cell biology 4 Flashcards
Ohm’s Law
DVfinal = I R, where I= current and R= the lumped resistance of the ion channels (called the ‘input resistance’ of the spherical cell).
Capacitance
the ability of a body to store an electrical charge.
Vm when the current is turned off
The shape of the fall of Vm when the current is turned off is exponential, and the ‘time constant’ (which is the time for ΔV to decay to 1/e or about 37% of its plateau value) is given simply as the product R.C, where C= the total capacitance of the spherical cell
cable properties of axons
uses mathematical models to calculate the electric current (and accompanying voltage) along passive[a] neurites, particularly the dendrites that receive synaptic inputs at different sites and times. Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances c_m and resistances r_m combined in parallel. The capacitance of a neuronal fiber comes about because electrostatic forces are acting through the very thin lipid bilayer. The resistance in series along the fiber r_l is due to the axoplasm’s significant resistance to movement of electric charge. The length constant, lambda, is a parameter that indicates how far a stationary current will influence the voltage along the cable. The larger the value of lambda, the farther the charge will flow. The larger the membrane resistance, rm, the greater the value of \lambda, and the more current will remain inside the axoplasm to travel longitudinally through the axon. The higher the axoplasmic resistance, r_l, the smaller the value of lambda, the harder it will be for current to travel through the axoplasm, and the shorter the current will be able to travel. Neuroscientists are often interested in knowing how fast the membrane potential, V_m, of an axon changes in response to changes in the current injected into the axoplasm. The time constant, tau, is an index that provides information about that value. The larger the membrane capacitance, c_m, the more current it takes to charge and discharge a patch of membrane and the longer this process will take. Thus membrane potential (voltage across the membrane) lags behind current injections. Response times vary from 1–2 milliseconds in neurons that are processing information that needs high temporal precision to 100 milliseconds or longer. A typical response time is around 20 milliseconds.
All-or-none principle
The amplitude of an action potential is independent of the amount of current that produced it. In other words, larger currents do not create larger action potentials. Therefore, action potentials are said to be all-or-none signals, since either they occur fully or they do not occur at all. The frequency of action potentials is correlated with the intensity of a stimulus. This is in contrast to receptor potentials, whose amplitudes are dependent on the intensity of a stimulus. Once threshold is exceeded, a miniature ‘explosion’ occurs. Remember, at threshold, not all sodium channels are conducting yet. But the sodium entering the channels that are conducting will depolarize the membrane further, and that depolarization will cause more sodium channels to start conducting, which will cause more sodium entry, which will cause more channels to open…. This is called ‘positive feedback.’ In a few tens of microseconds, the sodium channels are all open, and Vm is well on its way to ENa..
threshold potential
the critical level to which the membrane potential must be depolarized in order to initiate an action potential. every time the membrane potential must be depolarized to the same level before the action potential occurs. The threshold is not the point at which all of the Na+ channels open, as one might initially guess. In fact, there is no such point; the relation between PNa (the permeability of the membrane to Na+) and Vm is continuously graded with membrane potential.
What determines the threshold voltage?
The answer is a bit subtle; it’s the point at which sodium and potassium currents are exactly equal and opposite. Here is the explanation. Suppose we depolarize an axon exactly to threshold, and then turn off the stimulus. At that instant, some Na+ channels will have opened and Na+ ions will be entering, ‘trying’ to depolarize the cell even more. At the same time, however, potassium ions will be leaving the cell, ‘trying’ to pull Vm back towards EK. At the threshold, a very precarious balance is struck; if the K+ current should by chance slightly exceed the Na+ current, Vm will be pulled back towards the resting potential, Na+ channels will close, and there will be no AP. Conversely, if the inward Na+ current momentarily exceeds the outward K+ current, it will produce a little bit more depolarization, which will open more Na+ channels and the Na+ entry process will become ‘explosive’, producing an AP. Thus, while it is certainly easier to think of threshold as the point at which all of the sodium channels open, in fact threshold is defined as the point at which the Na+ and K+ currents are exactly equal and opposite.
Initiation of the action potential
It is important to remember that the concentration of Na+ is higher outside the cell than inside, and that the concentration of K+ is higher inside the cell than outside. Thus, if the membrane were permeable to Na+, Na+ ions would “want” to enter the cell, in order to balance their concentration inside and outside the cell. A typical value for ENa is 40mV, and a typical value for Ek is -90 mV. The actual membrane potential of the cell is determined by the relative permeability of the membrane to Na+ and K+. Since the typical membrane is much more permeable to K, Vm (-70mV) is much closer to Ek (-90mV) than ENa (40 mV). Within each square micrometer of typical axonal membrane are about 100 sodium channels which, at rest, do not permit any Na+ to cross the membrane. However, the channels start conducting when the cell is depolarized a little bit. Thus, the membrane permeability is drastically altered, from one that is largely permeable to potassium to one that is much, much more permeable to sodium. As sodium ions rush into the cell, the inside becomes more positive.
What is it like right at the peak of the AP?
The ‘struggle’ between Na+ and K+ goes on, as at rest, but PNa is now much greater than PK, and so Vm is very close to the sodium equilibrium potential.
