# Answers to homework

### Homework 1.3

    # One fast persistent calcium channel
    # Here is the equation
    dv/dt=(i+gl*(vl-v)+gca*minf(v)*(vca-v))/c

    #and the initial condition
    V(0)=-60

    # and the calcium current
    aux ica=gca*minf(v)*(v-vca)
    aux il=gl*(v-vl)
    # and the parameters
    param vl=-60,vca=120
    param i=0,gl=2,gca=4,c=20
    param v1=-1.2,v2=18

    # and the functions
    minf(v)=.5*(1+tanh((v-v1)/v2))
    done

### Homework 1.4b

    # nnet1.ode
    da/dt = (-a+w*f(a)+i)/tau
    f(a)=1/(1+exp(-beta*(a-theta)))
    par beta=2,theta=1,i=0,tau=1,w=1
    done

### PIR ODE file

    # PIR Model with GABA_A and GABA_B synapses
    p gca=1,vk=-90,fh=2,vca=120
    p gl=.1,vl=-70,i=0
    p gsyna=0,gsynb=0,vsyna=-85,vsynb=-90,tvsyn=-40
    p fka=2,rka=.08
    ph(v)=1/(1+exp((v+79)/5))
    ps(v)= 1/(1+exp(-(v+65)/7.8))
    tauh(v)= ph(v)*exp((v+162.3)/17.8)+20
    #
    v'= gl*(vl-v)+gca*(vca-v)*h*ps(v)^3+i
    h'= (ph(v)-h)*fh/tauh(v)
    #
    # GABA A synapse
    sa'= fka*ssyn*(1-sa)-rka*sa
    #
    # GABA B synapse
    tb'= 5*ssyn*(1-tb)-.007*tb
    sb'= .03*tb*(1-sb)-.005*sb
    #
    ssyn= 1/(1+exp(-(v+40)/2))
    done

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