Title: Membrane Potentials Subtitle: Ion Movement: Forces and Measurement Diomedes E. Logothetis, Ph.D. Lecture goals:

Transcription

1 Title: Membrane Potentials Subtitle: Ion Movement: Forces and Measurement Diomedes E. Logothetis, Ph.D. Lecture goals: This lecture will discuss the chemical and electrical forces determining the direction and magnitude of ion movement through permeable pathways across the plasma membrane, the resting membrane potential and the use of voltage clamp and patch-clamp techniques to study ion channel function. The Learning Objectives below define the topics and what students should know regarding each topic. Learning Objectives 1. Understand how distribution of unbalanced charges at the membrane boundary accounts for membrane potentials. 2. Know the distribution (low vs. high) of the four major ions in most mammalian cells. 3. Know the thermodynamic derivation of the Nernst Equation and be comfortable explaining it qualitatively. 4. Given a membrane potential be able to determine the flow of ions (for a particular distribution in and out of the cell) considering the relative magnitude and direction of the chemical and electrical forces. 5. Be able to use Ohm s law to determine the currents flowing through the cell membrane. 6. Given a membrane potential be able to determine the flow of ions (for a particular distribution in and out of the cell) considering Ohm s Law. 7. Know the different types of Ion Channels and the major features they possess. 8. Understand how the balance of currents determines the membrane potential. 9. Know the voltage clamp and all modes of the patch clamp techniques. 10. Predict how ion flux through a particular ion channel will influence the membrane potential. Readings See Lecture Notes and Physiology, 3 rd Edition, L.S. Costanzo, Saunders, pp 15-17

2 Electrical signaling Ion movement across the plasma membrane through ion channel proteins serves distinct signaling roles such as changes in internal Ca 2+ concentration or changes in the membrane potential, thus allowing rapid communication of the cell with its external environment. Although electrical signals are mainly thought to be the language of the nervous system, they are also generated in almost all cells in response to a variety of stimuli. Thus, the stereotypic electrical signals called spikes or action potentials serve as important signals in many non-neuronal types of cells: for example, eggs generate an action potential when they meet the first sperm, macrophages respond with a kind of action potential to certain factors in complement as part of their chemotactic reaction and secretory cells in many glands --- pancreas, pituitary, adrenal medulla for example -- undergo action potentials when the contents of their secretory granules are to be released. Membrane Potential and Cell Capacitance Sodium (Na + ), potassium (K + ), calcium (Ca 2+ ) and chloride (Cl - ) ions are unequally distributed on either side of the plasma membrane. Yet, electroneutrality is achieved in the bulk intracellular and extracellular solutions as positively and negatively charged molecules screen the charge of each other. Suppose that we have some way of taking individual positive ions (cations) out of the cytoplasm of a cell and placing them outside (we will see later ways in which this can be done). As we move more and more cations out of the cell it becomes more difficult (takes more work) to move each additional ion because the partners of the cations, the negatively charged ions (anions) that are left behind, attract additional cations from leaving. Moreover, we are building an excess of cations outside that repel more cations from coming out. The amount of work to transport one ion with valence z out of the cell is: Work = -ze 0 V eqn. 1 where e 0 is the elementary charge. This equation is the fundamental definition of the membrane potential V. It is equal to the work that it takes to move a charge of valence z across the membrane. Meanwhile, we just argued that the work increases the more ions we transport across the membrane. The relationship between the work and the total charge that has been transported turns out to be a simple proportionality, such that: V = Q / C eqn. 2 where we say that Q is the net unbalanced charge left inside the cell, and C is a quantity called the capacitance. From your physics courses you have learned that capacitance is simply the capability of an insulator to separate electric charge. The capacitance of the cell membrane resides specifically in the lipid bilayer, which insulates the extra- from the intracellular aqueous phase with its hydrophobic core. Clearly, if a cell has a large capacitance, you can move a lot of charge before V changes very much. The physical properties of a membrane, which determine its capacitance, are the dielectric constant ε, the membrane area A and the membrane thickness d. C = εa/4πd eqn. 3 Let's remember from eqn. 3, that the membrane capacitance is proportional to the membrane area (see below for the reason) and inversely proportional to the membrane thickness (the larger the distance between the plates of the capacitor the weaker the attractive forces that keep the charges on each side). As we shall see in later lectures, this has great significance for the understanding of the pathophysiology of demyelinating diseases such as multiple sclerosis.

