The Origin of Membrane Potentials

It is important to understand the origin of membrane potentials. Biological membranes are electrical insulators due to their phospholipid bilayer structure and are impermeable to ions, unless specific ion channels are temporarily open. In real cells, several different ion types, each with its own gradient contribute to this charge separation. Any ion that forms an ion gradient across a membrane, and that is permeable contributes to the actual membrane potential. At rest, most cells have a potential around -40 to -80mV indicating that they are dominated by K or Cl permeability (see table).

TABLE    Ion distribution across mammalian skeletal muscle membrane

Ion	Intracellular	Extracellular	Gradient	Nernst Potential
Na+	12 mM	145 mM	12 fold	+67 mV
K+	155 mM	4 mM	0.0026 fold (39 fold)	-98 mV
Ca++	0.001 mM	1.5 mM	15,000 fold	+129 mV
Cl-	4 mM	123 mM	29	-90 mV

[Note: a 10 fold gradient gives rise to ±60mV (see Nernst Potential below); Cl- concentrations can vary considerably from cell type to cell type; Source: Bertile Hille, Ion channels of excitable membranes, Sinauer, 1992]

While ion gradients are the result of pumps that move ions across membranes in an ATP dependent fashion (e.g. the Na/K-ATPase) charge separation is the result of ion selective channels used for rapid signaling events or prolonged voltage stabilization (resting conditions).

In general, transport processes are described by diffusion (diffusion coefficient D). For cell membranes diffusion is a two step process of moving ions from one aqueous compartment to an other across and within the hydrophobic core of the phospholipid bilayer. This is best characterized by the oil-water partition coefficient K (moving in and out of the bilayer) and the diffusion coefficient D within the bilayer. It is important to realize that the entire gradient spans only the thickness of a cell membrane, a distance of about 4-6 nm. Since measuring these parameters is fairly difficult to measure, a more accessible parameter, the permeability coefficient P, can be defined that includes both K and D.

Ion gradients can be mimicked, manipulated, and measured by electrodes attached to current generators and volt meters by a type of experimentation summarily known as electrophysiology. This can been done by modeling membranes as electrical circuits with resistance, capacitance, and charge (as in a battery) and correlated this circuit elements with structural features of cell membranes. Whatever the goal of an investigation may be, the important point is to define properties that can be measured experimentally. For membranes this includes the membrane potential (E) and membrane currents (I). Form these parameters we can calculate resistance (R), or its inverse the conductance (g), and permeability ratios. One basic equation, Ohm's law, describes the relationship between these parameters. It has been derived from flux rate analysis and, for charged particles:

E = RI or I = gE
Ohm's law

Concentration gradients of charged ions determine the membrane potential E as outlined above and the two parameters can be related using the thermodynamic or chemical equilibrium of transport phenomena. The equilibrium potential for a single ion species across a thin membrane separating two compartments with unequal concentration is described by the Nernst potential:

E(eq) = [RT/zF]ln{C(out)/C(in)}
Nernst equilibrium potential

R is the gas constant, T the actual temperature, z the number of charges of the ion species, F the Faraday constant, and C(out) and C(in) the extracellular and intracellular concentrations of the ion. Such a potential forms in the presence of a semi-permeable membrane. Consider that an ion species, e.g. K+ always comes with an anion neutralizing its charge. However, the two counter ions can be separated physically by some distance without violating the electroneutrality requirement of a salt solution. If the membrane separates an ion gradient, a potassium selective (semi-permeable) membrane would form a diffusion potential across the thin partition. The strength of this diffusion potential is captured by the Nernst equation, if the ion selectivity is absolute, i.e., the membrane is permeable for potassium ions only, but impermeable for the anion. Such absolute selectivities are never found in real cell membranes and potential equations are more complex than indicated for a single ion species. The most basic voltage equation that captures the relationship between ion gradients and membrane potential of excitable membranes (in neurons and muscle cells) is the Goldman-Hodgkin-Katz voltage equation, or GHK. It quantifies the relationship between equilibrium voltage, permeabilities and concentrations of Na, K, and Cl ions.

