Transport of Solutes and Water

Total-body water is the sum of the ICF and ECF volumes

Total-body water (TBW) N5-1 is ~60% of total-body weight in a young adult human male, ~50% of total-body weight in a young adult human female ( Table 5-1 ), and 65% to 75% of total-body weight in an infant. TBW accounts for a lower percentage of weight in females because they typically have a higher ratio of adipose tissue to muscle, and fat cells have a lower water content than does muscle. Even if gender and age are taken into consideration, the fraction of total-body weight contributed by water is not constant for all individuals under all conditions. For example, variability in the amount of adipose tissue can influence the fraction. Because water represents such a large fraction of body weight, acute changes in TBW can be detected simply by monitoring body weight.

N5-1

Determination of the Volume of Body Fluid Compartments

The TBW can be determined by the use of a volume-of-distribution technique. The first step is to infuse intravenously a known quantity of a tracer for water (deuterium oxide [ ² HOH] or tritiated water [ ³ HOH]) that will distribute everywhere there is water. Because water readily permeates most cell membranes, a tracer for water distributes into both the extracellular and ICF.

For example, suppose a 70-kg male is injected with 10 ⁸ counts per minute (cpm) of ³ HOH contained in a small volume of physiological saline. After an equilibration period of 2 hours, a sample of the blood plasma is drawn and the ³ HOH concentration in the plasma is found to be 2.5 × 10 ³ cpm/mL plasma. Measurement also reveals that 5 × 10 ⁵ cpm of ³ HOH has been lost in urine, as well as from the skin and lungs. From this information, we can calculate the volume of distribution of the tracer, which is the same as the TBW:

In this male, the TBW of 39.8 L is 57% of the 70-kg body weight.

How can we determine how this water is distributed among the various fluid compartments? In particular, we need to know the fraction of the TBW that is intracellular and the fraction that is extracellular. In practice, the ICF volume is calculated as the difference between TBW and ECF volume. The ECF volume is determined by using a marker that distributes uniformly throughout the compartments accessible to water but that does not enter the cells. Unfortunately, different markers thought to distribute within the ECF yield different values. For example, large polysaccharides (e.g., inulin) or polyalcohols (e.g., mannitol) that cannot cross cell membranes do not penetrate fully into dense connective tissue and bone. On the other hand, ions that are largely extracellular (e.g., Na ⁺ , Cl ⁻ ) are able to enter cells to some extent. Using the above techniques, the best estimate is that the total ECF represents between 20% and 25% of body weight (~40% of TBW). This leaves about 35% to 40% of the body weight (~60% of TBW) as intracellular water or ICF volume.

The plasma volume can be determined by measuring the volume of distribution of labeled albumin. Because albumin escapes only very slowly from the vascular compartment, measuring the final concentration of labeled albumin in the plasma and then using the above equation to compute the volume of distribution of the albumin label will yield the plasma volume.

The anatomy of the body fluid compartments is illustrated in Figure 5-1 . The prototypical 70-kg male has ~42 L of TBW (60% of 70 kg). Of these 42 L, ~60% (25 L) is intracellular and ~40% (17 L) is extracellular. ECF is composed of blood plasma, interstitial fluid, and transcellular fluid.

ICF is rich in K ⁺ , whereas ECF is rich in Na ⁺ and Cl ⁻

Not only do the various body fluid compartments have very different volumes, they also have radically different compositions, as summarized in Figure 5-1 . Table 5-2 is a more comprehensive listing of these values. ICF is high in K ⁺ and low in Na ⁺ and Cl ⁻ ; ECF (interstitial and plasma) are high in Na ⁺ and Cl ⁻ and low in K ⁺ . The cell maintains a relatively high K ⁺ concentration ([K ⁺ ] _i ) and low Na ⁺ concentration ([Na ⁺ ] _i ), not by making its membrane totally impermeable to these ions but by using the Na-K pump to extrude Na ⁺ actively from the cell and to transport K ⁺ actively into the cell.

TABLE 5-2

Approximate Solute Composition of Key Fluid Compartments

SOLUTE	PLASMA	PROTEIN-FREE PLASMA	INTERSTITIUM	CELL
Na + (mM)	142	153	145	15
K + (mM)	4.4	4.7	4.5	120
Ca 2+ (mM)	1.2 (ionized) 2.4 (total) *	1.3 (ionized)	1.2 (ionized)	0.0001 (ionized)
Mg 2+ (mM)	0.6 (ionized) 0.9 (total) *	0.6 (ionized)	0.55 (ionized)	1 (ionized) 18 (total)
Cl − (mM)	102	110	116	20
(mM)	22 †	24	25	16
and (mM)	0.7 (ionized) 1.4 (total) ‡	0.75 (ionized)	0.8 (ionized)	0.7 (free)
Proteins	7 g/dL 1 mmole/L 14 meq/L	—	1 g/dL	30 g/dL
Glucose (mM)	5.5	5.9	5.9	Very low
pH	7.4	7.4	7.4	~7.2
Osmolality (milliosmoles/kg H 2 O)	291	290	290	290

* Total includes amounts ionized, complexed to small solutes, and protein bound.

† Arterial value. The value in mixed-venous blood would be ~24 mM.

‡ As discussed on pages 1054–1056 , levels of total plasma inorganic phosphate are not tightly regulated and vary between 0.8 and 1.5 mM.

Transcellular fluids differ greatly in composition, both from each other and from plasma, because they are secreted by different epithelia. The two major constituents of ECF, the plasma and the interstitial fluid, have similar composition as far as small solutes are concerned. For most cells, it is the composition of the interstitial fluid enveloping the cells that is the relevant parameter. The major difference between plasma and interstitial fluid is the absence of plasma proteins from the interstitium. These plasma proteins, which cannot equilibrate across the walls of most capillaries, are responsible for the usually slight difference in small-solute con­centrations between plasma and interstitial fluid. Plasma proteins affect solute distribution because of the volume they occupy and the electrical charge they carry.

Volume Occupied by Plasma Proteins

The proteins and, to a much lesser extent, the lipids in plasma ordinarily occupy ~7% of the total plasma volume. Clinical laboratories report the plasma composition of ions (e.g., Na ⁺ , K ⁺ ) in units of milliequivalents (meq) per liter of plasma solution. However, for cells bathed by interstitial fluid, a more meaningful unit would be milliequivalents per liter of protein-free plasma solution because it is only the protein-free portion of plasma—and not the proteins dissolved in this water—that can equilibrate across the capillary wall. For example, we can obtain [Na ⁺ ] in protein-free plasma (which clinicians call plasma water) by dividing the laboratory value for plasma [Na ⁺ ] by the plasma water content (usually 93%):

Similarly, for Cl ⁻ ,

Table 5-2 lists solute concentrations in terms of both liters of plasma and liters of plasma water. If the plasma water fraction is <93% because of hyperproteinemia (high levels of protein in blood) or hyperlipemia (high levels of lipid in blood), the values that the clinical laboratory reports for electrolytes may appear abnormal even though the physiologically important concentration (solute con­centration per liter of plasma water) is normal. For example, if a patient's plasma proteins and lipids occupy 20% of plasma volume and consequently plasma water is only 80% of plasma, a correction factor of 0.80 (rather than 0.93) should be used in Equation 5-1 . If the clinical laboratory were to report a very low plasma [Na ⁺ ] of 122 meq/L plasma, the patient's [Na ⁺ ] relevant to interstitial fluid would be 122/0.80 = 153 meq/L plasma water, which is quite normal.

