Cell Physiology: Source Book

By Nicholas Sperelakis

A multi-authored and comprehensive text, Cell Physiology Source Book enables graduate students in various biological sub-disciplines to gain a thorough understanding of cell physiology. It begins with a reviewof the physical chemistry of solutions, protein structure, and membrane structure, and ends with an Appendix featuring reviews of electricity, electrochemistry, and cable properties of cells. In between, this book is loaded with information on membrane potentials, cell metabolism, signal transduction, transport physiology and pumps, membrane excitability and ion channels, synaptic transmission, sensory transduction, muscle contraction, excitation-contraction coupling, bioluminescence, photosynthesis, andplant cell physiology.
This exhaustive work provides graduate students with detailed and authoritative coverage of nearly all aspects of cell physiology. Such broad coverage of this field within a single source makes for a unique text.
Chapters written in a clear, concise, and didactic style, and appropriate reviews of basic physics and chemistry are among the many distinguishing features of this monumental treatise.

Comprehensive source-book of cell physiology
Authoritative and multi-authored by leading experts in the field
Unique features include broad coverage and review of relevant physics, chemistry, and metabolism
Clear, concise, and didactic
Includes reviews of physical chemistry of solutions, protein structure, membrane structure, electrochemistry, and electricity
Topic covered include plant cell physiology, photosynthesis, bioluminescence, effects of pressure, cilia, and flagellae
Detailed treatise on ion channels and their regulation

• Language: English
• Publisher: Academic Press
• Release date: Oct 22, 2013
• ISBN: 9781483293677

Book preview

Sperelakis

SECTION I

Biophysical Chemistry, Electrochemistry, Metabolism, Second Messengers, and Ultrastructure

Outline

Chapter 1: Biophysical Chemistry of Cellular Electrolytes

Chapter 2: The Physiological Structure and Function of Proteins

Chapter 3: Lateral Lipid Domains and Membrane Function

Chapter 4: Ultrastructure of Cells

Chapter 5: Diffusion and Permeability

Chapter 6: Origin of Resting Membrane Potentials

Chapter 7: Gibbs–Donnan Equilibrium Potentials

Chapter 8: Energy Production and Metabolism

Chapter 9: Signal Transduction

Chapter 10: Calcium as an Intracellular Second Messenger: Mediation by Calcium Binding Proteins

1

Biophysical Chemistry of Cellular Electrolytes

Jeffrey C. Freedman

Publisher Summary

Biophysical chemistry is defined as the application of the concepts and methods of physical chemistry to the study of biological systems. Physical chemistry includes physiologically relevant subjects, such as thermodynamics, chemical equilibria and reaction kinetics, solutions and electrochemistry, properties and kinetic theory of gases, transport processes, surface phenomena, and molecular structure and spectroscopy. This chapter discusses the basic concepts of cell physiology by describing certain physicochemical properties of electrolytes and proteins that are relevant to an understanding of the structure and function of cells. All living cells contain proteins, salts, and water enclosed in membrane-bounded compartments. These biochemical and ionic cellular constituents, together with a set of genes, enzymes, substrates, and intermediates, function to maintain cellular homeostasis and enable cells to perform chemical, osmotic, mechanical, and electrical work. Concepts of biophysical chemistry are exemplified by human red blood cells, which lack membrane-bounded intracellular organelles and are devoid of the complexities introduced by intracellular compartments.

I Introduction

Biophysical chemistry may be defined as the application of the concepts and methods of physical chemistry to the study of biological systems. Physical chemistry includes such physiologically relevant subjects as thermodynamics, chemical equilibria and reaction kinetics, solutions and electrochemistry, properties and kinetic theory of gases, transport processes, surface phenomena, and molecular structure and spectroscopy. Many cellular physiological phenomena are best understood by a rigorous and comprehensive understanding of physical chemistry. Physical chemistry texts that specifically emphasize biological applications include those by Tinoco et al. (1985) and Eisenberg and Crothers (1979). Several outstanding monographs on biophysical chemistry are also available: Edsall and Wyman (1958), Tanford (1961), Cantor and Schimmel (1980), van Holde (1985), Silver (1985), and Bergethon and Simons (1990). This chapter and the next will introduce some of the basic concepts of cell physiology by describing certain physicochemical properties of electrolytes and proteins that are relevant to an under-standing of the structure and function of cells.

All living cells contain proteins, salts, and water enclosed in membrane-bounded compartments. These biochemical and ionic cellular constituents, together with a set of genes, enzymes, substrates, and intermediates, function to maintain cellular homeostasis and to enable cells to perform chemical, osmotic, mechanical, and electrical work. Homeostasis means that certain parameters, such as the cellular volume, the intracellular pH, and the intracellular concentrations of salts are maintained relatively constant in resting cells. To understand how cellular homeostasis is achieved, the electrolyte composition and the functions of specific ions in cells will be described first followed by a consideration of some physi-cochemical aspects of water and of solutions of salts and proteins. In this chapter, some concepts of biophysical chemistry will be exemplified by human red blood cells, which lack membrane-bounded intracellular organelles and are thereby devoid of the complexities introduced by intracellular compartments.

II Cell Cations

Potassium, sodium, calcium, and magnesium are the predominant biological cations. The ionic composition of the intracellular and extracellular solutions may be de-picted on bar graphs known as Gamblegrams, named after the physiologist J. L. Gamble, who used such diagrams extensively in analyzing the electrolyte balance of the blood and body fluids (Gamble, 1964). A Gamblegram for human red blood cells is shown in Fig. 1. The most abundant ion in the intracellular solution is potassium (K +) at 143 mM, whereas sodium ion (Na+) is only 7 mM (Funder and Wieth, 1966). In the extracellular fluid, Na+ predominates at approximately 145 mM, whereas K+ is only about 5 mM. The Na, K-ATPase, a transport protein located in the plasma membrane, specifically selects K+ from the Na+-rich medium and pumps it against the K+ concentration gradient (and electrochemical gradient) into the cytoplasmic solution. The same ionic pump specifically selects Na+ from the K + -rich cytoplasmic solution and extrudes it from the cell against the Na+ concentration gradient. This coupled active transport of K+ and Na+ uses metabolic energy obtained from the hydrolysis of ATP (for reviews, see Glynn, 1985; Läuger, 1991). At the same time that K+ is actively accumulated in the cell, it is also continually leaking out of the cell through a parallel pathway down its concentration gradient. The same is true for Na+ leaking into the cell. Steady-state distributions of K+ and Na+ are achieved by a balance between active pumping and passive leakage.

FIG. 1 Gamblegram for human red blood cells. The bar graphs illustrate the ionic composition of the intracellular and extracellular solutions, designated by i and o, respectively. Organic phosphates are represented by P−.

A quantitative model of the pump-leak theory that predicted the steady state Na+ and K+ concentrations in high-K+ and low-K+ red blood cells found in genetic variants of sheep was developed by Tosteson and Hoffman (1960).

