What are the three factors that influence the movement of ions in and out of the cell?

Loss of Membrane Potential and Development of Arrhythmias

Many acquired abnormalities of cardiac muscle or specialized fibers that result in arrhythmias produce a loss of the resting membrane potential (less negative). This change should be viewed as a symptom of an underlying abnormality, analogous to fever or jaundice, rather than as a diagnosis in and of itself, because both the ionic changes resulting in cellular depolarization and the more fundamental biochemical or metabolic abnormalities responsible for the ionic alterations probably have a number of causative factors.

Cellular depolarization can result from elevated [K+]o or decreased [K+]i, an increase in membrane permeability to Na+ (PNa increases), or a decrease in membrane permeability to K+ (PK decreases). Reference to the GHK equation for voltage (see earlier) illustrates that these changes alone or in combination make the transsarcolemmal diastolic voltage less negative.

Normal cells perfused by an abnormal milieu (e.g., hyperkalemia), abnormal cells perfused by a normal milieu (e.g., healed myocardial infarction), or abnormal cells perfused by an abnormal milieu (e.g., acute myocardial ischemia and infarction) can exist alone or in combination and reduce the resting membrane voltage. Each of these changes can have one or more biochemical or metabolic causes. For example, acute myocardial ischemia results in decreased [K+]i and increased [K+]o, release of norepinephrine, and acidosis, which may be related to an increase in intracellular Ca2+ and Ca2+-induced transient inward currents and accumulation of amphipathic lipid metabolites and oxygen free radicals. All these changes can contribute to the development of an abnormal electrophysiologic environment and arrhythmias during ischemia and reperfusion.

Introduction

An excitable membrane has a stable potential when there is no net ion current flowing across the membrane. Two factors determine the net flow of ions across an open ionic channel: the membrane potential and the differences in ion concentrations between the intracellular and the extracellular spaces. Because cells have negative intracellular potentials, the electrical force will tend to direct positively charged ions (cations such as sodium, potassium, and calcium) to flow into a cell. Hence, electrical forces will direct an inward flow of sodium, potassium, and calcium ions and an outward flow of chloride ions. The direction of ion movement produced by the ‘concentration force’ depends on the concentration differences for the ion between the intracellular and the extracellular compartments. Sodium, calcium, and chloride ions have higher extracellular concentrations compared with intracellular concentrations. The intracellular concentration of potassium is greater than the extracellular concentration. Concentration forces direct an inward flow of sodium, calcium, and chloride ions and an outward flow of potassium ions. The membrane potential at which the electrical and concentration forces are balanced for a given ion is called the equilibrium or Nernst potential for a given ion. At the equilibrium potential, inward and outward current movements are balanced for a specific ion due to balancing of the electrical and concentration forces. For a given cation, at membrane potentials that are negative compared with the equilibrium potential, ions flow into the cell, and at membrane potentials that are more positive than the equilibrium potential, current carried by the specific ion will flow out of the cell. The direction of current movement for a specific ion always tends to bring the membrane potential back to the equilibrium potential for that specific ion. Examples of approximate equilibrium potentials for ions in skeletal muscle are shown in Table 1.

Table 1. Equilibrium potentials

The membrane potential represents a balance among the equilibrium potentials of the ions to which the membrane is permeable. The greater the conductance of an ion, the more that ion will influence the membrane potential of the cell. The principal conductances responsible for establishing the resting membrane potential are that of chloride, potassium, and sodium. Chloride conductance is large in skeletal muscle fibers, in which it is mediated by skeletal muscle chloride channels. Peripheral nerve fibers have smaller chloride conductances. In skeletal muscle, chloride is the dominant membrane conductance, accounting for approximately 80% of the resting membrane conductance. Chloride channels in skeletal muscle are unusual in that they are gated by the presence of ions at the intracellular and extracellular orifices rather than by the membrane potential. The channel is likely to open when a chloride ion presents itself. The unique gating properties of chloride channels result in the chloride ions being distributed across the membrane in accord with the membrane potential. Consequently, chloride conductance does not set the membrane potential.