Effect of Protein Charge

For noncharged solutes such as glucose, the correction for protein and lipid volume is the only correction needed to predict interstitial concentrations from plasma concentrations. Because plasma proteins carry a net negative charge and because the capillary wall confines them to the plasma, they tend to retain cations in plasma. Thus, the cation concentration of the protein-free solution of the interstitium is lower by ~5%. Conversely, because these negatively charged plasma proteins repel anions, the anion concentration of the protein-free solution of the interstitium is higher by ~5%. We consider the basis for these 5% corrections in the discussion of the Gibbs-Donnan equilibrium (see pp. 128–129 ).

Thus, for a monovalent cation such as Na ⁺ , the interstitial concentration is 95% of the [Na ⁺ ] of the protein-free plasma water, the value from Equation 5-1 :

For a monovalent anion such as Cl ⁻ , the interstitial concentration is 105% of the [Cl ⁻ ] of the protein-free water of plasma, a value already obtained in Equation 5-2 :

Thus, for cations (e.g., Na ⁺ ), the two corrections (0.95/0.93) nearly cancel each other. On the other hand, for anions (e.g., Cl ⁻ ), the two corrections (1.05/0.93) are cumulative and yield a total correction of ~13%.

All body fluids have approximately the same osmolality, and each fluid has equal numbers of positive and negative charges

Electroneutrality

All solutions must respect the principle of bulk electroneutrality: the number of positive charges in the overall solution must be the same as the number of negative charges. If we add up the major cations and anions in the cytosol (see Table 5-2 ), we see that the sum of [Na ⁺ ] _i and [K ⁺ ] _i greatly exceeds the sum of [Cl ⁻ ] _i and . The excess positive charge reflected by this difference is balanced by the negative charge on intracellular macromolecules (e.g., proteins) as well as smaller anions such as organic phosphates.

There is a similar difference between major cations and anions in blood plasma, where it is often referred to as the anion gap. The clinical definition of anion gap is

Note that plasma [K ⁺ ] is ignored. The anion gap, usually 9 to 14 meq/L, is the difference between ignored anions and ignored cations. Among the ignored anions are anionic proteins as well as small anionic metabolites. Levels of anionic metabolites, such as acetoacetate and β-hydroxybutyrate, can become extremely high, for example, in type 1 diabetic patients with very low levels of insulin (see Box 51-5 ). Thus, the anion gap increases under these conditions.

The differences in ionic composition between the ICF and ECF compartments are extremely important for normal functioning of the body. For example, because the K ⁺ gradient across cell membranes is a major determinant of electrical excitability, clinical disorders of extracellular [K ⁺ ] can cause life-threatening disturbances in the heart rhythm. Disorders of extracellular [Na ⁺ ] cause abnormal extracellular osmolality, with water being shifted into or out of brain cells; if uncorrected, such disorders lead to seizures, coma, or death.

These examples of clinical disorders emphasize the absolute necessity of understanding the processes that control the volume and composition of the body fluid compartments. These processes are the ones that move water and solutes between the compartments and between the body and the outside world.

In passive, noncoupled transport across a permeable membrane, a solute moves down its electrochemical gradient

We are all familiar with the way that water can flow from one side of a dike to another, provided the water levels on the two sides of the dike are different and the water has an open pathway (a breach in the dike) to move from one side to the other. In much the same way, a substance can passively move across a membrane that separates two compartments when there is both a favorable driving force and an open pathway through which the driving force can exert its effect.

When a pathway exists for transfer of a substance across a membrane, the membrane is said to be permeable to that substance. The driving force that determines the passive transport of solutes across a membrane is the electrochemical gradient or electrochemical potential energy difference acting on the solute between the two compartments. This electrochemical potential energy difference includes a contribution from the concentration gradient of the solute—the chemical potential energy difference—and, for charged solutes (e.g., Na ⁺ , Cl ⁻ ), a contribution from any difference in voltage that exists between the two compartments—the electrical potential energy difference.

This concept of how force and pathway determine passive movement of solutes is most easily illustrated by the example of passive, noncoupled transport. Noncoupled transport of a substance X means that movement of X across the membrane is not directly coupled to the movement of any other solute or to any chemical reaction (e.g., the hydrolysis of ATP). What, then, are the driving forces for the net movement of X? Clearly, if the concentration of X is higher in the outside compartment ([X] _o ) than in the inside compartment ([X] _i ), and assuming no voltage difference, the concentration gradient will act as the driving force to bring about the net movement of X across the membrane from outside to inside ( Fig. 5-2 ). If [X] is the same on both sides but there is a voltage difference across the membrane—that is, the electrical potential energy on the outside (ψ _o ) is not the same as on the inside (ψ _i )—this voltage difference will also drive the net movement of X, provided X is charged. The concentration gradient for X and the voltage difference across the membrane are the two determinants of the electrochemical potential energy difference for X between the two compartments. Because the movement of X by such a noncoupled mechanism is not directly coupled to the movement of other solutes or to any chemical reactions, the electrochemical gradient for X is the only driving force that contributes to the transport of X. Thus, the transport of X by a noncoupled, passive mechanism must always proceed “downhill,” in the direction down the electrochemical potential energy difference for X.

Regardless of how X moves passively through the membrane—whether X moves through lipid or through a membrane protein—the direction of the overall driving force acting on X determines the direction of net transport. In the example in Figure 5-2 , the overall driving force favors net transport from outside to inside (influx). However, X may still move from inside to outside (efflux). Movement of X across the membrane in one direction or the other is known as unidirectional flux. The algebraic sum of the two unidirectional fluxes is the net flux, or the net transport rate. Net transport occurs only when the unidirectional fluxes are unequal. In Figure 5-2 , the overall driving force makes unidirectional influx greater than unidirectional efflux, which results in net influx.

When no net driving force is acting on X, we say that X is at equilibrium across the membrane and there is no net transport of X across the membrane. However, even when X is in equilibrium, there may be and usually are equal and opposite movements of X across the membrane. Net transport takes place only when the net driving force acting on X is displaced from the equilibrium point, and transport proceeds in the direction that would bring X back to equilibrium.

Equilibrium is actually a special case of a steady state. In a steady state, by definition, the conditions related to X do not change with time. Thus, a transport system is in a steady state when both the driving forces acting on it and the rate of transport are constant with time. Equilibrium is the particular steady state in which there is no net driving force and thus no net transport.

How can a steady state persist when X is not in equilibrium? Returning to the dike analogy, the downhill flow of water can be constant only if some device, such as a pump, keeps the water levels constant on both sides of the dike. A cell can maintain a nonequilibrium steady state for X only when some device, such as a mechanism for actively transporting X, can compensate for the passive movement of X and prevent the intracellular and extracellular concentrations of X from changing with time. This combination of a pump and a leak maintains both the concentrations of X and the passive flux of X.

At equilibrium, the chemical and electrical potential energy differences across the membrane are equal but opposite

As noted in the preceding section, the driving force for the passive, uncoupled transport of a solute is the electrochemical potential energy difference for that solute across the membrane that separates the inside (i) from the outside (o). We define the electrochemical potential energy difference as follows: N5-3

N5-3

Electrochemical Potential Energy Difference for an Ion Across a Cell Membrane

The chemical potential energy, or partial molar Gibbs free energy, µ _X , of an uncharged solute X is

where [X] is the concentration (more precisely, the chemical activity) of the solute, R is the gas constant ( R = 8.314 joules/[K ⋅ mole]), and T is the temperature in kelvins (K = 273.16 + °C). Thus, µ _X has the units of energy per mole of X (joule/mole). Note that “potential” in the often-used term chemical potential is shorthand for “chemical potential energy.” In the case of a cell, we must consider the chemical potential energy both on the inside (µ _X,i ) and on the outside (µ _X,o ):

Thus, if µ _X,o > µ _X,i (i.e., if [X] _o > [X] _i ), then X will spontaneously move from the outside to the inside. On the other hand, if µ _X,o < µ _X,i , then X will spontaneously move from the inside to the outside.

We can define the chemical potential energy difference (Δµ _X ) as

If solute X is charged, we must also consider the difference in partial molar free energy (Δµ _X,elec ) due to the voltage difference across the cell membrane. If the voltage inside the cell is ψ _i and the voltage outside the cell is ψ _o , then this voltage difference is (ψ _i − ψ _o ), which is also known as the membrane voltage ( V _m ). This electrical portion of the partial molar free energy change is the electrical work (joules/mole) needed to move the charge, which is on X, across the membrane and into the cell. According to the laws of physics, the electrical work per mole is the product of the voltage difference and the amount of charge/mole moved. Thus, we must multiply the voltage difference (joules/coulomb) by the Faraday constant, F (coulombs/mole), and the valence of the ion X, z _X (unitary charges/ion):

The total free energy change (Δũ _X ) required to move X into the cell is simply the sum of the chemical and electrical terms:

Equation NE 5-6 is the same as Equation 5-6 on page 106 in the main text.

where z _X is the valence of X, T is absolute temperature, R is the gas constant, and F is the Faraday constant. The first term on the right-hand side of Equation 5-6 , the difference in chemical potential energy, describes the energy change (joules per mole) as X moves across the membrane if we disregard the charge—if any—on X. The second term, the difference in electrical potential energy, describes the energy change as a mole of charged particles (each with a valence of z _X ) moves across the membrane. The difference (ψ _i − ψ _o ) is the voltage difference across the membrane ( V _m ), also known as the membrane potential.

By definition, X is at equilibrium when the electrochemical potential energy difference for X across the membrane is zero:

Thus, Δũ _X is the net driving force ( units: joules/mole). When Δũ _X is not zero, X is not in equilibrium and will obviously tend either to enter the cell or to leave the cell, provided a pathway exists for X to cross the membrane.

It is worthwhile to consider two special cases of the equilibrium state (see Equation 5-7 ). First, when either the chemical or the electrical term in Equation 5-6 is zero, the other must also be zero. For example, when X is uncharged ( z _X = 0), as in the case of glucose, equilibrium can occur only when [X] is equal on the two sides of the membrane. Alternatively, when X is charged, as in the case of Na ⁺ , but the voltage difference (i.e., V _m ) is zero, equilibrium likewise can occur only when [X] is equal on the two sides of the membrane. Second, when neither the chemical nor the electrical term in Equation 5-6 is zero, equilibrium can occur only when the two terms are equal but of opposite sign. Thus, if we set Δũ _X in Equation 5-6 to zero, as necessary for a state of equilibrium,

This relationship is the Nernst equation, which describes the conditions when an ion is in equilibrium across a membrane. Given values for [X] _i and [X] _o , X can be in equilibrium only when the voltage difference across the membrane equals the equilibrium potential ( E _X ), also known as the Nernst potential. Stated somewhat differently, E _X is the value that the membrane voltage would have to have for X to be in equilibrium.
N5-4 If we express the logarithm to the base 10, then for the special case in which the temperature is 29.5°C,

N5-4

Difference Between V _m and E _X

Equation 5-6 on page 106 in the text (shown here as Equation NE 5-7 ) states that—for ion X—the electrochemical potential energy difference across the cell membrane is

Here, each of the three major terms enclosed by horizontal braces has the dimension of energy per mole (e.g., joules/mole or kcal/mole). If we divide Equation NE 5-7 through by z _X F we obtain:

Each of the three major terms in Equation NE 5-8 now has the dimension of voltage. In other words, in dividing an energy term ( units: joules/mole) by z _X F ( units: coulombs/mole), we are left with joules/coulomb, which is the definition of a volt. The first term on the right side of Equation NE 5-7 is nothing more than the negative of the Nernst potential that we introduced in Equation 5-8 . The second term on the right side of Equation NE 5-8 is, of course, membrane potential. When V _m = E _X , the ion is in equilibrium. Otherwise, the difference ( V _m − E _X ) is the net electrochemical driving force—expressed in units of volts—that acts on ion X as the ion crosses the membrane. On page 151 of the text, we use this force to derive an expression in Equation 6-15 for the electrical current carried by ion X as the ion crosses the membrane:

Equation NE 5-9 is written in such a way that an inward current (i.e., the movement of a positively charged species into the cell or of a negatively charged species out of the cell) is negative.

Equation NE 5-9 allows us to predict the direction that ion X will passively move (if indeed it can move at all) across the membrane. Of course, if V _m = E _X , there will be no net movement of the ion at all. If V _m is more negative than E _X , then the membrane voltage is too negative for X to be in equilibrium. As a result, if X is positive, the cation will tend to passively enter the cell. For example, Na ⁺ generally tends to enter cells passively because V _m (e.g., −80 mV) is generally more negative than E _Na (e.g., +67 mV in Fig. 6-10 ). If X is negative, the anion will tend to passively exit the cell. For example, Cl ⁻ generally tends to exit cells passively because, in most cells, V _m (−60 mV) is generally more negative than E _Cl (e.g., −47 mV).

The opposite is true, of course, if V _m is more positive than E _X .

At normal body temperature (37°C), the coefficient is ~61.5 mV instead of 60 mV. At 20°C, it is ~58.1 mV. N5-5

N5-5

60 mV per 10-fold Concentration Change

We start with Equation 5-8 (shown here as Equation NE 5-10 ):

R is 8.314 joules/(K ⋅ mole), F is 96,484 coulombs/mole, and T is the temperature in kelvins (K = 273.16 + °C). In order to convert the natural logarithm to the logarithm in base 10, we must multiply the “ln” term by ln(10), which is ~2.303. For the term 2.303 RT / F to be exactly 60 mV, the temperature must be 29.5°C (302.66 K):

Indeed, this is Equation 5-9 .

To illustrate the use of Equation 5-9 we compute E _X for a monovalent cation, such as K ⁺ . If [K ⁺ ] _i is 100 mM and [K ⁺ ] _o is 10 mM, a 10-fold concentration gradient, then

Thus, a 10-fold gradient of a monovalent ion such as K ⁺ is equivalent, as a driving force, to a voltage difference of 60 mV. For a divalent ion such as Ca ²⁺ , a 10-fold concentration gradient can be balanced as a driving force by a voltage difference of 60 mV/2, or only 30 mV.

( V _m − E _X ) is the net electrochemical driving force acting on an ion

When dealing with an ion (X), it is more convenient to think about the net driving force in voltage ( units: millivolts) rather than electrochemical potential energy difference ( units: joules per mole). If we divide all terms in Equation 5-6 by the product of valence and the Faraday constant ( z _X F ), we obtain

Because the energy terms previously expressed as joules per mole were divided by coulombs per mole (i.e., z _X F )—all three energy terms enclosed in braces are now in units of joules per coulomb or volts. The term on the left is the net electrochemical driving force acting on ion X. The first term on the right, as defined in Equation 5-8 , is the negative of the Nernst equilibrium potential (− E _X ). The second term on the right is the membrane voltage ( V _m ). Thus, a convenient equation expressing the net driving force is

In Table 5-3 , we use this equation—along with the values in Table 5-2 for extracellular (i.e., interstitial) and intracellular concentrations and a typical V _m of −60 mV—to compute the net driving force of Na ⁺ , K ⁺ , Ca ²⁺ , Cl ⁻ ,
, and H ⁺ . When the net driving force is negative, cations will enter the cell and anions will exit. Stated differently, when V _m is more negative than E _X (i.e., the cell is too negative for X to be in equilibrium), a cation will tend to enter the cell and an anion will tend to exit.

TABLE 5-3

Net Electrochemical Driving Forces Acting on Ions in a Typical Cell *

EXTRACELLULAR CONCENTRATION [X] o	INTRACELLULAR CONCENTRATION [X] i	MEMBRANE VOLTAGE V m	EQUILIBRIUM POTENTIAL (mV) E X = −( RT/z X F ) ln ([X] i /[X] o )	ELECTROCHEMICAL DRIVING FORCE ( V m − E X )
Na + 145 mM	15 mM	−60 mV	+61 mV	−121 mV
K + 4.5 mM	120 mM	−60 mV	−88 mV	+28 mV
Ca 2+ 1.2 mM	10 −7 M	−60 mV	+125 mV	−185 mV
Cl − 116 mM	20 mM	−60 mV	−47 mV	−13 mV
25 mM	16 mM	−60 mV	−12 mV	−48 mV
H + 40 nM pH 7.4	63 nM 7.2	−60 mV	−12 mV	−48 mV

* Calculated at 37°C using − RT / z _x F = −26.71 mV.

In simple diffusion, the flux of an uncharged substance through membrane lipid is directly proportional to its concentration difference

The difference in electrochemical potential energy of a solute X across the membrane is a useful parameter because it allows us to predict whether X is in equilibrium across the cell membrane (i.e., Is Δũ _X = 0?) or, if not, whether X would tend to passively move into the cell or out of the cell. As long as the movement of X is not coupled to the movement of another substance or to some biochemical reaction, the only factor that determines the direction of net transport is the driving force Δũ _X = 0. The ability to predict the movement of X is independent of any detailed knowledge of the actual transport pathway mediating its passive transport. In other words, we can understand the overall energetics of X transport without knowing anything about the transport mechanism itself, other than knowing that it is passive.

So far, we have discussed only the direction of net transport, not the rate. How will the rate of X transport vary if we vary the driving force Δũ _X ? Unlike determining the direction, determining the rate—that is, the kinetics —of transport requires knowing the peculiarities of the actual mechanism that mediates passive X transport.

Most transport systems are so complicated that a straightforward relationship between transport rate and Δũ _X may not exist. Here we examine the simplest case, which is simple diffusion. How fast does an uncharged, hydrophobic solute move through a lipid bilayer? Gases (e.g., CO ₂ ), a few endogenous compounds (e.g., steroid hormones), and many drugs (e.g., anesthetics) are both uncharged and hydrophobic. Imagine that such a solute is present on both sides of the membrane but at a higher concentration on the outside (see Fig. 5-2 ). Because X has no electrical charge and because [X] _o is greater than [X] _i , the net movement of X will be into the cell. How fast X moves is described by its flux ( J _X ); namely, the number of moles of X crossing a unit area of membrane (typically 1 cm ² ) per unit time (typically 1 second). Thus, J _X has the units of moles/(square centimeter ⋅ second). The better that X can dissolve in the membrane lipid (i.e., the higher the lipid-water partition coefficient of X), the more easily X will be able to traverse the membrane-lipid barrier. The flux of X will also be greater if X moves more readily once it is in the membrane (i.e., a higher diffusion coefficient ) and if the distance that it must traverse is short (i.e., a smaller membrane thickness ). We can combine these three factors into a single parameter called the permeability coefficient of X ( P _X ). N5-6 Finally, the flux of X will be greater as the difference in [X] between the two sides of the membrane increases (a large gradient ).

N5-6

Definition of the Permeability Coefficient

The permeability coefficient (P) is

D is the diffusion coefficient (in cm ² /s), β is the partition coefficient (concentration in the lipid divided by the concentration in the bulk aqueous phase; a dimensionless number), and a is the thickness of the membrane (in cm). Thus, the units of the permeability coefficient are cm/s.

These concepts governing the simple diffusion of an electrically neutral substance were quantified by Adolf Fick in the 1800s and applied by others to the special case of a cell membrane. They are embodied in the following equation, which is a simplified version of Fick's law:

As already illustrated in Figure 5-2 , we can separate the net flux of X into a unidirectional influx ( ) and a unidirectional efflux ( ). The net flux of X into the cell is simply the difference between the unidirectional fluxes:

Thus, unidirectional influx is proportional to the outside concentration, unidirectional efflux is proportional to the inside concentration, and net flux is proportional to the concentration difference (not the ratio [X] _o /[X] _i , but the difference [X] _o − [X] _i ). In all cases, the proportionality constant is P _X .

A description of the kinetic behavior of a transport system (see Equation 5-14 )—that is, how fast things move—cannot violate the laws of energetics, or thermodynamics (see Equation 5-6 )—that is, the direction in which things move to restore equilibrium. For example, the laws of thermodynamics (see Equation 5-6 ) predict that when the concentration gradient for a neutral substance is zero (i.e., when [X] _o /[X] _i = 1), the system is in equilibrium and therefore the net flux must be zero. The law of simple diffusion (see Equation 5-14 ), which is a kinetic description, also predicts that when the concentration gradient for a neutral substance is zero (i.e., [X] _o − [X] _i = 0), the flux is zero.

Some substances cross the membrane passively through intrinsic membrane proteins that can form pores, channels, or carriers

Because most ions and hydrophilic solutes of biological interest partition poorly into the lipid bilayer, simple passive diffusion of these solutes through the lipid portion of the membrane is negligible. Noncoupled transport across the plasma membrane generally requires specialized pathways that allow particular substances to cross the lipid bilayer. In all known cases, such pathways are formed from integral membrane proteins. Three types of protein pathways through the membrane are recognized:

• 1

  The membrane protein forms a pore that is always open ( Fig. 5-3 A ). Physiological examples are the porins in the outer membranes of mitochondria, cytotoxic pore-forming proteins such as the perforin released by lymphocytes, and perhaps the aquaporin water channels. A physical equivalent is a straight, open tube. If you look though this tube, you always see light coming through from the opposite side.

  

• 2

  The membrane protein forms a channel that is alternately open and closed because it is equipped with a movable barrier or gate (see Fig. 5-3 B ). Physiological examples include virtually all ion channels, such as the ones that allow Na ⁺ , Cl ⁻ , K ⁺ , and Ca ²⁺ to cross the membrane. The process of opening and closing of the barrier is referred to as gating. Thus, a channel is a gated pore, and a pore is a nongated channel. A physical equivalent is a tube with a shutter near one end. As you look through this tube, you see the light flickering as the shutter opens and closes.

• 3

  The membrane protein forms a carrier surrounding a conduit that never offers a continuous transmembrane path because it is equipped with at least two gates that are never open at the same time (see Fig. 5-3 C ). Between the two gates is a compartment that can contain one or more binding sites for the solute. If the two gates are both closed, one (or more) of the transiting particles is trapped, or occluded, in that compartment. Physiological examples include carriers that move single solutes through the membrane by a process known as facilitated diffusion, which is discussed in the next section. A physical equivalent is a tube with shutters at both ends. As you look through this tube, you never see any light passing through because both shutters are never open simultaneously.

Water-filled pores can allow molecules, some as large as 45 kDa, to cross membranes passively

Some membrane proteins form pores that provide an aqueous transmembrane conduit that is always open (see Fig. 5-3 A ). Among the large-size pores are the porins ( Fig. 5-4 ) found in the outer membranes of gram-negative bacteria and mitochondria. Mitochondrial porin allows solutes as large as 5 kDa to diffuse passively from the cytosol into the mitochondria's intermembrane space.

One mechanism by which cytotoxic T lymphocytes kill their target cells is the release of monomers of a pore-forming protein known as perforin. Perforin monomers polymerize within the target cell membrane and assemble like staves of a barrel to form large, doughnut-like channels with an internal diameter of 16 nm. The passive flow of ions, water, and other small molecules through these pores kills the target cell. A similar pore plays a crucial role in the defense against bacterial infections. The binding of antibodies to an invading bacterium (“classic” pathway), or simply the presence of native polysaccharides on bacteria (“alternative” pathway), triggers a cascade of reactions known as the complement cascade. This cascade culminates in the formation of a doughnut-like structure with an internal diameter of 10 nm. This pore is made up of monomers of C9, the final component of the complement cascade.

