Creating a channel from a kinetic scheme specification

Here we will implement a new voltage-gated macroscopic current whose properties are described by a family of chemical reactions.

This example draws on the khh mechanism, a three-state kinetic model of the HH potassium current that has been used in the hands-on NEURON Summer Course (see http://www.neuron.yale.edu/neuron/courses.html for a link to the summer course files -- look at the exercise called NMODL : Kinetic Scheme : potassium channel).

This mechanism has two closed states C1 and C2, and an open state O, that participate in this in-line reaction sequence

Each of the three states lies in the range [0,1] and their sum C1 + C2 + O is always equal to 1.

The current generated by the khh mechanism is: i_K = g_K (V - E_K)
where: g_K = gmax_khh O

The rate constants for transitions between states are governed by the Boltzmann equation. Assuming that the energy difference between states is linear with voltage, and that the energy barrier is also linear with voltage, the equations for the rate constants are

        a1 = K1/(tau1*(K1+1))
        b1 =  1/(tau1*(K1+1))
        a2 = K2/(tau2*(K2+1))
        b2 =  1/(tau2*(K2+1))

where

        tau1 = ta1*exp(tk1*vr)
        K1   = exp((k2*(d2 - vr)) - (k1*(d1 - vr)))
        tau2 = ta2*exp(tk2*vr)
        K2   = exp(-(k2*(d2 - vr)))
        vr   = v + 65

The parameters of this model were found by fitting it to voltage clamp measurements of potassium current in squid axon published by Hodgkin and Huxley (Fig. 3 on page 508 of "A quantitative description of membrane current and its application to conduction and excitation in nerve", J. Physiol. 117:500-544, 1952).

	gmax_khh = 0.02979 (Siemens/cm2)

        ta1 = 4.4 (ms)
        tk1 = -0.025 (/millivolt)
        d1  = 21 (millivolt)
        k1  = 0.2 (/millivolt)

        ta2 = 2.6 (ms)
        tk2 = -0.007 (/millivolt)
        d2  = 43 (millivolt)
        k2  = 0.036 (/millivolt)

Configuring the Channel Builder for this mechanism involves working through the same four steps that we followed in dealing with the HH-style mechanism (big hint : work through that example first, if you haven't already done so). Here we will emphasize procedures that are specific to implementing a model from a kinetic scheme description.

Step 1. Bring up a Channel Builder for a density mechanism: We already know how to do this.

Step 2. Specify the channel's basic properties

Channel Name should be mykhh (so it won't conflict with the khh mechanism in a side-by-side comparison)
Selective for k
Ohmic
Default gmax = 0.02979 (Siemens/cm2)

The Channel Builder will look like this when we're ready for the next step :

Step 3. Specify "channel gating," i.e. :: specify the states that control channel gating
specify transitions between kinetic scheme states
specify how voltage and ligands affect states and transitions

Step 4. Test the channel

Go back to the main page ("Using the Channel Builder") to work on a different tutorial.