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BIOMD0000000522 - Muraro2014 - Vascular patterning in Arabidopsis roots

 

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Reference Publication
Publication ID: 24381155
Muraro D, Mellor N, Pound MP, Help H, Lucas M, Chopard J, Byrne HM, Godin C, Hodgman TC, King JR, Pridmore TP, Helariutta Y, Bennett MJ, Bishopp A.
Integration of hormonal signaling networks and mobile microRNAs is required for vascular patterning in Arabidopsis roots.
Proc. Natl. Acad. Sci. U.S.A. 2014 Jan; 111(2): 857-862
Centre for Plant Integrative Biology, School of Biosciences, University of Nottingham, Loughborough LE12 5RD, United Kingdom.  [more]
Model
Original Model: BIOMD0000000522.origin
Submitter: Vijayalakshmi Chelliah
Submission ID: MODEL1403110000
Submission Date: 11 Mar 2014 15:44:32 UTC
Last Modification Date: 12 Mar 2014 12:15:07 UTC
Creation Date: 11 Mar 2014 15:56:38 UTC
Encoders:  Vijayalakshmi Chelliah
   Daniele Muraro
   Nathan Mellor
set #1
bqbiol:hasProperty Mathematical Modelling Ontology MAMO_0000046
bqbiol:hasTaxon Taxonomy Arabidopsis
bqbiol:isVersionOf Gene Ontology xylem and phloem pattern formation
Notes
Muraro2014 - Vascular patterning in Arabidopsis roots

Using a multicellular model, maintanence of vascular patterning in Arabidopsis roots has been studied. The model that is provided here is the single-cell version of the model. The two-cell and multicellular models described in the paper can be downloaded as python scripts (follow the curation tab to get these files).

This model is described in the article:

Muraro D, Mellor N, Pound MP, Help H, Lucas M, Chopard J, Byrne HM, Godin C, Hodgman TC, King JR, Pridmore TP, Helariutta Y, Bennett MJ, Bishopp A.
Proc Natl Acad Sci U S A. 2014 Jan 14;111(2):857-62.

Abstract:

As multicellular organisms grow, positional information is continually needed to regulate the pattern in which cells are arranged. In the Arabidopsis root, most cell types are organized in a radially symmetric pattern; however, a symmetry-breaking event generates bisymmetric auxin and cytokinin signaling domains in the stele. Bidirectional cross-talk between the stele and the surrounding tissues involving a mobile transcription factor, SHORT ROOT (SHR), and mobile microRNA species also determines vascular pattern, but it is currently unclear how these signals integrate. We use a multicellular model to determine a minimal set of components necessary for maintaining a stable vascular pattern. Simulations perturbing the signaling network show that, in addition to the mutually inhibitory interaction between auxin and cytokinin, signaling through SHR, microRNA165/6, and PHABULOSA is required to maintain a stable bisymmetric pattern. We have verified this prediction by observing loss of bisymmetry in shr mutants. The model reveals the importance of several features of the network, namely the mutual degradation of microRNA165/6 and PHABULOSA and the existence of an additional negative regulator of cytokinin signaling. These components form a plausible mechanism capable of patterning vascular tissues in the absence of positional inputs provided by the transport of hormones from the shoot.

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.

