into an inactive molecule, Nbar. Nbar diffuses back to the presynaptic membrane of the bouton where it binds to an uptake molecule with density Ns. The bound Nbar is taken up at rate Ku by the bouton and resynthesized to stored NT. (Note that this model neglects the quantal nature of NT storage and release from the bouton.)
The process model outlined above and in the figure can be modeled by a Simnon program. (Note that the kinetic process is linear in this problem.) The Simnon program uses an IPFM system as a source of periodic, presynaptic impulses. The frequency of the impulses is proportional to Vin. When Vfa = 0.1 V, the frequency is 100 pps. The program is as follows:
CONTINUOUS SYSTEM epsp" 02/05/2000 Use Euler integration with delT tau.
STATE v psNT bNT Nbar Ns NT DER dv dpsNT dbNT dNbar dNs dNT TIME t " t in milliseconds.
" IPFM SOURCE OF PERIODIC INPUT PULSES: dv = Vin - z w = IF v > phi THEN 1 ELSE 0 s = DELAY (w, tau) x = w - s y = IF x > 0 THEN x ELSE 0
yo = y/10 - .15 " yo for plotting z = y*phi/tau
Pin = y*Do/tau" Input pulses.
" Ko is fraction of NT released at every pulse.
dpsNT = -Kb*psNT + DELAY(Ko*NT*Pin, dT) " Conc. NT @ SSM. Kb is mono" molecular rate const for NT binding to receptors. dbNT = Kb*psNT - Kh*bNT " Relative density of NT bound to (XS) " receptors. Kh is hydrolysis rate constant. dNbar = Kh*bNT - Kd*Nbar " Conc. inactive NT in cleft. " Kd is diffusion rate constant.
dNs = Kd*Nbar - Ku*Ns " Relative density of Nbar bound to bouton " membrane. Ku is rate of active Nbar uptake by bouton.
dNT = c + Ku*Ns - Ko*NT*Pin " Conc. stored neurotransmitter in bouton.
" Note that NT is recycled with rate Ku.
Vm = Kv*bNT " epsp is proportional to bNT.
Vin = Vo + Kr*t " Causes the freq. of y to ramp up.
" CONSTANTS: phi:1 tau:.001 Vo:.10 Do:8 Ko:.05 Kb:1. Kh:2. Kd:0.5 Kv:10 Ku:5
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