Dorvash2019 - Dynamic modeling of signal transduction by mTOR complexes in cancer

  public model
Model Identifier
BIOMD0000000822
Short description
This model is based on: Dynamic modeling of signal transduction by mTOR complexes in cancer Author: Mohammadreza Dorvash, Mohammad Farahmandnia, Pouria Mosaddeghi, Mitra Farahmandnejad, Hosein Saber, Mohammadhossein Khorraminejad-Shirazi, Amir Azadi, Iman Tavassoly Abstract: Signal integration has a crucial role in the cell fate decision and dysregulation of the cellular signaling pathways is a primary characteristic of cancer. As a signal integrator, mTOR shows a complex dynamical behavior which determines the cell fate at different cellular processes levels, including cell cycle progression, cell survival, cell death, metabolic reprogramming, and aging. The dynamics of the complex responses to rapamycin in cancer cells have been attributed to its differential time-dependent inhibitory effects on mTORC1 and mTORC2, the two main complexes of mTOR. Two explanations were previously provided for this phenomenon: 1-Rapamycin does not inhibit mTORC2 directly, whereas it prevents mTORC2 formation by sequestering free mTOR protein (Le Chatelier’s principle). 2-Components like Phosphatidic Acid (PA) further stabilize mTORC2 compared with mTORC1. To understand the mechanism by which rapamycin differentially inhibits the mTOR complexes in the cancer cells, we present a mathematical model of rapamycin mode of action based on the first explanation, i.e., Le Chatelier’s principle. Translating the interactions among components of mTORC1 and mTORC2 into a mathematical model revealed the dynamics of rapamycin action in different doses and time-intervals of rapamycin treatment. This model shows that rapamycin has stronger effects on mTORC1 compared with mTORC2, simply due to its direct interaction with free mTOR and mTORC1, but not mTORC2, without the need to consider other components that might further stabilize mTORC2. Based on our results, even when mTORC2 is less stable compared with mTORC1, it can be less inhibited by rapamycin.
Format
SBML (L2V4)
Related Publication
  • Dynamic modeling of signal transduction by mTOR complexes in cancer.
  • Dorvash M, Farahmandnia M, Mosaddeghi P, Farahmandnejad M, Saber H, Khorraminejad-Shirazi M, Azadi A, Tavassoly I
  • Journal of theoretical biology , 9/ 2019 , Volume 483 , pages: 109992 , PubMed ID: 31493485
  • Pharmaceutical Sciences Research Center, Shiraz University of Medical Sciences, Shiraz, Iran; Cell and Molecular Medicine Student Research Group, Faculty of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran.
  • Signal integration has a crucial role in the cell fate decision and dysregulation of the cellular signaling pathways is a primary characteristic of cancer. As a signal integrator, mTOR shows a complex dynamical behavior which determines the cell fate at different cellular processes levels, including cell cycle progression, cell survival, cell death, metabolic reprogramming, and aging. The dynamics of the complex responses to rapamycin in cancer cells have been attributed to its differential time-dependent inhibitory effects on mTORC1 and mTORC2, the two main complexes of mTOR. Two explanations were previously provided for this phenomenon: 1-Rapamycin does not inhibit mTORC2 directly, whereas it prevents mTORC2 formation by sequestering free mTOR protein (Le Chatelier's principle). 2-Components like Phosphatidic Acid (PA) further stabilize mTORC2 compared with mTORC1. To understand the mechanism by which rapamycin differentially inhibits the mTOR complexes in the cancer cells, we present a mathematical model of rapamycin mode of action based on the first explanation, i.e., Le Chatelier's principle. Translating the interactions among components of mTORC1 and mTORC2 into a mathematical model revealed the dynamics of rapamycin action in different doses and time-intervals of rapamycin treatment. This model shows that rapamycin has stronger effects on mTORC1 compared with mTORC2, simply due to its direct interaction with free mTOR and mTORC1, but not mTORC2, without the need to consider other components that might further stabilize mTORC2. Based on our results, even when mTORC2 is less stable compared with mTORC1, it can be less inhibited by rapamycin.
Contributors
Submitter of the first revision: Szeyi Ng
Submitter of this revision: Szeyi Ng
Modellers: Szeyi Ng

Metadata information

is (2 statements)
BioModels Database BIOMD0000000822
BioModels Database MODEL1909250002

isDescribedBy (1 statement)
PubMed 31493485

hasProperty (4 statements)
Experimental Factor Ontology cancer
Mathematical Modelling Ontology Ordinary differential equation model
NCIt mTOR Inhibitor
NCIt Signal


Curation status
Curated


Tags

Connected external resources

Name Description Size Actions

Model files

Dorvash2019 - Dynamic modeling of signal transduction by mTOR complexes in cancer.xml SBML L2V4 file for the model 81.79 KB Preview | Download

Additional files

Dorvash2019 - Dynamic modeling of signal transduction by mTOR complexes in cancer.cps COPASI 4.24 (Build 197) file for the model 100.26 KB Preview | Download
Fig 4.png PNG plot of the model simulation Fig 4 27.56 KB Preview | Download
simbiodata.mat Matlab files attached in the publication 10.23 KB Preview | Download