As illustrated in Fig. 2, other transport systems that may also contribute to the steady-state intracellular ionic concentrations of red cells have since been discovered (for review, see Tosteson, 1981). These include Na/K/Cl co-transport and K/Cl cotransport (for review, see Dunham, 1990) and Na/H exchange. The pump-leak theory for red cells has been extended to include some of the effects of these additional cotransport pathways (Milanick and Hoffman, 1986).

FIG. 2 The principal membrane transport systems of human red blood cells. Starting with the Na+/K+ pump and the passive leakage pathways for Na+ and K+ on the right, and proceeding clockwise around the membrane, are K+/C1" cotransport, Na+/K+/Cl− cotransport, Cl−/HCO3− exchange, the Ca²+ pump with a Ca²+ leakage pathway, the Ca²+-activated K+ channel, and Cl− conductance. The steady-state concentrations of K+, Na+ and Ca²+ represent a balance between active pumping and passive leakage. Cl− and HCO3− are passively distributed at equilibrium with a membrane potential of −9 mV.

In excitable cells such as nerve and muscle, the Na+ and K+ concentration gradients created by the Na,K-ATPase are reduced by a small extent during each action potential. With each action potential, Na+ and K+ move down their concentration gradients through voltage-gated ion channels (see chapters on resting potential and excitability).

K+ also functions as a specific cofactor for the glycolytic enzyme pyruvate kinase. The maximal catalytic velocity follows the sequence K+ > Rb+ >> Cs+ ≥ Na+ > Li+. During in vitro protein synthesis, K+ maintains an active conformation of 50S ribosomal subunits that catalyze peptide bond formation. The order of selectivity for this effect is NH4+ ≥ Rb+ > K+ > Cs+; Na+ and Li+ are ineffective.

The widespread importance of calcium ion (Ca²+) in cellular physiology was first emphasized by L. V. Heilbrunn. Injections of various salts into frog skeletal muscle fibers revealed that Ca²+ is the only intracellular ion that induces muscle contraction. Ca²+ is pumped out of the sarcoplasm into the sarcoplasmic reticulum (SR), and also across the plasma membrane into the extracellular solution, by a Ca-ATPase. Release of Ca²+ from the SR initiates muscle contraction. Using skinned muscle fibers, in which the sarcolemma has been removed with fine needles, J. Gulati, R. J. Podolski, and others found that the tension exerted by myofilaments is directly proportional to the concentration of free Ca²+ in the sarcoplasm. Pumping of Ca²+ from the cytoplasm of muscle, red cells, and other cells across the plasma membrane normally results in a submicromolar steady-state intracellular concentration of Ca²+, whereas plasma Ca²+ is about 2.5 mM. The ratio of extracellular to intracellular Ca²+ concentrations is thus more than 1000, much greater than the ratio of about 25 for Na+. In human mammary glands, Ca²+ is secreted by exocytosis via the Golgi system into milk to a total concentration of about 10 mM. M. C. Neville and colleagues determined that about two-thirds of Ca²+ in milk is chelated to citrate and to casein or other proteins; the remainder is freely ionized in solution.

The classic experiments of S. Ringer established that plasma Ca²+ is essential for the sustained beating of isolated hearts. It is now known that an inward Ca²+ current down its concentration and electochemical gradient through an ion channel constitutes a major component of the cardiac action potential. Transient elevations of intracellular Ca²+ also occur in such processes as fertilization; cell division; exocytosis during neurotransmitter release; activation of platelets, neutrophils, and lymphocytes; and the hormonal activation of cells. Ca²+ is an essential cofactor in blood clotting and in the activation of complement and also has a structural role in membranes and in mineralization of bone, teeth, and other skeletal structures (for review, see Campbell, 1983).

Despite the importance of Ca²+ as a trigger and modulator in a variety of cell activities, too much intracellular Ca²+ is harmful to cells. For example, G. Gardos discovered that if intracellular Ca²+ rises to about 3 μM in human red blood cells, the K+ permeability dramatically increases (the Gardos effect). The increased K+ permeability is due to the opening of a Ca²+-activated K+ channel, resulting in loss of intracellular K+ and Cl−, accompanied by cell shrinkage (for review, see Schwarz and Passow, 1983). At higher levels of intracellular Ca²+, the smooth biconcave discoid form of human red cells converts first to an echinocytic form with spicules protruding from the membrane and then to a spherocytic form (Fig. 3). This effect of Ca²+ is a striking example of the profound influence that Ca²+ can exert on cell morphology. At still higher levels, Ca²+ activates a transglutaminase that cross-links cytoskeletal proteins. Ca²+ also activates degradative proteases and phospholipase C, which converts membrane phosphatidylcholine (lecithin) to diacylglycerol.

FIG. 3 Conversion of human red blood cell discocytes to echinocytes and then to spherocytes by elevated intracellular Ca²+ in the presence of the Ca²+ ionophore A23187, here shown with light microscopy using Nomarski interference contrast optics. The diameter of the normal discocytes is 8 μm.

In multicellular animals, the concentration of magne-sium ion (Mg²+) in both the extracellular and intracellular fluids is about 1 mM. Consequently, Mg²+, unlike Na+, K+, and Ca²+, does not act as a carrier of ionic current across ceil membranes or as a trigger for the initiation of cellular activities. Mg²+ ion, with a divalent positive charge and a diameter of 1.2 Å (Table 1), has the highest charge density of all of the ions found in cells. Consequently, Mg²+ binds readily to anionic sites, particularly to polyphosphates, such as ATP. MgATP is the substrate for all kinases and for some phosphatases, such as the Na,K-ATPase. Mg²+ is also a cofactor for the glycolytic enzyme enolase, glutamine synthetase, and other enzymes. Mg²+ is also tightly bound to porphyrin in chlorophyll, the primary biological molecule for capturing light energy (see chapter on photosynthesis).

TABLE 1

Ionic Diameters, Enthalpies of Hydration, and Mobilities

aRadii are from Pauling (1960).

bStandard enthalpies of hydration at 25°C are from Edsall and McKenzie (1978).

cMobilities in water at 25°C are from Hille (1992, p. 268).

III Cell Anions

The most abundant permeant anion in cells is chloride (Cl−), although its intracellular concentration is typically less than the extracellular concentration. Macromolecular cellular constituents, including nucleic acids and most cytoplasmic proteins, carry a net negative charge at physiological pH. Phosphorylated metabolic intermediates and organic acids are also negatively charged. In the red cell membrane, the phospholipids are distributed asymmetrically. The neutral phospholipids—phosphatidylcholine (PC) and sphingomyelin—are preferentially located in the outer hemileaflet of the lipid bilayer; the neutral phospholipid phosphatidylethanolamine (PE), together with phosphatidylinositol (PI) and phosphatidylserine (PS), both of which bear a net negative charge, are preferentially located in the inner hemileaflet with the negative charges facing the cytoplasm.

