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Table 3 Set of reactions and kinetic functions programmed in COPASI

From: Reconstruction of endosomal organization and function by a combination of ODE and agent-based modeling strategies

 

Name

Reaction

Inhibitor(s)

Activator(s)

Rab Dynamics

Kinetic function: \( \frac{\mathrm{kS}1}{\left(1+\left(\exp {\left(\mathrm{kS}2-\sum activators\right)}^{\mathrm{kS}3}\right)+\exp \left(-{\left(\mathrm{kS}4-\sum inhibitors\ \right)}^{\mathrm{kS}5}\right)\right)}\ast \prod substrates \)

kS1 = 11; kS2 = 0.8 ; kS3 = 2; kS4 = 0.2; kS5 = 13

 

RabA Activation

RabAc + Rab0 → RabAm

RabDm

RabAm

RabA Inactivation

RabAm → RabAc + Rab0

RabAm

RabDm

RabB Activation

RabBc + Rab0 → RabBm

 

RabBm

RabB Inactivation

RabBm → RabBc + Rab0

RabBm

 

RabC Activation

RabCc + Rab0 → RabCm

 

RabCm

RabC Inactivation

RabCm → RabCc + Rab0

RabCm

 

RabD Activation

RabDc + Rab0 → RabDm

 

RabDm, RabAm

RabD Inactivation

RabDm → RabDc + Rab0

RabDm, RabAm

 

RabE Activation

RabEc + Rab0 → RabEm

 

RabEm

RabE Inactivation

RabEm→RabEc + Rab0

RabEm

 

Kinetic function: k*[substrate]

k = 0.3

 

rA Influx

RabAcyto → RabAc

  

rA Outflux

RabAc → RabAcyto

  

rB Influx

RabBcyto → RabBc

  

rB Outflux

RabBc → RabBcyto

  

rC Influx

RabCcyto → RabCc

  

rC Outflux

RabCc → RabCcyto

  

rD Influx

RabDcyto → RabDc

  

rD Outflux

RabDc → RabDcyto

  

rE influx

RabEcyto → RabEc

  

rE Outflux

RabEc → RabEcyto

  

Endosome Acidification and Lipid Metabolism

Kinetic Function: k*[substrate]

k Proton Pump = 0.0008; k1 Proton leak = 0.04; k-1 Proton leak = 0.04; k Cholesterol depletion 10

 

Proton Pump

vATPase → proton + vATPase

  
 

Proton leak

protonCy ←→ proton

  
 

Chol depletion

cholesterol + RabD → RabD

  

Kinetic Function: k ∗ (10pH − pHlimit)enhancer ∗  ∏ substrates

pH = -log[proton]; k, pHlimit and enhancer for each reaction are listed bellow

HexaA binding: 1, 6, 1.5; HexA release: 2*10-4, 6, -1.5

 

HexA release

M6PR-HexA → HexA + M6PR

  
 

HexA binding

M6PR + HexA → M6PR-HexA

  

Kinetic Function: \( \frac{10^{-6}}{\left[\mathrm{cholesterol}\right]+{10}^{-6}}\ast {\left({10}^{\mathrm{pH}-5}\right)}^{-2}\ast \prod substrates \)

pH = -log[proton]

 

GM2 hydrolysis

GM2 + HexA → HexA

  
  1. Rab dynamics on endosomal membranes was modeled following the scheme shown in Fig. 1c, where each Rab activates its own activation and inhibits its inactivation. RabAc and RabAm refer to the GDP- and GTP-bound forms, respectively (idem for other Rabs). Rab0 refers to a Rab free membrane domain. The RabA → RabD switch was programmed adding RabD as an inhibitor of RabA activation and activator of RabA inactivation. In addition, RabA was added as an activator of RabD activation and inhibitor of RabD inactivation. The kinetic function used was able to handle Rab dynamics in all organelles with only five parameters. The parameters were adjusted to mimic the reported Rab5 → Rab7 conversion kinetics [5]. Membrane-associated Rab-GDPs were allowed to exchange with a cytosolic pool (cyto Rabs). Units in mM and seconds (see Additional file 5 and Additional file 7 for the specific unit of each parameter) For lipid metabolism, the pH of organelles was regulated by a proton pump and a leakage reaction. Cytosolic pH was set to 7. To model the dynamics of HexA association with its receptor (M6PR), a pH-dependent kinetics function was used [51]. Finally, the GM2 hydrolysis was controlled by a pH and cholesterol-dependent kinetic function [33]. All parameters were adjusted to qualitatively reproduce reported experimental observations. Units in mM and seconds (see Additional file 5 and Additional file 7 for the specific unit of each parameter)
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Biology Direct

ISSN: 1745-6150

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