Repolarization
occurs for two reasons: 1) PNa decreases. If we could artificially maintain the membrane potential at ENa (say by passing current through a second electrode), we would find that within a few milliseconds, none of the Na+ channels would be conducting, even though the membrane was still depolarized. This occurs because there exists a second gate in the sodium channel, which is open at rest, and closes upon depolarization. However, this gate (which we will call the inactivation, or h gate), swings more slowly than the Na+ gate we discussed previously (the activation, or m gate). Thus, at rest, the activation gate (m) is shut and the inactivation gate (h) is open. When the membrane is depolarized, they reverse states: the activation gate opens and the inactivation gate closes. Naturally, if the gates swung at the same rate, the channel would never conduct, because both gates have to be open in order for sodium ions to move through the channel. This is avoided because the activation gate swings faster than the inactivation gate, so that when the axon is first depolarized there is a brief instant when both gates are open and sodium can then rush into the cell. Then the inactivation (h) gates close (a delayed response to the depolarization), and PNa promptly declines. 2) PK increases. The closing of the Na+ channels at the peak of the AP would itself cause the axon to repolarize. In addition, the permeability of the membrane to K+ ions increases. This too of course promotes repolarization. The K+ channels open as the Na+ channel inactivation gates are closing. Because Vm is very far removed from EK, K+ ions rush out of the cell, and Vm plummets back towards its resting level. The K+ channel gates are closed at rest, and open in response to depolarization. However, they respond with a delay. This delay is certainly a good thing, for if K+ channels and Na+ channels opened simultaneously, the AP would be much reduced in height, or might not occur at all. The delay in K+ channel opening is timed to allow both maximum height of the AP and rapid repolarization. Notice that Vm “undershoots” the resting potential after repolarization. This is the result of the increased PK: repolarization will cause the K+ channels to close, but they respond with a delay, so that when Vm first gets back to resting level, the K+ channels are still open, and so Vm moves closer to EK. Then, as the K+ channels close, Vm finally relaxes back to its resting level. Notice that while the explosive opening of Na+ channels is an example of positive feedback, the K+ channel behavior is an example of negative feedback: depolarization causes them to open, which causes repolarization, which causes them to shut.
Role of potassium channels
What is gained by having voltage-gated potassium channels? After all, with the closure of the inactivation gates in the sodium channels, Vm would return to its resting level. The answer is: faster repolarization. The K+ channels provide additional pathways for potassium ions to leave the cell, pulling the membrane potential back to its resting value faster than in the absence of an increase in potassium ion permeability. Without the voltage-gated K+ channels, the membrane would indeed repolarize, but the repolarization would be slower, determined only by the passive (ungated) K+ channels responsible for the resting potential. Having lots of channels provides lots of pathways for rapid potential changes. And the faster the potential change, the more action potentials can be generated in a given period of time.
Refractory period
After producing an action potential, an axon cannot generate another one for a few milliseconds. This is called the refractory period. It can be subdivided into an absolute refractory period, during which time no stimulus, no matter how strong, can evoke another AP, followed by a relative refractory period, during which time a stronger-than-normal stimulus is required to evoke another AP. The refractory period results primarily from the fact that the sodium channel inactivation (h) gates require time to reopen after repolarization. If a stimulus is applied when some h gates are still closed, the sodium channel activation (m) gates may swing open, but no Na+ can flow owing to the closed inactivation gates. Whenever any channel is blocked by a closed inactivation gate, we say that the channel is inactivated. The potassium channels also contribute to refractoriness. After the axon repolarizes, it takes time (several msec) for the K+ channel gates to close again. The higher K+ conductance makes it harder for a stimulus to depolarize the axon.
Energy and action potentials
Clearly, an axon must pay a price for producing an action potential. During each AP, a few thousand Na+ ions enter through each Na+ channel, and about the same number of K+ ions exit through each K+ channel. Ultimately the Na+/K+ pump must be called upon to restore proper ion balances. If the pump is poisoned and an axon is stimulated repeatedly, gradually it will fill up with Na+ and lose K+. How quickly that happens depends mainly on the surface-to-volume ratio of the axon. Big axons have a relatively small surface area (compared to their volume), and so ‘run down’ relatively slowly, compared to small axons. The giant axon of the squid (about 1000 microns (1 mm) in diameter) can give over 100,000 AP’s without needing its sodium pump. Tiny neurons in the human cerebral cortex (about 10 μm in diameter) are much more sensitive to loss of their sodium pumps. In many cells, for one AP, intracellular Na+ concentration does not increase very much - probably by less than 0.1 mM. Thus, while the Na/K pump is necessary over the long run, most axons can give long bursts of AP’s without requiring pump activity. It’s an elegant system: a large reserve of stored energy (the Na+ and K+ ‘batteries’) can be tapped rapidly and repeatedly, and restored leisurely at a later time.
Propagation of the action potential along the axon
At the ‘active locus’, Na+ ions are rushing into the fiber, making the region positive with respect to the rest of the fiber. Current then flows through the axoplasm in both directions away from the active locus. This flow of current ahead of the active locus depolarizes the membrane to threshold; Na+ channels there will then open, so that this next stretch of membrane will itself become an active locus, and so on along the membrane to the right. A millisecond or so before the AP reached, the membrane behind the locus was itself an active locus. Now however, this patch of membrane is undergoing repolarization; Na+ channels have stopped conducting and K+ channels have opened. It is refractory. The inward membrane current at the active locus is of course carried by Na+ ions. The axoplasmic and outward membrane currents are carried principally by K+ ions.