The condition of bulk macroscopic electroneutrality requires that the total concentrations of cations and anions be equal in each cellular compartment. The intracellular cationic charge, primarily due to K+ plus Na+, is neutralized by the intracellular organic anions, Cl−, bicarbonate (HCO3−), phosphate, and sulfate. HCO3− and phosphate, along with proteins, are the principal buffers that regulate intracellular and extracellular pH. Although Cl− functions primarily to maintain bulk electroneutrality, some cells also use Cl− to carry ionic current. Halobacteria, for example, possess a light-driven Cl− pump.

In mammalian tissue and pulmonary capillaries, during the transport and elimination of metabolically produced CO2, exchanges of HCO3− with Cl− across the red cell membrane are mediated by capnophorin, a protein located in band 3 of SDS-polyacrylamide gels (for review, see Passow, 1986). Exchanges of Cl− for HCO3− also occur during the secretion of acid by the kidney and by epithelial cells of the gastrointestinal tract.

IV Trace Elements

In addition to the predominant electrolytes found in the intracellular and extracellular solutions, other ions are tightly associated with certain proteins and enzymes, known as metalloproteins. The transport of oxygen (O2) to all of the cells of the organism by red blood cells depends on the reversible association of O2 with ferrous ions (Fe²+) in the porphyrin groups of intracellular hemoglobin. Heme is an iron porphyrin, whereas chlorophyll is a magnesium porphyrin. Binding of O2 to Fe²+ in the muscle heme protein myoglobin provides a reservoir of O2 for muscular work. Catalase is another Feheme protein that protects cells by catalyzing the conversion of hydrogen peroxide into water and oxygen. Iron is stored in cells in the cavity of the protein ferritin, which can accommodate as many as 4500 ferric (Fe³+) ions. Iron (Fe²+, Fe³+) and copper (Cu+, Cu²+) are essential cofactors in cytochromes in the respiratory chain of mitochondria and in the photosystems of chloroplasts. Manganese ions are essential in Photosystem II in plant cells. Selenium is a cofactor in glutathione peroxidase, an enzyme that reduces hydrogen peroxide and organic peroxides and helps to prevent oxidative dam-age in cells. Zinc (Zn²+) and copper are cofactors in superoxide dismutase, an enzyme that scavenges superoxide anion (O−2) and helps to prevent oxidative damage from toxic free radicals. Zn²+ also functions as a cofactor in some proteolytic digestive enzymes, the zinc proteases, and stabilizes structures known as zinc fingers in certain DNA-binding proteins. A notable example of the binding of an ion to a nonprotein compound is that of cobalt (Co+) in vitamin B12.

V Measurement of Electrolytes

Ion concentrations in biological fluids may be expressed as millimoles per liter of solution (mMolar) or as millimoles per liter of water (mMolal). When a solution containing metallic ions is aspirated into a flame, each type of ion burns with a characteristic color, Na+ giving a yellow flame, K+ giving a violet flame, and Ca²+ giving a red flame. In flame photometry, the intensity of the emitted light, compared with that produced by solutions containing known concentrations of ions, provides a convenient measure of ion concentration in extracellular fluids and in acid extracts of cells. Under a uniform rate of aspiration, a flame photometer accurately measures the intensity of the emitted light, which is related linearly to suitably diluted cation concentrations. Atomic absorption spectroscopy, an alternative technique, measures the light absorbed by ions during electronic excitation in a flame. Flame photometry and atomic absorption spectroscopy both measure total ionic concentrations in cell extracts irrespective of any intracellular compartmentation and are sensitive in the millimolar range of cellular concentrations.

The development of ion-specific glass microelectrodes by G. Eisenman, and subsequently of selective liquid ion-exchange microelectrodes, made possible the direct determination of intracellular cation activities. The activity (a) is related to the chemical concentration (c) by the activity coefficient (γ):

a = γc.

The activity coefficient is unity for an ideal dilute solution and is typically less than unity in biological solutions because of nonideal interactions between ions (see Section X). L. G. Palmer and M. M. Civan found that for Na+, K+, and Cl− of Chironomus salivary gland cells, the ion activities are the same in the nuclear and cytoplasmic compartments. In a related study, Palmer, Civan, and T. J. Century observed that during development of frog oocytes, the ratio of the cytoplasmic concentration of Na+ to K+ increased, whereas the corresponding ratio of ion activities decreased. This observation probably reflects the development of yolk platelets and intracellular vesicles that contain ions at concentrations and activities different from those in the bulk cytoplasm.

K+, Na+, Ca²+, and other elements in single cells, or even in regions of single cells, may be measured by electron probe microanalysis, a technique that uses an electron beam to excite the emission of X rays with energies characteristic of the various elements in cells. With this technique, it was found that the elevated Ca²+ in red cells from patients with sickle cell anemia is sequestered in intracellular vesicles and that such vesicles are also present in normal red cells (Lew et al., 1985).

To measure transient changes in intracellular Ca²+ in the micromolar and submicromolar range, fluorescent chelator dyes such as Quin-2, Fura-2, Indo-1, and Fluo-3 have been developed (Tsien, 1988). Quin-2, Fura-2, and Indo-1 are fluorescent analogues of ethylenediaminetetraacetic acid (EDTA), which contains four carboxylate groups that specifically bind two divalent cations. Fluo-3 is a tetracarboxylate fluorescein analogue. EGTA is a nonfluorescent analogue with a greater binding affinity for Ca²+ than for Mg²+ and is thus useful in experiments in which the extracellular concentration of Ca²+ is systematically varied. Upon binding Ca²+, Fura-2 undergoes a shift in its excitation spectrum. By measuring the ratio of dye fluorescence upon excitation at two exciting wavelengths, changes in the concentration of Ca²+ may be monitored. The cells are incubated with a permeant ester form of the dye to enable these dyes to penetrate into cells; intracellular esterases then release the Ca²+-sensitive chromophore. The traces in Fig. 4 show the response of human neutrophils to activation by the chemotactic peptide formylmethionyl-leucyl-phenylalanine (fMLP). The upper trace shows a Ca²+ transient measured with Indo-1, and the lower trace shows the simultaneous monitoring of the transmembrane potential with a fluorescent cyanine dye (Lazzari et al., 1986). With video microscopy of cells stained with fluorescent Ca²+ indicators, it is also possible to obtain time-resolved and spatially resolved light microscopic images of the changes in intracellular Ca²+. Another fluorescent probe (SPQ), developed by A. S. Verkman, is used to measure intracellular Cl− and to study its transport across cell membranes.

FIG. 4 Changes in intracellular Ca²+ and membrane potential upon activation of human neutrophils by the chemotactic peptide formyl-methionyl-leucyl-phenylalanine (fMLP). A transient increase in intracellular Ca²+ is detected with the fluorescent indicator Indo-1 (top), while hyperpolarization of the membrane potential is detected simultaneously with a fluorescent cyanine dye (bottom). (Adapted from Fig. 1 of Lazzari et al., 1986, p. 9712, by copyright permission of The American Society for Biochemistry and Molecular Biology.)