One particular situation arises in the presence of a charged macromolecule (= poly-electrolyte) like a protein or nucleic acid on one side of the membrane. Due to electroneutrality consideration and the impermeability of the macromolecules, the latter affects the distribution of the smaller, diffusible ions (K, Na, Cl, Ca etc.) attracting the counterion to its side, while repelling the ion with the same charge. In the most simple case, a negatively charged macromolecule P on one side of a Na and Cl permeable membrane will cause the Na concentration to be slightly higher and the Cl concentration in the compartment with the macromolecule. The opposite side will have an equal amount of Cl and Na ions, yet both ions will have a gradient of equal but opposite strength such that:

Na(out)=Cl(out) & Na(in)=Cl(in)+zP(in)

Na(out)/Na(in) = Cl(in)/Cl(out)         Donnan ratio

The potential associated to this gradient is called Donnan potential or equilibrium. It is important to keep in mind that actual biological transport processes are not at their chemical equilibrium but rather follow a steady-state equilibrium and are best described as homeostatic systems. Thus all formal analysis using Nernst potentials are approximations because they assume equilibrium or near equilibrium conditions. The actual processes can be estimated quite well from these approximations.

Another important concept to keep in mind when analyzing bioelectric phenomena is the difference between macroscopic and microscopic processes. Macroscopic systems involve a very large number of units in a system and any quantification thereof describes averaged behavior. Concentration, voltage, current, flux rate, temperature are macroscopic properties of systems. Having an extraordinary good insight into molecular structures allows us to also analyze systems at their microscopic level. This type of analysis describes the behavior of individual molecules and proteins and their behavior is statistical and probabilities can be assigned to individual events. A good example (discussed below) is the open probability of an ion channel. Probabilities multiplied by the number of particles in a system must equal the macroscopic behavior. Thus, structural presentation (microscopic) of a biological system can be linked to experimental observation (macroscopic) allowing complete physical description of mechanisms.

Historically, it is thus no surprise that in the 1940s when electrophysiologists begun studying nerve potentials and currents readily proposed unit conductances (the quanta was already well established in the physical chemists mind) that could be decoded from the noise spectra of macroscopic currents. These unit conductances, it was understood, were most likely the result of individual protein channels that could switch between open and closed states. Experimental proof of the existence and structural features of these proteins took several decades.

Action potentials

Cell membranes have stable potentials (resting potentials) that depend on the gradients of permeable ions and in excitable cells can be induced to form self-propagating, dynamic action potentials. An action potential can be induced when the membrane potential changes electrotonically reaching a threshold needed to trigger an action potential. Electrotonic potential changes are passive and characterized by the time and space constants of the membrane and the membrane conductance does not change as the potential changes.

TABLE Cell Membrane Potentials

Type	Propagation	Property	Information encoding
Electrotonic	Passive, graded	Time & space constant Equilibrium*	Amplitude Threshold
Action Potential	Self-propagation	Activation and inactivation kinetics Non-equilibrium	Frequency Duration

* No cell membrane potential is ever at chemical equilibrium, but at a steady-state equilibrium.

Action potentials, however, are the result of ion flow through voltage gated channels. The number of open channels changes as the membrane potential changes and thus the membrane conductance changes as well. This phenomenon is known as rectification. As a result, the increasing number of open pores increases the ion flow (current) disproportional to Ohm's law. And as the membrane potential is a function of ion flow, and the ion flow a function of the membrane potential, cell membranes with voltage gated ion channels form dynamic systems (here action potentials) that can best described as feedback coupled loops that 'oscillate' and due to the spatial distribution of channels behave like self-propagating waves of oscillating shifts of membrane potentials.

One of the most important feature of action potentials is the kinetics of depolarization (making the membrane potential more positive by moving Na+ through Na-channels into the cell) and hyperpolarization (making it more negative by moving K+ through K-channels out of the cell; note that the sign of the voltage always refers to the inside or cytoplasmic side of the cell membrane). The kinetics of the action potential, how fast it depolarizes and hyperpolarizes and how fast it can propagate along a cell membrane depends on two physical features of cell membranes, i.e., its resistance Rm and capacitance Cm. Basically, the entire process depends on the ability of certain membrane proteins to undergo conformational changes in a changing electric field strength. This conformational changes as a function of voltage is known as voltage gating and affects both activation (pore opening) and inactivation (pore closure) of these channels. It is clear that both processes are not independent of each other and form a dynamic feedforward and feedback loop system driving the potential change like a wave along an axonal membrane.