local anesthetic
The anesthetic blocks sodium channels, keeping them from opening. The depolarization might spread passively farther along the axon, but it would become smaller and smaller the farther beyond the block. If the anesthetic was applied to a long enough length of axon, the membrane potential beyond the anesthetic block would not reach threshold, and the sodium channels there would not open, and the action potential would die. This is what happens when your dentist administers novocaine. Pain fibers in your tooth or gum may be firing action potentials like mad, but they don’t get past the novocaine block and your brain remains blissfully ignorant of the licensed violence being committed in your mouth. Greatest effect on axons that are: Smaller (lower safety factor), More active (channels must open). Preferentially affect pain over touch axons
Safety factor
the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load. In neurons, There must be enough Na+ channels to supply enough current to depolarize the next ring to threshold. This is the key to understanding action potential conduction. It turns out that axons have more than enough Na+ channels to do the job; their safety factor of transmission is 5-10 times the minimum required for successful propagation. Is this excess just a needless waste of Na+ channels? After all, for every Na+ channel that opens, the sodium pump must eventually pump out several thousand ions. There are several good reasons for this apparent extravagance. First, axons branch, sometimes rather profusely. At each branch point, the safety factor for transmission is reduced: the ring of membrane just before the branch must deliver sufficient current to depolarize both branches to threshold. A high safety factor thus insures that action potentials will spread down both branches of the axon. Another good reason for having a high safety factor concerns sodium channel inactivation. After an AP, the axon is refractory, in part because Na+ channel inactivation gates have shut. The absolute refractory period ends when enough inactivation gates have reopened to enable the axon to conduct again. This requires that a certain minimum number of inactivation gates must be open in each ring of membrane. That number will be reached sooner if there is a large excess of Na+ channels in the membrane. The upshot of this is simply that the axon will be able to transmit AP’s at higher frequency than if it had only the minimum number of Na+ channels required for propagation. Moreover, the velocity of propagation of the AP will be increased, because the excess Na+ channels will supply extra current, and so the ring ahead of the active locus will be depolarized to threshold quicker.
Conduction velocity
hrough the course of evolution, organisms that could react quickly to changes in their environment (such as the sudden appearance of a predator) naturally had a strong selective advantage over their slower peers. Reaction time is limited, in the end, by the velocity of action potential propagation along sensory and motor axons. A simple analysis of conduction velocity is as follows: conduction velocity will depend simply on A) the time it takes for an active locus to depolarize the membrane ahead of it to threshold, and B) on the length of axon membrane it can so depolarize. It turns out that conduction velocity depends only on axon diameter. Qualitatively, an active locus in a small diameter axon will depolarize a shorter length of membrane ahead of the active locus than will an active locus in a large diameter axon, and so the action potential will propagate more slowly in a small axon. Invertebrates have capitalized extensively on this fact, and generally those responses that are important for survival (such as ‘escape’ reflexes) are mediated by large, and therefore fast conducting, axons. The world record is held by the squid, which has an axon that may be over one millimeter (1000 microns) in diameter, and mediates the squid’s escape behavior. Now this is a lot of space to devote to one cell. Some human nerve trunks are only a millimeter wide, yet may contain over 100,000 individual axons! Such nerves can certainly convey very much more detailed information than the squid giant axon, albeit more slowly.
myelin
The multiple layers of myelin membrane form an electrical insulator, reducing the ‘leaky’ cable properties of the nerve fiber (Fig. 2). In other words, the effective resistance between the axoplasm and the extracellular fluid is increased by myelin. When a “node of Ranvier,” a region of the membrane without myelin, is depolarized to threshold, Na+ channels in the nodal membrane open and the node becomes an active locus. The current then spreads ahead to the next node, which becomes depolarized. Little current is lost between the nodes and the next node is depolarized to threshold very quickly. Because of this elegant specialization, the action potential “jumps” from node to node; this is called saltatory conduction (from the latin saltare, to jump). Myelination greatly increases conduction velocity; if the squid giant axon were myelinated its conduction velocity would increase by a factor of 100! Myelination also changes the quantitative relation between fiber diameter and conduction velocity; the relationship now becomes directly proportional so that doubling the diameter doubles the conduction velocity. In mammalian myelinated nerve the conduction velocity of myelinated fibers in meters/sec is roughly 6 times the diameter in microns. Generally speaking, nodes of Ranvier are spaced at intervals of 1-2 mm, and of the total thickness of a myelinated axon, about 2/3 is axon, and the rest myelin.
why aren’t all neurons big?
The answer concerns balancing speed versus content. There is simply not an unlimited amount of space or precursor materials in the body for axons. The choice then becomes whether to make all axons the same size, or make some big at the expense of others - one axon that can conduct at 90 m/sec takes up as much space as nine smaller axons that conduct at 30 m/sec. So for the sacrifice of several msec in conduction time, an enormous increase in information can be obtained - nine fibers can tell you a lot more than one fiber can. Furthermore, processing by the central nervous system of information of any complexity requires a fair amount of time (tens of msec), and supplying this information to the brain over 90 m/sec axons would be gross mismatching, because the long central delay precludes a very rapid response. Thus, Nature has struck a balance between conflicting needs in the evolution of the nervous system, and the outcome is an efficient and economical compromise between speed and content.
