- Email: [email protected]
Bioelectricity
CELL TO BEDSIDE
Bioelectricity Mario Delmar, MD, PhD From the Department of Pharmacology, SUNY Upstate Medical University, Syracuse, New York. Clinical cardiac electrophysiology (EP) serves as a great example of how basic scientific discovery eventually can translate into a medical revolution. Centuries have passed from Galvani’s detection of electrical events in living tissues, reported in 1791, to modern-day clinical EP. In the last ⬃200 years, information has flowed from basic physics to medical therapy and all fields in between, in a constant exchange of discoveries, progress, and applications that constitute the cardiac EP of today. It seems easy to ignore, while surrounded by the technical and medical complexities of clinical EP, the basic physical principles upon which this field is founded. The present article attempts to present, in a clinically relevant fashion, some of the basic principles of bioelectricity that serve as a foundation to understanding the electrical behavior of the heart.
Some basic definitions Electricity is based on the displacement of charge through conductors, as “propelled” by a driving force. Most elements in nature maintain an equal number of protons and electrons. However, under certain circumstances, electrons can be transferred from one element to another, thus creating an imbalance. This imbalance turns the element into a charged particle. For example, a sodium ion has an excess of positive charges, caused by the loss of an electron. A positively charged ion is called a cation. Conversely, negatively charged particles are called anions. Opposites attract. The attractions exerted by particles of different polarity establish much of the physical principles of electricity. Imagine a negatively charged particle (an anion) that enters the “area of influence” (i.e., the electrical field) of a cation. The natural attraction between the particles could only be countered by a force of opposing strength; in other words, work would be required to keep the anion away from its counterpart. Formally, the work required to displace a negatively charged particle from point A to point B in an electrical field is called potential difference (or voltage difference). In the context of bioelectricity, a voltage difference is created by the uneven accumulation of electric Address reprint requests and correspondence: Dr. Mario Delmar, Department of Pharmacology, SUNY Upstate Medical University, 766 Irving Avenue, Syracuse, New York 13210. E-mail address: [email protected]. (Received October 10, 2005; accepted October 20, 2005.)
charges on the sides of a cell membrane. In most cells, more anions are present inside than outside the cell. The uneven distribution of ions creates a membrane potential. Consider a source of voltage (a battery) with a positive pole and a negative pole. Imagine that each pole is connected to a plate, and each plate is immersed in a conductive material. Clearly, each pole will attract the opposing charge. Anions will flow to the positive plate and cations to the negative plate. This is a point of common confusion: the cathode is the negative plate because it attracts cations. Conversely, the anode is the positive plate because it attracts anions. Placing both ends in contact through a conductive material allows for the flow of charges toward the corresponding pole. This flow of charges establishes the electrical current. Formally, electrical current is defined as the amount of charge that passes through a cross-section of a conductor per unit of time. It is the accepted convention to designate the direction of electrical current according to the flow of the positive charges. The properties of the conductive material determine the amount of current that can move through it. Every material has a certain ability to conduct electricity. As stated earlier, a voltage difference applied across a conductive material will elicit a flow of current. The amount of current will be a function of (1) the amplitude of the voltage difference and (2) the resistance of the conductor to the flow of current. It seems intuitively obvious that the less resistive materials would allow for a larger current. On the other hand, the larger the voltage difference, the larger the current will be. These three variables (current, voltage, and resistance) relate to each other by the following formula: I ⫽ V⁄R, where I ⫽ current, V ⫽ voltage, and R ⫽ resistance. This simple equation, known as Ohm’s Law, is the very foundation of bioelectricity. In terms of units, current is measured in amperes (A), voltage in volts (V), and resistance in Ohms (⍀). Ohm’s law also can be written using the term conductance (G) to replace resistance. Simply, conductance is the inverse of resistance (G ⫽ 1/R), and Ohm’s law would be expressed as the following: I ⫽ VG. The unit of conductance is Siemens (S). The concepts of electricity can be visualized (all limitations notwithstanding) using running water as an analogy.
1547-5271/$ -see front matter © 2006 Heart Rhythm Society. All rights reserved.
doi:10.1016/j.hrthm.2005.10.023
Delmar
Bioelectricity
Figure 1 Electrical behavior of an ohmic resistor. A: Diagram of a simple electric circuit that includes a voltage source (V) connected to a resistor (R). Current flows from the anode to the cathode. B: Diagram of the time course of current (I) that would be expected in response to square voltage steps (V). C: Plot of current as a function of voltage, illustrating the position of traces a, b, and c per the diagram in B. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
Consider the case of a water tap connected to a hose. In that case, a closed valve holds a pressure gradient between the inside of a full pipe and the empty hose to which it is connected. If the valve were to be opened, a flow of water would move from the pipe through the hose. If the supply of water is constant, the water current moving through the hose will be a function of the resistance imposed by the hose (e.g., its diameter) as well as the water pressure at the tap. A small hose will be more resistive, thus allowing less current. If the pressure at the pipe decreases, the flow of water will decrease as well. One can see a direct proportionality between water pressure and current and an inverse relation between current and the resistive properties of the hose. Water runs along a pressure gradient: from the tap to the opening of the hose. Current moves from anode to cathode following the direction of flow of the positive charge. The principles established here apply to all movement of charge, no matter how complex the behavior of the parts. However, the simplest case to consider is that of a resistor of constant properties. The hose is rigid. Only the water pressure changes. If one correlates pressure with current, a linear function will arise. Similarly, if the resistor is constant, a larger voltage gradient will elicit a proportionately larger current. Figure 1 illustrates this situation. Voltage pulses of amplitudes a, b, and c are applied to the circuit illustrated in the left. Each voltage pulse generates a current flow of proportional amplitude. A plot of current as a function of voltage would show that the relation between the two variables is linear, and the slope of the straight line would be the conductance (inverse of the resistance). A linear relation between voltage and current is referred to as an ohmic IV relation. Voltage-independent resistors are also called ohmic resistors. Let us return to the example of the running water. Imagine a valve that allows for the flow of current in one direction but not in the other. The flow will increase proportionately with pressure, but only in one direction. Similarly, some conductors pass current in one direction only.
