Experimental evidence shows that the electric signals have a finite speed in axons, dendrites and cell body; furthermore, that within the cell, the overwhelming majority of propagation time is spent in the dendrites. The mathematical handling of finite speeds is not simple, especially within a biological cell, so we separate the cell into two regions and make the approximation that within the cell body the interaction is instant (that is, the Laws of electricity are valid), but outside the cell, in the dendrites the finite interaction speed leads to observable effects that significantly influence cell’s operation (we need different approximation; we must not apply automatically the equations borrowed from electricity). We set up a hybrid model: the cell body is equipotential (aka: can be described by a ’fast current’), but the dendrites (and they contribute the overwhelming majority of the signal path within the cell) are non-equipotential and they must be described by approximations based on the notion of a ’slow current’. With that model, we explain the up to now not understood features of neuronal charge processing, furthermore, why is that ’the interplay between the synaptic and neuronal dynamics, when the network is near a critical point, both recurrent spontaneous and stimulated phase transitions enable the phase-dependent processes to replace each other’ [72].
The commonly used physical picture (see, for example, [24], page 9) is only half of the truth: ”there is never any actual movement of charge across the insulating membrane … the charge merely redistributes itself across the two sides by the way of the rest of the circuit.” On the one side, redistribution of charge per definitionem means a current, on the other, that picture contradicts also the notion of ’specific conductance’: the rest of the circuit cannot participate in a ’leakage current’ through a distributed resistor. The cell has a resistance (see the AIS and an area, but still, no specific resistance can be interpreted. The charge moves in the proximal layer of the electrolytes (in the form of a ’slow current’ near to dendrites), then the circuit closes though the AIS and the extracellular segment. We explicitly introduce the notion of ’slow current’, and show that we need to divide the membrane’s ionic currents roughly into two categories, whether they flow directly between the intracellular and the extracellular space or within the layer on the surface of the membrane.
The physical difference is whether the movement of ions is assisted by the enormous potential gradient between the extra- and intracellular regions when passing the ion channels (’fast’ current) or they move in the electrolyte layer proximal to isolating membrane assisted by the electrostatic repulsion of ions in the same layer (’slow’ speed of a macroscopic current). Cardiatic slow currents have been discovered [60] (actually, current pulses of duration in several msecs range). It was correctly observed that ”the slow currents appear to have been caused by repeated openings of one or more channels” and their speed [61] was found in the range of . In neurophysiology, ion current speeds ranging from a few to dozens of has been observed.
These statements mean (assuming that those signals travel with the same speed in the dendrites) that the presence of a ’slow current’ of ions in neurons is experimentally underpinned, although the notion is not introduced (mainly because its mathematical handling is not solved). Assuming that the dendrites’ size is about and the synaptic signals appear at the AIS after their arrival to their presynaptic terminals, we can estimate the speed of ’slow current’ as (see our discussion on the signals appearing in the ’relative refractory’ period and [64]). This result is in line with our result derived the speed value [50] measured within a cell body and the axonal speed [9].