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An in-depth analysis of action potentials in neurons, focusing on the roles of sodium (na+) and potassium (k+) channels. It explains the mechanisms of depolarization, repolarization, and hyperpolarization, and discusses the effects of tetraethylammonium (tea) and tetradotoxin (ttx) on voltage-sensitive channels. The document also covers concepts such as conduction velocity, length constant, time constant, accommodation, propagation, and saltatory conduction. Additionally, it touches upon the impact of demyelination on axon function, as seen in conditions like multiple sclerosis and guillain-barré syndrome.
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Action Potential Suppose we have the following cell: 145 mM 5mM 11 0mM 15 mM 140 mM 20 mM Na+^ K+^ Cl- measured E = - 70mV Proteins- If only Na+^ channels open up and remain open. Assume ENa= + 6 0 mV. 6 0 mV 0 mV
If only K+^ channels open up and remain open. Assume EK = - 88 mV 6 0 mV 0 mV
Depolarization : An action potential can be generated only if a critical number of Na+ channels are recruited. Voltage sensitive Na+^ channels open up in a range of membrane potential (-70mV to +40mV). Threshold is achieved only when enough channels are open at the same time. When the stimulus is larger than the threshold, the size and shape of the action potential does not change. As far as action potentials go it's all or none. Repolarization : caused by voltage sensitive K+^ channels (these are different channels from the K+/Na+^ leaking channels). These voltage sensitive channels begin to open up as the membrane potential rises above - 90 mV (this varies depending upon cell type). They open up more slowly than the activation gates of the Na+^ channels. Repolarization occurs within a few msec. Neuroscientists use tetraethylammonium (TEA) to selectively block voltage sensitive K+^ channels.
Hyperpolarization : voltage sensitive K+^ channels are slow to close after repolarization, therefore the membrane potential becomes more negative than the resting potential. How would TEA affect the voltage change profile of an action potential? 6 0 mV 0 mV
Length (space) Constant : the distance over which the potential change decreases to 37% of its maximum value. Note: the maximum value is the difference between the highest and lowest potential recordings. Typically it’s 1-3 mm in mammalian nerves or muscle. By 5 mm, there is no measurable change. Threshold: amount of depolarization that is required to open enough voltage sensitive Na+ channels which leads to the initiation of an action potential.
Absolute Refractory Period: period following an action potential when another action potential cannot be initiated because the Na+^ channels will not open.
When the membrane potential becomes less negative than during the resting state, rising from - 90 mV toward between - 70 and - 50 mV, that causes a sudden conformational change in the activation gate, flipping it to an "open" open position. This is called the activation state. During this state, sodium ions can pour through the channel, increasing the sodium permeability of the membrane as much as 500- 5000 - fold. The same increase in voltage that opens the activation gate also closes the inactivation gate. The inactivation gate, however, closes a few 10,000ths of a second after the activation gate opens. That is, the conformational change that flips the inactivation gate to the closed state is a slow process, whereas the conformational change that opens the activation gate is a rapid process. Therefore, after the sodium channel has remained open for a few 10,000ths of a second, it closes and sodium ions can no longer pour to the inside of the cell. An important characteristic of the sodium channel inactivation process is that the inactivation gate will not re-open until the membrane potential returns either to or nearly to the original resting membrane potential level. Therefore, it is not possible for the sodium channels to open again without the nerve fiber first repolarizing.
Relative Refractory Period: period following an action potential when the cell membrane potential is hyperpolarized and a larger stimulus is required to initiate a new action potential. Neuroscientist use tetradotoxin (TTX) to selectively block voltage sensitive Na+^ channels. TTX is found in the ovaries, liver testes and eggs of the Pufferfish. Blocking these channels is the mechanism of local anesthetics, e.g. procaine (Novocaine) or tetracaine.
Conduction velocity : the speed at which the potential changes in the membrane and the velocity an action potential is propagated down an axon. The greater the diameter of the axon, the greater the conduction velocity. Cable theory of action potential Cable theory began in the 1800’s scientists developed mathematical models for signal decay in underwater telegraphic cables. By analogy, the idea is applied to a theoretical tube made of cell membrane, submerged in salt solution like fluid.
Many axons are insulated with myelin , which is produced by schwann cells in the peripheral nervous system and oligodendrocytes in the central nervous system. Gaps occur in the myelin sheath every 1 to 2 mm. These gaps are known as nodes of Ranvier , which are about 1 m wide. Very little ion movement occurs in regions of the axon that are wrapped with myelin. Myelin greatly increases the conduction velocity because of greater length constant. This is because there is less charge loss through the myelin. A myelinated nerve fiber Nodes of Ranvier Myelin Because the action potential appears to jump from one node to the next, the process is called saltatory conduction. Latin word saltare , to leap. Since ion flow is only at the nodes much less Na+^ conductance is needed to effect an action potential, by a factor of about 1000. Therefore, myelinated axons are more metabolically efficient because fewer Na+'s have to be pumped back out by Na+/K+^ ATPase pumps. Analogy: water hose with leaks throughout the surface.
