molecules, the plasma membrane intrinsically has a high electrical resistivity, in other words a low intrinsic permeability to ions. however, some of the molecules embedded in the membrane are capable either of actively transporting ions from one side of the membrane to the other or of providing channels through which they can move. in electrical terminology, the plasma membrane functions as a combined resistor and capacitor. resistance arises from the fact that the membrane impedes the movement of charges across it. capacitance arises from the fact that the lipid bilayer is so thin that an accumulation of charged particles on one side gives rise to an electrical force that pulls oppositely charged particles toward the other side. the capacitance of the membrane is relatively unaffected by the molecules that are embedded in it, so it has a more or less invariant value estimated at 2 μf/cm2 (the total capacitance of a patch of membrane is proportional to its area). the conductance of a pure lipid bilayer is so low, on the other hand, that in biological situations it is always dominated by the conductance of alternative pathways provided by embedded molecules. thus, the capacitance of the membrane is more or less fixed, but the resistance is highly variable. the thickness of a plasma membrane is estimated to be about 7-8 nanometers. because the membrane is so thin, it does not take a very large transmembrane voltage to create a strong electric field within it. typical membrane potentials in animal cells are on the order of 100 millivolts (that is, one tenth of a volt), but calculations show that this generates an electric field close to the maximum that the membrane can sustain—it has been calculated that a voltage difference much larger than 200 millivolts could cause dielectric breakdown, that is, arcing across the membrane. facilitated diffusion and transport facilitated diffusion in cell membranes, showing ion channels and carrier proteins the resistance of a pure lipid bilayer to the passage of ions across it is very high, but structures embedded in the membrane can greatly enhance ion movement, either actively or passively, via mechanisms called facilitated transport and facilitated diffusion. the two types of structure that play the largest roles are ion channels and ion pumps, both usually formed from assemblages of protein molecules. ion channels provide passageways through which ions can move. in most cases, an ion channel is permeable only to specific types of ions (for example, sodium and potassium but not chloride or calcium), and sometimes the permeability varies depending on the direction of ion movement. ion pumps, also known as ion transporters or carrier proteins, actively transport specific types of ions from one side of the membrane to the other, sometimes using energy derived from metabolic processes to do so. ion pumps the sodium-potassium pump uses energy derived from atp to exchange sodium for potassium ions across the membrane. ion pumps are integral membrane proteins that carry out active transport, i.e., use cellular energy (atp) to "pump" the ions against their concentration gradient. such ion pumps take in ions from one side of the membrane (decreasing its concentration there) and release them on the other side (increasing its concentration there). the ion pump most relevant to the action potential is the sodium–potassium pump, which transports three sodium ions out of the cell and two potassium ions in. as a consequence, the concentration of potassium ions k+ inside the neuron is roughly 20-fold larger than the outside concentration, whereas the sodium concentration outside is roughly ninefold larger than inside. in a similar manner, other ions have different concentrations inside and outside the neuron, such as calcium, chloride and magnesium. if the numbers of each type of ion were equal, the sodium–potassium pump would be electrically neutral, but, because of the three-for-two exchange, it gives a net movement of one positive charge from intracellular to extracellular for each cycle, thereby contributing to a positive voltage difference. the pump has three effects: (1) it makes the sodium concentration high in the extracellular space and low in the intracellular space; (2) it makes the potassium concentration high in the intracellular space and low in the extracellular space; (3) it gives the intracellular space a negative voltage with respect to the extracellular space. the sodium-potassium pump is relatively slow in operation. if a cell were initialized with equal concentrations of sodium and potassium everywhere, it would take hours for the pump to establish equilibrium. the pump operates constantly, but becomes progressively less efficient as the concentrations of sodium and potassium available for pumping are reduced. ion pumps influence the action potential only by establishing the relative ratio of intracellular and extracellular ion concentrations. the action potential involves mainly the opening and closing of ion channels not ion pumps. if the ion pumps are turned off by removing their energy source, or by adding an inhibitor such as ouabain, the axon can still fire hundreds of thousands of action potentials before their amplitudes begin to decay significantly. in particular, ion pumps play no significant role in the repolarization of the membrane after an action potential. another functionally important ion pump is the sodium-calcium exchanger. this pump operates in a conceptually similar way to the sodium-potassium pump, except that in each cycle it exchanges three na+ from the extracellular space for one ca++ from the intracellular space. because the net flow of charge is inward, this pump runs "downhill", in effect, and therefore does not require any energy source except the membrane voltage. its most important effect is to pump calcium outward—it also allows an inward flow of sodium, thereby counteracting the sodium-potassium pump, but, because overall sodium and potassium concentrations are much higher than calcium concentrations, this effect is relatively unimportant. the net result of the sodium-calcium exchanger is that in the resting state, intracellular calcium concentrations become very low. ion channels main articles: ion channel and passive transport despite the small differences in their radii, ions rarely go through the "wrong" channel. for example, sodium or calcium ions rarely pass through a potassium channel. ion channels are integral membrane proteins with a