115 In other words, their conductivity (or their resistance) varies depending on the voltage applied. An example of a voltage-dependent resistor is shown in Figure 2. Panel A shows that the current increases proportionately with voltage pulses of negative polarity. However, only a small current results when pulses of positive polarity are applied (panel B). Moreover, the current amplitude does not increase with the increase in voltage amplitude. In this case, the resistor is voltage dependent: its conductivity (or resistance) depends on the voltage that is applied. In the particular example shown in Figure 2, it is said that the resistor rectifies. In this case, Ohm’s law continues to apply, except the term R is no longer a constant. It is a variable that is a function of voltage (fV). Ohmic resistors are time independent, that is, current changes instantly with voltage and remains at the same level for as long as voltage does not change (e.g., see the current “traces” in Figures 1 and 2). However, there are resistors whose conductance changes as a function of time. If the voltage gradient is held constant, the current amplitude may change. An example is shown in Figure 3. A voltage step is applied and yet current remains almost at zero. However, slowly and progressively, the amplitude of the current increases even though the voltage is held constant. The resistor in this example is time dependent. As in the case of
Figure 2 Electrical behavior of a resistor with rectifying properties. A: Voltage steps of negative polarity cause a current response of proportional amplitude. B: Positive voltage steps, on the other hand, do not induce progressively increasing currents. The current-voltage (IV) relations on the right further illustrate the point that these resistors are conductive only for voltage steps of negative polarity. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
116
Figure 3 Example of a current trace (I) elicited by a voltage step (V) across a resistor with time- and voltage-dependent properties. Many ion channels behave as voltage- and time-dependent resistors. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
voltage dependence, the basic equation for Ohm’s law still holds, except that the term R is not a constant but a variable that, in this case, is a function of time (fT). Hence, Ohm’s law when applied to a resistor that is voltage and time independent would be expressed as follows: I ⫽ V⁄R共f V,T兲, that is, current is equal to voltage divided by the resistance, which is a variable that depends on time and voltage.
Concept of equilibrium potential and the origin of the membrane potential A cell membrane separates two environments of different ionic composition: the intracellular and the extracellular space. An uneven ionic composition translates into an uneven distribution of electric charge. The latter creates a voltage difference across the membrane. Membrane potential is therefore the consequence of the unequal distribution of cations and anions across the lipid bilayer. In other words, the membrane potential is electrochemical in origin. The physical basis for the establishment of electrochemical potentials are defined by the Nernst equation. The basis of the Nernst equation is illustrated in Figure 4. A vessel is divided by a semipermeable membrane, which allows the passage of, for example, potassium but not chloride. At the onset of the experiment (panel A), potassium chloride is placed in compartment a. A concentration gradient is therefore established, whereby both potassium and chloride ions would tend to move toward compartment b. Given that the membrane is only permeable to potassium, only cations are displaced. An electric gradient is created, where negative charges are left behind by the migration of the cations to compartment b. Equilibrium is reached when the magnitude of the force pushing ions along the concentration gradient (from compartment a to b) is equal and
Heart Rhythm, Vol 3, No 1, January 2006 opposite to the magnitude of the electric gradient that attracts potassium ions back into compartment a. If an electrometer (a device that measures voltage gradients) were placed between compartments a and b, a voltage difference would be detected, compartment a being electronegative in relation to compartment 2. It seems intuitively obvious that the magnitude of such a voltage difference (which is called equilibrium potential) would be a function of (1) the selectivity and permeability of the membrane and (2) the concentration of the permeable ion on each side of the membrane. The Nernst equation establishes that the equilibrium potential (E) for a given ion (in this case, potassium [K]) is defined by the relation: EK ⫽ RT ⁄ Fln关K兴2 ⁄ 关K兴1. where T ⫽ temperature, R ⫽ a constant derived from the gas law, F ⫽ the Faraday constant, and [K]2 and [K]1 ⫽ the final concentrations of potassium ions in compartments b and a, respectively. A more complicated situation would arise if the compartments had more than one type of salt (e.g., potassium chloride as well as sodium chloride), and the permeability of the dividing membrane was different depending on the specific ion. In that case, the final value of the voltage difference would result from the concentrations of the two salts (sodium chloride and potassium chloride) and the specific permeabilities of the membrane for each one of the ions, namely, sodium, potassium, and chloride. In such a complex situation, the electrometer placed between compartments a and b will read a given value of voltage (V) that will be different from the value of the equilibrium potential (E) of each individual ion. The difference between the value