The Hodgkin cycle describes such a dynamic self-referential system as the Na channel dependent upstroke of an action potential. Inward currents carried by sodium ions cause the membrane to depolarize. The depolarization causes more Na-channels to open increasing the sodium conductance which leads to more inward currents and more depolarization. The action potential does not rise indefinitely for three reasons. First, the activated Na-channels rapidly inactivate. Second, voltage sensitive K-channels are being activated allowing K ions to flow outward, counter balancing the influx of positive charges by moving positive charges out of the cell. Third, the Na currents become weaker as the membrane potential depolarizes towards the Nernst potential of Na which measures +55mV. There, the sodium current becomes zero and reverses if the potential becomes even more positive. The Na current would contribute to hyperpolarization of the membrane in conjunction with the K current.

The passive time course of charging/discharging a membrane is the result of its capacitance and resistance. When applying a current pulse to a membrane by means of a microelectrode, the resulting change in membrane potential (charging) follows an exponential time course (natural logarithm) expressed as time constant tau which is proportional to the resistance and capacitance.

t = RC

The smaller the resistance (i.e. many ion channels open) and the smaller the capacitance (local current circuit) the faster the charge/discharge kinetics.

V = V(eq)exp{-t/RC)

In the 1940s when the first electrophysiology experiments on giant axons from squids were performed, the replacement of various ions quickly demonstrated that both Na and K currents are responsible for action potentials. Over the next decades, the role of ion channels in action potentials, and for that matter all membrane potentials, has been well established. Besides artificially changing ion compositions and concentrations showing the existence of several channel proteins with unique ion selectivity, the use of pharmacological agents, mostly neurotoxins from snails, snakes, spiders, fish and plants, and now also synthetic analogues has helped elucidate most of the mechanisms underlying electrical excitability of neurons and muscle cells.

Membrane currents

Measuring membrane currents instead of potentials has been the way of understanding mechanisms underlying action potentials. Membrane currents are the result of opening ion selective channels which causes ions to flow across cell membranes. This flow is spontaneous because all ion types are distributed unevenly between cellular and extracellular compartments. In general, cell contain high loads of K+, but low Na+ and Ca++ ions, while extracellular fluids contain high Na+ and Ca++ ions, but low K+ concentrations. Accordingly, ion gradients ranging from 10 to 10,000 fold depending on the ion species exist. When channels are activated, ions will always start diffusing through the pores in either direction, although more ions will flow from the high to the low concentration (down hill). These ion diffusion is an important part of bioelectricity maintaining resting potentials and generating action potentials. It is also used to couple the transport of secondary solutes that can be upconcentrated inside or outside according to metabolic needs. Finally, ATP hydrolyzing pumps reverse the flow of ions regenerating the gradients dissipated by the activity of channels and secondary transporters. Summarily, chemical energy is used to maintain the formation and use of membrane potentials and ion gradients.

While almost all transporters somehow involve the flux of ions across membranes, ion channels are unique in their fast kinetics facilitating the flow of up to 10 million ions per second. Pumps work at a roughly 10,000 fold slower rate. Despite the impressive flux rate through ion channels, ion gradients are not dissipated quickly because ion channels stay open only for milliseconds at a time. Prolonging their open state usually causes sever stress on cells and eventual cell death. Small, ion channel forming peptides from microorganisms but also animals are used as defense mechanism because they can penetrate membranes of competitors or pathogenic microorganisms forming permanent ion channels in host cell membranes destroying the cells. Examples are bacterial Gramicidin A, bee venom mellittin, frog skin antimicrobial magainins, and intestinal defensins, ionophoric peptides of animals that serve as a first line of defense against pathogenic bacteria.

The methods to study membrane currents are voltage clamp (two electrodes) and patch clamp (one electrode) techniques. The latter allows the measurement of currents through single channel units, while the former is used to measure macroscopic currents, which are the result of the simultaneous activity of hundreds to thousands of channels. The noise recorded in the early days of electrophysiology indicated the presence of unit conductances which later have been correlated with the presence of ion channels, the physical units of electrical conductivity in cell membranes. Today, the activity of these channels, their distribution and regulation is well described and one of the few protein systems that can be studied at the single unit level. Accordingly, single channel recordings have allowed the detailed characterization of kinetic properties and the opening and closing of these proteins. High resolution structural analysis has corroborated the existence of these channels, their channel structure, the gating mechanism, ion selectivity, voltage sensing elements, and ligand binding sites (e.g. where neurotransmitters can bind and activate the channel).

