1. Describe the basic structure of an ion channel. Name 3 ways a channel can be "activated," and describe what occurs upon activation. What are some ways a channel can decide what is allowed to pass through? Structure: Not much detail necessary. The basic structure is 2 or more (but usually 4 to 6) pore-forming subunits which may be identical or different, through which the ions pass, and 0 or more auxiliary subunits which affect functional properties such as binding capacity and gating properties. The inner part of the pore is hydrophilic, and the outer membrane-facing parts of the protein are hydrophobic. Channels can be activated by ligand-binding (chemical), voltage change, or mechanical changes such as stretch. Upon activation, there can be a conformational change, either in one part of the pore or a global change in the protein shape, which opens the pore, and/or there could be the elimination of a blocking element. This blocking element can be part of the channel protein itself, or an ion (such as magnesium in NMDA receptors). Channel selectivity can be based on charge, particle size, or based on a selectivity filter, a specialized part of the pore which makes it energetically favorable for some ions but not others to shed their waters of hydration, (the water molecules that naturally surround the ion in solution) and pass through the channel. 2. What are the forces that drive ions through channels? What determines the net flux of an ion? (4 th p.128-131, figure 7-3; 3 rd p.84-87, figure 6-6) Ions are driven though channels by the sum of their chemical (concentration) gradient and their electrical potential gradient. The concentration gradient is simply the difference in concentration of an ion inside and outside the cell. Sodium, for example, is chemically driven into the cell because it is much more concentrated in the extracellular fluid, while potassium is driven out of the cell because it is concentrated in the cell. The electrical gradient is determined by the charge of an ion and by the voltage difference across the cell membrane. Sodium and potassium are both positively charged, so they are driven into the cell because there is a buildup of negative charge on the internal surface of the membrane. (Important to note that the net charge in the cell and out are neutral and that the membrane potential is only a change in the distribution of charge up against the cell membrane). The net flux flow for a given ion (I) is determined by the net driving force, which is the sum mentioned above, times the permeability of the channel to that particular ion. Permeability is determined by the abundance of non-gated channels for the specific ion.
3. Explain the Nernst Potential. What are the Nernst potentials for K +, Na +, and Cl -? How are these ions' potentials calculated? How do the individual Nernst potentials determine the resting membrane potential? If the permeability to sodium was increased, how would this affect its Nernst potential? How about the resting potential of the cell?(4 th - p.128; 3 rd - p.84) Use the following concentrations: Inside the cell Outside the cell Na + 440 50 K + 20 400 Cl - 560 52 The Nernst potential is the membrane potential at which the electrical and chemical driving forces are equal for a specific ion. Note that at the Nernst potential, a dynamic equilibrium exists (this is actually a steady state balance), i.e., flow of the specific ion has not stopped, but net inward and outward movement are equal. The Nernst potentials for K +, Na +, and Cl - are calculated using the Nernst equation: For K+, E = RT x ln [K+]o Which can be simplified to: 58 log ([K+]o) ZF [K+]i Z ([K+]i) (K+ is a cation, so Z = +1; whereas Cl- is an anion, so Z = -1) For K +, E = 58 x log (20/400) = -75.5 mv For Na +, E = 58 x log (440/50) = +54.8 mv For Cl -, E = -58 x log (560/52) = -59.9 mv The individual Nernst potentials determine the resting potential based on the relative permeabilities of the membrane to each ion. The resting potential will end up closest to the Nernst potential of the ion to which it is most permeable. Thus in our nerve cells, the resting potential ends up very close to the resting potential for potassium due to the high conductance (permeability) of this ion. The Goldman Equation is used to combine Nernst potentials and permeabilities and calculate the resting potential. Since ions are constantly leaking down their electrochemical gradient, the Na+/K+ ATPase-pump is necessary to maintain the concentrations of Na+ outside and K+ inside the cell, which are needed to maintain the resting membrane potential. Nernst potentials change only when the intracellular or extracellular concentrations are altered in selectively permeable membranes. They are not affected by permeability to the specific ion. Therefore a change in the permeability to sodium would not alter its Nernst potential, but would raise the resting potential closer to the Nernst potential of sodium.