VI Free Energy and the Gibbs Equation

The active production and maintenance of ion concentration gradients by membrane pumps, such as the Na,K-ATPase and the Ca-ATPase, represent chemical work and electrical work done by the cell. With isolated red cell membranes (ghosts), active transport of Na and K against their respective concentration gradients is observed directly by measurements of net fluxes. The energy required for continuous pumping of Na+ by resting frog sartorius muscles is estimated to represent 14-20% of the energy available from the hydrolysis of ATP. The passive flow of ionic currents down their concentration gradients through specific ion channel proteins constitutes negative work done by the cell.

The first law of thermodynamics, which is a statement of the conservation of energy, states that the increase in energy (dE) of a system is the sum of the gain in heat (dQ) minus the work (dW) done by the system:

The second law of thermodynamics defines the change in entropy (dS) of a system in terms of the heat gained (dQ) and the absolute temperature (T) as

Combining the first and second laws gives

dE = TdS – dW.

If the work done by the system, dW, includes pressure-volume work, pdV, then

where z is the ionic valence (equivalent/mole), F is the Faraday constant (coulomb/equivalent), and dn is the number of moles of solute transported across the membrane out of the cell. εm is the transmembrane potential, or the difference in electrical potential ψ, in volts (or joules/coulomb), between two compartments,

where the subscripts i and o represent the intracellular (inside) and extracellular (outside) compartments, respectively. The electrical potential ψ represents the work done in moving a unit positive test charge from infinity to a point in the solution. Note that when the transmembrane potential, εm, is negative, the electrical work is positive for pumping Na+ out of the cell, but negative for pumping K+ into the cell. The electrical work is negative when Na+ leaks into the cell, and positive when K+ leaks out of the cell.

According to the first and second laws, the change in energy of the system is

For systems of variable chemical composition, the free energy (G) is by definition G = H – TS + σμjnj, where the enthalpy H = E + PV, and the chemical potential (μj) of the jth solute in the system at constant T, P, and nk is defined by

nj and nk being the number of moles of the jth and kth solutes, respectively. The chemical potential, also called the partial molar free energy, represents the incremental addition of free energy to the system upon incremental addition of a solute. All solutes contribute to the free energy of a solution. Although the free energy itself is a parameter of state for the whole system, the chemical potential refers to a particular solute. The free energy is thus given by

Differentiating, we obtain

Substituting the above expression for dE gives

Simplifying yields the Gibbs equation,

which states that the free energy of a system of variable chemical composition is a function of the temperature, the pressure, and the number of moles of each component in the mixture, or G = G(T, P, nj). At constant temperature and pressure (dT = dP = 0), the Gibbs equation simplifies to

which states that the increase in free energy of a system is equal to the sum of the electrical work done on the system plus the total change in free energy due to changes in chemical composition. Furthermore, when the system is at equilibrium (with dn = dnj = 0), dG = 0. The second law of thermodynamics also implies that the change in free energy, dG, is negative for all spontaneous processes. Thus, the first and second laws of thermodynamics, when combined with the definitions of free energy and enthalpy, result in the Gibbs equation, which is the fundamental equation permitting estimation of free energy changes when water, ions, or other solutes cross cell membranes.

VII Cell Water Content Is Determined by Osmosis

Most cells contain about 80% of their weight as water, as is easily determined by drying a piece of tissue or a pellet of sedimented cells to a constant weight in a vacuum oven, allowing suitable corrections for extracellular space or trapped volume. Human red blood cells are somewhat more dense with only 66% water (100 × g water/g packed cells). According to the Boyle–van’t Hoff law, which is derived from the Gibbs equation (see Dick, 1959), the osmotic pressure (π) of a solution containing N moles of solute dissolved in Vw liters of water is given by

where ϕ is the osmotic coefficient of the solute, R is the gas constant, T is the absolute temperature, and c (= N/ Vw) is the total concentration (osmolal) of dissolved solutes. Osmolality is the total molal concentration of all dissolved solutes. Because salts are completely ionized in solution, a 1 molal solution of NaCl would be 2 Osmolal. The osmotic coefficient (ϕ) is unity for ideal dilute solutions; deviations of ϕ from unity are due to solute-solvent interactions and other nonidealities. The osmotic pressure (πi) of the intracellular solution is the sum of the osmotic pressures of each component of the mixture,

where cj (= Nj/Vw) is the concentration of the jth solute. The osmotic pressure of a mixture may also be expressed as

where ϕ1 is the osmotic coefficient of the intracellular mixture, a parameter that equals the sum of the osmotic coefficients of the components of the mixture, weighted according to their respective mole fractions.

Water will cross the membrane until the intracellular osmotic pressure equals the extracellular osmotic pressure, or πi = π0. Thus, osmotic equilibrium is reached when

In order to maintain the normal volume of cells incubated during physiological experiments, the osmolality of the medium should equal that of isotonic solution. Isotonic solution is defined as having an osmolality equal to that of normal plasma, or 289 mOsm. In isotonic solution, designated by the superscript⁰,

Dividing πi by πi⁰, setting πi = πo and πi⁰, = πo⁰, and rear-ranging yield the following expression for the equilibrium cell water content relative to that of cells in isotonic so-lution:

This expression quantifies the amount of cell shrinkage that will occur in hypertonic solution (with πo > πo⁰), and the amount of cell swelling that will occur in hypotonic solution (with πo < πo⁰)

In the case of red blood cells, the osmotic coefficient of hemoglobin increases as the square of the concentration of hemoglobin (Fig. 5), resulting in significant deviations from ideal osmotic behavior (Dick, 1959; Freedman and Hoffman, 1979). Human red blood cells maintain stable volumes when placed in isotonic, hypotonic, or hypertonic salt solutions (Fig. 6, top). In contrast, red cells from certain other species (including Amphiuma, duck, fish, dog, and a low K+ genetic variant of sheep) and other types of cells (including Ehrlich ascites tumor cells, human lymphocytes, human platelets, and renal and other epithelial cells) can alter their membrane permeability in response to an altered extracellular osmolality such that NT is changed, and their cell volumes are returned to normal (for review, see Hoffman and Simonsen, 1989). Examples of this volume regulatory decrease (VRD) and volume regulatory increase (VRI) exhibited by Amphiuma red blood cells are shown in the bottom panel of Fig. 6 (Cala, 1980). The mechanisms by which cells sense their altered volume before switching on a transport pathway and sense their normal volume when turning off a transport pathway are unknown.

FIG. 5 Osmotic coefficients of NaCl, KCl, and sucrose (top) and of hemoglobin (bottom). Data for NaCl, KCl, and sucrose are from the CRC Handbook of Chemistry and Physics, 58th ed. (R. C. Weast and M. J. Astle, Eds.), p. D-261, 1978-79, and from R. A. Robinson and R. H. Stokes, 1959.; Data for hemoglobin are from Adair, adapted from Fig. 7 of J. C. Freedman and J. F. Hoffman, The Journal of General Physiology, 1979,74, p. 177, by copyright permission of the Rockefeller University Press, and are drawn according to ϕHb = 1 + 0.0645[Hb] + 0.0258[Hb]².