Figure 4 Concept of electrochemical potential. A container is divided into two compartments by a semipermeable membrane, which allows the passage of cations but not of anions. A: An ionizable solution is placed in compartment 1. B: A chemical gradient drives the cations into the second compartment; however, as cations migrate, an electrical gradient is formed in the opposite direction, caused by the uneven distribution of charges. C: An equilibrium eventually is reached when the magnitude of the electrical gradient is equal and opposite to that of the chemical gradient. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
Delmar
Bioelectricity
of V and the value of E for each individual ion is the force that, under a given circumstance, could drive the movement of the ion across the membrane. In other words, the driving force for the flow of a given ion x across the membrane is calculated by the subtraction of V ⫺ Ex; this term then can be inserted into Ohm’s law: Ix ⫽ 共V ⫺ Ex兲 ⁄ Rx. In other words, the amplitude of a current carried by ion x is equal to the driving force for that current divided by the resistance imposed by the membrane to the flux of x. Or, if we choose to use the term conductance (G) instead of resistance, then Ix ⫽ 共V ⫺ Ex兲Gx. At rest, most cardiac cells present a higher permeability for potassium than for any other ion. Potassium is distributed unevenly across the membrane: more concentrated inside than outside of the cell. The solution of the Nernst equation for potassium yields a value for EK of approximately ⫺90 mV (negative inside the cell; the reference electrode stays in the extracellular solution). Resting potential (V) of a cardiac myocyte is approximately ⫺85 mV. In other words, the resting potential of a cardiac cell is governed, mostly, by the Nernst equilibrium of potassium across the membrane. Ion channels in the cell membrane can be compared with resistors that are time and voltage dependent. The fact that potassium channels govern the resting potential is consequent to the fact that, at rest, potassium channels are open whereas other channels are closed. We can see from Ohm’s law that, regardless of the driving force, if the conductance to a given ion is near zero, current also will be near zero (any number multiplied by zero is zero). However, if the conductance for a given ion were to abruptly change, a current would ensue. An action potential results from a series of sequential changes in the conductance of several channels, allowing for the temporary flow of charges that alter the membrane potential, first toward zero and then back toward rest. The best example would be the sodium current. Sodium is more concentrated outside than inside the cell. The equilibrium potential for sodium is approximately ⫹40 mV. However, this driving force does not contribute to the resting potential because, at rest, the sodium channels are closed (i.e., GNa is near zero). However, sodium channels act as voltage-dependent resistors, and, if the cell is slightly depolarized (to approximately ⫺65 mV), the conductance for sodium greatly increases. Now, GNa is a sizable number that is multiplied by the driving force (V ⫺ (⫹40 mV)), yielding a large value for INa. Sodium channels are also time dependent, and they close very shortly after they open. GNa then quickly drops to near zero again, and, with it, INa once again becomes negligible. This series of events is responsible for the upstroke of the action potential in all cardiac myocytes with the exception of nodal cells.
117
Frequently asked questions The previous paragraphs establish some simple principles. In the following paragraphs, I discuss a few additional concepts. To cover all areas of bioelectricity is a task that goes beyond the scope of this review. Instead, I have chosen to focus on a few questions that, at least in our experience, are often asked by those who begin their studies in basic EP. Given the limitations of space and subject, the range of questions is limited, but hopefully they will coincide with areas that the reader finds of interest.
Why do we refer to currents as “inward” or “outward”? The term relates to whether the charges are moving into or out of the cell. Remember that ions follow the direction of the concentration gradient as they flow through the corresponding channels. Also remember that the direction of current follows the direction of positive ions. For example, sodium is found at a higher concentration outside than inside of the cell. Consequently, once the sodium channels open, sodium ions flow into the cell. Because sodium carries a positive charge, the direction of the current is the same as the direction of the ion, and sodium currents are considered inwardly directed (or inward). By the same token, potassium ions are more concentrated in the intracellular than in the extracellular space. When the corresponding channels open, potassium ions will move from the inside to the outside of the cell, that is, in the outward direction. However, notice that the term refers not to the direction of flux of the ion but to the flow of the current. In the case of positive ions, both things coincide. However, a point of confusion arises when one defines the direction of current of an anion (i.e., an ion of negative charge). This issue is discussed below.
What is the direction of current of an anion? Remember that we follow the direction of the positive charge. Remember also that an anion moving in one direction is equivalent to a cation moving in the opposite direction. Imagine a chloride ion that is moving along a concentration gradient, from inside to outside of the cell. The direction of flux of the anion is outwardly. However, because we follow the positive charge, an outflow of an anion is considered an inward current (an influx of a cation). In summary, the direction of the chloride current (an anionic current) is opposite to the direction in which the actual chloride ion flows.