Instead, chloride conductance acts as a brake to make it more difficult for the membrane to depolarize. Therefore, chloride conductance provides an important stabilizing influence on the membrane potential.

The dominant ion in setting the resting membrane potential is potassium. Potassium conductance accounts for approximately 20% of the resting membrane conductance in skeletal muscle and accounts for most of the resting conductance in neurons and nerve fibers. This is primarily attributable to nongated ion channels, which are made up of inward rectifier and ‘slow-leak’ channels. Inward rectifier channels are responsible for maintaining the membrane potential in the absence of an excitation electrical current. It is the nongated ion channels that are responsible for differences in the electrical response of various cell types. For example, neurons, which contain nongated ion channels for potassium, sodium, and chloride, have a resting membrane potential that deviates from the calculated Nernst potential for K+ (especially at low concentrations) whereas glial cells, which contain nongated ion channels for only potassium, have a resting membrane potential that matches closely with the calculated Nernst potential for K+.

The small amount of sodium conductance in the resting skeletal muscle, or nerve membrane, results in the resting membrane potential being slightly positive or depolarized compared with the equilibrium potential for potassium (Table 2). The specific class of potassium channel that determines the resting membrane potential is the inward or anomalous rectifier potassium channel. Resting calcium conductance is exceedingly small. Therefore, calcium does not contribute to the resting membrane potential.

Table 2. Membrane potential under different conditions

During an action potential, Na+ channels open and the dominant membrane conductance is that of Na+. Consequently, the membrane potential is approximately the same as the Na+ equilibrium potential (Table 2).

Measuring the Membrane Potential

The method for measuring the membrane potential is simple in theory but often difficult in practice because of the small size of most of the cells and fibers.Figure 5-2 shows a small micropipette filled with an electrolyte solution. The micropipette is impaled through the cell membrane to the interior of the fiber. Another electrode, called theindifferent electrode, is then placed in the extracellular fluid, and the potential difference between the inside and outside of the fiber is measured using an appropriate voltmeter. This voltmeter is a highly sophisticated electronic apparatus that is capable of measuring small voltages despite extremely high resistance to electrical flow through the tip of the micropipette, which has a lumen diameter usually less than 1 micrometer and a resistance of more than 1 million ohms. For recording rapidchanges in the membrane potential during transmission of nerve impulses, the microelectrode is connected to an oscilloscope, as explained later in the chapter.

The lower part ofFigure 5-3 shows the electrical potential that is measured at each point in or near the nerve fiber membrane, beginning at the left side of the figure and passing to the right. As long as the electrode is outside the neuronal membrane, the recorded potential is zero, which is the potential of the extracellular fluid. Then, as the recording electrode passes through the voltage change area at the cell membrane (called theelectrical dipole layer), the potential decreases abruptly to −70 millivolts. Moving across the center of the fiber, the potential remains at a steady −70-millivolt level but reverses back to zero the instant it passes through the membrane on the opposite side of the fiber.

To create a negative potential inside the membrane, only enough positive ions to develop the electrical dipole layer at the membrane itself must be transported outward. The remaining ions inside the nerve fiber can be both positive and negative, as shown in the upper panel ofFigure 5-3. Therefore, transfer of an incredibly small number of ions through the membrane can establish the normal resting potential of −70 millivolts inside the nerve fiber, which means that only about 1/3,000,000 to 1/100,000,000 of the total positive charges inside the fiber must be transferred. Also, an equally small number of positive ions moving from outside to inside the fiber can reverse the potential from −70 millivolts to as much as +35 millivolts within as little as 1/10,000 of a second. Rapid shifting of ions in this manner causes the nerve signals discussed in subsequent sections of this chapter.

