Macroscopic membrane current

The whole-cell configuration has been extensively used to measure macroscopic membrane currents, either voltage-activated (see for example [23, 31]) or receptor-activated (see for example [32, 33]), being an excellent method to study the electrophysiology of small cells that cannot be efficiently voltage clamped using classical intracellular electrodes. This configuration has also been extensively used to study exocytosis, since with appropriate measurement protocols it is possible to monitor continuously the whole-cell membrane capacity [34, 35]. 

As explained, there are endoelectrogenic soiu-ces in the cell membranes. However, it is quite likely that some macroscopic membranes around organs are also the sites of electricity sources. Nordenstr0m (1983) proposed that there are closed DC circuits in the body with the well-conducting blood vessels serving as cables (e.g., a vascular-interstitial closed circuit). These DC currents can cause electro-osmotic transport through capillaries. Dental galvanism is the production of electricity by the metals in the teeth. 

Amplitude of current fluctuations. Two very simple properties of random variables allow to relate the amplitude of macroscopic and microscopic fluctuations. Let the membrane current, I, be the sum of the contributions arising from N identical but independent ionic channels ... 

Essentially all these experimental methods apply when we deal with high-porosity multipore membranes, which are the majority of the cases. However, polymer brush decoration of single nanometric pores on macroscopic membranes has been examined lately [8]. A quite interesting method for the characterization of this system is the measmement of the ionic current that flows through the channel in an electrolyte solution under different electric potential differences. The current-voltage (TV) response of the system can be correlated to the conductance of the polymer-decorated channel and consequently to the effective free cross section of the pore-brush structure. 

Preliminaries. In this chapter we shall address the simplest nonequilibrium situation—one-dimensional locally electro-neutral electrodiffusion of ions in the absence of an electric current. We shall deal with macroscopic objects, such as solution layers, ion-exchangers, ion-exchange membranes with a minimum linear size of the order of tens of microns. 

In 4.4 the theory of 4.2 will be applied to study electro-diffusion of ions through a unipolar ion-exchange membrane, separating two electrolyte solutions. This will include the classical treatment of concentration polarization in a solution layer adjacent to an ion-exchange membrane under an electric current. The validity limits of this theory, set by the violations of local electro-neutrality and caused by the development of a macroscopic nonequilibrium space charge, will be indicated. (The effects of the nonequilibrium space charge are to be discussed at some length in Chapter 5.)... 

The results in sections 2 and 3 describe the adsorption isotherms and diffusivities of Xe in A1P04-31 based on atomistic descriptions of the adsorbates and pores. The final step in our modeling effort is to combine these results with the macroscopic formulation of the steady state flux through an A1P04-31 crystal, Eq. (1). We make the standard assumption that the pore concentrations at the crystal s boundaries are in equilibrium with the bulk gas phase [2-4]. This assumption cannot be exactly correct when there is a net flux through the membrane [18], but no accurate models exist for the barriers to mass transfer at the crystal boundaries. We are currently developing techniques to account for these so-called surface barriers using atomistic simulations. 

However, the ionic currents measured using the voltage clamp technique were the result of fluxes through an ensemble of membrane channels. Until the 1970s, it had only been possible to study ion channels as macroscopic cur-... 

Another well-defined synthetic membrane is a planar bilayer membrane. This structure can be formed across a 1-mm hole in a partition between two aqueous compartments by dipping a fine paintbmsh into a membrane-forming solution, such as phosphatidyl choline in decane. The tip of the brush is then stroked across a hole (1 mm in diameter) in a partition between two aqueous media. The lipid film across the hole thins spontaneously into a lipid bilayer. The electrical conduction properties of this macroscopic bilayer membrane are readily studied by inserting electrodes into each aqueous compartment (Figure 12.14). For example, its permeability to ions is determined by measuring the current across the membrane as a function of the applied voltage. 

The same experiment was carried out several times with different pieces of Nafion 390 cut from a large sheet all data showed similar trends in current efficiency and electro-osmotic water with increasing current density. However, results from each membrane were nonidentical, presumably because of macroscopic inhomogeneities. 

The study of protein function is increasingly focused on the interactions between protein structure, electrochemical potentials, and molecular motion. For membrane proteins, insertion through a phospholipid bilayer imparts a defined orientation to the protein and a specified relation between the macroscopic electrical field and the axis of the molecule normal to the membrane. These constraints can be exploited to obtain detailed information about membrane protein function and dynamics, particularly for proteins that form aqueous pores through membranes. The ability to record currents that... 

In the electrochemical interpretation of metabolism presented here, we discount the significance of chemical reactions occurring under conditions well removed from equilibrium as important sources of heat production. Rather, we identify those processes associated with electronic and protonic current flow as the critical elements in heat production. The relationship between body surface area and heat production becomes more readily understandable when it is appreciated that these heat-producing processes take place within cellular membranes (or the microtrabecular lattice). Thus, the finding that heat production is a function of body surface area rather than tissue mass may be a macroscopic reflection of the fact that cellular electrochemical reactions occur in two dimensions, in contrast with three-dimensional, scalar chemical reactions. 

Determination of the coefficients based on understanding of the membrane microstructure and modelling of the interaction between the membrane and the two transported species, i.e. hydronium and water, would be better. Most desirable would be a proper mathematical transition from an exact microscopic description of the interaction of membrane, hydronium and water, towards a macroscopic model. Such information and description being currently unavailable, we have to rely on guidance from knowledge on the membrane morphology to devise assumptions on the functional dependence of the coefficients on temperature and water content. 

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