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Do neurons have a voltage or a current threshold for action potential initiation? (English) Zbl 0820.92004

Summary: The majority of neural network models consider the output of single neurons to be a continuous, positive, and saturating firing rate \(f(t)\), while a minority treat neuronal output as a series of delta pulses \(\Sigma \delta (t - t_ i)\). We here argue that the issue of the proper output representation relates to the biophysics of the cells in question and, in particular, to whether initiation of somatic action potentials occurs when a certain threshold voltage or a threshold current is exceeded. We approach this issue using numerical simulations of the electrical behavior of a layer 5 pyramidal cell from cat visual cortex. The dendritic tree is passive while the cell body includes eight voltage- and calcium-dependent membrane conductances.
We compute both the steady-state \((I_ \infty^{\text{static}} (V_ m))\) and the instantaneous \((I_ 0 (V_ m))I - V\) relationships and argue that the amplitude of the local maximum in \(I_ \infty^{\text{static}} (V_ m)\) corresponds to the current threshold \(I_{\text{th}}\) for sustained inputs, while the location of the middle zero- crossing of \(I_ 0\) corresponds to a fixed voltage threshold \(V_{\text{th}}\) for rapid inputs. We confirm this using numerical simulations: for “rapid” synaptic inputs, spikes are initiated if the somatic potential exceeds \(V_{\text{th}}\), while for slowly varying input \(I_{\text{th}}\) must be exceeded. Due to the presence of the large dendritic tree, no charge threshold \(Q_{\text{th}}\) exists for physiological input.
Introducing the temporal average of the somatic membrane potential \(\langle V_ m \rangle\) while the cell is spiking repetitively, allows us to define a dynamic \(I - V\) relationship \(I_ \infty^{\text{dynamic}} (\langle V_ m \rangle)\). We find an exponential relationship between \(\langle V_ m \rangle\) and the net current sunk by the somatic membrane during spiking (diode-like behavior). The slope of \(I_ \infty^{\text{dynamic}} (\langle V_ m \rangle) \) allows us to define a dynamic input conductance and a time constant that characterizes how rapidly the cell changes its output firing frequency in response to a change in its input.

MSC:

92C20 Neural biology
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