Bianchi2015 -Model for lymphangiogenesis in normal and diabetic wounds
Model Identifier
BIOMD0000000722
Short description
Format
SBML
(L2V4)
Related Publication
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A mathematical model for lymphangiogenesis in normal and diabetic wounds.
- Bianchi A, Painter KJ, Sherratt JA
- Journal of theoretical biology , 10/ 2015 , Volume 383 , pages: 61-86 , PubMed ID: 26254217
- Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, Scotland, EH14 4AS, UK. Electronic address: ab584@hw.ac.uk.
- Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis) very few have been proposed for the regeneration of the lymphatic network. Moreover, lymphangiogenesis is markedly distinct from angiogenesis, occurring at different times and in a different manner. Here a model of five ordinary differential equations is presented to describe the formation of lymphatic capillaries following a skin wound. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from experimental and clinical data. The system is then solved numerically and the results are compared with the available biological literature. Finally, a parameter sensitivity analysis of the model is taken as a starting point for suggesting new therapeutic approaches targeting the enhancement of lymphangiogenesis in diabetic wounds. The work provides a deeper understanding of the phenomenon in question, clarifying the main factors involved. In particular, the balance between TGF-β and VEGF levels, rather than their absolute values, is identified as crucial to effective lymphangiogenesis. In addition, the results indicate lowering the macrophage-mediated activation of TGF-β and increasing the basal lymphatic endothelial cell growth rate, inter alia, as potential treatments. It is hoped the findings of this paper may be considered in the development of future experiments investigating novel lymphangiogenic therapies.
Contributors
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan
Metadata information
is (2 statements)
isDescribedBy (1 statement)
hasTaxon (2 statements)
occursIn (1 statement)
hasProperty (3 statements)
isDescribedBy (1 statement)
hasTaxon (2 statements)
occursIn (1 statement)
hasProperty (3 statements)
Mathematical Modelling Ontology
Ordinary differential equation model
OMIT 0015769
Gene Ontology wound healing
OMIT 0015769
Gene Ontology wound healing
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
SBGN view in Newt Editor
| Name | Description | Size | Actions |
|---|---|---|---|
Model files |
|||
| Wound Healing with Normal health condition.xml | SBML file for the model. | 54.45 KB | Preview | Download |
Additional files |
|||
| Wound Healing with Diabetic health condition.cps | Copasi file for Diabetic wound simulations. | 99.76 KB | Preview | Download |
| Wound Healing with Normal health condition.cps | Copasi file for Normal health conditions. | 97.69 KB | Preview | Download |
- Model originally submitted by : Sarubini Kananathan
- Submitted: Nov 21, 2018 11:35:17 AM
- Last Modified: Nov 21, 2018 11:35:17 AM
Revisions
-
Version: 4
- Submitted on: Nov 21, 2018 11:35:17 AM
- Submitted by: Sarubini Kananathan
- With comment: Automatically added model identifier BIOMD0000000722
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
| Species | Initial Concentration/Amount |
|---|---|
| LECs lymphatic endothelial cell |
0.0 mmol |
| Capillaries 0003535 |
0.0 mmol |
| Active TGF beta TGF-beta 1 |
30.0 mmol |
| Macrophages inflammatory macrophage |
1875.0 mmol |
| VEGF Vascular endothelial growth factor C |
0.5 mmol |
Reactions
| Reactions | Rate | Parameters |
|---|---|---|
| => LECs; VEGF, Active_TGF_beta | Body*(c1+VEGF/(c2+c3*VEGF))*1/(1+c4*Active_TGF_beta)*LECs | c2 = 42.0; c1 = 0.42; c3 = 4.1; c4 = 0.24 |
| LECs => ; Macrophages, Capillaries | Body*(Macrophages+LECs+Capillaries)/k2*LECs | k2 = 471000.0 |
| LECs => Capillaries; VEGF | Body*sigma*(delta1+delta2*VEGF)*LECs | sigma = 0.0; delta2 = 0.001; delta1 = 0.05 |
| => Active_TGF_beta; Macrophages | Body*(a_p*p_0*exp((-a_p)*T_L*time)+a_M*Macrophages)*(T_L+r1*Macrophages) | p_0 = 250000.0; r1 = 3.0E-5; a_p = 0.029; T_L = 18.0; a_M = 0.45 |
| Active_TGF_beta => | Body*d1*Active_TGF_beta | d1 = 500.0 |
| => Macrophages | Body*s_M | s_M = 542.0 |
| Macrophages => ; Capillaries | Body*rho*Capillaries*Macrophages | rho = 1.0E-5 |
| => VEGF | Body*S_V | S_V = 1.9 |
| VEGF => ; LECs | Body*gamma*VEGF*LECs | gamma = 0.0014 |
Curator's comment:
(added: 21 Nov 2018, 11:34:50, updated: 21 Nov 2018, 11:34:50)
(added: 21 Nov 2018, 11:34:50, updated: 21 Nov 2018, 11:34:50)
Figure 10 of the reference publication has been reproduced. Initial conditions and values were taken from the publication. The main xml file attached is for wound healing in normal health conditions. To reproduce the figure, run the simulation with time step size of 0.1 and plot against data from both normal and diabetic wound healing simulations. The model was simulated using Copasi 4.24 and the figure was generated using Python 3.7.