FIG. 6 Stable osmotic response of human red blood cells (top) in contrast to the volume regulatory responses of Amphiuma red blood cells (bottom). Washed human red cells were incubated in hypotonic, isotonic, or hypertonic media, and the water contents were determined at selected times by drying packed cells to a constant weight in a vacuum oven (Freedman and Fazio, unpublished observations). When Amphiuma red cells are incubated in hypotonic medium (lower panel, upper trace) or hypertonic medium (lower panel, lower trace), the cell water content spontaneously returns toward its normal value, illustrating a volume regulatory decrease (VRD) or volume regulatory increase (VRI). (bottom panel adapted from Figs. 1 and 2 of P. M. Cala, The Journal of General Physiology, 1980, 76, pp. 688-689, by copyright permission of the Rockefeller University Press)

The long-term regulation of cell volume in renal cells and in brain cells also involves changes in NT by the biosynthesis of solutes known as osmolytes. In response to a chronically hypertonic plasma, synthesis of mMolar quantities of polyols (such as sorbitol and myo-inositol), betaine, and glycerophosphorylcholine occurs in renal cells, thereby increasing the intracellular osmolality and preventing cellular dehydration. In brain cells, osmolytes include taurine, glycine, alanine, and other nonessential amino acids. Upon sudden exposure to an isotonic plasma, brain cells containing elevated osmolytes would swell, causing extensive neurological damage. For this reason, restoration of an isotonic plasma in patients by intravenous fluid therapy is performed slowly to allow sufficient time for brain cells to readjust their osmolyte concentrations without deleterious changes in cell volume. Thus, the amount of water in cells is determined by the total concentration (osmolality) of salts, proteins, and organic metabolites as well as by certain nonideal effects expressed by the osmotic coefficients of the intracellular solutes. In the next section some pertinent properties of intracellular water are considered.

VIII Structure, Polarity, and Hydrogen Bonding of Liquid Water

Liquid water is a highly polar solvent, with a structure stabilized by extensive intermolecular hydrogen bonds (Fig. 7). The hydrogen bonds between adjacent water molecules are linear (O-H • • • O) but are able to bend by about 10°. Two covalent bonds (O-H) are present, and two hydrogen bonds may also occur, around each oxygen atom at angles of 104° 30’ in a tetrahedral array. The energy required to break hydrogen bonds is −20 to −30 kJ/mole. A joule (J) is the unit of work in the mks system and equals 1 newton-meter, or 0.239 calories (cal). Because of the high strength of hydrogen bonds, liquid water has unique physicochemical properties, including a high boiling point (100°C), a high heat capacity (76.02 J/mole • °K), a high heat of vaporization (40.66 kJ/mole at 1 atm), and a high surface tension (72.75 dyn/cm). As discussed by Bergethon and Simons (1990), all of these thermodynamic parameters are considerably higher than those of the analogous compound H2S, which boils at −59.6°C. The bond angle of H2S is only 92°20’; this structure does not fit into a tetrahedral array, and thus H2S cannot form a network of hydrogen bonds in solution.

FIG. 7 Hydrogen bonds in liquid water. The linear hydrogen bonds are indicated by dotted lines between adjacent water molecules (O – H … O). Two covalent bonds, O – H, indicated by solid lines, and two hydrogen bonds occur around each oxygen atom in a tetrahedral array. The blunt end of the solid lines, indicating covalent bonds, protrudes out of the plane of the page, while the sharp end goes into the plane of the page. The partial charge separation of the O – H dipoles is indicated on the upper right water molecule.

The coulombic force, Fcoul (newtons), between two ions in a vacuum is given by Coulomb’s law

where q+ and q- are the charges (in coulombs) of the two ions, ε0 is the permittivity constant (8.854 × 10−12 C²/ N.m²), and d is the distance (meters) between the two ions. The newton (= kg.m/sec²) is the unit of force in the mks system; the dyne (= g.cm/sec²) is the corresponding unit of force in the cgs system (1 newton = 10⁵ dynes). Coulomb’s law states that the force between two point charges is directly proportional to the magnitude of the charges, and inversely proportional to the square of the distance between the charges. Note that the term 4πr² represents the surface area of a sphere.

The dielectric constant (e) of a medium, called a dielectric, is defined as the ratio of the coulombic force (Fcoul) to the actual force (F):

Substituting and rarranging yield

The dielectric constant of a vacuum is unity, and that of air (1.00054) is close to unity. The dielectric constant of water at 25°C is 78.5, much greater than that of methanol (32.6), ethanol (24.0), or methane (1.7). In liquid water, the high dielectric constant weakens the coulombic attractive forces between oppositely charged particles and thus promotes ionization of salts.

Water also has a strong permanent dipole moment. Water molecules have no net charge, yet possess permanent charge separation within the molecule. Because oxygen is more electronegative than hydrogen, the unbonded electrons are preferentially located near the oxygen atom, conferring a partial negative charge and leaving the hydrogen atoms with a partial positive charge. The magnitude of the dipole moment of a chemical bond is computed as the product of the separated charge and the distance of separation. The dipole moment of a molecule is the vector sum of the dipole moments of each bond. For water the dipole moment is 1.85 Debye, where 1 Debye = 10−18 esu.cm. One esu (electrostatic unit), or statcoulomb, equals 3.336 × 10−10C.

The hydrogen-bonded structure of liquid water also con-tributes to high proton conductivity. In a hydrogen-bonded network, a single proton need not diffuse through the liquid to carry a current. Instead, the successive breakage and formation of hydrogen bonds can effectively contribute to proton translocation.

Although the thermodynamic properties of liquid water are explicable in terms of extensive hydrogen-bonding, the actual structure of water is still unknown (see Eisenberg and Kauzmann, 1969). In Klotz’s flickering cluster model, groups of 50-70 water molecules are constantly associating and dissociating on a picosecond time scale. Other theories treat water as mixtures of distinct states or as a continuum of states.

Despite these uncertainties concerning the structure of liquid water and the influence of macromolecules on its properties in cells (see Cooke and Kuntz, 1975), the ability of water to act as a solvent inside cells closely resembles that of extracellular water. Thus, a variety of nonelectrolytes that are permeant, hydrophilic, and nonmetabolized distribute at equilibrium across human red cell membranes with ratios of intacellular to extracellular concentrations that deviate from unity by less than 10%. In mouse diaphragm muscle, C. Miller found that several alcohols, diols, and monosaccharides exhibit distribution ratios within 2% of unity, whereas other sugars are apparently excluded from intracellular compartments. Some intracellular water is constrained in gels, which are cross-linked networks of fibrous macromolecules, but even this water has normal solubility properties. The diffusion of solutes within gels may be hindered by collisions and interactions with the macromolecules and by the tortuosity of the diffusion paths. In cultured fibroblasts, the fluid-phase cytoplasmic viscosity, as determined from the rotational motions of fluorescent probes on a picosecond time scale, is only 1.2 to 1.4 times that of pure water; this viscosity is the same as that in nucleoplasm and is unaffected by large decreases in cell volume or by disruption of the cytoskeleton with cytochalasin B (Fushimi and Verkman, 1991). The fluid-phase viscosity, as determined from fluorophore rotational motions, is affected much less by macromolecules than the bulk viscosity, thereby providing a more accurate picture of the physical state of the aqueous domain of the cytoplasm. These and other studies indicate that the bulk of cell water is not organized more extensively than the extracellular water and that the physicochemical properties of intracellular and extracellular water are similar.