pore through which ions can travel between extracellular space and cell interior. most channels are specific (selective) for one ion; for example, most potassium channels are characterized by 1000:1 selectivity ratio for potassium over sodium, though potassium and sodium ions have the same charge and differ only slightly in their radius. the channel pore is typically so small that ions must pass through it in single-file order. channel pores can be either open or closed for ion passage, although a number of channels demonstrate various sub-conductance levels. when a channel is open, ions permeate through the channel pore down the transmembrane concentration gradient for that particular ion. rate of ionic flow through the channel, i.e. single-channel current amplitude, is determined by the maximum channel conductance and electrochemical driving force for that ion, which is the difference between the instantaneous value of the membrane potential and the value of the reversal potential. depiction of the open potassium channel, with the potassium ion shown in purple in the middle, and hydrogen atoms omitted. when the channel is closed, the passage is blocked. a channel may have several different states (corresponding to different conformations of the protein), but each such state is either open or closed. in general, closed states correspond either to a contraction of the pore—making it impassable to the ion—or to a separate part of the protein, stoppering the pore. for example, the voltage-dependent sodium channel undergoes inactivation, in which a portion of the protein swings into the pore, sealing it. this inactivation shuts off the sodium current and plays a critical role in the action potential. ion channels can be classified by how they respond to their environment. for example, the ion channels involved in the action potential are voltage-sensitive channels; they open and close in response to the voltage across the membrane. ligand-gated channels form another important class; these ion channels open and close in response to the binding of a ligand molecule, such as a neurotransmitter. other ion channels open and close with mechanical forces. still other ion channels—such as those of sensory neurons—open and close in response to other stimuli, such as light, temperature or pressure. leakage channels leakage channels are the simplest type of ion channel, in that their permeability is more or less constant. the types of leakage channels that have the greatest significance in neurons are potassium and chloride channels. even these are not perfectly constant in their properties: first, most of them are voltage-dependent in the sense that they conduct better in one direction than the other (in other words, they are rectifiers); second, some of them are capable of being shut off by chemical ligands even though they do not require ligands in order to operate. ligand-gated channels ligand-gated calcium channel in closed and open states ligand-gated ion channels are channels whose permeability is greatly increased when some type of chemical ligand binds to the protein structure. animal cells contain hundreds, if not thousands, of types of these. a large subset function as neurotransmitter receptors—they occur at postsynaptic sites, and the chemical ligand that gates them is released by the presynaptic axon terminal. one example of this type is the ampa receptor, a receptor for the neurotransmitter glutamate that when activated allows passage of sodium and potassium ions. another example is the gabaa receptor, a receptor for the neurotransmitter gaba that when activated allows passage of chloride ions. neurotransmitter receptors are activated by ligands that appear in the extracellular area, but there are other types of ligand-gated channels that are controlled by interactions on the intracellular side. voltage-dependent channels voltage-gated ion channels, also known as voltage dependent ion channels, are channels whose permeability is influenced by the membrane potential. they form another very large group, with each member having a particular ion selectivity and a particular voltage dependence. many are also time-dependent—in other words, they do not respond immediately to a voltage change but only after a delay. one of the most important members of this group is a type of voltage-gated sodium channel that underlies action potentials—these are sometimes called hodgkin-huxley sodium channels because they were initially characterized by alan lloyd hodgkin and andrew huxley in their nobel prize-winning studies of the physiology of the action potential. the channel is closed at the resting voltage level, but opens abruptly when the voltage exceeds a certain threshold, allowing a large influx of sodium ions that produces a very rapid change in the membrane potential. recovery from an action potential is partly dependent on a type of voltage-gated potassium channel that is closed at the resting voltage level but opens as a consequence of the large voltage change produced during the action potential. reversal potential the reversal potential (or equilibrium potential) of an ion is the value of transmembrane voltage at which diffusive and electrical forces counterbalance, so that there is no net ion flow across the membrane. this means that the transmembrane voltage exactly opposes the force of diffusion of the ion, such that the net current of the ion across the membrane is zero and unchanging. the reversal potential is important because it gives the voltage that acts on channels permeable to that ion—in other words, it gives the voltage that the ion concentration gradient generates when it acts as a battery. the equilibrium potential of a particular ion is usually designated by the notation eion.the equilibrium potential for any ion can be calculated using the nernst equation. for example, reversal potential for potassium ions will be as follows: e e q , k + = r t z f ln ⁡ [ k + ] o [ k + ] i =\ln where eeq,k+= equilibrium potential for potassium, measured in volts r = universal gas constant, equal to 8.314 joules·k−1·mol−1 t = absolute temperature, measured in kelvins (= k = degrees celsius + 273.15) z = number of elementary charges of the ion in question involved in the reaction f = faraday constant, equal to 96,485 coulombs·mol−1 or j·v−1·mol−1 o= extracellular concentration of potassium, measured in mol·m−3 or mmol·l−1 i= intracellular concentration of potassium even if two different ions have the same charge (i.e., k+ and na+),