3 Below we see a diagram (Fig. 1) of what our negatively-charged cell is like: in both the interior and in the exterior solution almost all the ions have balancing counter ions. Figure 1. The net excess of positive charges outside and negative charges inside the membrane of a cell at rest represents a small fraction of the total number of ions inside and outside the cell (the ratio of the width of the region of charge separation to cell diameter is exaggerated here for purposes of illustration). There are two things to notice about this picture. First, the unbalanced charges are at the membrane boundary. That is because unbalanced charges repel each other; if two of them were somewhere in the middle of the cell or out in the extracellular solution, they would repel each other and start to move apart. Thus charges always congregate at boundaries, such as at the membrane, where they cannot move any further. This is why the capacitance depends on the membrane area: if the area is larger, the unbalanced charges are farther apart and there is less repulsion; that is, V is smaller. The second thing to notice is that the ions that are next to the membrane are not necessarily the same ones that we moved in the first place. Ions are always in motion, so they are often exchanging places. Also, if you were to introduce an extra ion into the center of the cell, it would start repelling its neighbors, causing them to move; they would repel their neighbors and so on, until the net effect occurs that one unbalanced charge winds up at the membrane surface. This process (which is just the conduction of electricity in an ionic solution) is much faster than diffusion. That is, it would take much longer for the original ion to diffuse over to the membrane than it takes for its electrical influence to be felt. This is the fundamental reason why electrical signaling is the fastest signaling process in cells. To calculate the fraction of uncompensated ions on each side of the membrane required to produce a specific membrane potential difference in a cell of a given geometry, consider the space-charge neutrality principle. According to this principle, in a given volume, the total charge of cations is approximately equal to the total charge of anions. The membrane capacitance of a typical cell is 1 μf/cm 2, which means that 10-6 uncompensated coulombs of charge on each side of the 1 cm 2 membrane are needed to produce 1 V across the membrane. The Nernst equation and the resting potential In the previous section we created a negative membrane potential (Fig. 1) by removing some cations out of the cytoplasm and placing them outside the cell, thus creating a charge imbalance. Indeed, when an experimenter records the potential difference across the membrane (potential difference between two microelectrodes, one inserted into a resting cell while the other outside the cell in the bath), (s)he records a

4 constant ("resting") membrane potential difference of -80 to -90 mv (defined as V in - V out ). What is the basis for this resting potential? Imagine that we could have a pathway that selectively allows for positive ions, that is lets cations go through but is impermeable to anions. As it turns out the negative resting potential of most cells, such as a muscle cell is caused by the fact that the resting membrane is almost exclusively permeable to potassium ions (i.e. specific proteins that allow potassium ions to leave the cell at rest). The membrane potential develops because K ions, which are 30 times more concentrated inside the cell, have a tendency to leave the cell (through specialized potassium permeable proteins). The resulting charge separation (less positive charge inside) sets up the negative membrane potential. The exact relation between concentration difference and membrane potential is given by the Nernst equation, which we will now derive. Let us start by remembering the extracellular and intracellular distribution of the main ions, in a muscle cell, for example: Extracellular Intracellular Na mm 15 mm K + 5 mm 145 mm Cl mm 10 mm Ca 2+ 2 mm mm (!!) We have already mentioned that ions cross membranes through specialized proteins that provide a hydrophilic pathway. We will now consider WHY the ions move. Ion movement through specialized proteins is energetically passive, that is, ions move towards a lower level of free energy. The free energy of an ion is the sum of two components: Chemical and electrical. The chemical energy varies with ion concentration and temperature and has the form: Chemical energy =μ o + RT ln [X] Here μ o is the standard free energy of a 1 molar solution, R is the universal gas constant, T the absolute temperature and [X] the concentration of ion X. The chemical energy represents the fact that random thermal motion tends to drive particles from regions where they are concentrated to regions where they are dilute. For our muscle cell, this means that for instance for K- ions there exists a chemical driving force for K-efflux from the cell. The magnitude of this chemical energy gradient is simply the difference between the two free energies inside and outside of the membrane: Chemical energy gradient = μ o + RT ln [X] i - (μ o + RT ln [X] o ) = RT ln ([X] i /[X] o ) The electrical energy is proportional to the potential and has the form: Electrical energy = zfv (per mole of ion) V is the potential, F the Faraday constant (96,500 coulombs/mole) and z the valence (+1 for potassium). An ion will want to move towards a potential of opposite sign to its charge, thus a cation will be attracted by a region of negative potential. The electrical driving force is the difference between the electrical energies inside and outside: Electrical energy gradient = zfv in - zfv out = zf (V in -V out )