IX Ionic Diffusion

Ions migrate as hard spheres that interact with water. The strength of the attraction between ions and water dipoles depends to a large extent on the ionic charge and radius. For the alkali metal cations, the energy of interaction with water decreases according to the following series:

Li+, the smallest of the alkali metal cations, has the strongest interaction with water because the center of charge in the ion nucleus can more closely approach the negative side of neighboring water dipoles. As the ionic radius increases in the alkali metal series, the filled outer shells of electrons effectively shield the cationic charge and reduce the distance of closest approach to water molecules. The enthalpy of hydration of an ion is a measure of the strength of the interaction between ions and water and is defined as the increase in enthalpy when one mole of free ion in a vacuum is dissolved in a large quantity of water. The enthalpy of hydration for the smallest alkali metal cation Li+ is quite large at −131 kcal/mole. With increasing ionic radius, the enthalpy decreases progressively for Na+, K+, and Rb+, reaching −71 kcal/mole for Cs+, the largest ion in the series (Table 1). For the divalent, alkaline earth metal ions Mg²+ and Ca²+, the enthalpies of hydration also follow the ionic radius and are considerably larger at −476 and −397 kcal/mole, respectively. As pointed out by Hille (1992), the magnitude of ionic hydration energies approximates that found in the ionic bonds of a salt crystal lattice.

Another indication of the strength of the interaction between ions and water is the decrease in the mobilities of the alkali cations in water as the ionic radius decreases (Table 1; for discussion, see Hille, 1992). The inner hydration shell refers to the water molecules in direct contact with the ion, but even these water molecules rapidly exchange with bulk water on a nanosecond time scale for Na+, K+, and Ca²+. Mg²+, however, with its high charge density, is approximately four orders of magnitude slower in exchanging its inner hydration water.

Some membrane channels are so narrow that ions and water permeate by a process of single-file diffusion in which water and ions cannot pass each other, at least in the narrowest part of the channel (Finkelstein and Andersen, 1981). In narrow channels, where the diameter of the permeating ion may approximate that of the channel itself, the hydration water is stripped from the ion and is probably replaced by dipolar groups of the proteins lining the channel walls, thus providing electrostatic stabilization of the permeating ion.

X Interactions between Ions

Interactions between ions may be weak or highly selective. Ions in solution attract ions of the opposite charge in accordance with Coulomb’s law. Because the attractive forces are inversely proportional to the square of the distance between charges, the interaction energies are greater in more concentrated solutions. Such ion-ion interactions are stabilizing, and lower the chemical potential of an ion from its value in an ideal infinitely dilute solution.

The activity (a) of an ion is defined in terms of the chemical potential (μ) as

where μ°(T,P) is the standard-state chemical potential, or the chemical potential when the activity is one. Increases in chemical activity increase the chemical potential. Recall that the activity is the product of the concentration (c) and the activity coefficient (γ).

Activity coefficients can be estimated by the Debye-Hückel theory, which hypothesizes that ions attract oppositely charged ions (or counterions) in an ion cloud (or atmosphere). The forces of coulombic attraction are opposed by the randomizing influence of the thermal motion of the ions. In dilute solutions, in which ions are treated as point charges relative to the size of the ion cloud, the activity coefficient (γ) for salt ions with charges z+ and z-, is given by

where I is the ionic strength, defined as

The constant A, which equals 0.51 at 25°C, contains the term 1/k, or the Debye length, which defines the effective radius of the counterion atmosphere. The Debye-Hückel equation given above predicts activity coefficients accurately only to concentrations of about 0.01 M. In more concentrated solutions, the finite radius (a, in Å) of the ion is taken into account in the extended Debye-Hückel equation, given by

where the constant A is still 0.51 at 25°C, and the constant B is 0.33 × 10⁸ for water at 25°C. The activity coefficients calculated by the Debye-Hückel theory indicate that the forces between ions in dilute solutions are weak and nonselective. The predicted activity coefficients depend on the ionic charge and the ionic strength of the solution and are independent of the specific ion within, for example, the alkali metal series. The mean ionic activity coefficients for NaCl and KCl as a function of salt concentration are shown in Fig. 8. At 0.1 M concentrations, the activity coefficient of NaCl is 0.77, whereas that of KC1 is 0.76. These relatively high activity coefficients correspond to ion-ion interaction energies of only about −0.3 kcal/mole (see Hille, 1992).

FIG. 8 Activity coefficients of NaCl and KCl. Data are from Robinson and Stokes (1959). The dashed vertical line indicates that at 0.1 M, the activity coefficients of NaCl and KCl are 0.77 and 0.76, respectively.

Studies were conducted in which the red cell membrane was made permeable to cations by exposure of the cells to the channel-forming antibiotic nystatin, thus allowing Na+ and K+ to reach equilibrium. The mean ionic activity coefficient of KC1 and NaCl in the concentrated intracellular hemoglobin solution was found to be within 2% of that in the extracellular solution (Freedman and Hoffman, 1979). Thus, even in a solution containing 34% hemoglobin, where the average distance between the surfaces of neighboring protein molecules is on the order of 10 Å, the salts apparently behave as if in dilute solution.

Specific effects of small anions on the solubility, aggre-gation, or denaturation of proteins often follow the Hofmeister (lyotropic) series in the following order of effectiveness:

The ions to the right of Cl− are referred to as chaotropic because they tend to destabilize proteins (for review, see Collins and Washabaugh, 1985). In human red cells, NO3−, I−, SCN−, and methanesulfonate (CH3SO3−), but not methyl sulfate (CH3SO4−), all bind to hemoglobin and alter its net charge, with a consequent small but significant change in cell volume in accordance with the Gibbs-Don-nan equilbrium (Payne et al., 1990; see Section XII).

Certain enzymes, ion channels, and membrane trans-port proteins interact with the alkali cations with a high degree of ionic selectivity. Considering the five alkali metal cations, there are 5! (= 120) possible orders of selectivity that might arise. However, only 11 cationic selectivity orders commonly occur in chemical and biological systems, as indicated in Table 2. G. Eisenman predicted these selectivity orders by calculating the ion-site interaction energies. If the field strength of a negatively charged site is weak, then the ions remain hydrated. In this case, Cs+, having the smallest hydrated ionic radius, is favored (Sequence I) because it can approach most closely to the site and thus has the strongest coulombic force of attraction. If the field strength of the site is strong, and the interaction energy between the ion and the site is stronger than that between the ion and water dipoles, then the ion loses its associated water and becomes dehydrated. In this case, Li+, having the smallest unhydrated ionic radius, becomes favored (Sequence XI). Under intermediate field strengths, ions partially dehydrate, giving rise to the intervening selectivity sequences. Other sequences are possible when the sites are assumed to be polarizable (for review, see Eisenman and Horn, 1983).