Why do sodium currents (in the voltage range of an action potential) have a negative sign and potassium currents a positive sign? We previously noted that membrane potential is measured in relation to an electrode that stays outside of the cell (the
118 reference electrode). At rest, there are more negative charges inside than outside of the cell and therefore the membrane potential is negative. Similarly, ionic currents are measured in relation to a reference electrode, which stays in the extracellular space. When the positive charges move away from the reference (into the cell), the current is negative. When the positive charges move toward the reference (out of the cell), the current is positive. This concept can be explained more formally if we use our knowledge of Ohm’s law and driving force. We said that the driving force for a current is the difference between the membrane potential and the equilibrium potential for the ion. Also, it is important to note that conductance (or resistance) is expressed as a positive number (there is no physical “negative resistance”). Therefore, if the cell is at, for example, ⫺60 mV and ENa is ⫹40 mV: INa ⫽ 共 ⫺ 60 ⫺ 共 ⫹ 40兲兲 GNa INa ⫽ ⫺ 100 共G兲, and the current is negative. On the other hand, the equilibrium potential for potassium in a normal cardiac ventricular myocyte is approximately ⫺90 mV. If the cell is at ⫺60 mV: IK ⫽ 共 ⫺ 60 ⫺ 共 ⫺ 85兲兲GK IK ⫽ 共 ⫺ 60 ⫹ 85兲 GK IK ⫽ 25 GK, and the current is of positive sign.
What is “inward-going rectification”? We discussed the fact that some resistors “rectify,” that is, their conductance is affected by the voltage gradient to which they are subjected. The first demonstration of rectification in a membrane channel was obtained by Frankenhaeuser1 in 1962. He observed that the outward potassium current in frog myelinated nerve was considerably greater than expected for a channel that behaved ohmically and referred to this phenomenon as outward-going rectification to indicate that the channels conducted more easily for outward-directed (outward-going) currents. It was not until years later that the opposite phenomenon was described in cardiac muscle (the current was called IK1). In this case, the current flowing inwardly is much larger than in the outward direction. In other words, the charges “go” when the voltage gradient brings them into the cell. To be consistent with the previously established terminology, this current was referred to as an inward-going rectifier. In summary, the type of rectification (inward-going or outward-going) is established in reference to the polarity with which the channel conducts.
Why is there little change in membrane voltage during the plateau phase of the action potential even though there are several active currents flowing through the membrane? Because membrane potential changes as a result of the net balance of currents, that is, the algebraic sum of charges
Heart Rhythm, Vol 3, No 1, January 2006 leaving and entering the cell. During the plateau phase, inward current (carried mostly by calcium ions) is countered by an outward current (carried by potassium) of similar amplitude but opposite direction. Hence, the balance of current is near zero (and membrane voltage changes very little), even though active currents are flowing in both directions. It is not until inward currents are inactivated that the balance shifts in favor of the outward currents and the cell repolarizes back to rest.
Why is rectification relevant to the morphology of the cardiac action potential? The IK1 current of a cardiac myocyte shows strong inward-going rectification. Accordingly, the channel prevents the passage of current in the outward direction. Because of this property, the amount of IK1 current flowing through the membrane within the voltage range of the plateau phase of the action potential is minimal. The importance of this phenomenon is better understood if we imagine what would happen in its absence. Without rectification, the amplitude of IK1 upon cell depolarization would be very large. Hence, the outward current would readily overcome the inward current during or immediately following the action potential upstroke. The membrane potential then would quickly return toward rest, giving no time for the calcium current to develop, thus interfering with the molecular processes that are fundamental to the contraction of the cell. Moreover, in the absence of a plateau phase, the refractory period of the ventricular cell would be greatly shortened. This would create the possibility of sustained contraction (tetanus) of the cardiac muscle. The latter, of course, would be incompatible with the normal mechanical function of the heart.
Can a channel be opened but pass no current? Yes. This happens when there is no driving force moving the current. For example, a gap junction channel can be opened, but if there is no voltage difference between the cells, there will be no flow of current. Similarly, the resting membrane potential of most cardiac myocytes is near the equilibrium potential for potassium. At that level of voltage, there is very little current flowing through IK1 channels, yet the channels are opened (they are conductive). If the membrane potential deviates from rest, a driving force is created, thus allowing for current to move across the channels. The latter explains why potassium channels can be an important determinant of cell excitability.
Summary and conclusion This article outlines some basic principles of bioelectricity. As in any attempt at reviewing a broad field of science, much has been left unaddressed. However, the
Delmar
Bioelectricity
topics covered in this review serve to provide the reader with some background that may aid in understanding basic cellular EP and, from there, to a better understanding of the physical principles that control the electrical behavior of the heart.
Reference 1. Frankenhaeuser B. Instantaneous potassium currents in myelinated nerve fibers of Xenopus laevis investigated with voltage clamp technique. J Physiol 1962;160:40 – 45.
119 Suggested reading 1. Noble D. The Initiation of the Heartbeat. Second edition. Oxford, UK: Oxford University Press, 1985. 2. Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999. 3. Luderitz B. History of the Disorders of Cardiac Rhythm. Armonk, NY: Futura Publishing Co., 2002. 4. Carmeliet E, Vereecke J. Cardiac Cellular Electrophysiology (Basic Science for the Cardiologist). New York: Springer, 2002. 5. Aidley DJ. The Physiology of Excitable Cells. Cambridge, UK: Cambridge University Press, 1998. 6. Hille B. Ion Channels of Excitable Membranes. Third edition. Sunderland, MA: Sinauer Associates, 2001.
