We consider the neuron as a simple automated voltage controller with a predefined structure (a biological oscillator with a constant capacity (membrane) and resistance (AIS)), unidirectional input (synapses) and output (axon) connections with the environment, some dynamic components (ionic currents in the temporarily formed electrolyte layers), and a single temporary ”stage variable” (the membrane’s potential). The circuit essentially collects charge (while it is leaking, furthermore, gates its inputs) in its ground state, and when the stage variable (the membrane’s potential) – undex external impact(s) – reaches a well-defined constant critical value (the threshold potential), it flushes the collected charge. By regulating the single stage variable, the system can pass from stage to stage, in a well-defined way. The neuron transmits the collected information to its downstream neurons: the ”Delivering” process transmits the charge carriers from the surface layer of the membrane to the AIS and the ion channels ’instantly’ deliver the ions to the beginning of the axon where they pass along as the laws of motion of electrodiffusion dictate; see also section 1.7.
In our (somewhat simplified) view, a neuron is an autonomous system that has a well-defined equilibrium state. We do not mention here the details needed to maintain the equilibrium state, furthermore, we subdivide the charge processing into subprocesses by their physical nature. In reply to the environment (mainly upstream neurons) the neuron lets a given amount of positive charges from the electrolyte layer (handled as a ”charged infinite sheet”) formed on the high-concentration side of its membrane to enter the low-concentration side where it forms temporarily a similar layer. This process is instant. The ions produce a voltage increase on the well-defined capacity of the neuron. That voltage serves as a driving force for removing the rushed-in ions through its axon, through the AIS with as well-defined resistance. The ions arrive through ion channels at different places of the membrane, so they need different times to reach their outflow point. The travel time can be interpreted as ”storing the charge for some time”, which can be modeled by a classic condenser (which is a discrete element and uses instant current). The resistance of the AIS limits the current on the surface to a value which is much less than the inflow through the membrane. We assume that the repulsion between charged particles in the electrolyte layer is remarkable that tends to make the charged layer equipotential. However, the different speeds for the mass and charge transport processes limits the propagation speed of ions. Equations (2.13) and (2.16) describe the processes, althought they must be combined with the geometry of the of the neuronal membrane. The result of the interference of those processes is known as Action Potential. Important to notice that the the charge transfer from the layer on the high-concentration side to the layer on the low concentration side is accompanied with considerable voltage and concentration changes in both layers during generating the AP, see also section 2.2.2. These changes manifest in considerable current (and voltage) gradients.
A physical neuron operates with current gradients that enables it using very precise timings, and cooperates with the fellow individual neurons and their assemblies. Its goal is implementing a computing unit, which receives input information in form of native current gradients or artificial current gradients through its synapses. In any case, the received current evokes a potential gradient, and the voltage gradient operates the neuron. In this abstract interpretation, the neuron is represented as a serial electric oscillator circuit, which implements some voltage gradient (or maybe current density) threshold. [63] provided evidence that a spike with sufficiently large slope of current density (in other words, potential gradient) is capable alone to evoke the critical voltage gradient needed to evoke an action potential.