Resistance to action potential The conduction velocity is a function of the resistances associated with the axon. Things that affect conduction velocity reconsidered.
There is a convenient index of how rapidly exponential functions change with time. The index is denoted by the symbol τ and called the time constant. It is defined as the amount of time it takes for the change in potential in a capacitor to reach 63% (charging) or 37% (discharging) of its final value. So the greater the the longer it takes for the potential to change. The time constant is a function of two properties of membranes, the membrane resistance (Rm) and the membrane capacitance (Cm). = RmCm Take home message: the smaller the the faster things happen in the neuron! Length constant Consider another thermal analogue. Take a long, metal rod that is again initially at 10 oC and consider the consequences of touching one end of the rod to a hotplate which is at 100oC. (Assume that it is placed there for a certain amount of time to allow the temperature changes to stabilize.) How would the temperature be distributed along the length of the rod? There would be a temperature gradient along the rod because of the increasing loss of heat with greater distances from the heat source. The temperature gradient can be described by an exponential function of distance because of the physical processes involved. As stated earlier in this section, the length constant is the distance over which the potential change decreases to 37% of its maximum value.
Conduction velocity ∝ We’ve described separate equations that indicate both the time constant and the space constant. The insight above allows us to make a new equation that combines the two. Conduction velocity ∝
You will note that myelin causes a decrease in membrane capacitance thereby decreasing , and if is decreased then conduction velocity is increased. How much Na+^ crosses an axon during action potential? In the range of 10-^12 at a given point (pmole). Therefore, the change in ion concentration inside vs outside the cell is not measurable with current instrumentation. In fact, each sequential action potential is not dependent upon the extrusion of Na+^ by the Na+/K+^ ATPase pump because there is ample Na +concentration gradient to drive the depolarization of the membrane thousands of time with no pumping of the Na+/K+^ ATPase.
Multiple Sclerosis. An unpredictable disease of the central nervous system, multiple sclerosis (MS) can range from relatively benign to somewhat disabling to devastating, as communication between the brain and other parts of the body is disrupted. Many investigators believe MS to be an autoimmune disease -- one in which the body, through its immune system, launches a defensive attack against its own tissues. In the case of MS, it is the nerve-insulating myelin that comes under assault. Such assaults may be linked to an unknown environmental trigger, perhaps a virus. Most people experience their first symptoms of MS between the ages of 20 and 40; the initial symptom of MS is often blurred or double vision, red-green color distortion, or even blindness in one eye. Most MS patients experience muscle weakness in their extremities and difficulty with coordination and balance. These symptoms may be severe enough to impair walking or even standing. In the worst cases, MS can produce partial or complete paralysis. Most people with MS also exhibit paresthesias, transitory abnormal sensory feelings such as numbness, prickling, or "pins and needles" sensations. Some may also experience pain. Speech impediments, tremors, and dizziness are other frequent complaints. Occasionally, people with MS have hearing loss. Approximately half of all people with MS experience cognitive impairments such as difficulties with concentration, attention, memory, and poor judgment, but such symptoms are usually mild and are frequently overlooked. Depression is another common feature of MS. Reasons that demyelination interferes with axon function: length constant is shortened, a number of voltage sensitive potassium channels near the node are exposed and become an influence during action potentials. Once myelin is removed the voltage sensitive potassium and sodium channels are re-distributed and alter normal function of the axon. Guillain-Barré Syndrome (GBS). It is a disorder in which the body's immune system attacks part of the peripheral nervous system. The first symptoms of this disorder include varying degrees of weakness or tingling sensations in the legs, feet first. In many instances the symmetrical weakness and abnormal sensations spread to the arms, hands first, and upper body. These symptoms can increase in intensity until certain muscles cannot be used at all and, when severe, the person is almost totally paralyzed. In these cases, the disorder is life threatening - potentially interfering with breathing and, at times, with blood pressure or heart rate - and is considered a medical emergency. Such an individual is often put on a ventilator to assist with breathing and is watched closely for problems such as an abnormal heart beat, infections, blood clots, and high or low blood pressure. Most individuals, however, have good recovery from even the most severe cases of Guillain-Barré syndrome, although some continue to have a certain degree of weakness. Guillain-Barré syndrome can affect anybody. It can strike at any age and both sexes are equally prone to the disorder. The syndrome is rare, however, afflicting only about one person in 100,000. Usually Guillain-Barré occurs a few days or weeks after the patient has had symptoms of a respiratory or gastrointestinal viral infection. Occasionally surgery will trigger the syndrome. Recently, some countries worldwide have reported an increased incidence of GBS following infection with the Zika virus. In rare instances vaccinations may increase the risk of GBS.