5 The sum of the chemical and electrical energy gradients is called the electrochemical gradient. The transmembrane electrochemical gradient is the real driving force for ion movement through specialized proteins. This driving force vanishes when the sum of the chemical and electrical gradient equals zero. This condition is called the equilibrium condition, because there is no net transmembrane flux anymore. At equilibrium, the concentration gradient is exactly counterbalanced by an electrical gradient of opposite sign. RT ln ([K] i /[K] o ) + zf (V in -V out ) = 0 Rearranging yields the familiar Nernst equation: V X = V in -V out = (RT/zF) ln ([X] o /[X] i ) (eqn. 4) = (RT/zF) ln (10) log ([X] o /[X] i ) V X is called the Nernst potential for ion X. It is the potential that a membrane selective for ion X would stabilize at. Other equivalent names for the Nernst potential are: equilibrium or reversal potential. To distinguish the Nernst potential of a particular ion from the membrane potential or the resting potential we will designate it with the letter E. With the physiological extra- and intracellular concentrations listed above, we can now calculate the Nernst potentials for the major ions. This will tell us, at what value of the transmembrane potential the net driving force for a particular ion would vanish. At 37 o C, the expression RT/F ln (10)= 61 mv. Since z=2 for Ca ions RT/F ln (10)= 30.5 mv E Na = 61 log (145/15) = 60 mv E K = 61 log (5/145) =-89 mv E Cl =-61 log (125/10) =-67 mv E Ca =30.5 log (2/.0001) =131 mv Thus, the measured value of the membrane resting potential in our muscle cell (-80 to -90 mv) is very close to the Nernst potential for K- ions. It is as if the cell membrane is K- selective. This is confirmed by the fact that changes in extracellular K lead to predictable changes in the membrane potential, while changes in the other ions have little effect on the resting potential. The resting muscle membrane behaves like a K-selective membrane because specific K-permeable proteins are the only pathway for ions to move under resting conditions. It is worth noting that at the resting potential there exists a large inwardly directed electrochemical driving force for both Na and Ca ions. It can therefore be anticipated, that if Na and/or Ca pathways were to be permeable abruptly, this would lead to a large inward current which would make the inside of the cell more positive than before this change in permeability. We will see in a later lecture that this is precisely the mechanism that leads to the generation of an action potential. Ohm's law is central Electrical phenomena arise whenever charges (denoted as Q, measured in Coulombs) of opposite sign are separated or can move independently. Any net flow of charges (or a change of charge with time, dq/dt) is called a current (I), measured in Amperes. For our discussion of cellular excitability we will mainly study the mechanisms determining current flow across the plasma membrane of a cell. The magnitude of a current flowing between two points (for instance from extracellular to intracellular) is determined by the potential difference (or "voltage", or "voltage difference") between the two points (denoted as V, in Volts) and the resistance to current flow, R, measured in Ohms.

6 I=V/R OHM'S LAW (eqn. 5a) (For those who are uncomfortable with electricity: try the hydraulic equivalent Q=P/R. Here the potential difference corresponds to the pressure difference P and the current corresponds to the flow Q, while R refers to resistance). When Ohm's law is applied to biological cell membranes, it is often advantageous to replace the electrical resistance by its reciprocal, the conductance g, measured in reciprocal Ohms, or Siemens. I=gV OHM's LAW (eqn. 5b) For simplicity, we will assume that all resistive elements in the cell membrane behave in an "ohmic way", i.e. that their current voltage relationship (abbreviated as I-V) is described by eqn. 7b: the I-V relation is linear with a slope given by the conductance g. This is shown graphically by the solid line in Fig. 2a, which represents the transmembrane current (I) measured at different transmembrane potentials (V) in a hypothetical cell. Fig. 2b shows the experimental arrangement, the so called voltageclamp technique, which enables us to construct I-V relationships and to study the conductance characteristics of the cell membrane. Using this technique, we have inserted two microelectrodes into our cell (glass microelectrodes have tip diameters of microns and can be inserted into many cells without apparent damage to the membrane). One is connected to a voltmeter to measure the transmembrane potential. The second microelectrode is hooked up to a tunable current source (battery of variable output), which allows us to inject current into the cell. These electrodes are then connected to a feedback circuit that compares the measured voltage across the membrane with the voltage desired by the experimenter. If these two values differ, then current is injected into the cell to compensate for this difference. This continuous feedback cycle, in which the voltage is measured and current is injected, effectively clamps the membrane at a particular voltage. If specialized proteins that can offer a hydrophilic path to ions (called ion channels, see below) were to open (allowing ions to flow through them), then the resultant flow of ions into or out of the cell would be Figure 4a Figure 4b