Bioelectricity Mario Delmar, MD, PhD From the Department of Pharmacology, SUNY Upstate Medical University, Syracuse, New York. Clinical cardiac electrophysiology (EP) serves as a great example of how basic scientific discovery eventually can translate into a medical revolution. Centuries have passed from Galvani’s detection of electrical events in living tissues, reported in 1791, to modern-day clinical EP. In the last ⬃200 years, information has flowed from basic physics to medical therapy and all fields in between, in a constant exchange of discoveries, progress, and applications that constitute the cardiac EP of today. It seems easy to ignore, while surrounded by the technical and medical complexities of clinical EP, the basic physical principles upon which this field is founded. The present article attempts to present, in a clinically relevant fashion, some of the basic principles of bioelectricity that serve as a foundation to understanding the electrical behavior of the heart.
Some basic definitions Electricity is based on the displacement of charge through conductors, as “propelled” by a driving force. Most elements in nature maintain an equal number of protons and electrons. However, under certain circumstances, electrons can be transferred from one element to another, thus creating an imbalance. This imbalance turns the element into a charged particle. For example, a sodium ion has an excess of positive charges, caused by the loss of an electron. A positively charged ion is called a cation. Conversely, negatively charged particles are called anions. Opposites attract. The attractions exerted by particles of different polarity establish much of the physical principles of electricity. Imagine a negatively charged particle (an anion) that enters the “area of influence” (i.e., the electrical field) of a cation. The natural attraction between the particles could only be countered by a force of opposing strength; in other words, work would be required to keep the anion away from its counterpart. Formally, the work required to displace a negatively charged particle from point A to point B in an electrical field is called potential difference (or voltage difference). In the context of bioelectricity, a voltage difference is created by the uneven accumulation of electric Address reprint requests and correspondence: Dr. Mario Delmar, Department of Pharmacology, SUNY Upstate Medical University, 766 Irving Avenue, Syracuse, New York 13210. E-mail address: [email protected]. (Received October 10, 2005; accepted October 20, 2005.)
charges on the sides of a cell membrane. In most cells, more anions are present inside than outside the cell. The uneven distribution of ions creates a membrane potential. Consider a source of voltage (a battery) with a positive pole and a negative pole. Imagine that each pole is connected to a plate, and each plate is immersed in a conductive material. Clearly, each pole will attract the opposing charge. Anions will flow to the positive plate and cations to the negative plate. This is a point of common confusion: the cathode is the negative plate because it attracts cations. Conversely, the anode is the positive plate because it attracts anions. Placing both ends in contact through a conductive material allows for the flow of charges toward the corresponding pole. This flow of charges establishes the electrical current. Formally, electrical current is defined as the amount of charge that passes through a cross-section of a conductor per unit of time. It is the accepted convention to designate the direction of electrical current according to the flow of the positive charges. The properties of the conductive material determine the amount of current that can move through it. Every material has a certain ability to conduct electricity. As stated earlier, a voltage difference applied across a conductive material will elicit a flow of current. The amount of current will be a function of (1) the amplitude of the voltage difference and (2) the resistance of the conductor to the flow of current. It seems intuitively obvious that the less resistive materials would allow for a larger current. On the other hand, the larger the voltage difference, the larger the current will be. These three variables (current, voltage, and resistance) relate to each other by the following formula: I ⫽ V⁄R, where I ⫽ current, V ⫽ voltage, and R ⫽ resistance. This simple equation, known as Ohm’s Law, is the very foundation of bioelectricity. In terms of units, current is measured in amperes (A), voltage in volts (V), and resistance in Ohms (⍀). Ohm’s law also can be written using the term conductance (G) to replace resistance. Simply, conductance is the inverse of resistance (G ⫽ 1/R), and Ohm’s law would be expressed as the following: I ⫽ VG. The unit of conductance is Siemens (S). The concepts of electricity can be visualized (all limitations notwithstanding) using running water as an analogy.
1547-5271/$ -see front matter © 2006 Heart Rhythm Society. All rights reserved.
doi:10.1016/j.hrthm.2005.10.023
Delmar
Bioelectricity
Figure 1 Electrical behavior of an ohmic resistor. A: Diagram of a simple electric circuit that includes a voltage source (V) connected to a resistor (R). Current flows from the anode to the cathode. B: Diagram of the time course of current (I) that would be expected in response to square voltage steps (V). C: Plot of current as a function of voltage, illustrating the position of traces a, b, and c per the diagram in B. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
Consider the case of a water tap connected to a hose. In that case, a closed valve holds a pressure gradient between the inside of a full pipe and the empty hose to which it is connected. If the valve were to be opened, a flow of water would move from the pipe through the hose. If the supply of water is constant, the water current moving through the hose will be a function of the resistance imposed by the hose (e.g., its diameter) as well as the water pressure at the tap. A small hose will be more resistive, thus allowing less current. If the pressure at the pipe decreases, the flow of water will decrease as well. One can see a direct proportionality between water pressure and current and an inverse relation between current and the resistive properties of the hose. Water runs along a pressure gradient: from the tap to the opening of the hose. Current moves from anode to cathode following the direction of flow of the positive charge. The principles established here apply to all movement of charge, no matter how complex the behavior of the parts. However, the simplest case to consider is that of a resistor of constant properties. The hose is rigid. Only the water pressure changes. If one correlates pressure with current, a linear function will arise. Similarly, if the resistor is constant, a larger voltage gradient will elicit a proportionately larger current. Figure 1 illustrates this situation. Voltage pulses of amplitudes a, b, and c are applied to the circuit illustrated in the left. Each voltage pulse generates a current flow of proportional amplitude. A plot of current as a function of voltage would show that the relation between the two variables is linear, and the slope of the straight line would be the conductance (inverse of the resistance). A linear relation between voltage and current is referred to as an ohmic IV relation. Voltage-independent resistors are also called ohmic resistors. Let us return to the example of the running water. Imagine a valve that allows for the flow of current in one direction but not in the other. The flow will increase proportionately with pressure, but only in one direction. Similarly, some conductors pass current in one direction only.
115 In other words, their conductivity (or their resistance) varies depending on the voltage applied. An example of a voltage-dependent resistor is shown in Figure 2. Panel A shows that the current increases proportionately with voltage pulses of negative polarity. However, only a small current results when pulses of positive polarity are applied (panel B). Moreover, the current amplitude does not increase with the increase in voltage amplitude. In this case, the resistor is voltage dependent: its conductivity (or resistance) depends on the voltage that is applied. In the particular example shown in Figure 2, it is said that the resistor rectifies. In this case, Ohm’s law continues to apply, except the term R is no longer a constant. It is a variable that is a function of voltage (fV). Ohmic resistors are time independent, that is, current changes instantly with voltage and remains at the same level for as long as voltage does not change (e.g., see the current “traces” in Figures 1 and 2). However, there are resistors whose conductance changes as a function of time. If the voltage gradient is held constant, the current amplitude may change. An example is shown in Figure 3. A voltage step is applied and yet current remains almost at zero. However, slowly and progressively, the amplitude of the current increases even though the voltage is held constant. The resistor in this example is time dependent. As in the case of
Figure 2 Electrical behavior of a resistor with rectifying properties. A: Voltage steps of negative polarity cause a current response of proportional amplitude. B: Positive voltage steps, on the other hand, do not induce progressively increasing currents. The current-voltage (IV) relations on the right further illustrate the point that these resistors are conductive only for voltage steps of negative polarity. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
116
Figure 3 Example of a current trace (I) elicited by a voltage step (V) across a resistor with time- and voltage-dependent properties. Many ion channels behave as voltage- and time-dependent resistors. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
voltage dependence, the basic equation for Ohm’s law still holds, except that the term R is not a constant but a variable that, in this case, is a function of time (fT). Hence, Ohm’s law when applied to a resistor that is voltage and time independent would be expressed as follows: I ⫽ V⁄R共f V,T兲, that is, current is equal to voltage divided by the resistance, which is a variable that depends on time and voltage.
Concept of equilibrium potential and the origin of the membrane potential A cell membrane separates two environments of different ionic composition: the intracellular and the extracellular space. An uneven ionic composition translates into an uneven distribution of electric charge. The latter creates a voltage difference across the membrane. Membrane potential is therefore the consequence of the unequal distribution of cations and anions across the lipid bilayer. In other words, the membrane potential is electrochemical in origin. The physical basis for the establishment of electrochemical potentials are defined by the Nernst equation. The basis of the Nernst equation is illustrated in Figure 4. A vessel is divided by a semipermeable membrane, which allows the passage of, for example, potassium but not chloride. At the onset of the experiment (panel A), potassium chloride is placed in compartment a. A concentration gradient is therefore established, whereby both potassium and chloride ions would tend to move toward compartment b. Given that the membrane is only permeable to potassium, only cations are displaced. An electric gradient is created, where negative charges are left behind by the migration of the cations to compartment b. Equilibrium is reached when the magnitude of the force pushing ions along the concentration gradient (from compartment a to b) is equal and
Heart Rhythm, Vol 3, No 1, January 2006 opposite to the magnitude of the electric gradient that attracts potassium ions back into compartment a. If an electrometer (a device that measures voltage gradients) were placed between compartments a and b, a voltage difference would be detected, compartment a being electronegative in relation to compartment 2. It seems intuitively obvious that the magnitude of such a voltage difference (which is called equilibrium potential) would be a function of (1) the selectivity and permeability of the membrane and (2) the concentration of the permeable ion on each side of the membrane. The Nernst equation establishes that the equilibrium potential (E) for a given ion (in this case, potassium [K]) is defined by the relation: EK ⫽ RT ⁄ Fln关K兴2 ⁄ 关K兴1. where T ⫽ temperature, R ⫽ a constant derived from the gas law, F ⫽ the Faraday constant, and [K]2 and [K]1 ⫽ the final concentrations of potassium ions in compartments b and a, respectively. A more complicated situation would arise if the compartments had more than one type of salt (e.g., potassium chloride as well as sodium chloride), and the permeability of the dividing membrane was different depending on the specific ion. In that case, the final value of the voltage difference would result from the concentrations of the two salts (sodium chloride and potassium chloride) and the specific permeabilities of the membrane for each one of the ions, namely, sodium, potassium, and chloride. In such a complex situation, the electrometer placed between compartments a and b will read a given value of voltage (V) that will be different from the value of the equilibrium potential (E) of each individual ion. The difference between the value
Figure 4 Concept of electrochemical potential. A container is divided into two compartments by a semipermeable membrane, which allows the passage of cations but not of anions. A: An ionizable solution is placed in compartment 1. B: A chemical gradient drives the cations into the second compartment; however, as cations migrate, an electrical gradient is formed in the opposite direction, caused by the uneven distribution of charges. C: An equilibrium eventually is reached when the magnitude of the electrical gradient is equal and opposite to that of the chemical gradient. (Reproduced with permission from Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999.)