  • Model originally submitted by : Szeyi Ng
  • Submitted: Sep 25, 2019 2:20:31 PM
  • Last Modified: Sep 30, 2019 11:14:47 AM
Revisions
  • Version: 6 public model Download this version
    • Submitted on: Sep 30, 2019 11:14:47 AM
    • Submitted by: Szeyi Ng
    • With comment: Automatically added model identifier BIOMD0000000822
  • Version: 3 public model Download this version
    • Submitted on: Sep 25, 2019 2:20:31 PM
    • Submitted by: Szeyi Ng
    • With comment: Automatically added model identifier BIOMD0000000822

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

Legends
: Variable used inside SBML models


Species
Species Initial Concentration/Amount
mTORC1

mTORC1
0.0 mol
mTOR

431220 ; mTOR Inhibitor
3.756228E-7 mol
mTORC1 Rapamycin

sirolimus ; mTORC1
0.0 mol
mTOR Rapamycin

sirolimus ; mTOR Inhibitor ; 431220
0.0 mol
Cytosolic Rapamycin

sirolimus ; Cytosol
0.0 mol
mTORC2

mTORC2
0.0 mol
Raptor

Regulatory-Associated Protein of mTOR
3.201594E-7 mol
Reactions
Reactions Rate Parameters
mTORC1 + Cytosolic_Rapamycin => mTORC1_Rapamycin compartment*(k_form_C1_Rapam*mTORC1*Cytosolic_Rapamycin-k_diss_C1_Rapam*mTORC1_Rapamycin) k_diss_C1_Rapam = 0.022 1/s; k_form_C1_Rapam = 1920000.0 1/(mol*s)
mTOR + Raptor => mTORC1 compartment*(k_form_C1*mTOR*Raptor-k_diss_C1*mTORC1) k_form_C1 = 1.6666666E7 1/(mol*s); k_diss_C1 = 0.08333 1/s
mTORC1_Rapamycin => mTOR_Rapamycin + Raptor compartment*(k_forward_Raptor_release*mTORC1_Rapamycin-k_reverse_Raptor_release*mTOR_Rapamycin*Raptor) k_forward_Raptor_release = 0.01 1/s; k_reverse_Raptor_release = 1.0E-5 1/(mol*s)
mTOR + Cytosolic_Rapamycin => mTOR_Rapamycin compartment*(k_form_mTOR_Rapam*mTOR*Cytosolic_Rapamycin-k_diss_mTOR_Rapam*mTOR_Rapamycin) k_form_mTOR_Rapam = 1920000.0 1/(mol*s); k_diss_mTOR_Rapam = 0.022 1/s
Cytosolic_Rapamycin => compartment*K_el_Rapam*Cytosolic_Rapamycin K_el_Rapam = 0.0718632 1/h
mTOR + Rictor => mTORC2 compartment*(k_form_C2*mTOR*Rictor-k_diss_C2*mTORC2) k_form_C2 = 1.6666666E7 1/(mol*s); k_diss_C2 = 0.08333 1/s
Curator's comment:
(added: 25 Sep 2019, 14:18:24, updated: 30 Sep 2019, 11:06:17)
I tried to reproduce figure 4 under the condition of low-dose and short-interval using the COPASI file and COPASI, by setting time=2500. The figure is exact for equilibrium state. However the conditions with drug are not exact. Please edit the drug intake using 'events'. Respond from the Author about drug: We described the doses and interval schedules in the "Methods § 2.3. Dose schedules for Rapamycin". To elaborate, after I developed the model based on the extracted rate constants, I ran the model and reach the previously mentioned steady-state concentrations for all the species in the absence of Rapamycin. Then, to start for finding a starting point for our Rapamycin doses, I converted the 15 ng/ml concentration of Rapamycin (the whole-blood concentration of rapamycin in transplant patients) to almost 8.0 * 10^-20 mole of rapamycin is present in every 5.0 * 10^-12 liter of their blood. I ran the simulations with these numbers and found out that it has a moderate effect on the concentrations of mTORC1 and mTORC2. Thus, I named 8.0*10^-20 moles of rapamycin the "low dose". As we wanted to show that how the dose AND interval of rapamycin affects the dynamics of the core components of mTOR complexes, and with a little inspiration from Mannick et al. 2014 study, I chose two intervals for our study: Daily (short interval) and weekly (long interval). Hence, low dose and short interval is 8.0E-20 mole/day. To have a weekly interval with the same cumulative dose as the "low dose short interval" we can multiply 8.0E-20 mole by 7 = 5.6E-19 moles but administer it weekly. Now, 5.6E-19 mole is the high dose. We can administer this high dose weekly (schedule III) or daily (schedule II). Now, with another inspiration from Mannick's work, the VERY high dose is 4 times greater than the high dose = 2.24E-18 moles and we administered it only as a weekly scheduled dose.