7 Figure 2. Measuring the resistive properties of the plasma membrane to the flow of specific ions. (a) A current-voltage relationship showing ohmic (linear) characteristics. Conventions are also shown, i.e. negative current means negative inside with respect to the outside, outward current means positive ions (e.g. K) moving from the inside to the outside. (b) A voltage clamp experiment using two electrodes. One measures voltage (inside with respect to the outside) and compares it to the voltage that the experimenter desires to hold (or clamp) the cell membrane at. To adjust the voltage to the desired level the experimenter injects through the second electrode (the current electrode) either positive or negative current. The current injected in order to keep the membrane voltage from changing is precisely matching the amount of current entering or leaving the cell through conducting pathways (at the desired membrane potential). compensated for by the injection of positive or negative current into the cell through the current-injection electrode. The current injected through this electrode is necessarily equal to the current flowing through. It is the injected current that is measured by the experimenter. mthe convention used in Fig.2a is that the voltage is expressed as the difference between the intracellular and the extracellular potential (V=V in -V out ). At negative values of V the cell is said to be hyperpolarized, whereas at positive membrane potentials it is said to be depolarized. Positive charge moving from inside to outside is called outward current and is represented as an upward (positive) current, while inward current is shown as a negative current deflection. Ion channels carry transmembrane current How does current actually flow through the cell membrane via the channel protein? The answer to this question is not obvious, since we know that cell membranes are composed of a lipid bilayer with a very highly hydrophobic center, which is practically totally impermeable to charged particles like ions. Thus, in electrical terms, a lipid bilayer presents an almost infinite resistance to ionic current flow. For this reason, over the last ~50 years the presence of specialized membrane structures called ion channels was postulated. Today we know that ion channels are large transmembrane protein molecules embedded in the lipid bilayer. Each channel forms a relatively hydrophilic central pore, which allows ions to cross from one side of the membrane to the other. Many different channel proteins exist and we will discuss some of them in detail. The two most important functional properties of ion channels are (1) the fact that the channels fluctuate between open (conducting) and closed (non-conducting) states. This property is called channel gating and its importance will become obvious when we will consider the factors that control it, and (2) their ability to distinguish between different ions (channel Figure 3. Schematic representation of the various types of ion channels. Depiction of a voltage gated channel showing three key features. A voltage sensor that somehow is coupled to the movement of a gate that opens the channel so that ions can flow down the electrochemical gradient. Ions are selected (e.g. K + versus Na + ) through the selectivity filter.

8 selectivity). The nomenclature of ion channels is based upon these two most important functional properties. Thus, they are classified into distinct categories according to the stimuli that cause them to open. Ion channels that open in response to changes in voltage across the membrane are called voltage-gated (see Figs 3 and 4), those that open in response to binding of a ligand are called ligand-gated, those that open in response to mechanical stress are called mechanically gated or mechanosensitive channels (see Fig 4). A class of potassium channels that are thought to be active at resting membrane potentials and as such to be major contributors to the negative resting potentials of cells are starting to be recognized as PIP 2 --gated (as they seem to be opened by interactions with the membrane phospholipid phosphatidylinositol-bis-phosphate). Within these categories ion channels that are selective for K + ions are called potassium channels, for Ca 2+ ions, calcium channels and so on. Thus, we have distinct K + channels that are voltage-gated, ligand-gated, or mechanosensitive. Always keep in mind, that for each channel type there are several to many forms (e.g. the count is over 100 for K + channels) The benefit of the voltage-clamp technique can be appreciated for voltage-gated currents in particular. These ionic currents are both voltage and time dependent; they become active at certain membrane potentials and do so at a particular rate. Keeping the voltage constant in the voltage clamp allows these two variables to be separated; the voltage dependence and the kinetics of the ionic currents flowing through the plasma membrane can be directly measured. The balance of currents determines the potential Figure 4 Four classes of ion channels: voltage gated, intra- or extracellular ligand gated and mechanically gated channels. Extracellular ligands include neurotransmitters, peptides, hormones. Intracellular ligands include signaling molecules such as camp, cgmp, Ca 2+, Na +, G proteins, PIP 2, etc. Mechanical stimuli include physical cell deformation, shear stress, osmotic pressure. The current-voltage relation we drew in Fig. 5 does not apply to a real cell since as we said there is a negative resting potential (i.e. at equilibrium where the net current is zero, the membrane potential is negative). Figure 5 draws the correct relation for a K-selective channel. It will now intersect the current axis at V K. Ohm's law still describes the I-V relation, but we have to introduce the voltage offset, and eqn. 4b becomes: I K = g K (V-E K ) (eqn. 6) V-E K is of course just the electrochemical driving force at any potential V. If K-channels are the only channels open, then as stated above, the membrane potential will be E K. However, if the cell membrane also has some other measurable conductance, then V will deviate from E K. Let us assume for instance, that the cell also has a measurable Na-