Hyperkalemia
hypokalemia is often chronic, not acute, and it is more challenging to diagnose, because ECF potassium may be nearly normal while ICF potassium is pathologically low. The causes are mostly due to K+ escaping from cells, combined with a kidney that can’t do its job of keeping [K+]o below about 5 mM. While getting the excess K+ out of the ECF (by having cells take it up, or by removing it from the body) is an important therapy, a more acute issue concerns EKG abnormalities, reflecting cardiac arrhythmias that are potentially life-threatening. During hyperkalemia, the conduction cells are at
risk. The depolarization moves Vm closer to threshold, making it easier to fire an action potential, but it also inactivates some sodium channels, making it harder to fire an action potential. Maverick pacemakers can arise for either reason. In the latter case (block of conduction), other pacemaker cells distal to the block will keep depolarizing spontaneously, and when they get to threshold, they will fire an AP. It’s bad news either way, because now these mavericks are driving part of the heart at a rate that is independent of the rest, and when heart muscle fibers don’t contract synchronously, the heart cannot pump blood effectively. If other maverick pacemakers arise, the situation can deteriorate rapidly, leading ultimately to ventricular fibrillation, a condition in which no blood is pumped. These maverick pacemakers can be silenced by administering calcium ions, as described below. n summary, pacemaker cells in the conduction system are depolarized by the high [K+]o, and APs are blocked in some. New pacemakers arise distal to the block. Calcium ions administered intravenously bind to surface membranes, increasing the threshold for AP generation. The clinical hope, of course, is that the normal pacemakers will take over once again and restore the normal excitation of the heart muscle.
the basics of the cardiac arrhythmias
In brief, there is a master clock in the wall of the right atrium that triggers each beat. The clock comprises a clump of a few thousand cells (the sino-atrial (SA) node) that depolarize spontaneously (and synchronously). When they reach threshold, each fires one action potential. Axon-like processes fan out to all of the muscle fibers, and each AP carries news to the muscle fibers that it’s time to contract. In fact, a kind of backup system exists, because all cells in the cardiac conduction system depolarize spontaneously. It’s just that the ones in the SA node depolarize fastest and so get to threshold first, setting the overall tempo of beats. But the backups make trouble during
hyperkalemia.
Calcium ions and excitability
Calcium ions are a relatively safe, short-acting pacifier for the maverick pacemakers in the heart, quieting things down and helping restore the normal pattern of excitation. Calcium ions act by binding to the outside surface of cells and, through a pure electrostatic action, sort of trick the sodium channels into thinking that the membrane has been hyperpolarized, thereby raising the threshold for action potential initiation. How do calcium ions exert this quieting effect on sodium channels? Calcium ions are one of the most important intracellular signaling molecules in the body, participating in a bewildering variety of important cellular events, such as muscle concentration, cellular motility, bone deposition, and exocytosis. You will study these mechanisms in the months ahead. Ca++ is also important in governing the threshold for the action potential, which is the rationale for giving calcium when cardiac arrhythmias emerge during hyperkalemia.
How does calcium affect AP threshold?
The key features are the effects of extracellular Ca++ on the surface negativity of the membrane. By way of introduction to this arcane but important phenomenon, the outside surfaces of all plasma membranes are studded with fixed negative charges (they are negative headgroups of phospholipid molecules and also anionic sugar residues bound to membrane proteins, including sodium channels). These fixed negative charges make the outside of the membrane a little bit more negative than it would otherwise be, but the negativity is exceedingly localized in space – a tiny nanodomain near the membrane surface. For example, if you were a positive ion in the ECF approaching the membrane, you would not even begin to detect the presence of the fixed negative charges until you were within a few nanometers of the surface (less than the thickness of the membrane itself!). That’s because all the other free ions and water molecules in the bulk ECF block your electrical ‘view’ of the fixed charges beyond this short distance. Membrane proteins, however, lie within the nanodomain, and thus ‘see’ that the outside of the membrane is negative. Making the outside of the membrane negative is equivalent to a depolarization. A microelectrode recording Vm would, however, never see this nanodomain. For example, a microelectrode would record a Vm of -80 mV, but the ‘local’ Vm perceived by sodium channels and other membrane proteins is less, only -70 mV, owing to the unscreened fixed negative charges on the outside surface of the membrane. In summary, unscreened fixed negative charges reduce the electric field across the membrane, making it easier for sodium channels to start conducting. giving extra calcium ions screens naked fixed negative charges, hyperpolarizing the local Vm, making it more difficult for the cell to fire an action potential. The binding of calcium is entirely electrical; no special ‘receptor’ is involved.
What is the basis of the membrane potential?
1)Electrochemical gradient for each ion: Eion, the ionic equilibrium potential: [Na+]o»_space; [Na+]I, [K+]o «_space;[K+]I. ENa ≈ +60 mV, Ek ≈ -90 mV. 2) Ionic membrane permeability. 2) Depolarization is transient. Voltage-gated Na+ channels inactivate: Na+ stops entering the cell.
Electrochemical gradients
K+ “wants” to exit the cell. If the membrane were permeable to K+ only: Vm = Ek ≈ -90mV. Na+ “wants” to enter the cell. If the membrane were permeable to Na+ only: Vm = ENa ≈ +60mV
Ionic membrane permeability
Permeability is determined by ion channels in the membrane- are they open or closed?
Resting membrane potential
Vm is determined by Ek, ENa, and the relative membrane permeability to K+ and Na+. Since the membrane is much more permeable to K+ than Na +, Vm is much closer to Ek: Vm=-70mV
What causes the depolarization in the first place?
