# microtubulesDog.ode

# XPP code for simulating growing and shrinking microtubule 
# plus ends according to Dogterom & Leibler PRL paper 

# upwind basic Euler scheme on spatial domain
# discretization:
par h=0.1
#L is the domain length, set to 10 micro-meters
L=h*100.0


# here ug is the density of growing plus ends of MT.
# and us is the density of shrinking plus ends 
# fgs=transition rate from ug to us
# fsg = transition rate from us to ug
#vg= growth rate
#vs=shrink rate


ug[1..100]'= vg*(ug[j-1]-ug[j])/h+ fsg*us[j]-fgs*ug[j]
us[0..99]'= vs*(us[j+1]-us[j])/h- fsg*us[j]+fgs*ug[j]

# equate fluxes for growing and shrinking tips at x=L
us[100]=ug[100]*vg/vs
# plus ends nucleated at x=0 so as to be at constant level there
ug0=1

# param values from Dogterom et al PNAS 1995
# in units of micro meter/min for veloc and sec^-1 for transitions
# (for this reason, need factor of 60 to convert f's to per min)
# vg=10,vs=15,fgs=60*0.012,fsg=60*0.02
param vg=10,vs=15,fgs=0.72,fsg=1.2

# param values from the Phys Rev Let paper footnote [9] are:
# vg=2,vs=20,fgs=60*0.004,fsg=60*0.05
# param vg=2,vs=20,fgs=0.24,fsg=3

# Note that a transition in the behaviour should take place
# when vs*fgs=vg*fsg  currently 0.18 vs 0.2

@ dt=.01,total=10
done