delcontezerail1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000174). Biomodels notes: This is the cut-out switch model for the Rab5 - Rab7 transition, also referred to as model 2 in the original publication. This model is not completely described in all details in the publication. Thanks go to Barbara Szomolay and Lutz Brusch for finding and clarifying this. According to Dr. Brusch this model represents the mechanism identified by the qualitative analysis in the article in the scenario deemed most useful by the authors. For the time-course simulations it was necessary to add a time dependency to one of the parameters, which is only verbally described in the article. As argued in the publication the switch between early and late endosomes can be triggered by a parameter change. While with fixed parameter values each switch just converges to one steady state from its initial conditions and stays there, endosomes should switch between two different states. These changes would in reality of course depend on many different factors, such as cargo composition and amount in the specific endosome, its location and some additional cellular control mechanisms and encompass many different parameters. To keep the model simple the authors chose to add a time dependency to only one reaction - ke in the activation of RAB5 is multiplied with a term monotonously increasing over time from 0 to 1. They also hard coded a time dependence in this term, 100 minutes, to make the switch occur after several hundred minutes. As long as this modulating term remains monotonic all resulting time courses should look similar, with the switching behavior depending on the initial conditions and whether the term is increasing or decreasing. Monotonic increase is a reasonable assumption for the described mechanism of cargo accumulation. Not explicitly described in the article: activation of Rab5 (time) : r*ke*time/(100+time) /(1+e(kg-R)*kf) instead of r*ke/(1+e(kg-R)*kf). 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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Membrane identity and GTPase cascades regulated by toggle and cut-out switches.

  • Perla Del Conte-Zerial
  • Lutz Brusch
  • Jochen C Rink
  • Claudio Collinet
  • Yannis Kalaidzidis
  • Marino Zerial
  • Andreas Deutsch
Mol. Syst. Biol. 2008; 4 : 206
Abstract
Key cellular functions and developmental processes rely on cascades of GTPases. GTPases of the Rab family provide a molecular ID code to the generation, maintenance and transport of intracellular compartments. Here, we addressed the molecular design principles of endocytosis by focusing on the conversion of early endosomes into late endosomes, which entails replacement of Rab5 by Rab7. We modelled this process as a cascade of functional modules of interacting Rab GTPases. We demonstrate that intermodule interactions share similarities with the toggle switch described for the cell cycle. However, Rab5-to-Rab7 conversion is rather based on a newly characterized 'cut-out switch' analogous to an electrical safety-breaker. Both designs require cooperativity of auto-activation loops when coupled to a large pool of cytoplasmic proteins. Live cell imaging and endosome tracking provide experimental support to the cut-out switch in cargo progression and conversion of endosome identity along the degradative pathway. We propose that, by reconciling module performance with progression of activity, the cut-out switch design could underlie the integration of modules in regulatory cascades from a broad range of biological processes.

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 second
1.0 mole litre^(-1.0)
1.0 second^(-1.0)
1.0 mole second^(-1.0) litre^(-1.0)
1.0 litre mole^(-1.0)
1.0 dimensionless
Id Name Spatial dimensions Size
endosome endosomal membrane 3.0 1.0
Id Name Initial quantity Compartment Fixed
R5 Rab5-GTP 0.001 endosome (endosomal membrane)
R7 Rab7-GTP 0.001 endosome (endosomal membrane)
r5 Rab5-GDP 1.0 endosome (endosomal membrane)
r7 Rab7-GDP 1.0 endosome (endosomal membrane)

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
reaction_0 recruitment of Rab5 ∅ > r5

endosome * K1
reaction_1 activation of Rab5 (time) r5 > R5

endosome * sig_act_t(r5, ke, time, kg, R5, kf)
reaction_2 extraction of Rab5 r5 > ∅

endosome * extraction(kminus1, r5)
reaction_3 recruitment of Rab7 ∅ > r7

endosome * K1
reaction_4 activation of Rab7 by GEF7 r7 > R7

endosome * hill_act(r7, ke, R7, h, kg)
reaction_5 activation of Rab7 by GEF5 r7 > R7

endosome * sig_act(ke, r7, kg, R5, kf)
reaction_6 hydrolysis of Rab5 by Rab7 R5 > r5

endosome * sig_act(ke, R5, kg, R7, kf)
reaction_7 extraction of rab7 r7 > ∅

endosome * extraction(kminus1, r7)
reaction_8 hydrolysis of Rab5 (intr.) R5 > r5

endosome * hydrolysis(kh, R5)
reaction_9 hydrolysis of Rab7 (intr.) R7 > r7

endosome * hydrolysis(kh, R7)

Global parameters

Id Value

Local parameters

Id Value Reaction
K1 1.0 reaction_0 (recruitment of Rab5)
ke 0.3 reaction_1 (activation of Rab5 (time))
kg 0.1 M reaction_1 (activation of Rab5 (time))
kf 2.5 reaction_1 (activation of Rab5 (time))
kminus1 1.0 reaction_2 (extraction of Rab5)
K1 0.483 reaction_3 (recruitment of Rab7)
ke 0.21 reaction_4 (activation of Rab7 by GEF7)
h 3.0 dimensionless reaction_4 (activation of Rab7 by GEF7)
kg 0.1 reaction_4 (activation of Rab7 by GEF7)
ke 0.021 reaction_5 (activation of Rab7 by GEF5)
kg 1.0 M reaction_5 (activation of Rab7 by GEF5)
kf 3.0 reaction_5 (activation of Rab7 by GEF5)
ke 0.31 reaction_6 (hydrolysis of Rab5 by Rab7)
kg 0.3 M reaction_6 (hydrolysis of Rab5 by Rab7)
kf 3.0 reaction_6 (hydrolysis of Rab5 by Rab7)
kminus1 0.483 reaction_7 (extraction of rab7)
kh 0.06 reaction_8 (hydrolysis of Rab5 (intr.))
kh 0.15 reaction_9 (hydrolysis of Rab7 (intr.))

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Definition
hydrolysis(kh, R) = kh * R
hill_act(r, ke, R, h, kg) = r * ke * pow(R, h) / (kg + pow(R, h))
extraction(kminus1, r) = kminus1 * r
sig_act_t(r, ke, t, kg, R, kf) = r * (ke * t / (100 + t)) / (1 + exp((kg - R) * kf))
sig_act(ke, r, kg, R, kf) = ke * r / (1 + exp((kg - R) * kf))
Trigger Assignments