2016_02_17_worksheet_membrane_potential (1)

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BBIO 351: Principles of Anatomy & Physiology I Winter 2016 Worksheet: Understanding Membrane Potential Goals  Review fundamental information about cell membranes, ions, and electrochemical gradients.  Understand and apply the Nernst and Goldman-Hodgkin-Katz (GHK) equations.  Determine whether an ion will go into or out of a cell if given the ion’s concentration gradient and the cell’s membrane potential. Group roles to assign  Discussion leader: introduces questions, allots time for solo work, gathers input  Lifeline: looks things up, gets instructor’s attention  Equity officer: ensures equal participation  Digression manager: keeps discussion on track General background Today we begin our coverage of the nervous system! Fundamentally, the nervous system is an electrical system, i.e., messages are transmitted via the movement of charged particles (ions). As you know from courses like BBio 220, the movement of a cation (such as Na + ) into a neuron has consequences very different from the movement of a cation out of that neuron. Since such ion movements underlie the functioning of the entire nervous system, it is vital to understand exactly why ions move in the directions that they move. I. Two sides of the membrane 1. In Figure 1, place a large plus sign on the side of the membrane with the most positive charges and a large minus sign on the side of the membrane with the fewest positive charges. Figure 1: A polarized membrane. From Patrick J.P. Brown, Anatomy & Physiology: A Guided Inquiry (2016). 1

BBIO 351: Principles of Anatomy & Physiology I Winter 2016 2. A membrane potential can be defined simply as the difference in electrical charge between the two sides of a membrane (inside vs. outside). Based on #1 above, is the inside of a typical cell more negative or more positive than the outside? 3. Figure 1 does not show any anions (negatively charged ions) on either side of the membrane. Name at least one anion that contributes to the overall charge on one or both sides. II. Electrical and chemical gradients 4. Does the membrane potential in #2 above – that is, the charge difference between the inside and outside of the cell – pull K + ions into the cell, or push them out of the cell? (This assumes that K + has open channels through which it can go in or out.) 5. Now consider potassium’s concentration gradient, as depicted in Figure 1. Does this concentration gradient, in and of itself, attract K + ions into the cell, or push them out of the cell? Notice that your answers to #4 and #5 are opposites; that is, the electrical gradient (membrane potential) favors movement of K + in one direction, while the concentration gradient (chemical gradient) favors movement of K + in the opposite direction. We have arrived at the fundamental concept that ions are governed by both gradients … and the fundamental dilemma that an ion’s direction of movement can be tricky to predict when the two gradients oppose each other. III. The Nernst equation: balancing electrical and chemical gradients To figure out which gradient will “win” in a given situation, we have the Nernst equation . For a given ion, the Nernst equation tells us the membrane potential (that is, the electrical gradient) that perfectly counterbalances that ion’s chemical gradient, so that there is no net movement of the ion into or out of the cell . This special membrane potential is called that ion’s equilibrium potential (abbreviated E for equilibrium) or Nernst potential. The Nernst equation can be written in several forms, depending on one’s assumptions. Figure 2 shows a “full” version and a simplified version, along with (of course!) the lyrics for a Nernst equation jingle. Note the logarithm in the equation. A logarithm is another word for exponent. For example, 1000 may be written as 10 3 , so log 10 (1000) is 3. 6. If the ratio [ion] extracellular /[ion] intracellular is less than 1 , the log 10 of this ratio will be _________. Therefore, any cation that is more concentrated inside the cell than outside (e.g., K + ) will have an equilibrium potential (E) that is _______. 2

BBIO 351: Principles of Anatomy & Physiology I Winter 2016 Figure 2: Nernst equation and song lyrics. From https://www.youtube.com/watch?v=XfxwK9mTlkw . 7. If the ratio [ion] extracellular /[ion] intracellular is greater than 1 , the log 10 of this ratio will be _______. Therefore, any cation that is more concentrated outside the cell than inside (e.g., Na + ) will have an equilibrium potential (E) that is _______. 8. Chloride (Cl - ), like Na + , is more concentrated outside the cell than inside, but its valence (z) is negative (-1, to be exact). What can you conclude about chloride’s equilibrium potential (E Cl )? 9. Use the Nernst equation to find E Cl for a cell whose extracellular [Cl - ] is 110 mM and whose intracellular [Cl - ] is 5 mM. You may use a calculator. Does your answer match your conclusion in #8 above? IV. A graphical approach to electrochemical gradients The Nernst equation tells you the membrane potential at which the electrical and chemical gradients are exactly counterbalanced. Generally, though, we will want to know whether a specific ion will flow in or out at a specific membrane potential that is not the equilibrium potential. Here is Dr. C’s recommended method for determining the direction of an ion’s flow at any membrane potential: A. Find the ion’s equilibrium potential (E). B. Set up a graph with membrane potential on the X axis and overall driving force on the Y axis. 3