Initial depolarization: Synaptic transmission. Typical cells have both excititory (drive closer to threshhold) and inhibitory (away). The cell integrates this in the trigger zone (hillock),
transient depolarization
Voltage-gated Na+ channels inactivate. Na+ stops entering the cell. Voltage-gated K+ channels open. Channel opening is delayed from when the threshold is reached. K+ exits the cell. Therefore, Vm is pulled back towards Ek
Return to resting potential
1)Voltage-gated channels close. Overshoot / hyperpolarization / after hyperpolarization. 2) Relative permeability to Na+ and K+ returns to resting baseline. 3) Role of Na+/K+ pump
cardiac muscle action potential
Cardiac muscle bears some similarities to skeletal muscle, as well as important differences. Like skeletal myocytes (and axons for that matter), in the resting state a given cardiac myocyte has a negative membrane potential. Within the cell, K+ is the principal cation, and phosphate and the conjugate bases of organic acids are the dominant anions. Outside the cell, Na+ and Cl- predominate. A notable difference between skeletal and cardiac myocytes is how each elevates the myoplasmic Ca2+ to induce contraction. When skeletal muscle is stimulated by somatic motor axons, influx of Na+ quickly depolarizes the skeletal myocyte and triggers calcium release from the sarcoplasmic reticulum. However, in cardiac myocytes the release of Ca2+ from the sarcoplasmic reticulum is induced by Ca2+ influx into the cell through voltage-gated calcium channels on the sarcolemma. This phenomenon is called calcium-induced calcium release and increases the myoplasmic free Ca2+ concentration causing muscle contraction. In both muscle types, after a delay (the absolute refractory period), potassium channels reopen and the resulting flow of K+ out of the cell causes repolarization. The voltage-gated calcium channels in the cardiac sarcolemma are generally triggered by an influx in sodium during the “0” phase of the action potential (see below). Cardiac muscle is a syncytium in which the cardiac muscle cells are so tightly bound that when one of these cells is excited the action potential spreads to all of them. This “plateau” phase of the cardiac action potential (absent in pacemaker cells), is sustained by a balance between inward movement of Ca2+
Passive current propagation
The distance that current will propagate depends on: Ri = internal resistance. Higher Ri -> smaller spread of current. Rm = membrane resistance. Higher Rm -> larger spread of current. Cm = membrane capacitance. Higher Cm -> slower spread of current. Axons are poor “cables”. Rm is low, Ri is high, and Cm is high. Therefore, for a typical axon, λ (Length constant of axon) is small: ~ 1mm. However, axons are well-built for active propagation. The membrane resistance is a function of the number of open ion channels, and the axial resistance is generally a function of the diameter of the axon.
Active propagation
Depends on voltage-gated Na+ channels
Conduction velocity
Ranges from 0.5 – 120 m/s. Depends on: Myelination and Axon width. Axons carrying the most time-sensitive information are larger and more myelinated
Demyelinating diseases
Multiple sclerosis- Damages myelin in central nervous system. Guillain-Barré syndrome- Immune response against myelin in axons innervating muscles. Myelin sheaths are damaged, slowing and/or blocking conduction (and therefore nervous system function)
Inhibitors of action potentials
Action potential generation and conduction depends on voltage-gated Na+ channels. If these channels are blocked, current can only be propagated passively
Neurotoxins
Extracellular blockers of voltage-gated Na+ channels – abolish action potentials: Tetrodotoxin (e.g., from pufferfish), Saxitoxin (e.g., from clams). Modulators of voltage-gated Na+ channel function – may shift voltage dependence; alter ion selectivity: Batrochotoxin (e.g., from frogs)
Length constant of axon
(λ) is a mathematical constant used to quantify the distance that a graded electric potential will travel along a neurite via passive electrical conduction. The greater the value of the length constant, the further the potential will travel. A large length constant can contribute to spatial summation—the electrical addition of one potential with potentials from adjacent areas of the cell. In the neuron it is the distance by which voltage has dropped to 37% of its initial value
nodes of ranvier
are the gaps (approximately 1 micrometer in length) formed between the myelin sheaths generated by different cells. A myelin sheath is a many-layered coating, largely composed of a fatty substance called myelin, that wraps around the axon of a neuron and very efficiently insulates it. At nodes of Ranvier, the axonal membrane is uninsulated and therefore capable of generating electrical activity. Demyelination may play a role in chronic pain. Nodes of Ranvier are disrupted. Isolated clusters of voltage-gated Na+ channels. This could contribute to the perception that there is pain present.
myelin
Myelin decreases capacitance and increases electrical resistance across the cell membrane (the axolemma). Thus, myelination helps prevent the electrical current from leaving the axon. It has been suggested that myelin permits larger body size by maintaining agile communication between distant body parts.
Capacitance and nerve cell membranes
A nerve cell (or indeed any cell) is surrounded by a plasma membrane, made of phospholipid. The cell can be seen as two electrically-conducting regions (the cytoplasm and the extracellular fluid, both electrolyte solutions), separated by a thin layer of insulator (the plasma membrane). The membrane therefore acts as a capacitor! For this reason, we portray charge as lined up on either side of the membrane, just as charge builds up on each plate of a capacitor. Because of the capacitance of the membrane, any change in voltage across the membrane, as for example the depolarization associated with an action potential, will take time to occur: the membrane has a time constant, τ. This will affect the velocity at which the action potential is propagated. If you think of myelin as effectively increasing the thickness of the cell membrane, you would expect this to decrease its capacitance (thicker insulating layer). Although this is a gross oversimplification of what is really happening, it turns out that myelination does have the effect of reducing membrane capacitance. However, myelination also increases the membrane resistance, so overall the time constant (= RC) might not actually change much. Myelination increases conduction velocity mainly because the increased membrane resistance increases the length constant, λ.
