Potential gradient, distribution

Ion Channels. The excitable cell maintains an asymmetric distribution across both the plasma membrane, defining the extracellular and intracellular environments, as well as the intracellular membranes which define the cellular organelles. This maintained a symmetric distribution of ions serves two principal objectives. It contributes to the generation and maintenance of a potential gradient and the subsequent generation of electrical currents following appropriate stimulation. Moreover, it permits the ions themselves to serve as cellular messengers to link membrane excitation and cellular... 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

A combination of continuum transport theory and the Poisson distribution of solution charges has been popular in interpreting transport of ions or conductivity of electrolytes. Assuming zero gradient in pressure and concentration of other species, the flux of an ion depends on the concentration gradient, the electrical potential gradient, and a convection... 

When only taking into account the concentration polarization in the pores (disregarding ohmic potential gradients), we must use an equation of the type (18.15). Solving this equation for a first-order reaction = nFhjtj leads to equations exactly like (18.18) for the distribution of the process inside the electrode, and like (18.20) for the total current. The rate of attenuation depends on the characteristic length of the diffusion process ... 

One of the main reasons for a lower specific activity resides in the fact that electrodes with disperse catalysts have a porous structure. In the electrolyte filling the pores, ohmic potential gradients develop and because of slow difiusion, concentration gradients of the reachng species also develop. In the disperse catalysts, additional ohmic losses will occur at the points of contact between the individual crystallites and at their points of contact with the substrate. These effects produce a nonuniform current distribution over the inner surface area of the electrode and a lower overall reaction rate. 

A one-dimensional random walk is not necessarily symmetric with respect to jumps toward the right and toward the left. If the chemical potential gradient is sufficiently weak we may still approximate the jump length distribution by an exponentially decaying function, but distinguish that toward the right from that toward the left. 

We have actually measured the electrical potential differences in intact purple membrane bacteria, using the distribution of a lipid-soluble cation as an indicator, and found values of up to 100 mV[E. Bakker,H. Rottenberg, and S. R. Caplan, Biochim. Biophys. Acta, 440, 557 (1976)]. These values obviously correspond to enormous potential gradients across the membrane. 

In a discussion of permeability it is important to recognize that we deal with operational definitions, since the act of measurement influences the state of the system. In your case, applying an electrical potential gradient and performing electrodialysis alter the distribution of ionophore within the membrane. I wonder whether you have attempted to measure permeability by isotopic tracer techniques In this method the distribution of ionophore would not be influenced. Furthermore, information can be obtained on the question of carriers versus channels or pores. It should not be difficult to determine the extent of possible isotope interaction between tracer species and abundant species in the membrane as discussed by Kedem and Essig [J. Gen. Physiol., 48, 1047 (1965)]. Positive isotope interaction would tend to suggest the presence of channels or pores, negative isotope interaction the presence of carriers. 

If we neglect the overpotential at the electrodes, then the boundary conditions for solving this problem are the constant electrode potentials. This type of problem has exact analogs in electrostatics, and many generalized solutions for symmetric configurations are available. In this type of problem, the current density is proportional to the potential gradient, and the current distribution can be calculated from Ohm s law ... 

Laplace s equation governs the potential distribution [Eq. (21)]. Since overpotential is ignored, the potential immediately adjacent to the electrodes is constant. At insulated surfaces the normal potential gradient must be zero. These two requirements dictate the boundary conditions for the differential equation. 

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