The correlation between single channel behavior and macroscopic currents is straight forward. The latter are the summation of single channel activities such that the macroscopic conductance g is the product of the single channel conductance g times the number of channels in the membrane studied. The macroscopic current is proportional to the product of the single channel conductance, times the number of channels, times the open probability and the effective driving force.

I = g(E-En) = NgPo(E-En)

where I is the membrane current, N the number of channels, g the membrane conductance, g the single channel conductance, Po the open probability of the single channel, E the membrane potential and En the Nernst potential of the ion species selective for the channel. The single channel conductance is an intrinsic property of a protein (channel) and differs with different ions used but is independent of the voltage or ion gradient. Membranes with multiple copies of the same channel show multiple distinct conductance levels of equal size. This observation has led to the concept of the unit conductance, one of several physical parameters by which ion channels can be distinguished (other parameters would be ion selectivity and pharmacological profile).

An other physical property that appears to be intrinsic to specific channel type is the probability of the channel being open and closed. Voltage-gated channels change their open probability with the membrane potential, a property known as rectification. In ligand gated channels, this probability increases with the proper ligand (e.g. neurotransmitter) bound to the channel. Yet other channels react to changes in pressure or temperature and function as mechanosensing or temperature sensing elements (e.g. in nociception, the perception of physiological pain).

Channel kinetics

The surprising observation is that voltage gating behavior found in current recordings can be kinetically described (fitting an equation to the observed macroscopic current of a Na current, for example) and correlated to structural elements of these proteins. Thus activation and inactivation processes are the result of structural changes in Na and K channels that response to changes in the electric field strength of a changing membrane potential. The structural elements of these proteins are referred to as voltage sensors that rely the stimulus to other structural components called the activation and inactivation gates. Sensors and gates are small domains in these channel proteins that shift their position affecting the quaternary structure of these multi-subunit and multi-domain proteins. Some gates function like a diaphragm while others literally swing in and out of an ion conducting pathway through the protein allow ions to flow across the membrane when both the activation and inactivation gates are open, but not when either one of the gates is closed.

Careful analysis of the kinetics and structural features of voltage-gated ion channels has shown that they contain an activation gate made of four voltage sensors that control the opening and closing of the pore, and one (Na-channel) or four (K-channel) inactivation gates. The movement of the voltage sensors in these channels depends on several positively charged amino acids that move in synchrony toward the outside and inside surface of the membrane. The movement of these positive charges can be measured electrophysiologically in the absence of mobile ions and is known as gating current. The inactivation gate is known as 'ball and chain' module where the N-terminal domain of the channel binds to the intracellular opening of the pore blocking ion flow.

The different amino acid sequences of different Na and K-channels can explain the differences in the gating behavior (i.e. kinetics) of these channels. Both types of channels are encoded for by many different genes. The voltage gated K-channels comprise a family of at least 50 different isoforms ranging from delayed rectifier (slow activation, very slow inactivation) to the A-type K-channel (fast activation, fast inactivation).

The kinetic analysis of single channel recordings has shown that channels, once activated, rapidly switch between an open and closed state, before they inactivate and stay silent until a new trigger activates them. These transitions between conducting and non-conducting states in an active conformation are randomly distributed and are well described by stochastic models. A stochastic model predicts that an event such as an opening transition is independent of its previous event (a closing). No definite mechanism for this opening and closing transitions have been found. Likely explanations are rapid conformational changes due to intrinsic internal motion of atoms or even kinetic models of oscillating changes of ion flow as the result of dynamic feed back loops between local fixed and mobile charges. The local transmembrane potential is affected by nearby mobile charges, while the number of mobile charges is affected by local surface potentials. As a result, local ion concentrations can drop temporarily below the resolution limit of modern electrophysiology equipment (about 0.1pA).

Ion Selectivity

All ion channels show selectivity and prefer certain ions while rejecting others. No channel has an absolute selectivity for a single ion species. Three basic types of selectivity mechanisms are found.

First, channels can be size selective where the size refers to the hydrated ion. Few channels depend solely on this size selectivity, but noted exception are the connexin forming gap junction channels bridging the double membrane structure of adjacent cells and mitochondrial and bacterial porins which serve as molecular sieves with a working cutoff size of 600 Dalton Gap junctions have a cutoff size selectivity around 1,000 Daltons. Thus, small metabolites like ions, sugars, nucleotides and amino acids can freely diffuse between neighboring cells. This process is known as metabolic coupling.

