% % Reference: Bertram et al., J. Neurophysiol., 90:1643-1653, 2003. % A minimal G protein model. Has V-dependent relief of inhibition, and % acts as a high-pass filter. Assumes constant level of G proteins. % HH Na current has been simplified by using the quasi-equilibrium assumption % for activation and (1-n) in place of h (see ref. 1191). # xpp parameters @ meth=cvode, atolar=1e-10, tolar=1e-10, dt=0.1, total=900, maxstor=10000, @ bounds=10000000000 @ xp=t, yp=vp @ xlo=0, xhi=900, ylo=-70, yhi=40 # For voltage clamp set autovp=0. # Initial Conditions # w=fraction of willing Ca channels. # v=presynaptic voltage. # vp=postsynaptic voltage. # s=fraction of bound postsynaptic receptors. init v=-65 init n=0.3 init w=0 init vp=-65 init np=0.3 init s=0 # Enter max number of pulses. params pulsenum=200 # For voltage clamp set autovp=0. params autovp=1,vclamp=-30 # G protein binding and unbinding rates. # Default: Gb3 - b1 params kp=0.004,kmbar=0.22 % voltage parameters params freq=20 number tf=5,tp=1,q10=1,gk=36,gna=120,vl=-55 number cm=1,gl=0.3,vna=40,vk=-77 % Stimulus Parameters params pulseiap=10 number offperiod=60, tstart=60 % Postsynaptic parameters params gsyn=0.3,vsyn=0 number kdmax=50,taus=1 period = 1000/freq % G protein binding/unbinding rates km = kmbar/(1+exp(-v/5)) % bound postsynaptic receptors. kd = kdmax*(1-w) sinf = 1/(1+exp(-(v-kd)/5)) % Multiply rates by 2 for shorter APs. Also apply q10 scaling. alphax = q10*2*0.1*(v+40)/(1-exp(-(v+40)/10)) betax = q10*2*4*exp(-(v+65)/18) alphan = q10*2*0.01*(v+55)/(1-exp(-(v+55)/10)) betan = q10*2*0.125*exp(-(v+65)/80) onperiod = period*pulsenum ts=t-tstart iaptmp = pulseiap*(heav(mod(ts,period)-tf)-heav(mod(ts,period)-(tf+tp))) iap = iaptmp*(heav(onperiod-ts)+heav(ts-(onperiod+offperiod-10))-heav(ts-(2*onperiod+offperiod-10))) % Postsynaptic currents alphaxp = q10*2*0.1*(vp+40)/(1-exp(-(vp+40)/10)) betaxp = q10*2*4*exp(-(vp+65)/18) alphanp = q10*2*0.01*(vp+55)/(1-exp(-(vp+55)/10)) betanp = q10*2*0.125*exp(-(vp+65)/80) isyn=gsyn*s*(vp-vsyn) % quasi-equilibrium assumption for HH Na current activation xinf=alphax/(alphax+betax) xinfp=alphaxp/(alphaxp+betaxp) % Differential Equations v' = -(gna*(xinf**3)*(1-n)*(v-vna)+gk*(n**4)*(v-vk)+gl*(v-vl)-iap)/cm n' = alphan*(1-n)-betan*n w' = km*(1-w) - kp*w vp' = autovp*(-(gna*(xinfp**3)*(1-np)*(vp-vna)+gk*(np**4)*(vp-vk)+gl*(vp-vl)+isyn)/cm) + (1-autovp)*(vclamp-vp) np' = alphanp*(1-np)-betanp*np s' = (sinf-s)/taus % Output aux Iap=iap aux winf=km/(km+kp) aux tsec=t/1000 done