0
kphos 0.0
ksyn 0.04
ksyn1 0.04
p 0.15
q 0.004
ratio 0.026666667

Local parameters

Id Value Reaction

Assignment rules

Definition
DegU_Total = DegU + DegUP + 2.0 * Dim
kdephos = q / ratio
kphos = ratio * p

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments