Lecture goals: Learning Objectives

Similar documents
Channels can be activated by ligand-binding (chemical), voltage change, or mechanical changes such as stretch.

Membrane Potentials, Action Potentials, and Synaptic Transmission. Membrane Potential

Membrane Protein Channels

MEMBRANE POTENTIALS AND ACTION POTENTIALS:

6.3.4 Action potential

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES

Neurophysiology. Danil Hammoudi.MD

Physiology Unit 2. MEMBRANE POTENTIALS and SYNAPSES

Overview Organization: Central Nervous System (CNS) Peripheral Nervous System (PNS) innervate Divisions: a. Afferent

Quantitative Electrophysiology

Voltage-clamp and Hodgkin-Huxley models

Voltage-clamp and Hodgkin-Huxley models

Quantitative Electrophysiology

لجنة الطب البشري رؤية تنير دروب تميزكم

Rahaf Nasser mohammad khatatbeh

Nerve Signal Conduction. Resting Potential Action Potential Conduction of Action Potentials

Neural Conduction. biologyaspoetry.com

STUDIES OF CHANGING MEMBRANE POTENTIAL * : 1. BASIC ELECTRICAL THEORY, 2. GRADED AND ACTION POTENTIALS 3. THE VOLTAGE CLAMP AND MEMBRANE POTENTIALS

Biomedical Instrumentation

Nervous Systems: Neuron Structure and Function

Νευροφυσιολογία και Αισθήσεις

Lecture 10 : Neuronal Dynamics. Eileen Nugent

Membrane Physiology. Dr. Hiwa Shafiq Oct-18 1

Transport of ions across plasma membranes

Introduction to electrophysiology 1. Dr. Tóth András

Neurons, Synapses, and Signaling

LESSON 2.2 WORKBOOK How do our axons transmit electrical signals?

BME 5742 Biosystems Modeling and Control

All-or-None Principle and Weakness of Hodgkin-Huxley Mathematical Model

COGNITIVE SCIENCE 107A

BIOL Week 5. Nervous System II. The Membrane Potential. Question : Is the Equilibrium Potential a set number or can it change?

General Physics. Nerve Conduction. Newton s laws of Motion Work, Energy and Power. Fluids. Direct Current (DC)

Supratim Ray

Fundamentals of the Nervous System and Nervous Tissue

! Depolarization continued. AP Biology. " The final phase of a local action

Lecture 2. Excitability and ionic transport

BIOELECTRIC PHENOMENA

Ion Channel Structure and Function (part 1)

Neurons and Nervous Systems

Action Potential (AP) NEUROEXCITABILITY II-III. Na + and K + Voltage-Gated Channels. Voltage-Gated Channels. Voltage-Gated Channels

Chapter 9. Nerve Signals and Homeostasis

4. Active Behavior of the Cell Membrane 4.1 INTRODUCTION

Action Potentials & Nervous System. Bio 219 Napa Valley College Dr. Adam Ross

Resting membrane potential,

Nervous System: Part II How A Neuron Works

Chapter 48 Neurons, Synapses, and Signaling

PROPERTY OF ELSEVIER SAMPLE CONTENT - NOT FINAL

Signal processing in nervous system - Hodgkin-Huxley model

Introduction to electrophysiology. Dr. Tóth András

Topics in Neurophysics

CELL BIOLOGY - CLUTCH CH. 9 - TRANSPORT ACROSS MEMBRANES.

Nervous System Organization

ACTION POTENTIAL. Dr. Ayisha Qureshi Professor MBBS, MPhil

Neuroscience 201A Exam Key, October 7, 2014

Chapter 1 subtitles Ion gradients

BIOLOGY 11/10/2016. Neurons, Synapses, and Signaling. Concept 48.1: Neuron organization and structure reflect function in information transfer

Lecture Notes 8C120 Inleiding Meten en Modelleren. Cellular electrophysiology: modeling and simulation. Nico Kuijpers

NEURONS, SENSE ORGANS, AND NERVOUS SYSTEMS CHAPTER 34

Cellular Electrophysiology. Cardiac Electrophysiology

Slide 1. Slide 2. Membrane Transport Mechanisms II and the Nerve Action Potential. Epithelia

Naseem Demeri. Mohammad Alfarra. Mohammad Khatatbeh

2401 : Anatomy/Physiology

Nervous Tissue. Neurons Neural communication Nervous Systems

Neurons, Synapses, and Signaling

Chapter 3. Voltage- Dependent Membrane Permeability. Overview. Ionic Currents Across Nerve Cell Membranes

QUESTION? Communication between neurons depends on the cell membrane. Why is this so?? Consider the structure of the membrane.

SUMMARY OF THE EVENTS WHICH TRIGGER AN ELECTRICAL IMPUSLE IN NERVE CELLS (see figures on the following page)

Mathematical Foundations of Neuroscience - Lecture 3. Electrophysiology of neurons - continued

9 Generation of Action Potential Hodgkin-Huxley Model

PHYSIOLOGY CHAPTER 9 MUSCLE TISSUE Fall 2016

Transmission of Nerve Impulses (see Fig , p. 403)

Housekeeping, 26 January 2009

Neurons. 5 th & 6 th Lectures Mon 26 & Wed 28 Jan Finish Solutes + Water. 2. Neurons. Chapter 11

STEIN IN-TERM EXAM -- BIOLOGY FEBRUARY 12, PAGE 1 of 7

The nerve impulse. INTRODUCTION

Nervous Tissue. Neurons Electrochemical Gradient Propagation & Transduction Neurotransmitters Temporal & Spatial Summation

Introduction and the Hodgkin-Huxley Model

In the experiment shown in Figure 3-8,

Ion Channels. 6 th December, Touqeer Ahmed PhD Atta-ur-Rahman School of Applied Biosciences National University of Sciences and Technology

6 Mechanotransduction. rotation

3.3 Simulating action potentials

Membrane Potentials and Action Potentials

Supplementary Figure 1

Module Membrane Biogenesis and Transport Lecture 15 Ion Channels Dale Sanders

Deconstructing Actual Neurons

Lecture 04, 04 Sept 2003 Chapters 4 and 5. Vertebrate Physiology ECOL 437 University of Arizona Fall instr: Kevin Bonine t.a.

PNS Chapter 7. Membrane Potential / Neural Signal Processing Spring 2017 Prof. Byron Yu

Neurons. The Molecular Basis of their Electrical Excitability

Control and Integration. Nervous System Organization: Bilateral Symmetric Animals. Nervous System Organization: Radial Symmetric Animals

Neurons, Synapses, and Signaling

Organization of the nervous system. Tortora & Grabowski Principles of Anatomy & Physiology; Page 388, Figure 12.2

Universality of sensory-response systems

Nervous Lecture Test Questions Set 2

Particles with opposite charges (positives and negatives) attract each other, while particles with the same charge repel each other.

Curtis et al. Il nuovo Invito alla biologia.blu BIOLOGY HIGHLIGHTS KEYS

Neural Modeling and Computational Neuroscience. Claudio Gallicchio

Peripheral Nerve II. Amelyn Ramos Rafael, MD. Anatomical considerations

Electrophysiology of the neuron

Nervous System AP Biology

UNIT I INTRODUCTION TO ARTIFICIAL NEURAL NETWORK IT 0469 NEURAL NETWORKS

Transcription:

Title: Membrane Potential in Excitable Cells 1 Subtitle: Voltage-Gated Ion Channels and the basis of the Action Potential Diomedes E. Logothetis, Ph.D. Lecture goals: This first of two lectures will use our understanding of voltage-gated Na + and K + channel function to explain how an action potential is generated. Learning Objectives 1. Describe the ion substitution experiments performed by Hodgkin and Huxley in elucidating the ion responsible for the biphasic currents obtained in their voltage clamp experiments with the squid giant axon. What pharmacological agents can also distinguish between these currents? 2. Know how to plot and explain the current-voltage relationship of voltage-gated K+ and Na+ currents. 3. Contrast the topology of various voltage-gated channels and discuss their distinguishing structural feature involved in voltage sensitivity. 4. Know how voltage dependence is recognized in single-channel records obtained from voltage steps to different potentials. Predict the result of an ensemble average of many single-channel current records in response to steps to a particular voltage. 5. Predict the result of an ensemble average of many single-channel current records in response to steps to a particular voltage. 6. Plot the probability of Na+ channel opening and the Na+ current obtained as a function of voltage. 7. Describe an action potential in terms of its dependence on the time course of gna and gk. 8. Discuss the mechanism of Na+ channel inactivation and its control of the refractory period for generation of multiple action potentials. Reading See Lecture Notes and Physiology 3 rd Edition, L.S. Costanzo, Saunders, pp 17-22

