# Resting potential

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The resting potential of a cell is the membrane potential that would be maintained if there were no action potentials, synaptic potentials, or other active changes in the membrane potential. In most cells the resting potential has a negative value, which by convention means that there is excess negative charge inside compared to outside. The resting potential is mostly determined by the concentrations of the ions in the fluids on both sides of the cell membrane and the ion transport proteins that are in the cell membrane. How the concentrations of ions and the membrane transport proteins influence the value of the resting potential is outlined below.

## Membrane transport proteins Edit

For determination of membrane potentials, the two most important types of membrane ion transport proteins are ion channels and ion pumps. Ion channel proteins create paths across cell membranes through which ions can passively diffuse without expenditure of energy. They have selectivity for certain ions, thus, there are potassium-, chloride-, and sodium-selective ion channels. Different cells and even different parts of one cell (dendrites, cell bodies, nodes of Ranvier) will have different amounts of various ion transport proteins. Typically, the amount of certain potassium channels is most important for control of the resting potential (see below). Some ion pumps such as the Na+/K+ATPase are electrogenic, that is, they produce charge imbalance across the cell membrane and can also contribute directly to the membrane potential. All pumps use energy to function.

## Equilibrium potentials Edit

For most animal cells potassium ions (K+) are the most important for the resting potential[1]. Due to the active transport of potassium ions, the concentration of potassium is higher inside cells than outside. Most cells have potassium-selective ion channel proteins that remain open all the time. There will be net movement of positively-charged potassium ions through these potassium channels with a resulting accumulation of excess positive charge outside of the cell. The outward movement of positively-charged potassium ions is due to random molecular motion (diffusion) and continues until enough excess positive charge accumulates outside the cell to form a membrane potential which can balance the difference in concentration of potassium between inside and outside the cell. "Balance" means that the electrical force (potential) that results from the build-up of ionic charge, and which impedes outward diffusion, increases until it is equal in magnitude but opposite in direction to the tendency for outward diffusive movement of potassium. This balance point is an equilibrium potential as the net transmembrane flux (or current) of K+ is zero. The equilibrium potential for a given ion depends only upon the concentrations on either side of the membrane and the temperature. It can be calculated using the Nernst equation:

$E_{eq,K^+} = \frac{RT}{zF} \ln \frac{[K^+]_{o}}{[K^+]_{i}} ,$

where

• Eeq,K+ is the equilibrium potential for potassium, measured in volts
• R is the universal gas constant, equal to 8.314 joules·K-1·mol-1
• T is the absolute temperature, measured in kelvins (= K = degrees Celsius + 273.15)
• z is the number of elementary charges of the ion in question involved in the reaction
• F is the Faraday constant, equal to 96,485 coulombs·mol-1 or J·V-1·mol-1
• [K+]o is the extracellular concentration of potassium, measured in mol·m-3 or mmol·l-1
• [K+]i is likewise the intracellular concentration of potassium

Potassium equilibrium potentials of about 70 millivolts (inside negative) are common in neurons. In cardiac cells, it is more negative than -80 mV.

## Resting potentials Edit

The resting membrane potential is not an equilibrium potential as it relies on the constant expenditure of energy (for ionic pumps as mentioned above) for its maintenance. It is a dynamic diffusion potential that takes mechanism into account—wholly unlike the equilibrium potential, which is true no matter the nature of the system under consideration. The resting membrane potential is dominated by the ionic species in the system that has the greatest conductance across the membrane. For most cells this is potassium. As potassium is also the ion with the most negative equilibrium potential, usually the resting potential can be no more negative than the potassium equilibrium potential. The resting potential can be calculated with the Goldman-Hodgkin-Katz voltage equation using the concentrations of ions as for the equilibrium potential while also including the relative permeabilities, or conductances, of each ionic species. Under normal conditions, it is safe to assume that only potassium, sodium (Na+) and chloride (Cl-) ions play large rôles for the resting potential:

$E_{m} = \frac{RT}{F} \ln{ \left( \frac{ P_{Na^+}[Na^+]_{o} + P_{K^+}[K^+]_{o} + P_{Cl^-}[Cl^-]_{i} }{ P_{Na^+}[Na^+]_{i} + P_{K^+}[K^+]_{i} + P_{Cl^-}[Cl^-]_{o} } \right) }$

This equation resembles the Nernst equation, but has a term for each permeant ion. Also, z has been inserted into the equation, causing the intracellular and extracellular concentrations of Cl- to be reversed relative to K+ and Na+, as chloride's negative charge is handled by inverting the fraction inside the logarithmic term.

• Em is the membrane potential, measured in volts
• R, T, and F are as above
• PX is the relative permeability of ion X in arbitrary units (e.g. siemens for electrical conductance)
• [X]Y is the concentration of ion X in compartment Y as above

Another way to view the membrane potential is using the Millman equation:

$E_{m} = \frac{P_{K^+}E_{eq,K^+} + P_{Na^+}E_{eq,Na^+} + P_{Cl^-}E_{eq,Cl^-}} {P_{K^+}+P_{Na^+}+P_{Cl^-}}$

or reformulated

$E_{m} = \frac{P_{K^+}} {P_{tot}} E_{eq,K^+} + \frac{P_{Na^+}} {P_{tot}} E_{eq,Na^+} + \frac{P_{Cl^-}} {P_{tot}} E_{eq,Cl^-}$,

where Ptot is the combined permeability of all species, again in arbitrary units. The latter equation portrays the resting membrane potential as a weighted average of the reversal potentials of the system, where the weights are the relative permeabilites across the membranes (PX/Ptot). During the action potential, these weights change.

If the permeabilities of Na+ and Cl- are zero, the membrane potential reduces to the Nernst potential for K+ (as PK+ = Ptot). Normally, under resting conditions PNa+ and PCl- are not zero, but they are much smaller than PK+, which renders Em close to Eeq,K+. Medical conditions such as hyperkalemia in which blood serum potassium (which governs [K+]o) is changed are very dangerous since they offset Eeq,K+, thus affecting Em. This may cause arrhythmias and cardiac arrest. The use of a bolus injection of potassium chloride in executions by lethal injection stops the heart by shifting the resting potential to a more positive value, which depolarizes and contracts the cardiac cells permanently, not allowing the heart to repolarize and thus enter diastole to be refilled with blood.

## Measuring resting potentials Edit

In some cells, the membrane potential is always changing (such as cardiac pacemaker cells). For such cells there is never any “rest” and the “resting potential” is a theoretical concept. Other cells with little in the way of membrane transport functions that change with time have a resting membrane potential that can be measured by inserting an electrode into the cell[2]. Transmembrane potentials can also be measured optically with dyes that change their optical properties according to the membrane potential.

## ReferencesEdit

1. ^  An example of an electrophysiological experiment to demonstrate the importance of K+ for the resting potential. The dependence of the resting potential on the extracellular concentration of K+ is shown in Figure 2.6 of Neuroscience, 2nd edition, by Dale Purves, George J. Augustine, David Fitzpatrick, Lawrence C. Katz, Anthony-Samuel LaMantia, James O. McNamara, S. Mark Williams. Sunderland (MA): Sinauer Associates, Inc.; 2001.
2. ^  An illustrated example of measuring membrane potentials with electrodes is in Figure 2.1 of Neuroscience by Dale Purves, et al (see reference #1, above).