Delmar
Bioelectricity
of V and the value of E for each individual ion is the force that, under a given circumstance, could drive the movement of the ion across the membrane. In other words, the driving force for the flow of a given ion x across the membrane is calculated by the subtraction of V ⫺ Ex; this term then can be inserted into Ohm’s law: Ix ⫽ 共V ⫺ Ex兲 ⁄ Rx. In other words, the amplitude of a current carried by ion x is equal to the driving force for that current divided by the resistance imposed by the membrane to the flux of x. Or, if we choose to use the term conductance (G) instead of resistance, then Ix ⫽ 共V ⫺ Ex兲Gx. At rest, most cardiac cells present a higher permeability for potassium than for any other ion. Potassium is distributed unevenly across the membrane: more concentrated inside than outside of the cell. The solution of the Nernst equation for potassium yields a value for EK of approximately ⫺90 mV (negative inside the cell; the reference electrode stays in the extracellular solution). Resting potential (V) of a cardiac myocyte is approximately ⫺85 mV. In other words, the resting potential of a cardiac cell is governed, mostly, by the Nernst equilibrium of potassium across the membrane. Ion channels in the cell membrane can be compared with resistors that are time and voltage dependent. The fact that potassium channels govern the resting potential is consequent to the fact that, at rest, potassium channels are open whereas other channels are closed. We can see from Ohm’s law that, regardless of the driving force, if the conductance to a given ion is near zero, current also will be near zero (any number multiplied by zero is zero). However, if the conductance for a given ion were to abruptly change, a current would ensue. An action potential results from a series of sequential changes in the conductance of several channels, allowing for the temporary flow of charges that alter the membrane potential, first toward zero and then back toward rest. The best example would be the sodium current. Sodium is more concentrated outside than inside the cell. The equilibrium potential for sodium is approximately ⫹40 mV. However, this driving force does not contribute to the resting potential because, at rest, the sodium channels are closed (i.e., GNa is near zero). However, sodium channels act as voltage-dependent resistors, and, if the cell is slightly depolarized (to approximately ⫺65 mV), the conductance for sodium greatly increases. Now, GNa is a sizable number that is multiplied by the driving force (V ⫺ (⫹40 mV)), yielding a large value for INa. Sodium channels are also time dependent, and they close very shortly after they open. GNa then quickly drops to near zero again, and, with it, INa once again becomes negligible. This series of events is responsible for the upstroke of the action potential in all cardiac myocytes with the exception of nodal cells.
117
Frequently asked questions The previous paragraphs establish some simple principles. In the following paragraphs, I discuss a few additional concepts. To cover all areas of bioelectricity is a task that goes beyond the scope of this review. Instead, I have chosen to focus on a few questions that, at least in our experience, are often asked by those who begin their studies in basic EP. Given the limitations of space and subject, the range of questions is limited, but hopefully they will coincide with areas that the reader finds of interest.
Why do we refer to currents as “inward” or “outward”? The term relates to whether the charges are moving into or out of the cell. Remember that ions follow the direction of the concentration gradient as they flow through the corresponding channels. Also remember that the direction of current follows the direction of positive ions. For example, sodium is found at a higher concentration outside than inside of the cell. Consequently, once the sodium channels open, sodium ions flow into the cell. Because sodium carries a positive charge, the direction of the current is the same as the direction of the ion, and sodium currents are considered inwardly directed (or inward). By the same token, potassium ions are more concentrated in the intracellular than in the extracellular space. When the corresponding channels open, potassium ions will move from the inside to the outside of the cell, that is, in the outward direction. However, notice that the term refers not to the direction of flux of the ion but to the flow of the current. In the case of positive ions, both things coincide. However, a point of confusion arises when one defines the direction of current of an anion (i.e., an ion of negative charge). This issue is discussed below.
What is the direction of current of an anion? Remember that we follow the direction of the positive charge. Remember also that an anion moving in one direction is equivalent to a cation moving in the opposite direction. Imagine a chloride ion that is moving along a concentration gradient, from inside to outside of the cell. The direction of flux of the anion is outwardly. However, because we follow the positive charge, an outflow of an anion is considered an inward current (an influx of a cation). In summary, the direction of the chloride current (an anionic current) is opposite to the direction in which the actual chloride ion flows.