Model
Publication ID: 24381155 Submission Date: 11 Mar 2014 15:44:32 UTC Last Modification Date: 12 Mar 2014 12:15:07 UTC Creation Date: 11 Mar 2014 15:56:38 UTC
Mathematical expressions
Rules
Assignment Rule (variable: F_AHP6) Assignment Rule (variable: F_ARR5) Assignment Rule (variable: F_CK) Assignment Rule (variable: F_IAA2)
Assignment Rule (variable: F_PIN1) Assignment Rule (variable: F_PIN3) Assignment Rule (variable: F_PIN7) Rate Rule (variable: Auxin)
Rate Rule (variable: Cytokinin) Rate Rule (variable: miRNA) Rate Rule (variable: PHBm) Rate Rule (variable: AHP6m)
Rate Rule (variable: IAA2m) Rate Rule (variable: ARR5m) Rate Rule (variable: PIN1m) Rate Rule (variable: PIN3m)
Rate Rule (variable: PIN7m) Rate Rule (variable: AHP6p) Rate Rule (variable: IAA2p) Rate Rule (variable: ARR5p)
Rate Rule (variable: PHBp) Rate Rule (variable: CKX3p)    
Physical entities
Compartments Species
compartment Auxin Cytokinin AHP6m
AHP6p IAA2m IAA2p
ARR5m ARR5p PHBm
PHBp CKX3m CKX3p
PIN3m PIN1m PIN7m
miRNA    
Global parameters
F_AHP6 F_CK F_IAA2 F_ARR5
F_PIN1 F_PIN7 F_PIN3 p_ax
p_ck d_ax d_ck phloem_rate_ax
all_section_rate_ax phloem_rate_ck all_section_rate_ck lambda_AHP6
lambda_IAA2 lambda_ARR5 lambda_PIN1 lambda_PIN3
lambda_PIN7 mu_m_PHB mu_m_AHP6 mu_m_IAA2
mu_m_ARR5 mu_m_PIN1 mu_m_PIN3 mu_m_PIN7
delta_PHB delta_AHP6 delta_IAA2 delta_ARR5
delta_PIN1 delta_PIN3 delta_PIN7 delta_CKX3
mu_p_PHB mu_p_AHP6 mu_p_IAA2 mu_p_ARR5
mu_p_PIN1 mu_p_PIN3 mu_p_PIN7 mu_p_CKX3
theta_Ax theta_Ck theta_AHP6 theta_ARR5
theta_PHB theta_CKX3 p_phb d_phb
p_mirna d_mirna d_mirna_mrna p_ckx3
d_ckx3 b_pin3 b_pin1 b_pin7
b_ahp6 b_arr5 b_iaa2 hill_ax
hill_ck hill_arr5 hill_ckx3 hill_ahp6
hill_phb      
Reactions (0)
Rules (22)
 
 Assignment Rule (name: F_AHP6) F_AHP6 = (b_ahp6+(Auxin/theta_Ax)^hill_ax)/(1+(Auxin/theta_Ax)^hill_ax+(PHBp/theta_PHB)^hill_phb)
 
 Assignment Rule (name: F_ARR5) F_ARR5 = (b_arr5+(Cytokinin/theta_Ck)^hill_ck)/(1+(Cytokinin/theta_Ck)^hill_ck+(AHP6p/theta_AHP6)^hill_ahp6)
 
 Assignment Rule (name: F_CK) F_CK = 1/(1+(CKX3p/theta_CKX3)^hill_ckx3)
 
 Assignment Rule (name: F_IAA2) F_IAA2 = (b_iaa2+(Auxin/theta_Ax)^hill_ax)/(1+(Auxin/theta_Ax)^hill_ax)
 
 Assignment Rule (name: F_PIN1) F_PIN1 = (b_pin1+(ARR5p/theta_ARR5)^hill_arr5)/(1+(ARR5p/theta_ARR5)^hill_arr5)
 
 Assignment Rule (name: F_PIN3) F_PIN3 = b_pin3
 
 Assignment Rule (name: F_PIN7) F_PIN7 = (b_pin7+(ARR5p/theta_ARR5)^hill_arr5)/(1+(ARR5p/theta_ARR5)^hill_arr5)
 
 Rate Rule (name: Auxin) d [ Auxin] / d t= phloem_rate_ax*p_ax-d_ax*Auxin
 
 Rate Rule (name: Cytokinin) d [ Cytokinin] / d t= phloem_rate_ck*p_ck*F_CK-d_ck*Cytokinin
 