Abstract

Membrane potential is a fundamental biophysical parameter common to all of cellular life. Traditional methods to measure membrane potential rely on electrodes, which are invasive and low-throughput. Optical methods to measure membrane potential are attractive because they have the potential to be less invasive and higher throughput than classic electrode based techniques. However, most optical measurements rely on changes in fluorescence intensity to detect changes in membrane potential. In this chapter, we discuss the use of fluorescence lifetime imaging microscopy (FLIM) and voltage-sensitive fluorophores (VoltageFluors, or VF dyes) to estimate the millivolt value of membrane potentials in living cells. We discuss theory, application, protocols, and shortcomings of this approach.

Calculating the Membrane Potential

Walther Nernst in 1888 studied quantitatively the equilibrium condition for membranes permeable to only one ion, deriving an equation that still bears his name.l The conceptual basis for the Nernst equation is simply that at equilibrium the work required to move a given ion across the electrical potential gradient is equal and opposite to the work required to move it against its concentration gradient. The work (We) required to move a mole of an ion across voltage V is:

7.11We=zFV

wherez is the valence of the ion andF is Faraday's constant (the charge in 1 mole of monovalent ions). Hence it takes work to move positive ions to a more positive potential, whereas moving them to a less positive potential can be a source of work.

The work (Wc) required to change the concentration of a mole of the same ion (X) from [X]1 to [X]2 is:

7.12Wc=RTln[X]2[X]1

whereR is the gas constant andT is the temperature in °K. Hence it takes work to concentrate the ion ([X]2 > [X]1), whereas diluting a solution can be a source of work ([X]2 < [X]1).

At equilibrium We + Wc = 0, so

7.13zFVX=−RTln [X]2[X]1=RTln[X]1[X]2

3.3.2 Ions passively diffuse according to membrane potential

Membrane potential is a potential gradient that forces ions to passively move in one direction: positive ions are attracted by the ‘negative’ side of the membrane and negative ions by the ‘positive’ one. If we suppose that there is no concentration gradient for any ions (there is the same concentration of each ion in the extracellular and intracellular media), ions will diffuse according to membrane potential only: at a membrane potential Vm = −30 mV (Figure 3.5b), positively charged ions, the cations Na+, Ca2+ and K+, will move from the extracellular medium to the intracellular one according to membrane potential. In contrast, anions (Cl−) will move from the intracellular medium to the extracellular one.

39.6.1 Distributive probes

Membrane potential and some pH probes distribute themselves between the cell and the external milieu according to the property being evaluated. In the case of membrane potentials, this is the net negative charge of the cell with respect to the buffer in which it is suspended. In the case of pH probes, it is the difference between the extra- and the intra-cellular pH. These probes will distribute into every compartment across whose membrane a potential or pH gradient, respectively, exists, and therefore will be distributed within all cellular organelles. Unless one uses an image-enhanced fluorometer, the net membrane potential or pH will therefore be an average over the whole cell, its organelles and interior compartments.

Abstract

The membrane potential is a key aspect of cellular function and cell-to-cell signaling, and thereby ultimately body functions. This article describes the basic principles regarding electrical and chemical properties of ions and membranes, how these forces combine to determine electrochemical gradients that, when combined with membrane permeability give rise to membrane potentials. The article quantifies these principles using a range of simple equations such as Ohm’s Law, the Nernst equation, and the Goldman–Hodgkin–Katz (GHK) equation, and illustrates how to calculate the number of ions flowing in or out of a cell during typical membrane potential changes. The role of active and passive transporters in generating membrane potentials is briefly described, with a focus on the important role of a channel’s selectivity filter and gating mechanism. The final section discusses ways to experimentally measure membrane potentials and some caveats to be aware of when using these approaches. The challenges associated with an accurate measurement of membrane potential is illustrated by the range of absolute values reported for the resting membrane potential in hippocampal pyramidal neurons, and it may be a little misleading to consider a membrane as ever at ‘rest.’ Changes in membrane potential are a major cellular unit of organ and body function. It is hoped this article provides a simple and clear outline of the membrane potential and its underlying principles and mechanisms to assist students and researchers in cell biology.

Long-range membrane potential correlation: slow rhythm is correlated, but fast fluctuations are not

Membrane potential fluctuations in neocortical neurons contain multiple frequency components. The slow oscillation introduces a strong low-frequency component, while during the active states high-frequency components are most pronounced in the membrane potential fluctuations (Mukovski et al., 2007; Steriade et al., 1996a,b; Timofeev et al., 2001). To disentangle the contribution of the slow oscillation to the overall strong membrane potential correlation in neuron pairs from a possible contribution of other rhythms, we have extracted the low-frequency (< 5 Hz) and the high-frequency (> 10 Hz) components of membrane potential fluctuations using fast Fourier transformation (FFT). To extract fluctuations at frequencies < 5 Hz, we performed FFT of the signal, then set in the result all coefficients which corresponded to frequencies > 5 Hz to zero, and then performed an inverse FFT (Mukovski et al., 2007; Volgushev et al., 2003). High-frequency components were extracted using the similar procedure, but Fourier coefficients corresponding to frequencies < 10 Hz were set to zero in this case. Figure 9 shows unprocessed membrane potential traces of two neurons, which exhibited strong overall correlation (Fig. 9a, peak r = 0.79), and low-frequency and high-frequency components extracted from the membrane potential (Fig. 9b and c). As expected, fluctuations of the low-frequency components which contained the slow rhythm were strongly correlated in two neurons (Fig. 9b, peak r = 0.87). In contrast, fluctuations at frequencies > 10 Hz showed little correlation (Fig. 9c, peak r = 0.11). These results substantiate the conclusion that high correlation of membrane potential changes during slow oscillations is due to the slow rhythm of synchronously occurring transitions between the states, while fluctuations at higher frequencies, which are most pronounced during the active states, are not synchronized in distant neurons (Steriade et al., 1996a,b).

1.42.4.3.2 Membrane Potential

Membrane potential is one of the most commonly used parameters to determine cell viability. Electrical potential differences across membranes of prokaryotic and eukaryotic cells reflect the differential distribution and activity of such ions as Na+, Cl+, H+, and especially K+ across these biological membranes. These ionic gradients are generated by diverse membrane electrogenic pumps, with a contribution from each ion’s intrinsic membrane permeability. This membrane potential plays a major role in processes involving external stimulation of the cell, such as photosynthesis, nutrient and ion transport across the membrane, and signal transduction. In eukaryotic cells, major examples are cytoplasmic, mitochondrial (inner membrane), and lysosome membrane potential, which are negative inside the cell (or inside the organelles) relative to the external medium [3, 5, 7, 10, 11, 12, 14].

Changes in membrane potential involve either depolarization (i.e., a decrease in transmembrane potential) or hyperpolarization (an increase in the potential difference across the membrane). Only live cells can maintain membrane potential, and although membrane depolarization means a decrease in cell activity, it does not imply cell death.

Dyes generally used in FC are molecules with a single negative or positive net charge and are highly hydrophobic. Cyanine dyes, like DiOC6, have one net positive electric charge at physiological pH, so their cellular partitioning is the contrary of oxonol dyes. These dyes also partially accumulate in some organelles with negative inner membrane potential, like the mitochondria and endoplasmic reticula, and they are relatively toxic to cells. The cellular fluorescence intensity reflects membrane potential from the plasma membrane, as well as the mitochondrial and endoplasmic reticulum membranes [3, 5, 7, 10, 11, 12, 14].

The carbocyanine dye JC-1 can be used to study mitochondrial potential. At low local dye concentrations (low potential), the molecule is in the monomeric state with green fluorescence emission (527 nm) when excited at 488 nm. When mitochondria are hyperpolarized, the local dye concentration increases and forms polymer conjugates (J-conjugates) with a shifted red fluorescence (590 nm). This property makes possible ratiometric red/green fluorescence measurements in FC [3, 5, 7, 10, 11, 12, 14].

Rhodamine 123 is a dye for which incorporation depends on the voltage gradient of the mitochondrial inner membrane, and it is less toxic than carbocyanine dyes. This dye is used in tests for early modifications of energy metabolism [3, 5, 7, 10, 11, 12, 14].