9 conductance, with g Na :g K = 1:5. I Na = g Na (V-E Na ) I Na will be zero at E Na and have a slope of 1/5 that of I K (see Fig. 5). The resting potential V R in this case will settle at a value between E Na and E K where net K efflux is exactly balanced by net Na influx. This point can easily be determined graphically from Since I Na =-I K g Na (V R -E Na ) = - g K (V R -E K ) Figure 5. Two linear (for the sake of simplicity) resting conductances are shown. One conducts K ions while the other Na (g Na : g K = 1:5). The dashed line shows the sum of the two conductances or the net conductance. Resting membrane potential can be appreciated graphically as the potential where inward and outward currents are equal or they add up to zero. V K and V Na are the same as E K and E Na. rearranging V R = (E Na g Na )/(g K +g Na )+(E K g K )/(g K +g Na ) (eqn. 7) So V R can have any value between E Na and E K. The actual value of V R becomes a weighted average of the two Nernst potentials for Na and K, where the weight is given by the relative conductances. In our example with the above values for E Na, E K and g Na :g K, V R = -64 mv. As expected, if g Na >>g K then V R =E Na and, if g K >>g Na then V R =E K V will however only stay constant as long as the ionic gradients do not change. If there was no independently operating, active transport system which maintains the ionic gradients (we will discuss this in the last lecture) these gradients would indeed run down, since at V R there is a constant K-efflux and Na-influx. The patch clamp technique The patch clamp technique (see Fig. 6), a variant of the voltage clamp technique described earlier, has revolutionized the study of ion channels. Erwin Neher and Bert Sakmann who are primarily responsible for this technique, received the Nobel Prize in This technique allows one to record current flow not only from hundreds to thousands of channels present in the plasma membrane but also ionic currents from a single channel protein. With this technique, a fire-polished glass micropipette with a tip diameter of around 1 μm is pressed against the plasma membrane of a cell. Application of a small amount of suction to the pipette greatly tightens the seal between the pipette

10 and the membrane. The result is a seal with extremely high resistance between the inside and outside of the pipette. Thus ion flow through open ion channels offers much less resistance than through the pipette-membrane seal. and outside of the pipette. Thus ion flow through open ion channels offers much less Figure 6. All modes of the patch-clamp technique start with a clean pipette pressed against an intact cell to form a gigaohm seal (the resistance to ion flow between and the membrane is in the order of gigaohms). Currents can be recorded in this on-cell or cell-attached mode as minute currents passing between the pipette solution and the cytoplasm. Additional suction can break the isolated patch without affecting the gigaohm seal, giving access to the cell cytoplasm and measuring currents from the whole-cell membrane (minus the small ripped patch). Pulling the patch pipette away from the cell can rip a small patch of membrane giving rise to the outside-out patch where the experimenter has easy access to the solution on the external side of the patch. Finally, an alternative configuration is the inside-out mode of recording, where the pipette is pulled away from the on-cell mode, exposing the inner surface of the membrane to the bath, where the experimenter can easily manipulate the internal solutions. This dramatically improves the signal to noise ratio and extends the utility of the technique to the whole range of channels involved in electrical excitability, including those with small conductance. The patch clamp technique is highly versatile, as one can record channel activity in different arrangements. The "cell-attached" recording records microscopic (from just one or a few ion channel) currents, while the intracellular environment of the cell is intact. Pulling away from the cell, a small patch of the membrane can be ripped away (inside-out or outside-out patch) allowing recording of single-channel currents under absolute control of the intracellular solution that can now be easily changed through the bath solution (e.g. for the inside-out patch). If one would like to record from many ion channels further suction can be applied to the cell attached mode to break the patch under the electrode and allow access to the remaining cell membrane containing many ion channels (whole cell). Since there are many different types of ion channels in the membrane, one has to take cautious care of adjusting the composition of the solutions and including pharmacological agents that will allow isolation of the current type that needs to be studied.