 Rate Rule (name: miRNA) d [ miRNA] / d t= 0
 
 Rate Rule (name: PHBm) d [ PHBm] / d t= (p_phb-d_phb*PHBm)-d_mirna_mrna*PHBm*miRNA
 
 Rate Rule (name: AHP6m) d [ AHP6m] / d t= lambda_AHP6*F_AHP6-mu_m_AHP6*AHP6m
 
 Rate Rule (name: IAA2m) d [ IAA2m] / d t= lambda_IAA2*F_IAA2-mu_m_IAA2*IAA2m
 
 Rate Rule (name: ARR5m) d [ ARR5m] / d t= lambda_ARR5*F_ARR5-mu_m_ARR5*ARR5m
 
 Rate Rule (name: PIN1m) d [ PIN1m] / d t= lambda_PIN1*F_PIN1-mu_m_PIN1*PIN1m
 
 Rate Rule (name: PIN3m) d [ PIN3m] / d t= lambda_PIN3*F_PIN3-mu_m_PIN3*PIN3m
 
 Rate Rule (name: PIN7m) d [ PIN7m] / d t= lambda_PIN7*F_PIN7-mu_m_PIN7*PIN7m
 
 Rate Rule (name: AHP6p) d [ AHP6p] / d t= delta_AHP6*AHP6m-mu_p_AHP6*AHP6p
 
 Rate Rule (name: IAA2p) d [ IAA2p] / d t= delta_IAA2*IAA2m-mu_p_IAA2*IAA2p
 
 Rate Rule (name: ARR5p) d [ ARR5p] / d t= delta_ARR5*ARR5m-mu_p_ARR5*ARR5p
 
 Rate Rule (name: PHBp) d [ PHBp] / d t= delta_PHB*PHBm-mu_p_PHB*PHBp
 
 Rate Rule (name: CKX3p) d [ CKX3p] / d t= delta_CKX3*CKX3m-mu_p_CKX3*CKX3p
 
 compartment Spatial dimensions: 3.0  Compartment size: 1.0
 
 Auxin
Compartment: compartment
Initial concentration: 0.0
 
 Cytokinin
Compartment: compartment
Initial concentration: 0.0
 
 AHP6m
Compartment: compartment
Initial concentration: 0.0
 
 AHP6p
Compartment: compartment
Initial concentration: 0.0
 
 IAA2m
Compartment: compartment
Initial concentration: 0.0
 
 IAA2p
Compartment: compartment
Initial concentration: 0.0
 
 ARR5m
Compartment: compartment
Initial concentration: 0.0
 
 ARR5p
Compartment: compartment
Initial concentration: 0.0
 
 PHBm
Compartment: compartment
Initial concentration: 0.0
 
 PHBp
Compartment: compartment
Initial concentration: 0.0
 
 CKX3m
Compartment: compartment
Initial concentration: 0.0
 
 CKX3p
Compartment: compartment
Initial concentration: 0.0
 
 PIN3m
Compartment: compartment
Initial concentration: 0.0
 
 PIN1m
Compartment: compartment
Initial concentration: 0.0
 
 PIN7m
Compartment: compartment
Initial concentration: 0.0
 
 miRNA
Compartment: compartment
Initial concentration: 0.0
 
Global Parameters (69)
 