Voltage-Gated Channels We will now consider voltage-gated ion channels, the class of ion channels that generate action potentials, the brief electrical signals by which excitable cells such as neurons, muscle and endocrine cells communicate with one another. I will present voltage-gated channels with a historical perspective, to underscore the monumental work of two British scientists, Hodgkin and Huxley (Nobel laureates 1963) whose work has influenced physiologists in as major a way as Watson and Crick influenced molecular biologists. Hodgkin and Huxley, used the voltage-clamp technique to study a relatively easy preparation, the squid giant axon. The experiment shown in Fig. 1 illustrates the currents they obtained using different voltage-clamp protocols. Figure 1. An axon is bathed in sea water and voltage clamped by the axial wire method. The membrane potential is held at 65 mv and then hyperpolarized in a step to 130 mv or depolarized in a step to 0 mv. Outward ionic current is shown as an upward deflection. The membrane permeability mechanisms are clearly asymmetrical. Hyperpolarization produces only a small inward current, while depolarization elicits a larger and biphasic current. A hyperpolarizing step from -65 mv (resting potential) to -130 mv failed to produce a sizable ionic current (Fig. 1A). In contrast when the axon was depolarized to 0 mv, a large transient inward current and a later outward sustained current was elicited. The ionic permeability of the membrane was changed in a dramatic manner by the step depolarization. Hodgkin and Huxley set out to determine which ions carry the current and how the underlying membrane permeability mechanisms work. First they reasoned that each ion seemed to move passively down its electrochemical gradient, so basic thermodynamic arguments could be used to predict whether the net movement of an ion would be inward or outward at a given membrane potential. For example current carried by Na + ions should be inward at potentials negative to the equilibrium potential E Na, and outward at potentials positive to E Na. If the membrane was voltage clamped to E Na, Na + ions should make no contribution to the membrane current, and if the current reverses sign around E Na, it is possibly carried by Na + ions. The same argument could be applied to K +, Ca 2+, and Cl -. Second, ions could be easily added to or removed from the external solutions. In the extreme, if a permeant ion were totally replaced by an impermeant ion, one component of current would be abolished. Using these approaches Hodkin and Huxley in 1952 identified two major components, I Na and I K, in the ionic current. They first noticed that the early transient currents reverse their sign from inward to outward at around +60 mv (also referred to as the "reversal potential") as would be expected if they are carried by Na + ions. The late currents, however, are outward at all test potentials (more positive to -65 mv), as would

be expected for a K + current with a reversal potential more negative than -65 mv. The identification of I Na was then confirmed by replacing most of the NaCl of the external medium by choline chloride (Fig. 2). Figure 2. An illustration of the classical a ionic substitution method for analyzing the ionic basis of voltage-clamp currents. Ionic currents are measured in a squid axon membrane stepped from a holding potential b of 65 mv to 9 mv. The component carried by Na + ions is dissected out by substituting impermanant choline ions for most of the external sodium. (a) The voltage protocol applied to an axon in c seawater, showing inward and outward ionic currents. (b) Axon in low-sodium solution with 90% of the NaCl substitued by choline chloride, showing only outward ionic current. (c) Algebraic difference between experimental records A and B, showing the transient inward component of current due to the inward movement of external Na + ions. The early inward transient current seen in the control ("100% Na + ") disappears in low Na + ("10% Na + "), while the late outward current remains. Subtracting the low-na + record from the control record reconstructs the transient time course of the Na + current, I Na, shown below. The properties of I Na and I K are frequently summarized in terms of current-voltage relations. Figure 3 shows the peak I Na and the late I K plotted as a function of the voltage-clamp potential. Figure 3. The axon membrane potential is stepped under voltage clamp from the negative holding ptential (V H or E H ) to various test potentials. Peak transient sodium current and steady-state potassium current from each trace are polotted against the test potential. The curvature of the two I-E relations between 50 to 20 mv reflects the voltage-dependent opening of Na + and K + channels. With modern terminology we would describe the Hodgkin and Huxley results to indicate that the axon membrane has two major types of ionic channels: Na + channels with a positive reversal potential, E Na, and K + channels with a negative reversal potential, E K. Both channels are largely closed at rest and they open with depolarization at

different rates. Nowdays, pharmacological tools exist to isolate Na + from K + current. Tetrodotoxin (TTX), a paralytic poison of some puffer fish, block selectively Na + channels. Tetraethylammonium ion (TEA) selectively blocks I K. Figure 4 shows a family of voltage steps producing a family of curents before and after application of the selective blockers. It is from traces like these that I-V curves are constructed. Figure 4. Pharmacological dissection of I Na and I K. A node of Ranvier under voltage clamp is held at 95 mv, hyperpolarized for 40 ms to 120 mv, and then depolarized to various potentials ranging from 60 to +60 mv in 15-mV steps. (A) Normal I Na and I K in Ringer s solution. (B) Same node after external addition of 300 nm TTX. Only I K remains. (C) Control measurements in another node. (D) Same node after external addition of 6 mm TEA. Only I Na remains. Voltage-gated channels are comprised of four (six membrane-spanning-segment) subunits as compared to the inward rectifier K + channels (having only two membranespanning-segments) that are not voltage-gated and are critical determinants of the resting potential. Figure 5. Topology of the intracellular ligand-gated channels we considered in the last lecture, compared to voltage-gated channels discussed in this lecture. Each of the four subunits in these channel proteins is thought to contain either two (M1-M2 for inward rectifier K + channels) or six membrane-spanning α helixes, S1-S6. In voltagegated channels the S4 segment contains several positively charged amino acids and is the voltagesensing α helix. The porelining P segment lies between S5 and S6. The N- terminus of the polypeptide, located in the cytosol, contains a globular domain essential for inactivation of the open channel.

What characterizes voltage-gated channels from other channel proteins is a unique motif found in the fourth transmembrane domain (S4), where in this predicted α helix K + channels are coded in single subunits just like the CNG channels. Na + and Ca 2+ voltagegated channels exist as four-subunit transcripts all coded in a single gene.every third amino acid residue is a positively charged arginine or lysine. Strong evidence has implicated this segment as an integral part of the molecular voltage sensor that upon depolarization moves away from the internal membrane surface and pulls the gate open allowing ions to flow down their electrochemical gradient (Fig. 5). Channel gating underlies variable conductance As mentioned above, ion channels fluctuate between open and closed states, the process we have called channel gating. With patch-clamp recordings, it has been possible, to measure the openings and closings of a single channel molecule directly. Figure 6 shows such recordings from a tiny "patch" of membrane that contains just one voltage-gated K + -channel. Two voltage steps are shown, one at -20 and the other at +20 mv. The current level fluctuates between the zero current level (closed channel) and a distinct open level. As expected for a K + channel, the current through the open channel is outward at both potentials, but the outward current is larger at +20 mv. The other important difference between the two current traces is the fact that the channel is open more often at the positive potential. The fraction of time a channel spends in the open state is called the open probability Po (Po ranges between 0 and 1). Figure 6. Single-channel recordings from a voltage-gated K + channel. The step to +20 mv elicits single channel currents of larger amplitude that the step to -20 mv, simply because of the greater driving force. Similarly, the step to +20 mv shows that the channel spends more time in the open state that it does during the step to -20 mv. It is precisely this increase in open probability seen at more depolarized voltages that characterizes these channels as voltage sensitive. Below in Figure 7 we see records from a patch-clamp experiment, where a single voltage-gated K + channel has been isolated (e.g. in the on-cell, inside-out or outside-out modes). The membrane voltage is clamped between two levels, first at 100 mv for a relatively long period of time and next to +50 mv for 40 ms. Below we see the gating of a single K + channel in response to this voltage step repeated nine times (top trace). Each voltage step produces a current record as shown in each of the records shown below. The dashed line indicates the zero current level (the channel is closed), while the transition to the positive current indicates the potassium flow for as long as the channel stays in the open position. Each time the channel opens and closes stochastically. This probabilistic nature of ion channel activity is very representative of single molecular function at large. If we were to signal average current records obtained from a voltage step of the membrane to the same value repeated many times (e.g. forty times in this example), we

would obtain the ensemble average record shown at the bottom of the figure. This macroscopic record is identical to what one would obtain if forty K + channels were to open simultaneously during a voltage step to the same potential. Figure 7. Gating in single K + channels. (a) Nine consecutive depolarizations yield noninactivating K+ channels. Notice the channel re-openings and the relatively long times for the first channel opening following the voltage stimulus (compare to figure 8 showing single Na + channel activity). (b) Ensemble average of 40 repeats of the same protocol. (From Hille: Ionic Channels of Excitable Membranes, 1992, Sinauer Press, p. 69) Figure 8 shows recordings of single Na + channels in response to a voltage pulse. Notice that currents are elicited with a smaller delay than K + currents, they activate more rapidly than K + currents and inactivate despite the maintenance of the depolarizing stimulus, a phenomenon termed inactivation (more about inactivation below). Figure 8. Cell-attached patch-clamp recording of unitary Na currents in a toe muscle of adult mouse during a voltage step from -80 to -40 mv. (A) Ten consecutive depolarization steps. One can see two superimposed channel openings in the first record but not in any of the others. Dashed line indicates the current level when Na channels are closed. (B) The ensemble mean of 352 repeats of the same protocol. (From Patlak and Ortiz, from Hille: Ionic Channels of Excitable Membranes, 1992, Sinauer Press, p. 68)

Figure 9 shows the behavior of macroscopic Na + currents (top two panels) and compares it to that of the total current in a neuron (containing K + channels as well bottom panel). If we were to plot the normalized current as a function of voltage (maximum current at 0 mv would be 100%) we can obtain a plot of the probability that Na + channels would be open at a given membrane potential (top panel). If we were to plot the macroscopic current flowing through many Na + channels, as a function of the membrane voltage steps that we clamp the plasma membrane, we would obtain the I-V plot shown in the middle panel. Figure 9 The open probability (Po) of Na channels increases steeply with depolarization. Thus, the effective Na + conductance is voltage dependent. The sodium current I Na = g Na (V-V Na ) with its voltage dependent conductance g Na = g max Po. g max is the (maximal) conductance of a Na channel when Po = 1. Net ionic current, obtained as the sum of the Na + current and the current through the resting membrane, here represented as I R =g R (V-V R ). Note N-shaped form with three zero-current intersects. Middle intersect is threshold; more about that in the next lecture. Many mechanisms exist which can alter Po in an ion channel. For the ion channels, which generate the action potential, the most important regulator of Po is the transmembrane voltage (membrane potential). These voltage-gated ion channels, contain as we mentioned earlier a voltage sensor connected to a "gate", which keeps the channel shut at negative potentials and opens it at more positive potentials. It is this voltage dependent change in Po of Na + and K + channels that underlies the conductance changes which lead to the nerve action potential. Note that a change in membrane potential has two independent effects on voltage-gated channels: (1) It changes the driving force for ion movement and thus the current through an open channel. (2) It changes the open probability Po. The voltage dependence of Po for voltage-gated Na + channels is shown in the top panel of Fig. 9. The second panel shows the voltage dependence of the Na + current where we have now scaled the maximum conductance g max (conductance of an open Na + channel) with Po to obtain I Na =g max Po (V-E Na ). The third panel of Fig. 9 finally shows the net membrane current as the sum of the Na + channel properties and the conductance of the resting membrane (mainly K + channels). For simplicity's sake we have not taken into account that Po for K + -channels is also voltage dependent. The net ionic membrane current has an N-shaped form with three intersects of the zero-current axis.

We will examine this panel in greater detail in the next lecture in an attempt to determine the threshold for action potential generation. For now, let us just consider the strikingly different effects of an increase in the Na + or K + conductance by membrane depolarization: Figure 10. Effect of membrane potential of voltage-gated K + and Na + channels. Thus, a depolarization which activates only K + channels terminates itself (negative feedback) whereas a depolarization which activates Na + channels becomes regenerative through positive feedback between depolarization and further opening of Na + channels. This positive feedback leads to the explosive upstroke of the action potential, once the threshold is reached (see below). The last property of Na + channels necessary for the understanding of the action potential is Na + channel inactivation. The voltage dependent increase of the opening probability of Na + channels is not maintained in time, but is rapidly transient. When Na + channels are depolarized rapidly, but then held at a positive potential, they open first but then enter soon a non conducting "inactivated" state (see Fig.8). The word "inactivated" means that as long as a Na + channel is in that state, it cannot be opened again by a subsequent depolarization. This property of Na + channels is an important factor in terminating the action potential (along with the K + channel mediated hyperpolarization). A cartoon of the three important functional states of a voltage gated Na + -channel is shown in Fig. 11. Figure 11. Ball-and-chain model of inactivation gating. Three gating states of the channel: Resting (R), Open (O) and Inactivated (I). The part of the channel that interacts with the inactivation ball becomes exposed only upon opening of the channel. Return of Na + channels from the inactivated to the resting (closed) state requires repolarization of the cell membrane. Another action potential can only be elicited after a large fraction of Na + channels have returned from the inactivated to the resting state, i.e. the Na + channels have become available to open once again. The time necessary for this

recovery from inactivation determines the so called "refractory period", the minimal time required before the cell can be excited again to fire the next action potential. In nerve and muscle cells, this refractory period is very short (a few milliseconds) but it is greatly prolonged in heart cells. Because inactivation of Na + channels during the action potential shuts down the inward current carried by those channels, Na + channel inactivation helps terminate the action potential. Maintained depolarizations will tend (after an initial Na + channel opening) to drive Na + channels into the inactivated state and therefore render a cell unexcitable. The relative number of resting versus inactivated Na + channels is steeply voltage dependent between -80 and -40 mv, so steady depolarizations in this potential range will greatly reduce the number of available (resting) Na + channels, and therefore the excitability of a cell. An example of a clinically important case of maintained depolarization is that of elevated serum potassium levels. Variable conductances: the generation of the action potential When excitable cells are depolarized from their resting potential beyond a certain level (threshold more about this in the next lecture), they respond with a relatively large, stereotyped potential change, the action potential. It is the action potential propagating away from the site of origin, which underlies impulse conduction in nerve, muscle and heart. We will deal with impulse conduction below but first let us consider the ionic basis for the generation of the action potential. Figure 12 shows the typical configuration of a nerve action potential. An initial depolarization from the resting potential leads into a very rapid depolarization, called the upstroke of the action potential. After the upstroke, the action potential peaks at a value positive to +30 mv and then repolarizes. In many cells repolarization is followed by an "undershoot" (afterhyperpolarization) of the membrane potential, which returns to its resting value a few milliseconds after the end of the action potential. Figure 12 We have seen in the last paragraph that the membrane potential is determined by the relative conductances of the ion channels in the cell membrane. ~45 years ago Hodgkin and Huxley concluded that the nerve action potential is generated by rapid conductance changes of Na + and K + channels. For this work which was the first successful utilization of the voltage clamp technique Hodgkin and Huxley received the Nobel Prize in 1963. In the presence of Na + and K + channels, the membrane potential can swing between E K =-90 mv and E Na =+60 mv as these channels open. At rest, g K >>g Na, and V is just slightly more positive than E K. Upstroke and peak of the action potential are the result of a massive increase of g Na, such that at the peak of the action potential the membrane potential approaches E Na because now g Na >>g K. Repolarization occurs because g Na falls back to its resting low level and g K increases. The resulting afterhyperpolarization marks the closest agreement between V m and E K, at this time g K >>>g Na. As g K returns to its normal level, V m depolarizes to the resting level. The timecourse of the changes in g Na and g K underlying the generation of the nerve action potential is also shown in the bottom panel.

How can an action potential be triggered? Where does the initial depolarizing stimulus come from in a real cell that triggers an action potential? The depolarizing stimulus can come from two sources. 1. Through electrical connections: From a cell that generates its own action potentials (i.e. a pacemaker cell such as in the heart or some neurons) and through specialized channels called gap junctions (that connect pacemaker cells to other non-pacemaking cells - see last lecture) current travels from one cell to another depolarizing the membrane and triggering an action potential. This is equivalent to injecting current through a microelectrode into a cell. 2. Through other channels: The initial depolarization can come from other channels, for example channels opened by neurotransmitters. Those could be the extracellular ligand-gated (neurotransmitter-activated) ion channels we encountered in the last lecture, such as the nicotinic acetylcholine receptor (AChR) [we will discuss in greater detail in a later lecture]. This channel is opened by the binding of two acetylcholine molecules and acts to depolarize the membrane of a skeletal muscle fiber (see last lecture). It is about equally permeable to both K + and Na +, so its equilibrium (or reversal) potential is near 0 mv. This means that it would carry inward current when V m <0 mv, for example at the resting potential. Another way to think about it is that near the resting potential there would be less driving force for K + ions to leave the cell (closer to E K ) than for Na + ions to enter the cell (farther away from E Na ). So when AChR channels open and the cell is at the resting potential, there will be a net inward current that can cause the initial depolarization that brings the cell membrane to the threshold potential. Cell capacitance, the metabolic cost of an action potential and The capacitance of a membrane determines the metabolic "cost" of an action potential, because as you may remember from my first lecture, the higher the capacitance, the more charge must be moved to generate the voltage of an action potential. The charge is supplied by the ionic current, and the greater the current, the more energy must be expended by the Na + /K + ATPase (see next lecture) to restore the ion gradients. Since the specific capacitance of a lipid bilayer is fairly constant at 1 μf/cm 2, we can calculate the number of Na + ions, which have to enter a cell to produce the typical depolarization of ~ 100 mv associated with the action potential upstroke. Let's assume a spherical cell (e.g. a nerve cell body) with a diameter of 20 μm. Membrane area = 4πr 2 = 1267 μm 2 Capacitance = 1267 μm 2 x 1 μf/cm 2 = 12.67 pf (1pF = 10-12 F) Charge = 12.67 pf x 100 mv = 1.267 x 10-12 C Each Na + ion carries the elementary charge of 1.6 x 10-19 C, so 1.267 x 10-12 C/1.6 x 10-19 C/Na + ion = 7.91 x 10 6 Na + ions/action potential. Will this lead to a measurable increase of the intracellular Na + concentration? Our cell has a volume of 4/3πr 3 = 4187 μm 3. At [Na + ] i = 15mM the cell contains

0.015 moles/liter x 6x10 23 ions/mole x 4187x10-15 liter = 3.77 x 10 10 Na + ions/cell So, each action potential will increase [Na + ] i by about 0.05 %, an increase that is not measurable chemically. After prolonged activity however, i.e. hundreds of action potentials, [Na + ] i will start rising and active pumping is required to maintain the transmembrane gradient. The relative change in ion concentration produced by each action potential also varies with the surface to volume ratio of a cell. Since in our example we have chosen a spherical cell (minimal surface to volume ratio), the relative Na + accumulation can be higher in cells of different geometries.

Practice Questions Choose the correct answer. 1. Voltage-dependent Na + channels show the following characteristics: a. They activate and inactivate rapidly at depolarized potentials b. The display a linear current-voltage relationship c. They display negative feedback regulation d. They underlie the repolarization phase of the action potential 2. Voltage-dependent K + channels underlying the squid giant axon action potential described by Hodgkin and Huxley show the following characteristics: a. They activate and inactivate rapidly at depolarized potentials b. They display a biphasic current-voltage relationship c. They display negative feedback regulation d. They underlie the upstroke phase of the action potential 3. The action potential of the squid giant axon is characterized by: a. At rest g K < g Na, and V R is just slightly positive than E K b. The upstroke and peak of the action potential are the result of a massive increase in g Na c. Repolarization occurs because g Na inactivates d. During the afterhyperpolarization g K < g Na Answer the following: 4. You are using the patch clamp technique to study the characteristics of a voltagedependent Na + channel from human cells. 5. How would you set up the patch clamp experiment to ensure that you measure sodium current alone? 6. If you performed the same experiment in the presence of tetrodotoxin (TTX), what would occur?