11 Ionic currents recorded by the patch clamp technique Figure 7 shows single channel records of a K channels found in cardiac cells. 150 mm K bathed the patch from each side. At 0 mv no single channel openings were observed (E K = 0 mv). As the membrane potential was held to increasingly more and more negative levels, the channel openings became larger and larger (difference from the dotted zero line). When the single channel currents obtained at each membrane voltage was plotted (for both the negative potentials shown, as well as the positive potentials not shown) a linear ohmic relationship was obtained (labeled control). If the external K concentration was adjusted to 30 mm or the internal K concentration was changed to 45 mm, while leaving the K concentration on the other side to 150 mm, the I-V curves shown were obtained. Do the E K values obtained experimentally match the values predicted by the Nernst equation? Figure 8 shows whole cell records from a cation selective (Na, Ca and Mg), cyclic nucleotide-gated channel from the rod outer segment membrane (see next lecture). 1 mm cgmp activated this current linearly at both negative and positive membrane potential changes. Figure 7. left: Singlechannel currents recorded from an inwardly rectifying K channel in the open cellattached configuration. Numbers to the left of each current trace refer to holding potential. The electrode was filled with Ca-free, high-k solution. The dotted line indicates zero-current level. right: Single-channel I-V relationships obtained from similar patches as those shown on the left. From: H. Matsuda, A. Saigusa & H. Irisawa, 1987 Nature 325: and H. Matsuda, 1991, Journal of Physiology 435:

12 Figure 8. Macroscopic current-voltage relation at a saturating cyclic GMP concentration. A, recordings from one patch. The membrane potential was held at 0, and positive/negative voltage steps of +/- 10 mv increments and lasting 1 s were delivered, in the absence and the presence of 1000 μm-cyclic GMP. The steady-state current amplitude at the end of each voltage step was measured. The current measurements in the two runs without cyclic GMP were averaged and then subtracted from the corresponding measurements with cyclic GMP. B, averaged current-voltage relation from seven patches. The current in each experiment was normalized to unity at 60 mv before averaging was done. Black circles show averaged current values; the horizontal bars show standard deviations of the currents, which are very small. The straight line is drawn through points between 0 and 60 mv, and is extrapolated linearly to positive voltages. From L. W. Haynes and K. W. Yau, 1990, Journal of Physiology (London) 429:

13 Practice Questions Choose the correct answer. 1. If a few positive charges were moved from the inside to the outside of a cell, the unbalanced negative charges would a. distribute uniformly in the cytoplasm b. end up at the membrane boundary c. diffuse from the place they were left unbalanced to their final destination d. violate the principle of electroneutrality 2. The Nernst potential describes a. The electrical force that together with the chemical force drive ions to move in a particular direction b. The resting potential of a cell c. The electrical force that balances the chemical force so that there is no net ion movement d The potential at which ion current reverses direction from an inward (Na + ) to an outward (K + ) current 3. The patch-clamp technique is a versatile technique enabling recording of ion channel activity in several modes a. The on-cell or cell-attached recording records the activity of all the channels present in the entire cell b. The whole-cell configuration records the activity of one or a few channel molecules out of the whole cell c. The excised patch recordings (inside-out or outside-out) enable the experimenter to easily change the intracellular solution (i.e. bath solution) d. The gigaohm seal between the membrane and the glass pipette increases the signal to noise ratio so greatly that one can resolve the activity of a single protein in real time. 4. A particular mammalian cell displays a chloride equilibrium potential of -60 mv. Due to a high resting potassium conductance (K + equilibrium is at -90 mv) the cell s resting potential is at -80 mv. Please check the correct answer. a) What would the direction of the chloride and potassium currents be at rest? Chloride: inward outward no net current Potassium: inward outward no net current b) What would the direction of the chloride and potassium ion movements be at rest? Chloride: inward outward no net movement Potassium: inward outward no net movement Answer the following: 5. Assume that a particular cell is equally permeable to chloride and potassium ions and that g K = g Cl. If the equilibrium potential for chloride is -60 mv, while for potassium is -90 mv, what would you predict the resting membrane potential to be? Show all work. 6. Describe how the voltage clamp technique works to keep the membrane voltage from changing.