pain axons
usually smaller and myelinated, therefore propagation speed is slower
skin mechano-reception axons
slightly larger and myelinated, therefore slighlty faster propagation speed
ion channels
Ion Channels are Membrane Proteins that open and close (“gate”). When open, they only allow certain substances to pass (“selectivity”). Ion channels are present both in the plasma membrane and in membranes of intracellular organelles. Their gating is controlled by a vast array of stimuli including: temperature (hot/cold), mechanical deformation, membrane potential, Extracellular chemicals (taste, olfaction, neurotransmitters), Intracellular second messengers (ATP, cAMP, Ca2+). Some channels respond to multiple stimuli (e.g., both hot and capsaicin; cold and menthol, voltage and Ca2+)
Naming ion channels
There is no consistent method for naming channels. Thus, some are named according to their gating stimuli: e.g., nicotinic acetylcholine receptors (AChRs), GABAA receptors. Some are named for their selectivity (sodium channels, potassium channels, aquaporins), and others given names that reflect neither gating nor selectivity (TransientReceptorPotential channels, Orai, ryanodine receptors).
cell types with ion channels
Ion channels are essential for function of diverse cell types including muscle (triggering contraction/relaxation), neurons (sensory transduction, signal propagation, neurotransmitter release, postsynaptic responses, plasticity), T lymphocytes (activation), and pancreatic β cells (insulin release).
ion channels as targets
Ion channels are important targets of natural products that are used for predation (cone snails, spiders, kraits, cobras, scorpions) and defense (puffer fish, bees, plant alkaloids). Ion channels are important therapeutic targets (pain, arrhythmia, hypertension).
mutated ion channels
Mutations of ion channels are responsible for diverse human diseases (severe chronic pain, complete lack of pain, periodic paralysis, familial hemiplegic migraine, arrhythmias, diabetes mellitus, immunodeficiency, congenital cataracts and nephrogenic diabetes insipidus)
structure of ion channels
Ion channels have diverse structures. Voltage gated channels of the KV, NaV and CaV families have four membrane-spanning domains, each of which contains six alpha helices (S1 through S6). In KV channels, each domain is a separate polypeptide, and four of these assemble to form the channel. In NaV and CaV the four domains (I, II, III, and IV) are linked into a single polypeptide. For both, the S4 helices have positively charged residues (lys or arg) at every third position and are the structures that “sense” voltage. Also for both, the S5 and S6 helices and the “P loop”, which connects them, assemble to form the ion conducting pathway. The predominant selectivity of these channels is indicated by their names. These channels are essential for the function of nerve and muscle cells.
Neurotransmitter receptors
are either directly coupled to ion channels (i.e. the receptor and channel are part of the same protein), or activate second messenger pathways which can affect physically separate ion channels. The former are called ionotropic receptors, and the latter are called metabotropic (and are not a topic of this lecture). A given neurotransmitter typically is able to activate both ionotropic and metabotropic receptors.
pentameric ligand gated channels
Within the ionotropic category are the pentameric ligand gated channels, also called the Cys-loop family of neurotransmitter receptor channels, including the GABAARs, GlyRs, nAChRs and 5-HT3Rs (all of which are named after the ligand most important for controlling their gating). These channels are heteropentamers. Each subunit has four transmembrane alpha helices (M1 through M4), with M2 assembling around the central, ion-conducting pathway. These channels are either selective for the permeation of chloride (inhibitor receptor), or allow permeation of both sodium and potassium (with a slight preference for sodium) (excititory receptor).
Ionotropic glutamate receptors
The ability of synapses to modify their synaptic strength in response to activity is a fundamental property of the nervous system and may be an essential component of learning and memory. There are four classes of ionotropic glutamate receptors, namely NMDA receptor, AMPA receptor, Delta receptor and kainate receptors. They are believed to play critical roles in synaptic plasticity. At many synapses in the brain, transient activation of NMDA receptors leads to a persistent modification in the strength of synaptic transmission mediated by AMPA receptors and kainate receptors can act as the induction trigger for long-term changes in synaptic transmission. Ionotropic glutamate receptors are tetrameric ligand gated channels. In the case of the kind of glutamate receptors called NMDA receptors, two of the four subunits bind glutamate (causes channel to open or close) and the other two bind glycine (constitutively bound).
Chloride channels
Chloride channels of the CLC family are dimers in which each subunit has an ion permeation pathway. Each permeation pathway can gate open and closed independently of the other, although there is also another gate which controls both pathways simultaneously. Some members of the CLC family are H+-Cl- exchangers. The CLC chloride channels are important for stabilizing the resting membrane potential
Aquaporin water channels
are tetramers in which each of the subunits contains a permeation pathway for water molecules. Strictly speaking, these are “anti-ion” channels since they exclude all ions including protons. Aquaporins are expressed in cells/tissues where rapid movement of water is important, such as the kidney. In addition to the four water channels, the assemblage of the four subunits also produces a central pore which may allow ion permeation and be gated between open and closed.
Channel Selectivity
Selective permeation depends on a number of factors. Selectivity varies. Some channels are highly selective. For example, only about 1:10,000 ions permeating a KV channel is not K+, and CaV channels select for Ca2+ over Na+ by ~3000:1. Others are moderately selective (1 ion in 12 permeating NaV channels is not sodium). Others display little selectivity: nicotinic AChRs show only a slight preference for Na+ over K+ (~1.3 fold).
charge selectivity
an important determinant of what substances will pass through a channel. Channels that are cation selective do not allow permeation of anions, and those that are anion selective do not allow permeation of cations. Ionic valence is also important.
size selectivity
ions larger than the narrowest part of the pore will be rejected. However, size is by no means the only determinant: the crystal ionic radius of sodium is smaller than that of potassium, yet KV channels are highly selective (only about 1 ion In 10,000 is not K+).
