Heinrich Model Simplified ODE:4

heinrich 4 XY constant size 4 vesicle types antisymmetric norm.nb

Heinrich Model Simplified ODE:4

Original Heinrich model was a differential equation system for a two-compartment model with two SNARE pairs (X,U and Y,V) and one cargo (C) and transport vesicles with coats A or B
J.Cell Biol.10.1083/jcb.200409087 Heinrich et al.Supplement

The model was adapted to Mathematica by John S. McCaskill and simplified
- to only two snares X and Y and no cargo
- and then to constant compartment sizes s1 and s2
- and hence also numbers of transport vesicles of types A and B, and then to ignore differences in vesicle origin for fusion rates.
- and finally the
antisymmetric situation where snare X on compartment 1 or vesicle type A is equivalent to snare Y on compartment 2 or vesicle type B.
Result is 4 coupled ODEs for amounts of
snares X and Y amounts on compartments 1 (2) and on vesicles of type A  (2) total = 2+2 = 4 ODEs


Basic notation

Fusion processes

Budding processes

Differential equations

Analysis of behavior near x1==y1 for strong binding discrimination

Time dept variables and ODEs rewritten with explicit time dependence

Initial conditions, for the figure in the paper (see intro above)


Simulation run

Auxiliary quantitites of interest

Simulation run with iteration

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