  The application of systems and control theory to membrane physiology is
presented here. Modeling efforts have focused on describing those
physiologically realistic mechanisms which govern the regulation of membrane
permeability in nerve. The motivation behind identifying such mechanisms lies
in understanding the morphology of neural activity on a meaningful and
analytically tractable level. The suggested merit of integrating control theory
into the analysis lies in providing how a membrane effectively adapts to
changes in permeability and through what governing mechanisms. The value in
producing such an understanding lies in mirroring biological reality in a more
formal manner than could be achieved solely through experimental means. A
bang-bang control policy describing the permeability correction mechanisms is
developed using Liapunov's Stability Criteria. Both changes in membrane
potential and kinetic rates are required to implement the policy. The policy
describes the inherent mechanisms of the membrane which act to drive its
permeability from unstable firing to the resting potential state. It is shown
that these permeability changes in state are governed by a switching function
that depends on the membrane potential and a dominant controlling parameter.
The control policy is discussed in the context of solutions of the
Hodgkin-Huxley Equations of Ionic Hypothesis.