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BBIO 351: Principles of Anatomy & Physiology I Winter 2016 C. Plot 2 easy points: the X-intercept (when Y=0) and the Y-intercept (when X=0). D. Connect the dots! The chemical gradient is assumed to be constant throughout this process. To see how this method actually works, let’s do an example with Cl - ions, using the information given above. Step A: See #9 above. (Did you get -78 mV?) Step B. Note that “net driving force” (Y axis) represents the combined influence of the electrical and chemical gradients. Step C. The X- intercept, when Y=0, is simply the E Cl you calculated from the Nernst equation. The Y- intercept is the point representing the net driving force when there is no electrical gradient, i.e., when the membrane potential is 0 mV. In this case, there is only a chemical gradient, and since you know that Cl - is more concentrated outside the cell, that gradient drives Cl - inward. 4

BBIO 351: Principles of Anatomy & Physiology I Winter 2016 Step D. Once you draw a line through the 2 points, this line will show you the direction of the ion’s flow (in or out) at any membrane potential. Notice that all possible membrane potentials can be divided into the 3 regions labeled at the bottom. 10. Based on the method and data above, which way will Cl - flow (into the cell or out of the cell) at a membrane potential of +78 mV? 11. Based on the method and data above, which way will Cl - flow (into the cell or out of the cell) at a membrane potential of -90 mV? 12. Now try the following problem, which was on a quiz in a previous quarter…. Imagine an alien animal with neurons like ours except with different ions, different ion channels, and a resting membrane potential of -100 mV. The Nernst equation still holds true. If ion X 2+ is at a concentration of 10 mM inside the cell and 100 mM outside the cell, fill in each empty box of the following chart with INTO CELL, OUT OF CELL, or NEITHER. You may use IN/OUT/NEITHER for short. Note that log 10 (1/10) = -1 and log 10 (10) = 1. Membrane potential Direction X 2+ is driven, considering only the electrical gradient Direction X 2+ is driven, considering only the chemical gradient Direction X 2+ is driven, considering the overall electrochemical gradient -100 mV -58 mV -29 mV 0 mV 29 mV 58 mV 100 mV 5

BBIO 351: Principles of Anatomy & Physiology I Winter 2016 V. The Goldman-Hodgkin-Katz (GHK) equation: calculating membrane potential based on multiple ions The Nernst equation only considers one ion at a time. The Goldman-Hodgkin-Katz equation essentially combines the Nernst equations for multiple ions to calculate a membrane potential (V m ; V is for voltage) based on these ions’ intracellular and extracellular concentrations and the membrane’s permeability to these ions. Below is one form of the GHK equation (with subscripts i for inside and o for outside). Figure 3: GHK equation and song lyrics. From https://www.youtube.com/watch?v=jhoREcHVCj8 . Permeability reflects the density of open ion channels; the more open channels there are, the higher the permeability. The membranes of resting neurons are about 25 times more permeable to K + than to Na + because more K + channels are open. VI. Computer modeling of neurons We will now use a computer program to further explore the Nernst and GHK equations. Go to http://nernstgoldman.physiology.arizona.edu and click the “Launch now” button (or download the stand-alone program). Notice the four tabs at the upper right: Nernst, Nernst @37°C, Goldman, and Goldman @37°C. Also notice the lower-right menu of ion/permeability presets: default, generic cell, squid axon, skeletal muscle, red cell. Load the preset of a generic (mammalian) cell. 13. According to this program, what are the extracellular and intracellular Na + concentrations [Na + ] o and [Na + ] i (o is for outside and i is for inside)? 6

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BBIO 351: Principles of Anatomy & Physiology I Winter 2016 14. What is E Na for this generic cell, according to this program? (Is this a Nernst question or a GHK question?) Confirm that the sign of your answer (positive or negative) is what you would expect, based on the ion’s charge and concentration gradient. 15. Much of the pioneering work on how neurons function was done with squid, a marine animal whose bodily fluids somewhat resemble seawater. What are the extracellular and intracellular Na + concentrations for a squid axon, according to this program? 16. How does a squid axon’s E Na compare to a generic mammalian cell’s E Na ? 17. Now use a Goldman tab to determine the membrane potential (V m ) of a generic mammalian cell and a squid axon. How do the two compare? 18. Based on your above answers, does evolution seem to keep any or all of the following parameters within narrow limits?  extracellular ion concentrations  intracellular ion concentrations  equilibrium potentials  membrane potentials 19. Notice that, in the Goldman tabs, the relative permeabilities (P K and P Na ) are adjustable. Increase the membrane’s permeability to Na + . How does the membrane potential change? To what phase of an action potential does this change correspond? 20. Now bring the Na + permeability back to its original value and increase the K + permeability. What happens to the membrane potential now? 22. According to the GHK equation, the membrane potential (V m ) will always be somewhere between E Na and E K . What determines whether V m is closer to E Na or closer to E K ? 7

2016_02_17_worksheet_membrane_potential (1)

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