The nuclear pore complex (NPC), which regulates traffic into and out of the nucleus (see p. 21 ), is remarkably large. The NPC is made up of at least 30 different proteins and has a molecular mass of 10 ⁸ Da and an outer diameter of ~100 nm. It can transport huge molecules (approaching 10 ⁶ Da) in a complicated process that involves ATP hydrolysis. In addition to this active component of transport, the NPC also has a passive component. Contained within the massive NPC is a simple aqueous pore with an internal diameter of ~9 nm that allows molecules <45 kDa to move between the cytoplasm and nucleus but almost completely restricts the movement of globular proteins that are larger than ~60 kDa.

The plasma membranes of many types of cells have proteins that form channels just large enough to allow water molecules to pass through. The first water channel to be studied was aquaporin 1 (AQP1), a 28-kDa protein. AQP1 belongs to a larger family of aquaporins (AQPs) that has representatives in organisms as diverse as bacteria, plants, and animals. In mammals, the various AQPs have different tissue distributions, different mechanisms of regulation, and varying abilities to transport small neutral molecules other than water. In the lipid bilayer, AQP1 ( Fig. 5-5 ) exists as tetramers. Each monomer consists of six membrane-spanning helices as well as two shorter helices that dip into the plane of the membrane. These structures form a permeation pathway for the single-file diffusion of water. For his discovery of the aquaporins, Peter Agre shared the 2003 Nobel Prize in Chemistry. N5-7

Gated channels, which alternately open and close, allow ions to cross the membrane passively

Gated ion channels, like the AQPs just discussed, consist of one or more polypeptide subunits with α-helical membrane-spanning segments. These channels have several functional components (see Fig. 5-3 B ). The first is a gate that determines whether the channel is open or closed, with each state reflecting a different conformation of the membrane protein. Second, the channel generally has one or more sensors that can respond to one of several different types of signals: (1) changes in membrane voltage, (2) second-messenger systems that act at the cytoplasmic face of the membrane protein, or (3) ligands, such as neurohumoral agonists, that bind to the extracellular face of the membrane protein. These signals regulate transitions between the open and closed states. A third functional component is a selectivity filter, which determines the classes of ions (e.g., anions or cations) or the particular ions (e.g., Na ⁺ , K ⁺ , Ca ²⁺ ) that have access to the channel pore. The fourth component is the actual open channel pore (see Fig. 5-3 B ). Each time that a channel assumes the open conformation, it provides a continuous pathway between the two sides of the membrane so that ions can flow through it passively by diffusion until the channel closes again. During each channel opening, many ions flow through the channel pore, usually a sufficient number to be detected as a small current by sensitive patch-clamp techniques (see p. 154 ).

Some carriers facilitate the passive diffusion of small solutes such as glucose

Carrier-mediated transport systems transfer a broad range of ions and organic solutes across the plasma membrane. Each carrier protein has a specific affinity for binding one or a small number of solutes and transporting them across the bilayer. The simplest passive carrier-mediated transporter is one that mediates facilitated diffusion. Below, we will introduce cotransporters (which carry two or more solutes in the same direction) and exchangers (which move them in opposite directions).

All carriers that do not either hydrolyze ATP or couple to an electron transport chain are members of the solute carrier (SLC) superfamily, N5-8 which is organized according to the homology of the deduced amino-acid sequences ( Table 5-4 ). Each of the 52 SLC families contains up to 53 genes that encode proteins that share a relatively high amino-acid sequence identity (20% to 25%). Moreover, each gene may encode multiple variants (see Fig 4-19 ). Members of an SLC family may differ in molecular mechanism (i.e., facilitated diffusion, cotransport, exchange), kinetic properties (e.g., solute specificity and affinity), regulation (e.g., phosphorylation), sites of membrane targeting (e.g., plasma membrane versus intracellular organelles), tissues in which they are expressed (e.g., kidney versus brain), or developmental stage at which they are expressed.

TABLE 5-4

The SLC Superfamily of Solute Carriers
N5-8

FAMILY	DESCRIPTION	EXAMPLES
SLC1 (7) *	Glutamate transporters	EAAT1, 2, 3, 4, 5 ASCT1, 2
SLC2 (14)	Facilitated transport of hexoses	GLUT1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14; HMIT
SLC3 (2)	Heavy subunits of heterodimeric amino-acid transporters (with SLC7)	rBAT system 4F2hc system
SLC4 (10)	exchangers and cotransporters	AE1, 2, 3 (Cl-HCO 3 exchangers) NBCe1, 2 (electrogenic Na/HCO 3 cotransporters) NBCn1, 2 (electroneutral Na/HCO 3 cotransporters) NDCBE (Na + -driven Cl-HCO 3 exchanger)
SLC5 (12)	Na/glucose cotransporters	SGLT1, 2, 3, 4, 5 (glucose); NIS (iodide); SMIT1, 2(myoinositol) SMCT1, 2 (monocarboxylates) SMVT (biotin) CHT (choline)
SLC6 (21)	Na + - and Cl − -coupled cotransport of “neurotransmitters”	B 0 AT1 (Na + -coupled amino acid) GAT1, 2, 3; GBT1 (Na + - and Cl − -coupled GABA) ATB 0+ (Na + - and Cl − -coupled amino acids) NET (norepinephrine transporters) SERT (serotonin) DAT (dopamine)
SLC7 (14)	Transporter subunits of heterodimeric amino-acid transporters (with SLC3)	LAT1, 2; y + LAT1, 2 CAT1, 2, 3, 4
SLC8 (3)	Na-Ca exchangers	NCX1, 2, 3
SLC9 (13)	Na-H exchangers	NHE1, 2, 3, 4, 5, 6, 7, 8, 9 NHA1, 2 Sperm-NHE
SLC10 (7)	Na/bile-salt cotransporters	ASBT
SLC11 (2)	H + -driven metal-ion cotransporters	DMT1 NRAMP1
SLC12 (9)	Cation-coupled Cl − cotransporters	NKCC1, 2 (Na/K/Cl cotransporter) NCC (Na/Cl cotransporter) KCC1, 2, 3, 4 (K/Cl cotransporter)
SLC13 (5)	Na + -coupled sulfate and carboxylate cotransporters	NaDC1, 3 (mono-, di-, and tricarboxylates) NaS1, 2 (sulfate)
SLC14 (2)	Facilitated transport of urea	UT-A1, 2, 3, 4, 5, 6; UT-B1, 2
SLC15 (4)	H + -driven oligopeptide cotransporters	PepT1, 2 PhT1, 2
SLC16 (14)	Monocarboxylate transporters	MCT1, 2, 3, 4 (H + -coupled monocarboxylate cotransporter) MCT8, 10 (facilitated diffusion of aromatic amino acids)
SLC17 (9)	Type I Na/phosphate cotransporters and vesicular Glu transporters	NaPi-I NPT1, 3, 4 VNUT VGLUT1, 2, 3
SLC18 (4)	Vesicular monoamine transporters	VMAT1, 2 (H + -amine exchanger) VAChT (H + -acetylcholine exchanger)
SLC19 (3)	Folate/thiamine transporters	RFC ThTr1, 2
SLC20 (2)	Type III Na/phosphate cotransporters	PiT-1, 2
SLC21 (11) or SLCO	Organic anion and cation transporters	OATP1, 2, 3, 4, 5, 6 (bile salts, thyroid hormones, prostaglandins)
SLC22 (23)	Organic cation, anion, zwitterion transporters	OCT1, 2, 3 (facilitated diffusion of organic cations ) OCTN1 (organic cation -H exchanger) OCTN2 (Na/organic cation cotransporter) OAT1, 2, 3, 4, 5, 7, 10 (exchange or facilitated diffusion of organic anions ) URAT1 (urate exchanger)
SLC23 (4)	Na/ascorbic acid transporters	SVCT1, 2, 3, 4
SLC24 (5)	Na + /(Ca 2+ -K + ) exchanger	NCKX1, 2, 3, 4, 5
SLC25 (53)	Mitochondrial carriers	ANC1, 2, 3, 4 (ANT1, 2, 3, 4)
SLC26 (11)	Multifunctional anion exchangers	DRA (Cl-HCO 3 exchanger) Pendrin (exchanges , Cl − or I − ) Prestin (exchanges Cl − , formate, oxalate; a motor in cochlear hair cells) CFEX (exchanges Cl − , , oxalate, formate)
SLC27 (6)	Fatty-acid transporters	FATP1, 2, 3, 4, 5, 6
SLC28 (3)	Na/nucleoside transporters	CNT1, 2, 3
SLC29 (4)	Facilitative nucleoside transporters	ENT1, 2, 3, 4
SLC30 (10)	Zinc efflux transporter	ZnT1, 2, 3, 4, 5, 6, 7, 8, 9, 10
SLC31 (2)	Copper importer	CTR1, 2
SLC32 (1)	Vesicular inhibitory amino-acid transporter	VIAAT (exchange of H + for GABA or glycine)
SLC33 (1)	Acetyl–coenzyme A transporter	ACATN1
SLC34 (3)	Type II Na/phosphate cotransporters	NaPi-IIa, b, c
SLC35 (30)	Nucleoside-sugar transporter	HFRC CST UGT PAPST1, 2
SLC36 (4)	H + -coupled amino-acid cotransporters	PAT1, 2, 3, 4
SLC37 (4)	Sugar-phosphate/phosphate exchanger	SPX1, 2, 3, 4
SLC38 (11)	Na + -driven neutral amino acids (system A and N)	SNAT1, 2, 4 (system A, cotransports amino acids with Na + ) SNAT3, 5 (system N, cotransports amino acids with Na + in exchange for H + )
SLC39 (14)	Metal-ion transporters	ZIP1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 (uptake of Zn 2+ )
SLC40 (1)	Basolateral Fe 2+ transporter	Ferroportin (FPN1)
SLC41 (3)	MgtE-like magnesium transporter	MgtE
SLC42 (3)	, CO 2 channels	RhAG, RhBG, RhCG
SLC43 (3)	Na + -independent, system L–like amino-acid transporter	LAT3, 4 EEG1
SLC44 (5)	Choline-like transporter	CTL1, 2, 3, 4, 5
SLC45 (4)	Putative sugar transporter	Past-A MATP Prostein
SLC46 (3)	Folate transporter	PCFT TSCOT
SLC47 (2)	Multidrug and toxin extrusion transporter	MATE1, 2
SLC48 (1)	Heme transporter	HRG-1 (heme responsive gene 1)
SLC49 (4)	FLVCR-related transporter	FLVCR1, 2 MFSD7 DIRC2
SLC50 (1)	Sugar efflux transporter	SWEET1
SLC51 (2)	Steroid-derived molecule transporters	OSTα, OSTβ
SLC52 (3)	Riboflavin transporter	RFVT1, 2, 3

