middleton1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000422) Biomodels notes: This model corresponds to the full model that is described in the reference publication. The model parameter corresponds to wild-type and reproduces Figure 4C wild-type with R=1. The simulation runs for 500 time units (minutes) to allow the system to approach its steady state, then adds exogenous hormone for 120 time units, before removing the exogenous hormone until a total time of 800. So, the total run time is 800 minutes, having exogenous hormone between time points 500 and 620 (120 mins). In the paper, time is shifted so that t=0 corresponds to the addition of hormone, i.e. 500mins. The plot here show the time-course simulation between 500 mins(t=0 in the paper) and 800 mins (t=300 in the paper). The y-axis scale in the paper is in nM, whereas in the model it is in ?M. The plot date were obtained by simulating the model using Copasi v4.8 (Build 35). The plot was generated using Gnuplot. 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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Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling.

  • Alistair M Middleton
  • Susana Úbeda-Tomás
  • Jayne Griffiths
  • Tara Holman
  • Peter Hedden
  • Stephen G Thomas
  • Andrew L Phillips
  • Michael J Holdsworth
  • Malcolm J Bennett
  • John R King
  • Markus R Owen
Proc. Natl. Acad. Sci. U.S.A. 2012; 109 (19): 7571-7576
Abstract
The hormone gibberellin (GA) is a key regulator of plant growth. Many of the components of the gibberellin signal transduction [e.g., GIBBERELLIN INSENSITIVE DWARF 1 (GID1) and DELLA], biosynthesis [e.g., GA 20-oxidase (GA20ox) and GA3ox], and deactivation pathways have been identified. Gibberellin binds its receptor, GID1, to form a complex that mediates the degradation of DELLA proteins. In this way, gibberellin relieves DELLA-dependent growth repression. However, gibberellin regulates expression of GID1, GA20ox, and GA3ox, and there is also evidence that it regulates DELLA expression. In this paper, we use integrated mathematical modeling and experiments to understand how these feedback loops interact to control gibberellin signaling. Model simulations are in good agreement with in vitro data on the signal transduction and biosynthesis pathways and in vivo data on the expression levels of gibberellin-responsive genes. We find that GA-GID1 interactions are characterized by two timescales (because of a lid on GID1 that can open and close slowly relative to GA-GID1 binding and dissociation). Furthermore, the model accurately predicts the response to exogenous gibberellin after a number of chemical and genetic perturbations. Finally, we investigate the role of the various feedback loops in gibberellin signaling. We find that regulation of GA20ox transcription plays a significant role in both modulating the level of endogenous gibberellin and generating overshoots after the removal of exogenous gibberellin. Moreover, although the contribution of other individual feedback loops seems relatively small, GID1 and DELLA transcriptional regulation acts synergistically with GA20ox feedback.

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
1.0 mole
1.0 litre
1.0 metre^(2.0)
1.0 metre
1.0 second
Id Name Spatial dimensions Size
default 3.0 1.0 volume
Id Name Initial quantity Compartment Fixed
s1 GA4 0.01 default
s11 ga20ox_source 0.0 default
s15 gid_source 0.0 default
s16 DELLA 0.01 default
s2 GID 0.01 default
s22 DELLA_U 0.01 default
s23 GA12 0.01 default
s24 GA15 0.01 default
s25 GA24 0.01 default
s26 GA9 0.01 default
s27 GA20ox 0.01 default
s28 GA3ox 0.01 default
s29 GA9-GA3ox 0.01 default
s3 GA12_source 0.0 default
s30 GA24-GA20ox 0.01 default
s31 GA15-GA20ox 0.01 default
s32 GA12-GA20ox 0.01 default
s33 GID_source 0.0 default
s34 della_source 0.0 default
s35 ga3ox_source 0.0 default
s36 GA4-GID-DELLA2 0.01 default
s39 ga20ox 0.01 default
s40 della 0.01 default
s41 ga3ox 0.01 default
s42 gid 0.01 default
s45 GA4-GID-DELLA1 0.01 default
s5 GA3ox_source 0.0 default
s6 GA20ox_source 0.0 default
s62 GA4-GID-closed 0.01 default
s65 GA4-GID 0.01 default
s66 GA4_source 0.0 default
s67 sa5_degraded 0.0 default
s68 sa6_degraded 0.0 default
s69 sa7_degraded 0.0 default
s7 DELLA_source 0.0 default
s70 sa8_degraded 0.0 default
s71 sa1_degraded 0.0 default

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
re1 GA4-GID association s1 + s2 > s65

la * s1 * s2
re10 GA15-GA20ox association s24 + s27 > s31

ka15 * s24 * s27
re11 GA15.GA20ox dissociation s31 > s24 + s27

kd15 * s31
re12 GA24 production s31 > s27 + s25

km15 * s31
re13 GA24-GA20ox association s25 + s27 > s30

ka24 * s25 * s27
re14 GA24.GA20ox dissociation s30 > s25 + s27

kd24 * s30
re15 GA9 production s30 > s27 + s26

km24 * s30
re16 GA9-GA3ox association s26 + s28 > s29

ka9 * s26 * s28
re17 GA9.GA3ox dissociation s29 > s26 + s28

kd9 * s29
re18 GA4 production s29 > s28 + s1

km9 * s29
re19 GA4.GID lid closing s65 > s62

q * s65
re2 GA4.GID dissociation s65 > s2 + s1

ld * s65
re20 GA4.GID-Closed lid opening s62 > s65

p * s62
re21 della translation s7 > s16

deltaDELLA * s40
re22 ga20ox translation s6 > s27

deltaGA20ox * s39
re23 ga3ox translation s5 > s28

deltaGA3ox * s41
re24 gid translation s33 > s2

deltaGID * s42
re27 ga20ox transcription (activated by DELLA) s11 > s39

muGA20ox * s16 / (s16 + thetaGA20ox)
re28 gid transcription (activated by DELLA) s15 > s42

