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Code: Select all

NEURON {
    POINT_PROCESS syn
    RANGE gmax, tau0, tau1, e_rev, i
    NONSPECIFIC_CURRENT i
}

UNITS {
        (nA) = (nanoamp)
        (mV) = (millivolt)
        (uS) = (micromho)
}

PARAMETER {
    tau0 =  0.3 (ms)
    tau1 =  5.0 (ms)
    gmax =  0.0 (uS)
    e_rev = 0.0 (mV)
}

ASSIGNED {
    i   (nA)
    g   (uS)
    v   (mV)
}

UNITSOFF

INDEPENDENT { t FROM 0 TO 1 WITH 1 (ms) }

FUNCTION conductance(x) {
    conductance = gmax*(1-exp(-t/tau0))*(exp(-t/tau1))
}

BREAKPOINT {
    g = conductance(t)
    i = g*(v - e_rev)
}

UNITSON

Code: Select all

FUNCTION conductance(x (ms)) (uS) {
    conductance = gmax*(1-exp(-x/tau0))*(exp(-x/tau1))
}

Code: Select all

:synapse.mod
TITLE Synaptic conductances of CA3 neurons

COMMENT
    synaptic current modeled with monoexponential rise 
    and decay conductances defined by:

        i = g * (v-e_rev), 
    
    where i is current in nA, g is conductance in microhms, 
    v is membrane potential (in mV) and e_rev is the reversal potential 
    of the synapse (in mV)

        g = 0 for t < tonset and
        g = ( (1-exp(-(t-tonset)/tau0)*(exp(-(t-tonset)/tau1))) for t > tonset
    the function is normalized to the time of the peak so that gmax is the peak of the conductance.

ENDCOMMENT

NEURON {
    POINT_PROCESS synapse
    RANGE gmax, tonset, tau0, tau1, e_rev, i
    NONSPECIFIC_CURRENT i
}

UNITS {
        (nA) = (nanoamp)
        (mV) = (millivolt)
        (uS) = (micromho)
}

PARAMETER {
    tonset = 0.0 (ms)
    tau0 =  0.3 (ms)
    tau1 =  5.0 (ms)
    gmax =  0.0 (uS)
    e_rev = 0.0 (mV)
}

ASSIGNED {
    i   (nA)
    g   (uS)
    v   (mV)
}

FUNCTION biexponential(x (ms)) {
    biexponential = (1-exp(-(x-tonset)/tau0))*(exp(-(x-tonset)/tau1))
}

: Tpeak was solved arithmetically with Sage 
: Tpeak is a as function of tau0, tau1 and tonset

LOCAL norm 

FUNCTION conductance(x (ms)) (uS) { 
    LOCAL tpeak
    tpeak = tau0*log(tau1/tau0 + 1) + tonset
    : function is normalized to tpeak
    norm = biexponential(x)/biexponential(tpeak)

    if (x < tonset) {
        conductance = 0
    }
    else {
         : now the peak conductance is in gmax
        conductance = gmax*norm
    }

}

BREAKPOINT {

    g = conductance(t)
    i = g*(v - e_rev)
}