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
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)
Auxiliary quantitites of interest
| Created by Mathematica (January 9, 2007) |  |