GABA, gamma-aminobutyric acid.

* In parentheses is the number of human genes in the family. Members of individual families generally are named SLCxAy (e.g., SLC4A4), where x is a number identifying the family and y is a number identifying the gene within that family.

Carrier-mediated transport systems behave according to a general kinetic scheme for facilitated diffusion that is outlined in Figure 5-3 C . This model illustrates how, in a cycle of six steps, a carrier can passively move a solute X into the cell.

This mechanism can mediate only the downhill, or passive, transport of X. Therefore, it mediates a type of diffusion, called facilitated diffusion. When [X] is equal on the two sides of the membrane, no net transport will take place, although equal and opposite unidirectional fluxes of X may still occur.

In a cell membrane, a fixed number of carriers is available to transport X. Furthermore, each carrier has a limited speed with which it can cycle through the steps illustrated in Figure 5-3 C . Thus, if the extracellular X concentration is gradually increased, for example, the influx of X will eventually reach a maximal value once all the carriers have become loaded with X. This situation is very different from the one that exists with simple diffusion—that is, the movement of a solute through the lipid phase of the membrane. Influx by simple diffusion increases linearly with increases in [X] _o , with no maximal rate of transport. As an example, if X is initially absent on both sides of the membrane and we gradually increase [X] on one side, the net flux of X ( J _X ) is described by a straight line that passes through the origin ( Fig. 5-6 A ). However, with carrier-mediated transport, J _X reaches a maximum ( J _max ) when [X] is high enough to occupy all the carriers in the membrane (see Fig. 5-6 B ). Thus, the relationship describing carrier-mediated transport follows the same Michaelis-Menten kinetics as do enzymes:

This equation describes how the velocity of an enzymatic reaction (V) depends on the substrate concentration ([S]), the Michaelis constant ( K _m ), and the maximal velocity ( V _max ). The comparable equation for carrier-mediated transport is identical, except that fluxes replace reaction velocities:

Thus, K _m is the solute concentration at which J _X is half of the maximal flux ( J _max ). The lower the K _m , the higher the apparent affinity of the transporter for the solute.

Historically, the name carrier suggested that carrier-mediated transport occurs as the solute binds to a miniature ferryboat that shuttles back and forth across the membrane. Small polypeptides that act as shuttling carriers exist in nature, as exemplified by the antibiotic valinomycin. Such “ion carriers,” or ionophores, bind to an ion on one side of the membrane, diffuse across the lipid phase of the membrane, and release the ion on the opposite side of the membrane. Valinomycin is a K ⁺ ionophore that certain bacteria produce to achieve a selective advantage over their neighbors. However, none of the known carrier-mediated transport pathways in animal cell membranes are ferries.

Examples of membrane proteins that mediate facilitated diffusion are the GLUT glucose transporters ( Fig. 5-7 ), members of the SLC2 family (see Table 5-4 ). The GLUTs have 12 membrane-spanning segments as well as multiple hydrophilic polypeptide loops facing either the ECF or the ICF. They could not possibly act as a ferryboat shuttling back and forth across the membrane. Instead, some of the membrane-spanning segments of carrier-mediated transport proteins most likely form a permeation pathway through the lipid bilayer, as illustrated by the amphipathic membrane-spanning segments 7, 8, and 11 in Figure 5-7 . These membrane-spanning segments, as well as other portions of the protein, probably also act as the gates and solute-binding sites that allow transport to proceed in the manner outlined in Figure 5-3 C .

The SLC2 family includes 14 transporters (GLUTs). Whereas GLUT1 is constitutively expressed on the cell surface, GLUT4 in the basal state is predominantly present in the membranes of intracellular vesicles, which represent a storage pool for the transporters. Because a solute such as glucose permeates the lipid bilayer so poorly, its uptake by the cell depends strictly on the activity of a carrier-mediated transport system for glucose. Insulin increases the rate of carrier-mediated glucose transport into certain cells by recruiting the GLUT4 isoform to the plasma membrane from the storage pool (see p. 1047 ).

Two other examples of transporters that mediate facilitated diffusion are the urea transporter (UT) family, which are members of the SLC14 family (see Table 5-4 ), and the organic cation transporter (OCT) family, which are members of the SLC22 family. Because OCT moves an electrical charge (i.e., carries current), it is said to be electrogenic.

