# Morris-Lecar beta-cell (based on Utah model with kca instead of s)
# kmer rewritten using forms used in biophan 11/17/03

# For ACh effect, set per=0.009 and gl=5.

init v=-60.8, n=0.00013, c=0.087, d=0.297, cer=190

# equations
dv/dt=(i+gl*(vl-v)+gk*n*(vk-v)- Ica(v) - Ikca(v,c) + gkatp*(vk-v))/cm
dn/dt=(ninf(v)-n)/taun
dc/dt = fcyt*(Jmem + Jer)
# dc/dt=f*(-alpha*ica(v) - kpmca*c) + jertot/lambdaer
dd/dt = ka*((tot-d)-d*exp(r*(1.0-(c/r1))))
# dcer/dt = -Jer/(lambdaer*sigmaer)
dcer/dt = -fer*vcytver*Jer
# dcer/dt = -vcytver*Jer

par lambdaer=1, per0=0.0002, per1=0.009, sigmaer=0.032, kserca=0.4, epser=1

par tstep=75000

per = per0 + (per1 - per0)*heav(t - tstep)

# where
ninf(v) = 1/(1+exp((vn-v)/sn))
minf(v) = 1/(1+exp((vm-v)/sm))

param gkcastar=100, auto=0, gkatpstar=180, freezeatp=1
param vk=-75, vl=-20, vca=25
param i=0, gk=2700, gl0=0, gl1=5, gca=1000, cm=5300
num vm=-20, sm=12, vn=-16, sn=5, taun=20
param gkca=500, kd=0.5, nh=2

gl = gl0 + (gl1 - gl0)*heav(t - tstep)

# Ikca
ikca(v,c) = auto*gkcastar*(v-vk) + (1-auto)*gkca/(1+(kd/c)^nh)*(v-vk)

# Calcium Handling
par alpha=4.50e-6, kpmca=0.18, fcyt=0.01, fer=0.01

vcytver=1/sigmaer

# Ikatp
par gkatpbar=6000

# ADP parameters (from Smolen-Keizer)
p kone=0.45,ktwo=0.012,ka=5.0e-6,r=1.2,r1=0.35,tot=1

# ICa
ica(v) = gca*minf(v)*(v-vca)

# IKATP
gkatp = freezeatp*gkatpstar + (1-freezeatp)*gkatpbar*(1.0+d/kone)/(1.0+d/kone+(tot-d)/ktwo)

# Ca fluxes
Jmem = -(alpha*Ica(v) + kpmca*c)

Jserca = kserca*c
Jleak = per*(cer - c)
Jer = epser*(Jleak - Jserca)/lambdaer


# track some currents
aux tsec=t/1000
aux Condkca=gkca/(1+(kd/c)^nh)
aux Ica=gca*minf(V)*(V-Vca)
aux Ik=gk*n*(V-Vk)
aux Curkca=Ikca(v,c)
aux gkatpact = gkatp

@ meth=cvode, atol=1.0e-6, tol=1.0e-6, dt=5, total=150000, maxstor=100000
@ xp=tsec, yp=v, bound=100000000
@ xlo=0, xhi=150, ylo=-70, yhi=-10

done