Intracellular capacitive effects of polarized proteins in dendrites

Passive dendrites become active as a result of electrostatic interactions by dielectric polarization in proteins in a segment of a dendrite. The resultant nonlinear cable equation for a cylindrical volume representation of a dendritic segment is derived from Maxwell's equations under assumptions: (i) the electric field is restricted longitudinally along the cable length; (ii) extracellular isopotentiality; (iii) quasi-electrostatic conditions; (iv) isotropic membrane and homogeneous medium with constant conductivity; and (v) protein polarization contributes to intracellular capacitive effects through a well defined nonlinear capacity-voltage characteristic; (vi) intracellular resistance and capacitance in parallel are connected to the membrane in series. Under the above hypotheses, traveling wave solutions of the cable equation are obtained as propagating fronts of electrical excitation associated with capacitive charge-equalization and dispersion of continuous polarization charge densities in an Ohmic cable. The intracellular capacitative effects of polarized proteins in dendrites contribute to the conduction process.