The physical structures of pores, channels, and carriers are quite similar

Pores, ion channels, and carriers all have multiple transmembrane segments surrounding a solute permeation pathway. Moreover, some channels also contain binding sites within their permeation pathways, so transport is saturable with respect to ion concentration. However, pores, channels, and carriers are fundamentally distinct kinetically ( Table 5-5 ). Pores, such as the porins, are thought to be continuously open and allow vast numbers of particles to cross the membrane. No evidence suggests that pores have conformational states. Channels undergo conformational transitions between closed and open states. When they are open, they are open to both intracellular and extracellular solutions simultaneously. Thus, while the channel is open, it allows multiple ions, perhaps millions, to cross the membrane per open event. Because the length of time that a particular channel remains open varies from one open event to the next, the number of ions flowing through that channel per open event is not fixed. Carriers have a permeation pathway that is virtually never open simultaneously to both intracellular and extracellular solutions. Whereas the fundamental event for a channel is opening, the fundamental event for a carrier is a complete cycle of conformational changes. Because the binding sites in a carrier are limited, each cycle of a carrier can transport only one or a small, fixed number of solute particles. Thus, the number of particles per second that can move across the membrane is generally several orders of magnitude lower for a single carrier than for a single channel.

We have seen how carriers can mediate facilitated diffusion of glucose, which is a passive or downhill process. However, carriers can also mediate coupled modes of transport. The remainder of this section is devoted to these carriers, which act as pumps, cotransporters, and exchangers.

The Na-K pump, the most important primary active transporter in animal cells, uses the energy of ATP to extrude Na ⁺ and take up K ⁺

Active transport is a process that can transfer a solute uphill across a membrane—that is, against its electrochemical potential energy difference. In primary active transport, the driving force needed to cause net transfer of a solute against its electrochemical gradient comes from the favorable energy change that is associated with an exergonic chemical reaction, such as ATP hydrolysis. In secondary active transport, the driving force is provided by coupling the uphill movement of that solute to the downhill movement of one or more other solutes for which a favorable electrochemical potential energy difference exists. A physical example is to use a motor-driven winch to lift a large weight into the air (primary active transport) and then to transfer this large weight to a seesaw, on the other end of which is a lighter child. The potential energy stored in the elevated weight will then lift the child (secondary active transport). For transporters, it is commonly the favorable inwardly directed Na ⁺ electrochemical gradient, which itself is set up by a primary active transporter, that drives the secondary active transport of another solute. In this and the next section, we discuss primary active transporters, which are also referred to as pumps. The pumps discussed here are all energized by ATP hydrolysis and hence are ATPases.

As a prototypic example of a primary active transporter, consider the nearly ubiquitous Na-K pump (or Na,K-ATPase, NKA ). This substance was the first enzyme recognized to be an ion pump, a discovery for which Jens Skou shared the 1997 Nobel Prize in Chemistry. N5-9 The Na-K pump is located in the plasma membrane and has both α and β subunits ( Fig. 5-8 A ). The α subunit, which has 10 transmembrane segments, is the catalytic subunit that mediates active transport. The β subunit, which has one transmembrane segment, is essential for proper assembly and membrane targeting of the Na-K pump. Four α isoforms and two β isoforms have been described. These isoforms have different tissue and developmental patterns of expression as well as different kinetic properties.

With each forward cycle, the pump couples the extrusion of three Na ⁺ ions and the uptake of two K ⁺ ions to the intracellular hydrolysis of one ATP molecule. By themselves, the transport steps of the Na-K pump are energetically uphill; that is, if the pump were not an ATPase, the transporter would run in reverse, with Na ⁺ leaking into the cell and K ⁺ leaking out. Indeed, under extreme experimental conditions, the Na-K pump can be reversed and forced to synthesize ATP! However, under physiological conditions, hydrolysis of one ATP molecule releases so much free energy—relative to the aggregate free energy needed to fuel the uphill movement of three Na ⁺ and two K ⁺ ions—that the pump is poised far from its equilibrium and brings about the net active exchange of Na ⁺ for K ⁺ in the desired directions.

Although animal cells may have other pumps in their plasma membranes, the Na-K pump is the only primary active transport process for Na ⁺ . The Na-K pump is also the most important primary active transport mechanism for K ⁺ . In cells throughout the body, the Na-K pump is responsible for maintaining a low [Na ⁺ ] _i and a high [K ⁺ ] _i relative to ECF. In most epithelial cells, the Na-K pump is restricted to the basolateral side of the cell.

The Na-K pump exists in two major conformational states: E ₁ , in which the binding sites for the ions face the inside of the cell; and E ₂ , in which the binding sites face the outside. The Na-K pump is a member of a large superfamily of pumps known as E ₁ -E ₂ ATPases or P-type ATPases. It is the ordered cycling between these two states that underlies the action of the pump. Figure 5-8 B is a simplified model showing the eight stages of this catalytic cycle of the α subunit:

• Stage 1: ATP-bound E ₁ ⋅ ATP state. The cycle starts with the ATP-bound E ₁ conformation, just after the pump has released its bound K ⁺ to the ICF. The Na ⁺ -binding sites face the ICF and have high affinities for Na ⁺ .

• Stage 2: Na ⁺ -bound E ₁ ⋅ ATP ⋅ 3Na ⁺ state. Three intracellular Na ⁺ ions bind.

• Stage 3: Occluded E ₁ -P ⋅ (3Na ⁺ ) state. The ATP previously bound to the pump phosphorylates the pump at an aspartate residue. Simultaneously, ADP leaves. This phosphorylation triggers a minor conformational change in which the E ₁ form of the pump now occludes the three bound Na ⁺ ions within the permeation pathway. In this state, the Na ⁺ -binding sites are inaccessible to both the ICF and ECF.

• Stage 4: Deoccluded E ₂ -P ⋅ 3Na ⁺ state. A major conformational change shifts the pump from the E ₁ to the E ₂ conformation and has two effects. First, the pump becomes deoccluded, so that the Na ⁺ -binding sites now communicate with the extracellular solution. Second, the Na ⁺ affinities of these binding sites decrease.

• Stage 5: Empty E ₂ -P state. The three bound Na ⁺ ions dissociate into the external solution, and the protein undergoes a minor conformational change to the empty E ₂ -P form, which has high affinity for binding of extracellular K ⁺ . However, the pore still communicates with the extracellular solution.

• Stage 6: K ⁺ -bound E ₂ -P ⋅ 2K ⁺ state. Two K ⁺ ions bind to the pump.

• Stage 7: Occluded E ₂ ⋅ (2K ⁺ ) state. Hydrolysis of the acylphosphate bond, which links the phosphate group to the aspartate residue, releases the inorganic phosphate into the intracellular solution and causes a minor conformational change. In this E ₂ ⋅ (2K ⁺ ) state, the pump occludes the two bound K ⁺ ions within the permeation pathway so that the K ⁺ -binding sites are inaccessible to both the ECF and ICF.

• Stage 8: Deoccluded E ₁ ⋅ ATP ⋅ 2K ⁺ state. Binding of intracellular ATP causes a major conformational change that shifts the pump from the E ₂ back to the E ₁ state. This conformational change has two effects. First, the pump becomes deoccluded, so that the K ⁺ -binding sites now communicate with the intracellular solution. Second, the K ⁺ affinities of these binding sites decrease.

• Stage 1: ATP-bound E ₁ ⋅ ATP state. Dissociation of the two bound K ⁺ ions into the intracellular solution returns the pump to its original E ₁ ⋅ ATP state, ready to begin another cycle.

Because each cycle of hydrolysis of one ATP molecule is coupled to the extrusion of three Na ⁺ ions from the cell and the uptake of two K ⁺ ions, the stoichiometry of the pump is three Na ⁺ to two K ⁺ , and each cycle of the pump is associated with the net extrusion of one positive charge from the cell. Thus, the Na-K pump is electrogenic.

