Vso:1000 END

Figure 4.1-5 illustrates the response of the antifacilitating synaptic model to three pulses. Trace 1 = x1; 2 = x2 (basic response), 3 = xo (antifacilitated epsps), #4 = ff (antifacilitation factor). Simulation parameters are the same as in the program. Note that an exponential factor was used to effect antifacilitation. A Hill function can also be used; thus, ff =--4.1-9

Figure 4.1-6 shows the antifacilitation response of the model to six pulses with a period of 3 ms. In this case: a = b = 1, c = 0.1, d = 0.3, k = 2. Note that the antifacilitated output, 3, grows steadily less than the basic responses, 2.

There are several types of inhibitory synapses. Those that produce a strong negative (hyperpolarizing) psp generally gate potassium ions. The Nernst equilibruim potential for K+ across a neuronal membrane is given by

FIGURE 4.1-5 The modeled response of an antifacilitating ballistic filter simulation using the Simnon program, ANTIFAC.t. Scales: vertical, arbitrary units; horizontal milliseconds. Traces: 1, x1 (state); 2, x2 (simple linear BF output); 3, xo (antifacilitated epsp); 4, ff (the antifacilitation factor). Parameters: a = b = 1; c = d = 0.3; k = 1. Note that the epsp pulses, 3, grow progressively smaller.

FIGURE 4.1-5 The modeled response of an antifacilitating ballistic filter simulation using the Simnon program, ANTIFAC.t. Scales: vertical, arbitrary units; horizontal milliseconds. Traces: 1, x1 (state); 2, x2 (simple linear BF output); 3, xo (antifacilitated epsp); 4, ff (the antifacilitation factor). Parameters: a = b = 1; c = d = 0.3; k = 1. Note that the epsp pulses, 3, grow progressively smaller.

FIGURE 4.1-6 The modeled response of an antifacilitating ballistic filter simulation using the Simnon program, ANTIFAC.t. Scales: vertical, arbitrary units; horizontal milliseconds. Traces: 1, x1 (state); 2, x2 (simple linear BF output); 3, xo (antifacilitated epsp); 4, ff (the antifacilitation factor). Different parameters: a = b = 1; c = 0.1; d = 0.3; k = 2. Note that the epsp pulses, 3, grow progressively smaller with each successive presynaptic input.

FIGURE 4.1-6 The modeled response of an antifacilitating ballistic filter simulation using the Simnon program, ANTIFAC.t. Scales: vertical, arbitrary units; horizontal milliseconds. Traces: 1, x1 (state); 2, x2 (simple linear BF output); 3, xo (antifacilitated epsp); 4, ff (the antifacilitation factor). Different parameters: a = b = 1; c = 0.1; d = 0.3; k = 2. Note that the epsp pulses, 3, grow progressively smaller with each successive presynaptic input.

Thus, as more and more SSM K+ channels open in a potassium inhibitory synapse, the inhibitory subsynaptic membrane potential tends to go toward -75 mV, that is, to hyperpolarize, giving a definite "ballistic" ipsp. Summed ipsps force the generator potential away from the firing threshold of the SGL.

Chloride ion-mediated inhibition is found in spinal motoneurons and in CNS interneurons. A typical Nernst equilibrium potential for Cl- is -69 mV. If for some reason the resting potential across the SSM were -69 mV, upon stimulation of the chloride-gated inhibitory synapse, one would see no ipsp, nor would there be any Cl- flux through the gated channels. Although no visible ipsp is present, the transient high Cl- conductance effectively clamps the SSM to the -69 mV potential, preventing epsps from moving the SGL generator potential toward the firing threshold. If the nerve membrane potential is artificially hyperpolarized to -80 mV by a voltage clamp apparatus, stimulation of a chloride inhibitory synapse will produce a positive-going ipsp! This ipsp is positive because the membrane voltage tries to reach ECl = -69 mV. If the membrane potential is clamped at -60 mV, the Cl- ipsp will be negative-going as it tries to reach -69 mV.

One means of modeling the clamping effect of gated chloride inhibition is to assume that the inhibitory synapse makes contact with the postsynaptic neuron (PSN) soma (axosomatic synapse) near the SGL. In this position, one inhibitory synapse can have a greater effect in attenuating the net epsp excitation at the SGL. If the excitatory generator potential is Vex,

where Vek = the kth epsp generated either on the soma or dendrites of the PSN. kn = nth synaptic weighting function. (In general, the farther from the SGL, the smaller kn.) Hi is an attenuating Hill function emulating increased chloride conductance in the SSM when the inhibitory synapse is activated. The Simnon program, ClInh1.t, illustrates the dynamics of a chloride, axosomatic, inhibitory synapse:

continuous system Cllnhl " 3/12/99 STATE xl x2 x3 x4 vl f g DER dxl dx2 dx3 dx4 dvl df dg TIME t " ms.

dxl = -a*xl + Vsl " BF for axodendritic synapse l. dx2 = -b*x2 + a*b*xl Vel = DELAY (x2, Dl)

dx3 = -a*x3 + Vs2 " BF for axodendritic synapse 2. dx4 = -b*x4 + a*b*x3 Ve2 = DELAY (x4, D2)

df = -c*f + Vi " BF for axosomatic inhibitory synapse dg = -d*g + c*d*f

Hi = l/(l + g*Ki) " Hill function for Cl- inhibitory synapse. Vex = (Vel*kl + Ve2*k2) *Hi " Sum 2 epsps; inhib with Cl- synapse.

dv1 = -c1*v1 + c1*Vex - z 1 "RPFM SGL w1 = IF v1 > phi THEN 1 ELSE 0 s 1 = DELAY (w1, tau) q1 = w1 - s1

" INPUTS:

" PARAMETERS : tau : . 001 " ms ti:1 dt:.001 Vso:1000 phi:.1 c1:.3 a:1 b:1 c:.5 d:.5 D1:0.3 D2:0.1 k1:.5 k2:.9 Ki:5

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