Second, channels can be cation or anion selective using mechanisms of electrostatic screening. A well understood example is the nicotinic acetylcholine receptor which has a ring of negatively charged glutamate residues on each side of the channel attraction cations but repelling chloride ions.

Third, most ion channels are ion selective such that they can discriminate between sodium, potassium, or calcium ions, all cations. Obviously, a simple electrostatic model cannot account for this selectivity. The high resolution structure of a bacterial potassium channel (KcsA; non-voltage gated) with a conserved pore structure with voltage gated K-channels shows that the difference in dehydration energy of hydrated K+ and Na+ ions favors the binding of K+ ions in what is called the selectivity filter. This structure comprises a narrow portion of the pore that requires ions to lose their hydration shell. The protein surface mimics the hydration shell with a series of backbone carbonyls pointing toward the channel center. These carbonyls structurally mimics the oxygen binding states of water molecules in a hydration shell. Nicotinic acetylcholine receptor pores are wider and both K and Na ions can diffuse across the pore without stripping off their hydration shell.

Channel Blockers and Toxins

Molecules interfering with ion channel activity can exploit different mechanisms. In the most simple case, they act as blockers of the channel entrance cutting off the flow of ions across the membrane. These are the channel blockers and can be relatively small (entering the pore partially as is the case for local anesthetics like lidocaine derivatives) or fairly large, as is the case for spider toxins conotoxins specific against Ca-channels or saxitoxin and tetrodotoxin, two Na-channel specific neurotoxins.

TABLE Examples of channel toxins

Function	Na channel	K channel	Ca channel
Blockers	Tetrodotoxin	Tetraethylammonium	Verapamil
	Saxitoxin	Charybtotoxin	Diltiazem
	Chlorpromazine	4-Aminopyridine	alpha-conotoxin
	local anesthetics	local anesthetics	SDZ(-)202791
Activators	Batrachotoxin	Pinacidil	SDZ(+)202791
	Veratridine		BayK 8644

Other toxins can be considered inhibitors or antagonists because they force the channel to close without directly interacting with the pore structure. This works through an allosteric mechanism where the toxin may bind to a voltage sensor or ligand binding site preventing the activation of the gating mechanism. Such allosteric mechanisms can also have the opposite effect such that a toxin may continuously activate a pore leading to overstimulation of a cell and depletion of ion gradients necessary to maintain resting conditions. Most of these toxins are highly specific for certain channel types and can be classified as Na, K, or Ca channel toxins. Specificity can be exquisite such that stereoisoforms of the same chemical function as agonists and antagonist as is the case for the synthetic Ca-channel ligand SDZ 2002791.

A broader range of blocking activity has been observed for the lidocaine group of toxins that function as open channel blockers of Na and K-channels (but also Ca-channels and nicotinic acetylcholine receptors). Lidocains are commonly used in dentist's offices. They are small amphipathic molecules with a hydrophobic methylated benzene ring attached to a positively charged tertiary amine. The molecule diffuses with its positive charge into the open pore of a channel and gets stuck with its hydrophobic tail. As they effectively block Na and K currents local anesthetics suppress the formation and propagation of action potentials.

Another class of inhibitors includes the general anesthetics which are not thought to bind directly to channel proteins, but accumulate in the membranes of excitable cells. Some K and Na channels, but also gap junction channels are known to be inactivated by general anesthetics in cell culture experiments. By altering the physical properties of the lipid bilayer they cause a loss of consciousness. This loss of consciousness in the central nervous systems occurs before peripheral nerves and muscle tissue stop working. The potency of general anesthetics correlates well with the oil-gas partition coefficient of small volatile molecules and high pressure induces loss of consciousness at lower concentrations.

Axonal Propagation and Myelination

Most of what is known from action potential propagation comes from measurement on axons of myelinated and unmyelinated neurons. The portions of a neuron simply transmits an electrical signal over fairly large distances measured in millimeters or centimeters. Initiation and encoding of the action potential occurs on other portions of the neuron, the post-synaptic membrane adjacent to synaptic buttons that interact with dendritic extensions and the cell body of neurons. These cell regions are rich in many different types of channels - ligand gated and voltage gated - and are more complex in composition and distribution than axonal membranes.