TABLE 2

Eisenman’s Selectivity Sequences for Binding of Alkali Cations to Negatively Charged Sites

XI Ionophores

Ionophores are a class of compounds that form complexes with specific ions and facilitate their transport across cell membranes (for review, see Pressman, 1976). An ionophore typically has a hydrophilic pocket (or hole) that forms a binding site specific for a particular ion. The exterior surface of an ionophore is hydrophobic, allowing the complexed ion in its pocket to cross the hydrophobic membrane. A list of ionophores showing the ion specificity of each is. given in Table 3. Ionophores are useful tools in cell physiology. Nystatin forms a channel in membranes for monovalent cations and anions and is useful for altering the cation composition of cells. Gramicidin forms dimeric channels specific for monovalent cations. Valinomycin carries K+ across membranes with a high selectivity and is used extensively to impose a high K+ permeability on the cell membrane. Monensin is a carrier with specificity for Na+. Hemisodium is a new synthetic Na+ ionophore with an even greater degree of selectivity for Na+. The Ca²+ ionophore A23187 is used extensively to permit entry of Ca²+ into cells that normally have a low native permeability to Ca²+, thereby activating a variety of cellular processes that are regulated by Ca²+ (see Campbell, 1983). Nigericin exchanges K+ for protons (H+) and is used in many studies of mitochondrial bioenergetics to alter electrical and chemical gradients for protons (for review, see Harold, 1986). Ionophores such as FCCP and CCCP are specific for protons. In addition to the utility of ionophores in cell physiology experiments, studies of the mechanism of membrane transport that they mediate have provided important conceptual insights (e.g., Stark and Benz, 1971; Finkelstein and Andersen, 1981) relevant to the understanding of ion transport mediated by native transport proteins.

TABLE 3

lonophores and Their Ion Selectivities

XII Nernst Equation and Its Derivation

A solute is said to be at equilibrium when its concentration is constant over time, without requiring the continuous input of energy from metabolism or other sources. In human red blood cells, Cl−, HCO3−, and H+ are at thermodynamic equilibrium; that is, they are passively distributed. In contrast, the concentrations of Na+, K+, and Ca²+ are at a steady state. Their concentrations are constant in time, but are dependent on the continuous hydrolysis of ATP by the Na,K pump and the Ca pump. Active transport uses energy and results in steady-state distributions that represent a deviation from equilibrium. Passive transport is the movement of solutes toward a state of equilibrium.

The Nernst equation describes the relationship between voltage across a semipermeable membrane and the ion concentrations in the compartments adjacent to the mem-brane. The equation provides a simple method of testing whether or not a particular solute is at equilibrium. Consider a membrane permeant only to cations separating two solutions of KC1 of differing concentrations. The process of moving dn moles of K+ ions out of the cell from compartment i to compartment o involves a change in free energy, dG, of the system. The process will occur spontaneously only if dG < 0, and the system will be at equilibrium if dG = 0.

Using the Gibbs equation, the change in free energy in moving dn moles of K+ ions from compartment i to compartment o is given by

For this process, -dni = dn0 = dn, and

For charged solutes, the electrochemical potential (μj) of the jth solute is defined to be the sum of a chemical and an electrical component. The electrical contribution to the electrochemical potential is zFψ, and the chemical contribution is RT ln a.

The chemical potential in each solution is

For the system under consideration, μoi = μoo, and thus,

At equilibrium, dG = 0, and thus -zFεm - RT ln(ai/ ao) = 0.

Note that a fundamental condition of equilibrium is that the difference in electrochemical potential between compartments i and o is zero. The electrochemical potential of the solute is the same in each compartment to which that solute has access.

Rearranging yields the Nernst equation for a cationic concentration cell,

Converting the natural logarithm to base 10 yields

The value of 2.303RT/F is 58.7 mV at 23°C and 61.5 mV at 37°C.

The Nernst equation is independent of the mechanism of transport and is often used for ascertaining whether an intracellular ion is at electrochemical equilibrium. If so, then

If z = 0, as for nonelectrolytes, then ai = ao, and the activities of the solutes will be the same at equilibrium on both sides of the membrane, as was found to be nearly the case for the distribution of nonelectrolytes in red blood cells. If z does not equal zero, as for electrolytes, then at equilibrium each permeant monovalent ion will reach the same ratio of intracellular to extracellular activity. Such is the case for the passive distribution of Cl−, HCO3−, and H+ in human red blood cells:

Na+, K+, and Ca²+, however, deviate from this ratio because of the action of the Na/K pump and Ca pump. The transmembrane potential is usually measured by means of open-tipped microelectrodes, such as those developed and used by G. N. Ling and R. W. Gerard (1949) to obtain accurate and stable measurements of the membrane potential of frog skeletal muscle. In studies of human red blood cells, stable potentials have not been achieved with microelectrodes. P. C. Laris and J. F. Hoffman (1974) used fluorescent cyanine dyes as an optical alternative technique for monitoring and measuring red cell membrane potentials. Fluorescent cyanines, merocyanines, oxonols, styryls, rhodamines, and other dyes have since been used in numerous electrophysiological studies of red cells, neutrophils, platelets, and other nonexcitable cells and organelles that are too small for the use of microelectrodes (for review, see Freedman and Novak, 1989a). The equilibrium distribution of permeant, lipophilic, radioactively labeled ions, such as triphenylmethylphosphonium (TPMP+), may also be used to assess the membrane potential (see Freedman and Novak, 1989b).

XIII Gibbs-Donnan Equilibrium

An understanding of the Gibbs-Donnan equilibrium is critical for properly incubating cells in physiological ex-periments. Human red blood cells, for example, swell in acid and shrink in alkaline media. Red cells swell and hemolyze upon exposure to compounds that increase the normal low permeability of the membrane to cations, a phenomenon termed colloid osmotic hemolysis. Muscle cells swell when the external concentration of K+ is raised in equimolar substitution for Na+ without simultaneously lowering the concentration of Cl−. Increasing the external K+ would reduce the resting potential of muscle cells, and Cl−, if passively distributed, would then enter the cells and increase the intracellular osmolality, thereby resulting in swelling.

