Membrane bioelectrical models

In 1848 du Bois-Reymond [21] suggested that the surfaces of biological formations have a property similar to the electrode of a galvanic cell and that this is the source of bioelectric phenomena observed in damaged tissues. The properties of biological membranes could not, however, be explained before at least the basic electrochemistry of simple models was formulated. The thermodynamic relationships for membrane equilibria were derived by Gibbs in 1875 [29], but because the theory of electrolyte solutions was formulated first by Arrhenius as late as 1887, Gibbs does not mention either ions or electric potentials. 

Autonomous phenomena in multicellular systems are considered in the section on bioelectric patterning in cell aggregates. A mathematical model is considered which describes the cell aggregate via macroscopic variables--concentrations and voltage. Cells are "smeared out" to formulate the theory in terms of continuum variables. A nonlinear integral operator is introduced to model the intercellular transport that corrects the cruder diffusion-like terms usually assumed. This transport term is explicitly related to the properties of cell membranes. 

M. A. Habib and J. O M. Bockris, Charge Transfer Across Biological Membrane/ Solution Interface Test of an Electrodic Model, J. Bioelectricity 3, 247 (1984). 

Membranes also have a finite and distributed electric resistance both across their thickness and along their length. These resistances tend to short circuit the membrane capacitor and cause its stored charge to decay to zero if the membrane ion pumps cease. There are several different models of the cell membrane that describe its static and transient bioelectric behavior. Models of the cell membrane are useful because they help explain the propagation of action events, such as that along a nerve. 

Fig. 2. Electric model used by the method BIS-STEP to interpret current response i to a step voltage of magnitude Vd. The extracellular resistance - Re, intracellular resistance - Ri, and membrane capacitance -Cm, stand for the biological segmental bioelectric impedance model. The capacitances - Ce and resistances - Rb are associated to the impedances of the two electrode-tissue interfaces.

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