The action potential as described above can be modeled by assuming the coordinated activity of Na and K channels. The experimental data for this simple model comes from the squid giant axon membrane, a non-myelinated excitable membrane. The speed of action potential propagation depends on what have been called passive electrical properties. These include the time constant of charging and discharging a membrane capacitor and the space constant, a measurement of how far a local membrane potential can spread in the absence of an action potential (i.e., in the absence of voltage gated ion channels). Like the time constant, the space constant follows a single exponential decay. While the time constant increases with increasing membrane capacitance and membrane resistance, the space constant increases with the square root of the membrane resistance and diameter of the axonal segment (modeled after cable properties). It decreases with an increasingly larger internal resistance of the axonal cytoplasm.

The overall velocity of spreading an electrotonic potential increases with a shorter time and larger space constant. Now we can estimate if an axonal membrane is suitable for fast potential propagation. The propagation velocity increases with the diameter of the axonal segment and decreases with high membrane resistance and capacitance. Thus both decreasing the membrane resistance and capacitance speeds up the propagation velocity. In higher vertebrates, the myelination of long axonal segments provides such an adjustment helping to increase propagation speed without unduly increasing the thickness of the axon.

Myelination structurally divides long axons into 'compartments' of alternating high conductance (node of Ranvier where action potentials are generated) and low capacitance (myelination or internodal segments) that passively propagate the potential from node to node, called saltatory conductance. The role of myelination has traditionally been modeled after coaxial cable properties of transatlantic underwater telephone cables (before the invention of satellites and cell phones). However, the mechanism of neuronal membranes are quite different than those found in an insulated copper cable. Myelination influences the distribution of Na and K channels and the actual electrical properties of myelinated neurons and their equivalent circuits are more complex than the traditional cable model suggests. Particularly, there is good reason to believe that the parameters used in the cable theory are not independent variables.

There is now strong evidence for histological and immuno-histochemical analysis of channel distribution that the nodes have a high density of Na channels depolarizing the axonal membrane, while hyperpolarization is controlled by K-channels located within the internodal regions and the myelin membranes themselves. In such a model, the local ion current loops underlying an action potential, instead of being narrowly localized in the nodes only, are physically spread out between the nodes (depolarization) and nearby internodal membranes where K-channels are located (hyperpolarization). Demyelination diseases are shown to have abnormal Na and K channel distribution (not localized) and much slower signal propagation.

Encoding of Action Potentials

Action potentials are used as information carriers and information is encoded in the way action potentials can be generated and how often the can be generated. Information thus is carried as a function of the frequency of action potential, the so called firing pattern of nerve cells, and depends on the number of stimulating events needed to reach threshold. Generation and encoding of action potential occurs in the dendritic and somatic (cell body) portion of neurons, while axonal membranes merely propagate a series of action potentials.

The propagation of sequential action potentials can occur at a rate of up to 200 per second (200 Hz) which is the rate found in unmyelinated axons of the squid giant axon. This high frequency rate basically translates into one action potential generated every 5 ms. The lower range of the time period between successive action potentials is determined by the refractory period (absolute and relative period) of an excitable membrane. The absolute refractory period means that within this time period no action potential can be triggered by a current pulse following an initial pulse. This inability to trigger more than one action potential within a 1-3ms time frame is the result of the inactivation and relaxation kinetics of voltage gated Na-channels. Basically, activated Na channels inactivate and switch into a conformation I (inactive) that cannot be activated by a depolarizing pulse. The channel first has to change into a closed but active state that is susceptible to depolarization. During the relative refractory period a membrane cannot be completely depolarized because a fraction of the Na-channels is still in an inactive conformation.

The 200 Hz firing pattern observed with giant axons is among the highest frequencies observed in excitable membranes and usually not found on dendrites or cell bodies. Usually, firing frequencies range from as high as 100 to slow one every second. This range of frequencies indicates that neurons are able to generate firing patterns over a very wide range and plays the essential role in information processing (encoding). Frequency modulation thus is a major mechanism of excitable membranes and can be explained by the presence of voltage and ligand gated ion channels in addition to the two basic Na and K-channels (delayed rectifier) found in axonal membranes that can fire at very high rates. These additional channels contribute to either prolonged hyperpolarization or prolonged depolarization. They must facilitated outward currents (hyperpolarization) or inward currents (depolarization).