A Gibbs-Donnan equilibrium occurs whenever a membrane separates an aqueous salt solution from a salt solution that also contains impermeant charged electrolytes, such as intracellular charged proteins and organic phosphates. For human red cells, the permeability of the membrane to Na+ and K+ is considerably less than that to Cl− and HCO3−. Red blood cells represent a double-Donnan system, with one Donnan equilibrium being established by the slowly permeant cations and the other by hemoglobin (Hb) and organic phosphates. From the principle of bulk electroneutrality in the intracellular and extracellular solutions

where rCl, is the Donnan ratio for Cl−, and z is the average net charge on impermeant cell solutes (μeq/mole Hb). The net charge on hemoglobin depends on intracellular pH as the constituent amino acids are titrated. The titration curve of hemoglobin is approximately given by

where m is the slope of the titration curve, or buffer capacity, and pI is the isoelectric point of the cell contents, or the pH at which the net charge is zero (pI = 6.8 at 25°C in human red cells). As the intracellular pH decreases, hemoglobin becomes more positively charged and, because Na+ and K+ are relatively less permeant, Cl− enters the cell to balance the increased positive charge on hemoglobin. Because the total intracellular solute concentration has now increased, the red cells swell. In contrast, when the intracellular pH increases, hemoglobin becomes more negatively charged, and Cl− leaves the cell, resulting in cell shrinkage.

Colloid osmotic hemolysis occurs when the red cell membrane is exposed to pore-forming ionophores, such as nystatin or gramicidin, or when the normal low perme-ability to cations increases upon exposure to detergents or other chemicals. At equilibrium at the isoelectric pH, where the Donnan ratio equals unity and the membrane potential is zero, the intracellular concentrations of Na+, K+, and Cl− equal those of the extracellular solution. The osmotic pressure of hemoglobin is unbalanced by any extracellular solute and draws water into the cell, leading to swelling and hemolysis. Colloid osmotic hemolysis occurs at any pH when the membrane is permeant to both cations and anions. The Na+ pump, working against the leakage pathways and any significant cotransport pathways, establishes the steady-state intracellular cation concentrations, whereas Cl− and HCO3− move to maintain electroneutrality.

In the Gibbs-Donnan equilibrium, cellular electrolyte concentrations and water contents are determined by three principles: (1) bulk electroneutrality, (2) osmotic equality of the intracellular and extracellular solutions, and (3) equality of the Donnan ratios for all permeant ions of the same charge. The Donnan ratio for monovalent anions is equal to the inverse of the Donnan ratio for monovalent cations.

For human red blood cells, the equations expressing these constraints, including the activity and osmotic coef-ficients of the salts and of hemoglobin, have been form-ulated into a computer program designated IONIC (Freedman and Hoffman, 1979). For a given composition of the extracellular medium, and certain cellular parameters, the program predicts the cell volume, the intracellular pH and ion concentrations, the membrane potential, and the charge on hemoglobin and organic phosphates. The predictions of the model generally agree with experimental results within a few percent; for example, the predicted and experimentally determined dependence of the Donnan ratios for Cl− on pH are shown in Fig. 9. Beginning with a model of the Gibbs-Donnan equilibrium, Lew and Bookchin (1986) have developed an integrated kinetic model of red cell transport that includes parameters describing the known transport systems and begins to describe the time course of the changes in cell volume, intracellular salt concentrations, and membrane potential that occur when the extracellular conditions are changed.

FIG. 9 Comparison of measured and predicted Donnan ratios in human red blood cells. The equilibrium Donnan ratios for Cl− and the cell water contents were determined at varied extracellular pH. The solid lines are predictions of the program IONIC (adapted from Fig. 3 of R. B. Gunn, M. Dalmark, D. C. Tosteson, and J. O. Wieth, The Journal of General Physiology, 1973, p. 193, by copyright permission of the Rockefeller University Press); (adapted from Fig. 3 of J. C. Freedman and J. F. Hoffman, The Journal of General Physiology, 74, 1979, p. 174, by copyright permission of the Rockefeller University Press).

XIV Summary

This chapter introduces the functions and properties of the predominant cellular electrolytes—K+, Na+, Ca²+, Mg²+, Cl−, and HCO3−. Steady-state concentrations of K+, Na+, and Ca²+ are established by the Na+/K+-ATPase and Ca²+-ATPase, which use metabolic energy to pump ions against their electrochemical gradients. The passive flow of K+, Na+, and Ca²+ down their electrochemical gradients through voltage-gated ion channels constitutes the ionic currents that form action potentials in excitable cells, such as nerve and muscle. Intracellular K+ also activates the glycolytic enzyme pyruvate kinase and is required for peptide bond formation in protein synthesis.

Changes in cell Ca²+ initiate and modulate a variety of cellular functions, but excess Ca²+ inside cells can be harmful. Mg²+, with its high charge density, binds tightly to polyphosphates and is a cofactor in all kinases and some phosphatases including the Na+/K+-ATPase. HCO−3 and phosphate, along with proteins, are the principal biological buffers that regulate pH. Cl− primarily serves to maintain bulk electroneutrality. Trace ions, including those of iron, copper, manganese, zinc, selenium, and cobalt, are important cofactors in nutritional and bioenergetic pathways and in enzymes that protect cells from oxidative and peroxidative damage.

Cell cations are measured by means of flame photometry, atomic absorption spectroscopy, ion-specific electrodes, electron probe microanalysis, and fluorescent chelator dyes. Membrane-bounded compartments in cells may contain ion concentrations different from those in the bulk cytoplasm. All of the solutes in a cell contribute to the free energy of the intracellular solution. The Gibbs equation, which is derived by combining the first and second laws of thermodynamics, enables estimation of the changes in free energy when solutes cross cell membranes. The change in free energy is zero at equilibrium and negative for spontaneous processes. Solutes will redistribute until the electrochemical potential is the same in every compartment to which that solute has access. The amount of water in cells is determined by the Boyle-van’t Hoff law of osmotic equilibrium. At osmotic equilibrium, the total intracellular and extracellular osmolalities are equal. With human red blood cells, significant deviations from osmotic ideality are due to the effect of the osmotic coefficient of hemoglobin. Other cells are capable of adjusting their intracellular solutes by altering membrane transport systems to regulate their volume, even when exposed to hypotonic or hypertonic media. Still other cells synthesize osmolytes in response to altered extracellular tonicity.

Intracellular water is polar and extensively hydrogen-bonded, but exhibits thermodynamic properties similar to extracellular water. Salts and nonelectrolytes dissolve in cell water with the same solubility and activity as in extracellular water. Ions migrate through water as hard spheres that interact with water dipoles according to the ionic radius and charge. Weak nonspecific interactions between ions in solution are described by the Debye-Hückel theory, which enables calculation of the activity coefficients of ions. Selective ion interactions with sites on enzymes or ion channels occur in certain predictable specific patterns that depend on the relative energy of interaction between the ions and water dipoles and the binding sites. Ionophores with a high degree of ion selectivity are useful tools in cell physiology experiments. The study of ion transport mediated by ionophores has provided instructive models for understanding membrane transport.

The Nernst equation, which follows from the Gibbs equation, tests whether a solute is in electrochemical equi-librium across a cell membrane. The Gibbs-Donnan equi-librium describes the passive distribution of ions and water across membranes that separate aqueous salt solutions from solutions containing impermeant charged electrolytes. Computer programs have been devised that permit estimation of Gibbs–Donnan equilibria for human red blood cells as well as prediction of the time course of changes in the cellular volume, the intracellular pH, the membrane potential, and the intracellular salt concentrations when the extracellular conditions are altered.

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