From control theory, it is known that the goal of a controlled system is to govern the application of system inputs to drive the system to a desired state while minimizing delay and overshoot, steady-state error, and ensuring control stability. The neuron implements a controller that monitors the controlled process variable (the membrane voltage) and compares it with the reference or setpoint (the resting potential). Recall that the geometry, the composition, and the concentration of electrolytes define the setpoint, as discussed in section 2.6. The difference between the process variable’s actual and desired values, known as the error signal, represents the actual offset potential. It is applied as a feedback to generate a control action that brings the controlled process variable to the setpoint value.
From a control theoretical point of view, the condenser geometry and the ion concentrations set the ’always the same’ value (the set-point; see also Figure 2.8) and the currents serve to keep or restore that value. After introducing a finite-width membrane into an electrolyte, a potential difference between the two membrane surfaces is created; see Eq. (2.71). When adjusting the membrane’s potential, we must consider its ground and excited states separately, given that the perturbations in these two cases are vastly different. Nature employs various mechanisms to maintain the ground state and recover it after generating a spike. Although nature’s tools are remarkably similar (channels and pumps; here, for discussing ’downhill’ channels, we must consider the charge-up of different components), the significant difference in current intensity warrants a separate discussion.