14 Answers to Practice Questions: 1b 2c 3d 4a: Chloride current is inward; Potassium current is outward 4b: Chloride ion movement is outward; Potassium ion movement is outward 5. At rest I K = -I Cl (inward and outward currents are equal and opposite in direction so there is no net current). Thus g K (V r - E K ) = -g Cl (V r - E Cl ) g K (V r - (-90 mv)) = -g Cl (V r - (-60 mv)) g K (V r +90 mv) = -g Cl (V r +60 mv) (V r +90 mv) = -(V r +60 mv) 2V r = -150 mv V r = -75 mv 6. Two microelectrodes are inserted into a cell: one is connected to a voltmeter to measure the transmembrane potential; the second is hooked up to a tunable current source (battery of variable output), which allows us to inject current into the cell. These electrodes are then connected to a feedback circuit that compares the measured voltage across the membrane with the voltage desired by the experimenter. If these two values differ, then current is injected into the cell to compensate for this difference. Thus the amount of current we provide equals the amount of current passing through the cell membrane. Hence with a voltage clamp experiment we get both the amount of current flowing at the particular membrane voltage that we are clamping the membrane. Measuring the amount of current flowing at different membrane voltages allows us to plot the current-voltage relationship for a particular ion channel thus revealing its conductance (inverse of resistance) characteristics.

15 Extra Problems (Answers to be provided on eboard) 1. One use of concentration gradients of ions across cell membranes is to drive the flow of ions during action potentials of excitable cells. A concentration gradient of ions across a membrane may be expressed in terms of an electrical potential at equilibrium by use of the Nernst Equation. a) The concentrations of some of the ions inside (i) and outside (o) of a particular muscle cell are as follows: Na + o = 140 mm Na + i = 10 mm K + o = 4 mm K + i = 140 mm Ca 2+ o = 1 mm Ca 2+ i = 10-4 mm Calculate the equilibrium potential for each of the ions in the muscle cell. b) The actual measured membrane potential for the muscle cell was -90 millivolts. From this information, what conclusion can you draw concerning the relative conductances of sodium and potassium in these cells at rest (i.e. in the absence of action potentials) assuming that sodium and potassium are the only ions that contribute to membrane potentials. Is this last assumption valid? c) The value of the membrane potential at the peak of the action potential is +25 mv. Which ion species is most conductive at the peak of the action potential? 2. One way to measure membrane potentials in cells or organelles relies on the use of lipid-soluble ions like TPP +, which distribute themselves passively across membranes and achieve transmembrane concentration gradients which depend on the membrane potential. A suspension of mitochondria is exposed to 10 μm TPP +. At equilibrium, the intramitochondrial TPP + concentration is measured as 3 mm. What is the membrane potential across the mitochondrial membrane? 3. Suppose there were a neurotransmitter which selectively opened channels for protons. If the external ph is 7.4 and the intracellular ph is 7.0, and the resting potential is 90 mv, would the transmitter be excitatory (depolarizing) or inhibitory (hyperpolarizing)? 4. Cl - ions permeate skeletal muscle membranes and are (almost) passively distributed. In an unstimulated skeletal muscle fiber, where does the Nernst equilibrium potential for Cl - lie relative to V Na and V K? a) Does the presence of a chloride permeability have any effect on the shape of the action potential (assume that the chloride permeability is not voltage dependent but that it is time-dependent)? b) Is there a net influx or efflux of Cl - ions during the action potential? Gamma-amino-butyric acid (GABA) is a neurotransmitter which opens chloride selective channels (e.g. in spinal cord neurons). c) In a neuron with a resting potential of 80 mv, what happens to the membrane potential when GABA is added? d) Will GABA change the threshold for action potential generation (assume no direct action of GABA on any channels other than Cl - channels)? e) If so, in which direction will the threshold move?

16 5. Assume that at rest a particular neuron is permeable to potassium and sodium ions. If you are given values for E K = -89 mv and for E Na = +60 mv then calculate the resting potential given that in this cell g k = 5 g Na.