The neuron as a system aims to collect inputs from its upstream neurons and to provide an intense output that informs the downstream neurons. A large number of voltage-gated ion channels, distributed in the neuron’s wall, implements the input charge of this overshoot and the overshoot output current flows through a similarly large number of persistently open ion channels concentrated in AIS. The intense slow current produces a condenser-like behavior (capacitive current); the phenomena called polarization and hyperpolarization (not polarization, instead a complete charge separation) of the membrane provide the necessary positive and negative error signals for the controller in the transient state.
We considered that the neuron has a stable base state. On the one side, this resting state must be dynamically stabilized for little perturbations (and to provide a mechanism when the cell grows, divides, or ages). On the other side, it must be able to restore the state after rough perturbations, causing short-time transients (when restoring the membrane’s potential after issuing a spike). The two states need different physical mechanisms: a set of ungated low-current ion channels for the resting state, and a set of high-intensity ion channels for the transient state. Of course, for starting a spike, the input channels must be gated while the output ion channels can work without gating.
From control theory, it is known that the goal of the system is to govern the application of system inputs to drive the system to a desired state while minimizing any delay, overshoot, or steady-state error and ensuring control stability. The neuron implements a controller that monitors the controlled process variable (membrane voltage) and compares it with the reference or setpoint (the resting potential). The difference between the process variable’s actual and desired values called the error signal, is the actual offset potential. It is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point.
Biology uses such a simple controller. The gradients are used to adjust the process variable by their positive and negative contributions, and the different speeds of the thermodynamical and electrical interactions minimize the delay (i.e., provide the maximum speed of operations, vital for survival). The difference between the process variable’s actual and desired values called the error signal, is the actual offset potential. It is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. The steady-state error is minimized by setting the process variable to the reference point using long-term stable parameters (geometry and overall concentration). The low-intensity current through the always-open resting ion channels provides dynamic stability in the steady state. The permanently zero error signal indicates a lack of operations. In contrast, the permanently nonzero error signal is a sign of abnormal operation and is likely a symptom of a neurological disease. See also section 1.5.2.
The system aims to provide an intense output that informs the downstream neurons. This overshoot is implemented by a large number of voltage-gated ion channels distributed in the neuron’s wall. The overshoot current flows through a similarly large number of persistently open ion channels concentrated in AIS. The intense slow current produces a condenser-like behavior (capacitive current); the phenomena called polarization and hyperpolarization (not polarization, which is a complete charge separation instead) of the membrane provide the necessary positive and negative error signals for the controller in the transient state.