# 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