muGID * s16 / (s16 + thetaGID)
re29 della transcription (repressed by DELLA) s34 > s40

muDELLA * thetaDELLA / (s16 + thetaDELLA)
re3 GA4.GID-DELLA1 association s62 + s16 > s45

ua1 * s62 * s16
re30 ga3ox transcription (activated by DELLA) s35 > s41

muGA3ox * s16 / (s16 + thetaGA3ox)
re31 della decay s40 > s34

muDELLA * s40
re32 gid decay s42 > s15

muGID * s42
re33 ga20ox decay s39 > s11

muGA20ox * s39
re34 ga3ox decay s41 > s35

muGA3ox * s41
re35 GA20ox decay s27 > s6

gammaGA20ox * s27
re37 GID decay s2 > s33

gammaGID * s2
re38 GA3ox decay s28 > s5

gammaGA3ox * s28
re39 GA4.GID-DELLA2 association s62 + s16 > s36

ua2 * s62 * s16
re4 GA4.GID.DELLA1 dissociation s45 > s62 + s16

ud1 * s45
re40 GA4.GID.DELLA2 dissociation s36 > s62 + s16

ud2 * s36
re41 GA4 supply s66 > s1

Pmem * A1 * omegaGA4
re42 degradation of GA12 s23 > s67

muGA * s23
re43 degradation of GA15 s24 > s68

muGA * s24
re44 degradation of GA24 s25 > s69

muGA * s25
re45 degradation of GA9 s26 > s70

muGA * s26
re46 degradation of GA4 s1 > s71

(muGA + Pmem * B1) * s1
re5 DELLA ubiquitination s45 > s62 + s22

um * s45
re6 GA12 supply s3 > s23

omegaGA12
re7 GA12-GA20ox association s23 + s27 > s32

ka12 * s23 * s27
re8 GA12.GA20ox dissociation s32 > s23 + s27

kd12 * s32
re9 GA15 production s32 > s27 + s24

km12 * s32

Global parameters

Id Value
Pmem 2.66664 substance
R 1.0 substance
appliedGA4 2.0 substance
muDELLA 0.070794578438414 substance
muGA 0.290804218727464 substance
muGA20ox 0.047770755070625 substance
muGA3ox 0.102600014140148 substance
muGID 0.045708818961487 substance
omegaGA12 <assignment rule> substance
omegaGA12ga13 0.006602803853512 substance
omegaGA4 0.0 substance
tGA4off 620.0 substance
tGA4on 500.0 substance

Local parameters

Id Value Reaction
la 1.35 substance re1 (GA4-GID association)
ld 2.84315148627376 substance re2 (GA4.GID dissociation)
ua1 10.0 substance re3 (GA4.GID-DELLA1 association)
ud1 0.133045441797809 substance re4 (GA4.GID.DELLA1 dissociation)
um 6.92208879449283 substance re5 (DELLA ubiquitination)
ka12 2904.11853677638 substance re7 (GA12-GA20ox association)
kd12 2.67298621993027 substance re8 (GA12.GA20ox dissociation)
km12 198.80427707769 substance re9 (GA15 production)
ka15 2073.22402517968 substance re10 (GA15-GA20ox association)
kd15 0.008827838388125 substance re11 (GA15.GA20ox dissociation)
km15 763.777072066507 substance re12 (GA24 production)
ka24 3099.18915892587 substance re13 (GA24-GA20ox association)
kd24 0.01588492846351 substance re14 (GA24.GA20ox dissociation)
km24 2.58846077319221 substance re15 (GA9 production)
ka9 2073.22402517968 substance re16 (GA9-GA3ox association)
kd9 0.008827838388125 substance re17 (GA9.GA3ox dissociation)
km9 763.777072066507 substance re18 (GA4 production)
q 0.025118864315096 substance re19 (GA4.GID lid closing)
p 0.077624711662869 substance re20 (GA4.GID-Closed lid opening)
deltaDELLA 0.000527749140286577 substance re21 (della translation)
deltaGA20ox 0.192990314378105 substance re22 (ga20ox translation)
deltaGA3ox 0.019299031437811 substance re23 (ga3ox translation)
deltaGID 19.2990314378105 substance re24 (gid translation)
thetaGA20ox 0.6383 substance re27 (ga20ox transcription (activated by DELLA))
thetaGID 0.00055995 substance re28 (gid transcription (activated by DELLA))
thetaDELLA 0.01 substance re29 (della transcription (repressed by DELLA))
thetaGA3ox 0.0082 substance re30 (ga3ox transcription (activated by DELLA))
gammaGA20ox 3.514 substance re35 (GA20ox decay)
gammaGID 3.514 substance re37 (GID decay)
gammaGA3ox 3.514 substance re38 (GA3ox decay)
ua2 316.2278 substance re39 (GA4.GID-DELLA2 association)
ud2 2.8184 substance re40 (GA4.GID.DELLA2 dissociation)
A1 0.0307 substance re41 (GA4 supply)
B1 0.00039795 substance re46 (degradation of GA4)

Assignment rules

Definition
omegaGA12 = R * omegaGA12ga13

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments
gt(time, tGA4on) omegaGA4 = appliedGA4
gt(time, tGA4off) omegaGA4 = 0