effects of dehydration on ion channels
Ions are energetically stabilized in solution by waters of hydration, which make the ions effectively larger in size. Furthermore, the waters of hydration essentially mask small differences in the size of the ions. Thus, ions must be substantially de-hydrated before they pass through the channel pore, To compensate for this dehydration, which is energetically unfavorable, the ion is stabilized within the pore by energetic interactions with the amino acids forming the pore (but not too much, or the ion would stay “stuck” in the pore). The energetic interactions of the ion with the pore can occur with amino acid side chains (positive/basic residues: lysine or arginine; negative/acidic residues glutamate or aspartate), with backbone carbonyls (negative) or alpha helix dipoles (N-terminal: positive; C-teminal: negative). These and other interactions depend on the sign, valence and size of the ion.
multiple binding sites in ion channels
Multiple binding sites can increase selectivity: If an ion interacts with multiple sites while traversing the channel pore, even relatively slight differences in the strength of interaction between preferred and non-preferred ions at each site can result in a significant enhancement of overall selectivity for the preferred ion.
Gating of KV and NaV channels
This section discusses the gating of the channels important for generating the electrical impulse (action potential) in nerve and skeletal muscle, which will be discussed in detail in subsequent lectures. For both KV and NaV, gating is controlled by membrane potential (Vm). If one experimentally controls the voltage and steps it from a steady negative potential where the channels are in their resting state to a more positive steady voltage, the opening of the channels produces a current whose time course is a reflection of how many channels are open. A typical K+ current (IK) in response to a step from -60 mV to +20 mV is shown above, together with a cartoon summarizing the underlying mechanism. Specifically, the channel has an “activation gate”, which can rotate around a center pivot point. This rotation is controlled by a “voltage-sensing” charge, indicated by the “+” sign on the activation gate. When the inside of the cell has a negative potential with respect to the outside, the gate is held in its closed position and the current is zero. When the inside is made positive, the gate rotates to its open position and K+ ions flow out of the cell (upward deflection in the current). This process is called activation. When the inside of the cell is made negative the gate rotates back to the closed position and the current decays away. This process is the reverse of activation and is called deactivation. The gating of NaV channels is more complicated because they have both an activation gate and an inactivation gate. The operation of the NaV activation gate is similar to that of the KV activation gate. At negative potentials it is closed and making the inside of the cell positive causes the NaV activation gate to swing open (“activate”) and sodium ions to flow into the cell (INa). The second gate, the inactivation gate, is open at the resting potential because the activation gate occludes access to a site within the inner end of the pore at which the inactivation gate can bind. However, after the activation gate opens, the inactivation gate closes, a process called “inactivation,” causing the current to decay to zero during a maintained depolarization. Note that inactivation is not the same process as deactivation. Also, the reversal of inactivation is called “removal of inactivation.
Kv and Nav structure
Actual KV and NaV structures important for selectivity and gating. Selectivity occurs within a central, ion conducting pathway formed by the four KV subunits or four repeats of NaV, where this central pathway is surrounded by S5 and S6 helices and connecting P loop contributed by the each of the four subunits or repeats (see above for the structures of NaV and KV). Voltage sensing (the + sign in the cartoon activation gate) is accomplished by the S4 helices. These helices contain positively-charged Lys or Arg residues at every third position and translocate in response to changes in voltage across the membrane. It is not known precisely how the translocation of the S4 helices (4 per channel) cause activation, although the movement corresponding to the opening of the activation gate likely corresponds to a hinge-like motion of the S6 segments around a conserved glycine. This hinge-like re-orientation can be seen by comparing the crystal structures of the closed and open states of two bacterial K+ channels which are related to, but simpler than, KV channels (the bacterial channels have four subunits, each with only two transmembrane helices).Note that when the activation gates are closed, they occlude access to an enlarged space (“vestibule”) through which the ions pass before/after transiting a narrower constriction (the “selectivity filter” nearer to the extracellular side. The inactivation gate of NaV channels is formed by the cytoplasmic loop which connects repeats III and IV. When this cytoplasmic III-IV linker folds over the inner end of the central ion-conducting pathway, the channels is in a closed/inactivated state.
Sidedness and state-dependence of agents acting on KV and NaV.
The location of the selectivity filter near the extracellular side, and of the vestibule nearer the intracellular side of the KV/NaV channels, together with the location of the activation/inactivation gates near the intracellular side, has the result that many channel modifying reagents have access to their sites of action only from one side of the membrane, and that this access may require that the channel be open. For example, tetrodoxin (TTX) is a charged molecule that cannot cross the membrane. When it is added to the extracellular side, it binds within the entrance of the pore, just above the selectivity filter of NaV. The binding of TTX is essentially independent of the position of the activation/inactivation gates; TTX has no effect when added intracellularly. The binding of the commonly used local anesthetic, lidocaine, is much different. Lidocaine is a tertiary amine and equilibrates between de-protonated (neutral) and protonated (positively charged) forms. The protonated form is dominant at physiological pH and cannot cross the membrane, whereas the de-protonated form can. Protonated lidocaine has no effect on NaV from the extracellular side but can block the channel from the intracellular side (thereby producing local anesthesia). The block from the intracellular side can only occur if the protonated lidocaine can access the vestibule, which requires that the activation gate be open and that the inactivation gate not be closed. That is, the lidocaine block is “state-dependent.” Note that if lidocaine is at its binding site within the vestibule, it can be trapped there if the activation or inactivation gates are closed.