Frequency modulation, i.e., control over the length between successive action potentials is achieved by specific hyperpolarizing currents mainly due to K-channels. Two different K-channels have been characterized that contribute to so called slow after-hyperpolarizing potentials (AHP); the transient A-current (Kv4 or shaker K(A)-channels) and calcium activated K-channels (K(Ca)-channels). The transient A currents are activated when the membrane potential is between -45 and -65mV. Thus, an outward K+ current is activated at a time when the delayed rectifier K-channels that drive the fast after-hyperpolarization phase of an action potential are closed (delayed rectifiers open at potentials more positive than -40mV). Because these transient outward currents kick in when the cell membrane is hyperpolarized and close to rest, any depolarizing inward currents counterbalance and prevent the cell membrane from depolarizing. However, having a depolarizing inward current source of sufficient strength overpowers the effect of the transient A currents causing a fast paced triggering of action potentials. If the stimulating inward current is low, a large number of K(A) channels can delay depolarization and the firing rate of the membrane is decreased. The K(A)-channels are active only for brief periods (thus the name transient A current) as they have a fast inactivation kinetics. As a result, the time period during which they can prevent repetitive action potential generation is limited.

Some excitable membranes show resting periods (no action potentials generated) much longer than can be explained by the presence of transient A-currents. In these membranes, a calcium gated K-channel is expressed. Calcium gating is independent of voltage, but is sensitive to changes in the cytoplasmic calcium concentration. How is the cytoplasmic calcium concentration modulated in these cells? Voltage gated Ca-channels are activated during action potentials (depolarization) contributing inward calcium currents which produce prolonged action potentials and increased cytoplasmic calcium concentrations. Repetitive firing results in the rapid accumulation of internal calcium which results in the increased opening of the Ca-gated K-channels contributing a hyperpolarizing outward current. As a result, the time periods between successive action potentials are increased due to increasingly long after-hyperpolarizing potentials (AHP) until this outward current dominates the cell membrane and no depolarizing current reaches threshold. As a result, the entire cell comes to rest for several seconds during which Ca-pumps remove cytoplasmic calcium which removes K-channel activation and loss of slow AHP. The cell switches back to fast paced firing pattern until the cycle of inflowing Ca++ repeats and puts the membrane to rest. Overall, these cells exhibit a precisely timed bursting activity interrupted by long resting states the length of which is determined by the rate of calcium pumping, an ATP dependent mechanism.

The slow AHPs generated by various K-channels are not the only factors controlling the frequency of firing patterns. These hyperpolarizing outward currents (K+; and Cl- inward currents) are counterbalanced by depolarizing inward currents (Na+, Ca++; and K+ inward rectifiers) which are the result of ligand gated ion channels localized on post-synaptic membranes. Thus, the generation of an action potential depends on a membrane reaching its threshold potential which is the sum of depolarizing and hyperpolarizing current activity. This combination of depolarizing and hyperpolarizing currents occurs on specialized membrane regions called post-synaptic membranes. These post-synaptic membranes are apposed to presynaptic membranes found on chemical synapses.

Synaptic Transmission

Action potentials are generated on cell bodies where they form contact with innervating cells through synaptic buttons. These buttons are cell extensions that synthesize and store chemical neurotransmitters in small organellar vesicles. Upon an action potential stimulus arriving via the axonal membrane, voltage gated calcium channels trigger a signaling cascade using calcium ions that trigger membrane fusion between the storage vesicles and the presynaptic membrane. An exocytotic event releases the stored chemicals into the synaptic cleft where the rapidly diffuse towards and bind to ligand-gated receptors. Receptor activation triggers a post-synaptic membrane current in the receiving cell charging the potential to different levels. Thus the electrical signal is transmitted chemically between neurons and neurons and muscle cells.

Synapses can stimulate both depolarizing and hyperpolarizing currents depending on the neurotransmitter and their respective receptor used. Activating cation selective ion channels causes excitatory (depolarizing) post-synaptic potentials (EPSP) while activation of anion selective ion channels causes inhibitory (hyperpolarizing) post-synaptic potentials (IPSP). Chemical synapses produce so-called miniature endplate potential (called this way because they have first been characterized on the endplate regions of neuromuscular junctions) that are the result of a single pulse of exocytotic event. Each vesicle releasing neurotransmitter contains more or less the same amount of ligands activating a certain number of post-synaptic receptors which results in a uniform depolarizing pulse - the miniature endplate potential (MEPP). Usually, neurotransmitters from dozens of vesicles are released resulting in the local summation of many MEPPs eventually reaching threshold of the post-synaptic membrane that causes voltage gated Na-channels to open. The chemical transmission is complete.