Why do sodium currents (in the voltage range of an action potential) have a negative sign and potassium currents a positive sign? We previously noted that membrane potential is measured in relation to an electrode that stays outside of the cell (the
118 reference electrode). At rest, there are more negative charges inside than outside of the cell and therefore the membrane potential is negative. Similarly, ionic currents are measured in relation to a reference electrode, which stays in the extracellular space. When the positive charges move away from the reference (into the cell), the current is negative. When the positive charges move toward the reference (out of the cell), the current is positive. This concept can be explained more formally if we use our knowledge of Ohm’s law and driving force. We said that the driving force for a current is the difference between the membrane potential and the equilibrium potential for the ion. Also, it is important to note that conductance (or resistance) is expressed as a positive number (there is no physical “negative resistance”). Therefore, if the cell is at, for example, ⫺60 mV and ENa is ⫹40 mV: INa ⫽ 共 ⫺ 60 ⫺ 共 ⫹ 40兲兲 GNa INa ⫽ ⫺ 100 共G兲, and the current is negative. On the other hand, the equilibrium potential for potassium in a normal cardiac ventricular myocyte is approximately ⫺90 mV. If the cell is at ⫺60 mV: IK ⫽ 共 ⫺ 60 ⫺ 共 ⫺ 85兲兲GK IK ⫽ 共 ⫺ 60 ⫹ 85兲 GK IK ⫽ 25 GK, and the current is of positive sign.
What is “inward-going rectification”? We discussed the fact that some resistors “rectify,” that is, their conductance is affected by the voltage gradient to which they are subjected. The first demonstration of rectification in a membrane channel was obtained by Frankenhaeuser1 in 1962. He observed that the outward potassium current in frog myelinated nerve was considerably greater than expected for a channel that behaved ohmically and referred to this phenomenon as outward-going rectification to indicate that the channels conducted more easily for outward-directed (outward-going) currents. It was not until years later that the opposite phenomenon was described in cardiac muscle (the current was called IK1). In this case, the current flowing inwardly is much larger than in the outward direction. In other words, the charges “go” when the voltage gradient brings them into the cell. To be consistent with the previously established terminology, this current was referred to as an inward-going rectifier. In summary, the type of rectification (inward-going or outward-going) is established in reference to the polarity with which the channel conducts.
Why is there little change in membrane voltage during the plateau phase of the action potential even though there are several active currents flowing through the membrane? Because membrane potential changes as a result of the net balance of currents, that is, the algebraic sum of charges
Heart Rhythm, Vol 3, No 1, January 2006 leaving and entering the cell. During the plateau phase, inward current (carried mostly by calcium ions) is countered by an outward current (carried by potassium) of similar amplitude but opposite direction. Hence, the balance of current is near zero (and membrane voltage changes very little), even though active currents are flowing in both directions. It is not until inward currents are inactivated that the balance shifts in favor of the outward currents and the cell repolarizes back to rest.
Why is rectification relevant to the morphology of the cardiac action potential? The IK1 current of a cardiac myocyte shows strong inward-going rectification. Accordingly, the channel prevents the passage of current in the outward direction. Because of this property, the amount of IK1 current flowing through the membrane within the voltage range of the plateau phase of the action potential is minimal. The importance of this phenomenon is better understood if we imagine what would happen in its absence. Without rectification, the amplitude of IK1 upon cell depolarization would be very large. Hence, the outward current would readily overcome the inward current during or immediately following the action potential upstroke. The membrane potential then would quickly return toward rest, giving no time for the calcium current to develop, thus interfering with the molecular processes that are fundamental to the contraction of the cell. Moreover, in the absence of a plateau phase, the refractory period of the ventricular cell would be greatly shortened. This would create the possibility of sustained contraction (tetanus) of the cardiac muscle. The latter, of course, would be incompatible with the normal mechanical function of the heart.
Can a channel be opened but pass no current? Yes. This happens when there is no driving force moving the current. For example, a gap junction channel can be opened, but if there is no voltage difference between the cells, there will be no flow of current. Similarly, the resting membrane potential of most cardiac myocytes is near the equilibrium potential for potassium. At that level of voltage, there is very little current flowing through IK1 channels, yet the channels are opened (they are conductive). If the membrane potential deviates from rest, a driving force is created, thus allowing for current to move across the channels. The latter explains why potassium channels can be an important determinant of cell excitability.
Summary and conclusion This article outlines some basic principles of bioelectricity. As in any attempt at reviewing a broad field of science, much has been left unaddressed. However, the
Delmar
Bioelectricity
topics covered in this review serve to provide the reader with some background that may aid in understanding basic cellular EP and, from there, to a better understanding of the physical principles that control the electrical behavior of the heart.
Reference 1. Frankenhaeuser B. Instantaneous potassium currents in myelinated nerve fibers of Xenopus laevis investigated with voltage clamp technique. J Physiol 1962;160:40 – 45.
119 Suggested reading 1. Noble D. The Initiation of the Heartbeat. Second edition. Oxford, UK: Oxford University Press, 1985. 2. Jalife J, Delmar M, Davidenko J, Anumonwo JMB. Basic Cardiac Electrophysiology for the Clinician. Armonk, NY: Futura Publishing Co., 1999. 3. Luderitz B. History of the Disorders of Cardiac Rhythm. Armonk, NY: Futura Publishing Co., 2002. 4. Carmeliet E, Vereecke J. Cardiac Cellular Electrophysiology (Basic Science for the Cardiologist). New York: Springer, 2002. 5. Aidley DJ. The Physiology of Excitable Cells. Cambridge, UK: Cambridge University Press, 1998. 6. Hille B. Ion Channels of Excitable Membranes. Third edition. Sunderland, MA: Sinauer Associates, 2001.