transient receptor potential channels
a group of ion channels located mostly on the plasma membrane of numerous human and animal cell types. There are about 28 TRP channels that share some structural similarity to each other. TRP ion channels are widely expressed in many different tissues and cell types, where they are involved in diverse physiological processes, such as sensation of different stimuli or ion homeostasis. Most TRPs are non-selective cation channels, only few are highly Ca2+ selective, some are even permeable for highly hydrated Mg2+ ions. This channel family shows a variety of gating mechanisms, with modes of activation ranging from ligand binding, voltage and changes in temperature to covalent modifications of nucleophilic residues. Activated TRP channels cause depolarization of the cellular membrane, which in turn activates voltage-dependent ion channels, resulting in a change of intracellular Ca2+ concentration; they serve as gatekeeper for transcellular transport of several cations (such as Ca2+ and Mg2+), and are required for the function of intracellular organelles (such as endosomes and lysosomes). Because of their function as intracellular Ca2+ release channels, they have an important regulatory role in cellular organelles.
malignant hypethermia suspetability
Malignant hyperthermia susceptibility (MHS) is a pharmacogenetic disorder of skeletal muscle calcium regulation associated with uncontrolled skeletal muscle hypermetabolism. Manifestations of malignant hyperthermia (MH) are precipitated by certain volatile anesthetics (i.e., halothane, isoflurane, sevoflurane, desflurane, enflurane), either alone or in conjunction with a depolarizing muscle relaxant (specifically, succinylcholine). The triggering substances release calcium stores from the sarcoplasmic reticulum and may promote entry of calcium from the myoplasm, causing contracture of skeletal muscles, glycogenolysis, and increased cellular metabolism, resulting in production of heat and excess lactate. Affected individuals experience: acidosis, hypercapnia, tachycardia, hyperthermia, muscle rigidity, compartment syndrome, rhabdomyolysis with subsequent increase in serum creatine kinase (CK) concentration, hyperkalemia with a risk for cardiac arrhythmia or even arrest, and myoglobinuria with a risk for renal failure. In nearly all cases, the first manifestations of MH (tachycardia and tachypnea) occur in the operating room; however, MH may also occur in the early postoperative period. There is mounting evidence that some affected individuals will also develop MH with exercise and/or on exposure to hot environments. Without proper and prompt treatment with dantrolene sodium, mortality is extremely high. Variations of the CACNA1S and RYR1 genes increase the risk of developing malignant hyperthermia. Malignant hyperthermia susceptibility is inherited in an autosomal dominant pattern, which means one copy of the altered gene in each cell is sufficient to increase the risk of a severe reaction to certain drugs used during surgery. In most cases, an affected person inherits the altered gene from a parent who is also at risk for the condition.
Nicotinic acetylcholine receptors (nAChR)
neuron receptor proteins that signal for muscular contraction upon a chemical stimulus. They are cholinergic receptors that form ligand-gated ion channels in the plasma membranes of certain neurons and on the presynaptic and postsynaptic sides of the neuromuscular junction. As ionotropic receptors, nAChRs are directly linked to ion channels and do not use second messengers (as metabotropic receptors do). Nicotinic acetylcholine receptors are the best-studied of the ionotropic receptors.
nuclear pore complex (NPC)
are multiprotein aqueous channels that penetrate the nuclear envelope connecting the nucleus and the cytoplasm. NPCs consist of multiple copies of roughly 30 different proteins known as nucleoporins (NUPs). Due to their essential role in controlling nucleocytoplasmic transport, NPCs have traditionally been considered as structures of ubiquitous composition. The overall structure of the NPC is indeed conserved in all cells, but new evidence suggests that the protein composition of NPCs varies among cell types and tissues. Moreover, mutations in various nucleoporins result in tissue-specific diseases. These findings point towards a heterogeneity in NPC composition and function. This unexpected heterogeneity suggests that cells use a combination of different nucleoporins to assemble NPCs with distinct properties and specialized functions. Although a recent report suggests that large ribonucleoprotein (RNP) complexes can be exported from the nucleus by budding of the nuclear membrane2, the vast majority of nucleocytoplasmic exchange occurs through NPCs
nucleoporins (Nups).
NUPs contain a very limited set of domains, including transmembrane domains (which are found in only four mammalian and yeast NUPs), α-helices, β-propellers, WD domains and FG repeats. FG repeats are the most common domains found in NUPs. NUPs carrying 4 to 48 FG repeats fill the central channel of the NPC, thereby forming a meshwork that is responsible for controlling nucleocytoplasmic transport and that determines the pore permeability limit. Most NUPs associate in biochemically stable subcom- plexes that, due to the eightfold rotational symmetry of the NPC, are present in eight or multiples of eight copies. nuclear pores are highly dynamic and plastic molecular assemblies that can adapt in response to cellular changes.
karyopherins
a group of proteins involved in transporting molecules between the cytoplasm and the nucleus of a eukaryotic cell. The inside of the nucleus is called the karyoplasm (or nucleoplasm). Generally, karyopherin-mediated transport occurs through the nuclear pore, which acts as a gateway into and out of the nucleus. Most proteins require karyopherins to traverse the nuclear pore.
Ran GDP/GTP cycle
Ran is a small G protein that is essential for the translocation of RNA and proteins through the nuclear pore complex. During nuclear import, cargo release occurs when the transport receptor interacts with the small RAN GTPase bound to GTP (RAN·GTP) inside the nucleus. On the other hand, in nuclear export RAN·GTP is required for the assembly of the receptor–cargo complex, and cargo release takes place upon GTP hydrolysis.