Answers to Practice Questions: 1a 2c 3b 4. Establish a gigaseal with the patch presumably containing the sodium channel. Only sodium should be present in the pipette. 5. In order to insure that no K + channels are functioning, TEA can be added. 6. Na + channel would be inhibited, thus no current would be observed at any test potentials.

Extra Problems (Answers to be provided on eboard) (1) The unicellular organism Paramecium caudatum shows a resting potential (RP) and an action potential (AP) that are similar in many respects to corresponding neural potentials. With the cell in typical pond water, the following measurements were made with an intracellular electrode: If one varies [K + ] out only, or [Ca 2+ ] out only, one observes the following: In the following questions, assume that the membrane of P. caudatum is normally permeable only to K +, Ca 2+, and water. (a) In the resting state, which of these is true? Explain concisely. i. G K > G Ca

ii. iii. G K = G Ca G K < G Ca (b) Which is true during the peak of the AP? Explain concisely. (c) Compared to the ionic concentrations of typical pond water, is [K + ] in greater than, equal to, or less than [K + ] out? Explain. (d) Compare also [Ca 2+ ] in with [Ca 2+ ] out. (e) When the posterior end of the organism is mechanically tapped, the membrane transiently hyperpolarizes. What conductance change(s) might be responsible? Explain. (2) You are using the technique of patch clamping to study the characteristics of a voltage-dependent Na + channel from human cells. (a) How would you set up the patch clamp experiment to ensure that you measure sodium current alone? (b) In experiment I, you maintain the membrane potential at 55 mv and determine the ability of Na + to move through the channel. You do the same in experiments II, III, and IV, but you maintain the membrane potentials at 40 mv, -20 mv, and +20 mv, respectively. The results in terms of Na + permeability are presented below: Experiment Clamped Membrane Potential Na + Permeability (mv) I -55 Absent II -40 Absent III -20 Present IV +20 Present Explain these results. What can you say about the approximate magnitude of the threshold potential for these cells? (c) If you performed the same experiment in the presence of tetrodotoxin (TTX), what would occur? (3) Ionic currents involved in the action potential of a cardiac muscle fiber have been studied by the voltage-clamp technique. When membrane potential is stepped from its resting value of 77 mv to 50 mv, an initial inward current is seen, which is carried by Na +. (a) Assume internal Na + concentration is normally 30 mm, and external Na + concentration is normally 150 mm. Draw to approximate scale the initial current traces for a step to 0 mv (zero mv) when external Na + concentration is normal; and when external Na + concentration is reduced to 30 mm, to 10 mm, and to 1 mm by replacement of Na + with an impermeable cation.

(b) If the peak inward Na + current with normal Na + concentration is 1 ma/cm 2, calculate the peak Na + current in each of the cases. (c) External Na + concentration is adjusted so that the initial inward current during a voltage clamp step to 50 mv is abolished. However, when the membrane potential is stepped from 77 mv to 20 mv, a longer-lasting inward current is recorded. Can this be due to the opening of further Na + channels at this membrane potential? Explain in one sentence. Assuming that internal and external K + and Cl - concentrations are comparable to those of frog muscle, could it be due to the opening of K + channels or of Cl - channels? Explain each answer. (d) The suggestion has been made that Ca 2+ carries the current. If external Ca 2+ concentration is 2.5 mm and internal Ca 2+ concentration is less than 10-2 mm, in what range is E Ca? Would the Ca 2+ current at a membrane potential of 20 mv be in the right direction to account for the observed current? Justify your answer. (4) When a normal, healthy squid axon is voltage-clamped in artificial sea water, one obtains the following membrane current record in response to a step change in membrane potential from V m = -70 mv to V m = 0 mv. Draw similar plots of I m vs. t (when V m is stepped from 70 mv to 0 mv) when the recordings are made under each of the following experimental conditions. For each of your plots, explain in one or two sentences how and why your graph differs from that drawn above. (a) TTX is added to the bath surrounding the axon. (b) TEA (tetraethylammonium) is added to the interior of the axon. (c) [Na + ] out is adjusted so that [Na + ] out = [Na + ] in. (d) [K + ] out is adjusted so that [K + ] out = [K + ] in. Ouabain, the specific inhibitor of the Na + -K + pump, is added to the bath five minutes before the experiment.