Download Electrical potentials on surfaces, Debye length, and transmembrane

Electrical potentials on surfaces, Debye length, and transmembrane potentials
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Proteins carry a net charge, o If another protein is nearby, they don’t feel each other until they are a certain distance apart‐ due to region of charge o Region of charge also helps orient/ move them 
A dry protein will have ions with it as ion pair or protonated groups. The overall particle must be neutral. In aqueous solution, ions will tend to leave protein by thermal motion but are also attracted back by electrostatic attraction. The electrical field produced depends on how many charged ions are in the solution/ around a structure (membrane, protein) 
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What is the situation at equilibrium?  If the structure has a negative charge, the potential energy is negative on the surface and becomes zero as farther away.  For simplicity, consider a flat surface.  The distribution of both cations and anions depend on the profile of the potential. After all, at equilibrium the chemical potential for each mobile ion must be the same at all points in the solution, whether close or far from the surface.  The Boltzmann distribution says: [C x ]  [C ]e
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Fx =>Volts*Coulombs/mole= J/mole RT=Thermal energy/ mol [Cx]= the concentration of cations at any point [C∞] = the concentration of cations far from the membrane (in the bulk phase) The potential acts on both cations and anions [ Ax ]  [ A ]e
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 zC F x
RT
 z A F x
RT
The way that the electric field changes with distance: o Slope can only change if there is a charge density o There is a relationship between charge density, ρ, and the electric d
field, E (remember that E 
): dx
dE
4
…the Poisson equation 
dx

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 x  z C F [C x ]  z A F [ Ax ] …since the valencies are opposite, the 
concentrations will subtract leaving the charge density which is the concentration of charge. For monovalent ions:  x  F [C  ](e
 F x
RT
e
F x
RT
) …fitting into the Poisson equation and solving for low potentials:
 x   0 e  x
1/Κ= length unit called “Debye Length”
 0 RT
1


2 FIS
IS= Ionic strength = 0.5 ci z i 2
i
…where ci is the concentration of each ion and zi is the respective valency
… it has units of concentration and corrects for the greater effect of polyvalent ions
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the potential decays exponentially with distance from the surface Every Debye‐length, the potential will decrease by 1/e The Debye Length diminishes as the square root of the ionic strength Ionic Strength Debye Length 10 mM 3 nm 100 mM 1 nm 1 M 0.3 nm ‐‐ more ions take the place of the counter ions and thus the potential decays more rapidly with distance from the charged surface ‐‐‐ the more dilute, the longer the Debye Length The chemical potential of the cations does not change with distance from the membrane. The concentration of the cation changes. Similarly for all mobile ions. At equilibrium there cannot be any change in energy with distance. Membrane Enclosing a Solution
 The membrane encloses the compartment including the charged substances (ions).  An electrical potential can be generated across the membrane by translocating mobile ions across the membrane. Trans-Membrane Potential
 Is generated by moving ions across the membrane.  The cell membrane is a neutral barrier  For example: If there is a pump that pumps out some positive charges, their counterions will be left behind. These will attract each other across the thin membrane. o Have to do work to pump positive charges into a positively‐charge region and the work needed increases as the membrane potential increases  Potential energy o Is going to be lowered by positive charges on one side of the membrane interacting with negative charges on the other side o Is going to depend on surface area of the cell because charges can spread out over the surface thus reducing their mutual repulsion. o   SA  The membrane acts as a capacitor o In order for a cell to develop a transmembrane potential by pumping ions out of the cell it needs to charge the capacitator o The amount of charge that needs to be pumped depends on membrane thickness, surface area and the polarizability (0)of the membrane o The thickness and 0 are essentially the same for all membranes (first order approximation)  If the surface area is larger then more ions will need to be pumped out of the cell to achieve a specific transmembrane potential. Thus more energy will be expended with a larger surface area. q= C
charge in Coulombs = (capacitance in Farads) x (transmembrane potential in Volts)
the unit capacitance of a typical membrane is 1 µFarad/cm2