Due to the nature of this quantized neurotransmitter release and a very large number of post-synaptic receptors clustered in the synaptic region high frequency signals from stimulating neurons result in temporal or spatial summation of MEPPs when a neuron is innervated by several synapses coming from the same or different neurons, respectively. Summation can also be the result of balancing excitatory and inhibitory synapses such that several neurons can control the firing pattern of a receiving neuron which integrates the signals coming from different regions of the body/brain. The complexity of neuronal signaling using combinations of excitatory and inhibitory synapses is indeed great and the numbers of active synapses or how strongly they can signal can be modified by metabolic feed back mechanism. This variability is known as synaptic plasticity and is invoked in models of learning and memory.

Some synapses are electrically rather than chemically coupled. These electrical synapses are composed of large gap junction plaques that contain thousands of gap junction channels. These channels are cell-to-cell channels spanning across two adjacent cell membranes directly connecting the cytoplasmic compartments of two neighboring cells. Gap junctions are found in all cells that are interacting with neighboring cells, not just neurons. Their major function is metabolic coupling of dozens of cells that can rapidly exchange metabolites without using extra-cellular exchange routes. A second function of gap junction is the electrical coupling of cell membranes. Thus, action potentials generated on one cell can rapidly spread to neighboring cells without extracellular chemical signaling molecules. Electrical communication is an order of magnitude faster than chemical synaptic transmission. The mechanisms of metabolic and electrical coupling are not completely understood particularly regarding the ability of many gap junctions to promote unidirectional information flow.

Channels and Diseases

Malfunctioning channels can be the cause of many diseases. Voltage gated ion channels contribute to arrhythmias in the heart because of their involvement in shaping action potentials and firing patterns of neurons and muscle cells. Understanding diseases requires a step up from individual cells to larger tissue and organ systems. Arrhythmias particularly are not a property of single cells but the entire heart pumping in carefully controlled time periods. Electrocardiograms capture the propagation of currents flowing across membranes in different parts of the heart during the pumping cycle. The EKG starts with the P-wave as the result of depolarization of atrial cells followed by the QRS-complex measuring the current spreading through the ventricles. The cycle ends with the T-wave that is characteristic of the repolarization of the ventricle.

The Long QT syndrome is diagnosed as an abnormal extension of the QRS complex to the end of the T wave in an electrocardiogram (extracellular recording) and that most cases are caused by mutations in a subunit of the ventricular K-channel I(Ks). In this cardiac membranes, I(Ks) is a heteromeric channel mixture composed of both delayed rectifier and shaker-type (transient A-currents) subunits giving rise to the characteristic firing pattern of ventricular membranes (see OMIM entry 607542). Delayed repolarization of the ventricle increases the refractory period of the ventricular myocardium delaying its subsequent depolarization. The wave of excitation may then 'pursue a distinctive pathway around a focal point in the myocardium (circus reentrant rhythm), leading to ventricular tachycardia, hemodynamically ineffective contraction of the ventricles, syncope, and, possibly, sudden death' (for more information go to eMedicine).

A variety of myotonias (dysfunctional coordination of muscle contraction-elongation) can be traced to defects in voltage gated chloride channels. These channels control the time interval between action potentials since inward chloride currents (due to their negative charge) contribute to hyperpolarization. When chloride channels are defective or blocked, slow after-hyperpolarization potentials disappear and cells begin to fire rapidly during a depolarizing inward current that can lead to muscle stiffness.

Gap junctions are found in large numbers in heart myocardium that allows the rapid spreading of electrical signals from neuromuscular junctions across large muscle fibers. They are also found in myelin sheets where they contribute to electrical coupling and K+ current circuit of action potential propagation. Mutations in connexins (the proteins that make gap junction channels) cause demyelination and are known to affect propagation behavior of peripheral neurons. A known peripheral neuropathy related to connexin mutations is Charcot Marie Tooth syndrome progressive degeneration of the muscles in the foot, lower leg, hand, and forearm. Some forms of hearing loss are also related to connexin mutations. In both diseases, the lack of gap junction coupling between cells causes a disruption of local K+ currents essential for the maintenance of electrical excitability of neurons or hair cells.

Read more about membranes and diseases.