When researching the electric operation, ’foreign’ currents and voltages (as opposed to the ’native’ ones) are applied. Our model can describe the effects of such artificial invasions. The synaptic control can be best understood on the example of modeling constant external current. As we discussed, a constant current (in ’steady-state’, after the transients relaxed) can be modelled as adding a constant term to the sum of the voltage time derivatives directing the neuron’s AP. Figure 3.15 calls attention to some important consequences of applying artificial currents and shows how our model handles them. (Notice that the subfigures share the logarithmic time scale the begins at the arrival of the first synaptic input. For the sake of simplicity we use an arbitrary voltage scale, and imitate synaptic inputs with an instant membrane voltage step). For understanding the terms and notions, see also Figures 1.6 and 8.1.
The bottom subfigure displays the action potential observable on the AIS. The ’0’ case is a simple delivering (see section 3.7.4), when no external invasion is present. The AP is as experimentally observed: in the ’Relaxing’ stage the neuron receives three synaptic inputs. When the first input arrives, the neuron passes to stage ’Computing’. For the effect of the third input, the neuron membrane exceeds the threshold voltage and the neuron passes to stage ’Delivering’. First the rushed-in ions increase the membrane’s potential, then the AIS decreases it to its resting value. As we discussed, the synaptic inputs are disabled in the ’Delivering’ stage. The top subfigure shows how the synaptic inputs are enabled/disabled during generating the AP when the threshold level crossed. The synapses are OFF only during the ’Delivering’ stage (conventionally considered as the ’absolute refractory’ period). For the sake of simplicity, for this figure we assumed an instant re-enabling, that is, that after crossing the threshold potential value, the re-enabled synaptic inputs appear at the AIS without delay. The background also displays the voltage caused by the ions. The voltage scale is arbitrary, but the time scale is true: the neuronal condenser ”stores” the ions and the stored current will reverse its direction when the rush-in current reaches its peak value; the reverse current appears as a negative current (decreases membrane’s potential below the value of its resting potential).
If the external invasion is relatively small (codename ’2’), the stages are reached at different ’local time’ values compared to the case without external invasion. The stage ’Delivering’ begins practically at the same time, but the polarization and hyperpolarization peak voltages are remarkable higher for the ’2’ case). Notice that the synaptic inhibition time is considerably longer: the extra charge extends the time until the membrane’s potential can decrease below the threshold level. If the invasion is stronger (codename ’4’), the hyperpolarization still exists, but the membrane’s voltage decreases only for a short period below the threshold: the external input will increase the voltage above the threshold again. Notice that (on the top subfigure) the synaptic inputs are re-enabled at a much later time, and they remain enabled only until the membrane’s current exceeds the threshold again (actually, the synaptic inputs can approach an ill-defined state). At a slightly higher invasion current, the membrane’s voltage cannot decrease below the threshold: due to that ’foreign’ current, the synaptic inputs get ’forever’ disabled (’blocked’). The experimental evidence was published in [147]; also displaying that some protection exists in neurons against ’overloading’.