   F_AHP6  
 
   F_CK  
 
   F_IAA2  
 
   F_ARR5  
 
   F_PIN1  
 
   F_PIN7  
 
   F_PIN3  
 
   p_ax
Value: 0.06
Constant
 
   p_ck
Value: 2.0
Constant
 
   d_ax
Value: 1.0
Constant
 
   d_ck
Value: 10.0
Constant
 
   phloem_rate_ax
Value: 1.0
Constant
 
   all_section_rate_ax
Value: 1.0
Constant
 
   phloem_rate_ck
Value: 1.0
Constant
 
   all_section_rate_ck
Value: 1.0
Constant
 
   lambda_AHP6
Value: 2.0
Constant
 
   lambda_IAA2
Value: 10.0
Constant
 
   lambda_ARR5
Value: 20.0
Constant
 
   lambda_PIN1
Constant
 
   lambda_PIN3
Constant
 
   lambda_PIN7
Value: 1.0
Constant
 
   mu_m_PHB
Value: 1.0
Constant
 
   mu_m_AHP6
Value: 1.0
Constant
 
   mu_m_IAA2
Value: 10.0
Constant
 
   mu_m_ARR5
Value: 10.0
Constant
 
   mu_m_PIN1
Constant
 
   mu_m_PIN3
Constant
 
   mu_m_PIN7
Value: 1.0
Constant
 
   delta_PHB
Value: 1.0
Constant
 
   delta_AHP6
Value: 1.0
Constant
 
   delta_IAA2
Value: 10.0
Constant
 
   delta_ARR5
Value: 10.0
Constant
 
   delta_PIN1
Constant
 
   delta_PIN3
Constant
 
   delta_PIN7
Value: 5.0
Constant
 
   delta_CKX3
Value: 1.0
Constant
 
   mu_p_PHB
Value: 1.0
Constant
 
   mu_p_AHP6
Value: 1.0
Constant
 
   mu_p_IAA2
Value: 10.0
Constant
 
   mu_p_ARR5
Value: 10.0
Constant
 
   mu_p_PIN1
Constant
 
   mu_p_PIN3
Constant
 
   mu_p_PIN7
Value: 1.0
Constant
 
   mu_p_CKX3
Value: 1.0
Constant
 
   theta_Ax
Value: 0.25
Constant
 
   theta_Ck
Value: 0.5
Constant
 
   theta_AHP6
Value: 0.04
Constant
 
   theta_ARR5
Value: 0.1
Constant
 
   theta_PHB
Value: 0.4
Constant
 
   theta_CKX3
Value: 0.05
Constant
 
   p_phb
Value: 2.0
Constant
 
   d_phb
Value: 1.0
Constant
 
   p_mirna
Value: 32.5
Constant
 
   d_mirna
Value: 1.0
Constant
 
   d_mirna_mrna
Value: 10.0
Constant
 
   p_ckx3
Value: 5.0
Constant
 
   d_ckx3
Value: 1.0
Constant
 
   b_pin3
Value: 1.0
Constant
 
   b_pin1
Constant
 
   b_pin7
Constant
 
   b_ahp6
Constant
 
   b_arr5
Constant
 
   b_iaa2
Constant
 
   hill_ax
Value: 2.0
Constant
 
   hill_ck
Value: 2.0
Constant
 
   hill_arr5
Value: 3.0
Constant
 
   hill_ckx3
Value: 5.0
Constant
 
   hill_ahp6
Value: 3.0
Constant
 
   hill_phb
Value: 3.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000522

Curator's comment: (updated: 11 Mar 2014 15:56:24 GMT)

The paper has multi-cellular, two-cell and single-cell model that describes vascular patterning in Arabidopsis roots. This model correspond to single-cell model. There is no corresponding plot in the paper for this single-cell model. Here, the plot that is generated using the python script sent by the author for single-cell model is reproduced by simulating the model in Copasi v4.12 (Build 72). The plot was obtained using Gnuplot.

The python scripts corresponding to the two-cell and multicellular model can be downloaded from the links below.

Additional file(s)
  • Two cell model:
    The python code (and associated figures) - to generate the figures in the steady state analysis described in section 4 of the supplementary information (as provided by the authors).
    [The scripts use the package pyDSTool (http://www.ni.gsu.edu/~rclewley/PyDSTool/FrontPage.html), which in turn uses the Numpy and Matplotlib libraries. It takes a while to run and generate the plots.]
  • Multi cell model::
    The python code (and associated figures) - to obtain the simulation results represented in Movie S9 of the paper. The same directory has its associated single cell model (run_cell_model.py), as well. The above model (BIOMD0000000522) is the SBML version of this single cell model.
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