Intracellular capacitive effects of polarized proteins in dendrites

Abstract

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.

Solitonic conduction of electrotonic signals in neuronal branchlets with polarized microstructure

“…This is a simplification that suffices for the conduction process, focusing on homogeneous dielectric polarization 20 without exploring the physicochemical nature of excitation. Consequently in the context of conduction process, ionic polarizability of individual molecules is not taken into account, but instead a continuum of molecular ions with macroscopic charge densities are used as a phenomenological description of the electrostatic interactions and transfer of information due to the interactions among the molecular ions in a fluid environment within neuronal branchlets.…”

“…3 then the nonlinear cable equation with polarized microstructure can be written as ref. 20:where V is the membrane potential (mV), γ = τ ρ /τ m  ≪ 1 and κ = γ (λ 2 /πr 2 ) are both positive constants (dimensionless), τ p  = 2ε r ε o /σ < 1msec (Maxwell’s time constant), ε r  = 81 is the relative permittivity of sea water (dimensionless), ε o  = 7 × 10 —12  F/cm is the fluid permittivity, τ m  = c m r m (passive membrane time-constant in msec), λ = √(r m /r i ) (electrotonic space-constant in cm), dimensionless time T = t/τ m and dimensionless space X = x/λ, r i is the core-resistance (or intracellular resistance) per unit length r i  = 1/(πr 2 σ) (Ω/cm), r m is the membrane resistance across a unit length of passive membrane cylinder (Ωcm), c m is the membrane capacitance per unit length of cylinder (F/cm). Note the core-resistance (or intracellular resistance) per unit length differs slightly from the intracellular resistivity R i  = 1/(2σ) (Ωcm) or volume resistivity of the intracellular medium, also referred to as specific resistance (1/σ) where σ is the electrical conductivity (S/cm).…”

“…The first new term γ ∂ 3 V/∂T∂X 2 is a linear dissipative term due to surface-charge equalization between polarized intracellular free charges on endogenous structures within the microstructure 19 . The other new term ∂{C(V)V}/∂T is the charge ‘soakage’ due to polarization current within the microstructure produced by the bounded charges on endogenous structures 20 . In a neuronal branchlet with microstructure, voltage created by charge ‘soakage’ produces intracellular capacitive effects.…”

“…For example, if a quadratic capacitance-voltage characteristic C(V) = 2αV 2 is used instead of (2) then a ‘kink’ shaped soliton solution (i.e., waveform) results upon solving (1); see ref. 20. Therefore C(V) is the main source of nonlinearity responsible for both shape and stability of the electrotonic signal.…”

“…The model was further developed by including polarization current due to dispersion of bound charge on the surface of endogenous structures in the cytoplasm 20 . This resulted in polarization current arising from electrostatic interactions between charges/dipoles in the cytoplasm at slow varying electric fields (e.g., quasi-electrostatic conditions) causing self-excitability with a variety of different electrical signaling patterns created by charges held by the microstructure.…”