4. Describe the activation of a voltage-gated sodium channel, including the resting, active and inactive (refractory) states. How can an elevated resting potential lead to a decreased action potential amplitude? Voltage-gated sodium channels have two gates, an activation gate (m-gate) and an inactivation gate (h-gate). At the resting potential, the activation gate is closed and the inactivation gate is open. Depolarization rapidly opens the m-gate and begins the slow closure of the h-gate. For a short time, the channel is open, until the h-gate fully closes. The membrane now repolarizes, closing the m-gate and slowly opening up the h-gate again. Voltage-gated sodium channels vary in their threshold of activation. If the resting potential is elevated above its normal number, some voltage-gated sodium channels will always be in the inactive state, having been activated by the current membrane potential. So if action potential is initiated at a higher than normal resting potential, its amplitude will be diminished because some sodium channels will be in the inactive state. 5. Describe the steps involved in initiation and resolution of an action potential. What types of ion channels are involved, and what role do they each play? An action potential is initiated by a depolarization of the cell membrane, which may be caused by the binding of a neurotransmitter to a ligand-gated sodium channel, for example, or by a sodium channel activated by stretch or some other chemical or mechanical stimulus. This initial depolarization is called a synaptic potential. If the initial depolarization is enough to reach threshold, an action potential is fired. About threshold: Every time a little sodium current comes through the membrane, raising its potential, two things happen which prevent the start of an action potential. First, there is an increase in the potassium driving force because of the change in membrane potential. Second, a few voltage-gated potassium channels open and bring the potential back down. Threshold is the point at which the rapidly-opening voltage-gated sodium channels cause inward sodium current to exceed outward potassium current. A large number of voltage-gated sodium channels will open, and the influx of sodium will open more voltage-gated sodium channels, and the membrane potential approaches the Nernst potential for sodium. The sodium channels gradually inactivate, decreasing the sodium conductance, and at the same time, voltage-gated potassium channels open, increasing the outflow of potassium and bringing the membrane potential back down toward the Nernst potential for potassium. There is a transient hyperpolarization, the undershoot, after the action potential. This occurs because some of the voltage-gated potassium channels which opened during the action potential have not yet closed when the membrane potential returns to its normal
resting value. The increased permeability to potassium compared to its normal permeability pushes the membrane potential closer to the Nernst potential for potassium. Remember, permeability affects the relative strength of an ion in pushing the membrane potential where it wants it to go. After the action potential, there is a refractory period which can be divided into two parts. In the absolute refractory period, most sodium channels are still inactivated so no stimulus can bring on an action potential. In the relative refractory period, some sodium channels are still inactive and there are still some open potassium channels, so a new action potential would require a very large stimulus. 6. The cell membrane is often compared to a capacitor. Explain what is meant by membrane capacitance. What determines capacitance? What effect does capacitance have on changes in membrane potential and on the propagation of an action potential? How have organisms evolved their capacitance to speed up their action potential propagation? (p142) A simple capacitor consists of 2 plates separated by a gap. In the case of the cell membrance, the plates are the intra- and extracellular surfaces of the membrane, and the membrane thickness itself is the gap. The membrane exhibits the behavior of a capacitor because the membrane potential rises and decays more slowly than sudden changes in current applied to it (with a simple resistor, the changes would be instantaneous). In effect, the membrane capacitance acts as a bucket with the voltage represented by how high the bucket is filled. If you have a big fat bucket (big capacitance), it takes longer to fill it to a certain height (achieve a certain voltage). If you have a very thin bucket (small capacitance) it reaches that height (voltage) more quickly. Mathematically, V=Q/C (if the capacitance is equal to 1, then a change in current results in an immediate and proportional change in voltage, i.e. a simple resistor. If the capacitance is greater than 1, as in the cell membrance, the voltage changes is slower and smaller.) Therefore, capacitance serves to slow down changes in membrane potential and, by extension, slow down the propagation of an action potential. Capacitance itself is determined by the equation C=A/d where A is the area of the plates and d is the size of the gap. Therefore cells with a bigger gap (a thicker membrane due to myelination) have a lower capacitance and propagate action potentials quicker. Saltatory conduction is a faster mode of action potential propagation in which action potentials are generated only at the nodes of Ranvier in a myelinated axon. 7. What is the length constant for action potential propagation? How do the components of the length constant affect propagation? How have cells' length constants evolved to have faster propagation? What is the mathematical relationship between axonal resistance, capacitance, and rate of passive current spread? (p143-148) The length constant describes how far a voltage change due to the injection of current will travel within an axon before it decays. So, big length constant = more propagation. (Lambda= square root of Rm/Ra) Rm = resistance of the membrane (how much current
can escape across the membrane - bad for propagation) and Ra = resistance on axon (how easily current can flow down the axon - good for propagation). So, the bigger the Rm and the smaller the Ra, the less current will escape from the axon across the membrane and the more will travel down it. Cells increase Rm by myelination and decrease Ra by increasing axon diameter. The rate of propagation of an action potential is inversely related to the sum of capacitance and axonal resistance (C*Ra). SO, to increase rate, you want to decrease C*Ra. Note: Increasing axon diameter also increases capacitance by increasing the membrane surface area, remember from above that C=A/d. However, the Ra decreases in proportion to the square of the increased diameter while C increases in direct proportion to the diameter, (resistance goes down faster than capacitance goes up) so the net effect is to decrease C*Ra. 8. Draw a circuit representing a neuron at rest. To what does each element correspond? (4 th - p. 135, figure 7-10; and p147) Referring to figure 7-10, Cm represents the membrane itself as a capacitor (see above for explanation). The resistors / battery combinations in parallel represent the ion channels and Nernst potentials for Cl, K, and Na. Note the current flowing across the Na and K channels: in a cell at rest, the K current would be much larger. The two current generators in the diagram represent the Na/K pump which is working to counteract the constant leak of current across the Na and K channels. Finally, this figure only represents a tiny patch of membrane. To describe an entire axon, multiple segments like this one should be linked up in parallel with resistors that represent the axonal resistance (Ra). 9. What is the difference between patch clamping and voltage clamping? What is each one used to study? Be sure to say TTX and TEA at least once each in your answer. (p152-153, p162) The basic answer is that voltage clamping studies the electrical properties of the whole cell while patch clamping studies one channel. In both techniques, the cell (or channel in the case of patch clamping) is impaled with an electrode and it's voltage "clamped" at a desired level. The flow of current is then measured to determine what channels are opening and when. TTX is used in voltage clamping to block voltage gated Na channels so you can study the K current alone. TEA blocks the K so you can study the Na.