Just as glucose flux through the GLUT1 transporter is a saturable function of [glucose], the rate of active transport by the Na-K pump is a saturable function of [Na ⁺ ] _i and [K ⁺ ] _o . The reason is that the number of pumps is finite and each must bind three Na ⁺ ions and two K ⁺ ions. The transport rate is also a saturable function of [ATP] _i and therefore depends on the metabolic state of the cell. In cells with high Na-K pump rates, such as renal proximal tubules, a third or more of cellular energy metabolism is devoted to supplying ATP to the Na-K pump.

A hallmark of the Na-K pump is that it is blocked by a class of compounds known as cardiac glycosides, examples of which are ouabain and digoxin; digoxin is widely used for a variety of cardiac conditions. These compounds have a high affinity for the extracellular side of the E ₂ -P state of the pump, which also has a high affinity for extracellular K ⁺ . Thus, the binding of extracellular K ⁺ competitively antagonizes the binding of cardiac glycosides. An important clinical correlate is that hypokalemia (a low [K ⁺ ] in blood plasma) potentiates digitalis toxicity in patients.

Besides the Na-K pump, other P-type ATPases include the H-K and Ca pumps

The family of P-type ATPases—all of which share significant sequence similarity with the α subunit of the Na-K pump—includes several subfamilies.

The F-type and the V-type ATPases transport H ⁺

F-type or F _o F ₁ ATPases

The ATP synthase of the inner membrane of mitochondria, also known as an F-type or F _o F ₁ ATPase, catalyzes the final step in the ATP synthesis pathway. N5-11

N5-11

ATP Synthase

A Pump in Reverse

The apparent paradox of how the same “pump” protein can act both as an ATP ase and an ATP synthase can be resolved if we recognize that the pump can either hydrolyze ATP and use the energy to pump H ⁺ out of the mitochondrion or—in the physiological direction—use the energy of the inwardly directed H ⁺ gradient to synthesize ATP.

The F _o F ₁ ATPase of mitochondria ( Fig. 5-9 A ) looks a little like a lollipop held in your hand. The hand-like F _o portion is embedded in the membrane and serves as the pathway for H ⁺ transport. The F _o portion has at least three different subunits (a, b, and c), for an overall stoichiometry of ab ₂ c _10–12 . The lollipop-like F ₁ portion is outside the plane of the membrane and points into the mitochondrial matrix. The “stick” consists of a γ subunit, with an attached ε subunit. The “candy” portion of F ₁ , which has the ATPase activity, consists of three alternating pairs of α and β subunits as well as an attached δ subunit. Thus, the overall stoichiometry of F ₁ is α ₃ β ₃ γδε. The entire F _o F ₁ complex has a molecular mass of ~500 kDa.

A fascinating property of the F _o F ₁ ATPase is that parts of it rotate. We can think of the hand, stick, and candy portions of the F _o F ₁ ATPase as having three distinct functions. (1) The hand (the c proteins of F _o ) acts as a turbine that rotates in the plane of the membrane, driven by the H ⁺ ions that flow through the turbine—down the H ⁺ electrochemical gradient—into the mitochondrion. (2) The stick is an axle (γ and ε subunits of F ₁ ) that rotates with the turbine. (3) The candy (the α and β subunits of F ₁ ) is a stationary chemical factory—energized by the rotating axle—that synthesizes one ATP molecule for each 120-degree turn of the turbine/axle complex. In addition, the a and b subunits of F _o , and possibly the δ subunit of F ₁ , form a stator that holds the candy in place while the turbine/axle complex turns. Paul Boyer and John Walker shared part of the 1997 Nobel Prize in Chemistry for elucidating this “rotary catalysis” mechanism. N5-12

N5-12

Paul Boyer and John Walker

For more information about Paul Boyer and John Walker and the work that led to their Nobel Prize, visit http://www.nobel.se/chemistry/laureates/1997/index.html (accessed October 2014).

Under physiological conditions, the mitochondrial F _o F ₁ ATPase runs as an ATP synthase (i.e., “backward” for an H pump)—the final step in oxidative phosphorylation—because of a large, inwardly directed H ⁺ gradient across the inner mitochondrial membrane (see Fig. 5-9 B ). The citric acid cycle captures energy as electrons and transfers these electrons to reduced nicotinamide adenine dinucleotide (NADH) N5-13 and reduced flavin adenine dinucleotide (FADH ₂ ). NADH and FADH ₂ transfer their high-energy electrons to the electron transport chain, which consists of four major complexes on the inner membrane of the mitochondrion (see Fig. 5-9 B ). As this “respiratory chain” transfers the electrons from one electron carrier to another, the electrons gradually lose energy until they finally combine with 2 H ⁺ and O ₂ to form H ₂ O. Along the way, three of the four major complexes of the respiratory chain (I, III, IV) pump H ⁺ across the inner membrane into the intermembrane space (i.e., the space between the inner and outer mitochondrial membranes). These “pumps” are not ATPases. The net result is that electron transport has established a large out-to-in H ⁺ gradient across the mitochondrial inner membrane.

N5-13

NADH/NAD ⁺ versus NADPH/NADP ⁺

NADH and NAD ⁺ are, respectively, the reduced and oxidized forms of nicotinamide adenine dinucleotide (NAD) and their close analogs are NADPH and NADP ⁺ , the reduced and oxidized forms of nicotinamide adenine dinucleotide phosphate (NADP). The coenzymes NADH and NADPH each consist of two nucleotides joined at their phosphate groups by a phosphoanhydride bond. NADPH is structurally distinguishable from NADH by the additional phosphate group residing on the ribose ring of the nucleotide, which allows enzymes to preferentially interact with either molecule.

Total concentrations of NAD ⁺ /NADH (10 ⁻⁵ M) are higher in the cell by approximately 10-fold compared to NADP ⁺ /NADPH (10 ⁻⁶ M). Ratios of the oxidized and reduced forms of these coenzymes offer perspective into the metabolic activity of the cell. The high NAD ⁺ /NADH ratio favors the transfer of a hydride from a substrate to NAD ⁺ to form NADH, the reduced form of the molecule and oxidizing agent. Therefore, NAD ⁺ is highly prevalent within catabolic reaction pathways where reducing equivalents (carbohydrate, fats, and proteins) transfer protons and electrons to NAD ⁺ . NADH acts as an energy carrier, transferring electrons from one reaction to another. Conversely, the NADP ⁺ /NADPH ratio is low, favoring the transfer of a hydride to a substrate oxidizing NADPH to NADP ⁺ . Thus, NADPH is utilized as a reducing agent within anabolic reactions, particularly the biosynthesis of fatty acids.

References

• Nelson DL, Cox MM: Lehninger Principles of Biochemistry.6th ed2012.AH FreemanNew York
• Wikipedia. s.v. Nicotinamide adenine dinucleotide. http://en.wikipedia.org/wiki/Nicotinamide_adenine_dinucleotide

The F _o F ₁ ATPase—which is complex V in the respiratory chain—can now use this large electrochemical potential energy difference for H ⁺ . The H ⁺ ions then flow backward (i.e., down their electrochemical gradient) into the mitochondrion through the F _o F ₁ ATPase, which generates ATP in the matrix space of the mitochondrion from ADP and inorganic phosphate. The entire process by which electron transport generates an H ⁺ gradient and the F _o F ₁ ATPase harnesses this H ⁺ gradient to synthesize ATP is known as the chemiosmotic hypothesis. Peter Mitchell, who proposed this hypothesis in 1961, received the Nobel Prize in Chemistry for his work in 1978. N5-14

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Peter Mitchell

For more information about Peter Mitchell and the work that led to his Nobel Prize, visit http://nobelprize.org/nobel_prizes/chemistry/laureates/1978/index.html (accessed October 2014).

The precise stoichiometry is unknown but may be one ATP molecule synthesized for every three H ⁺ ions flowing downhill into the mitochondrion (one H ⁺ for each pair of αβ subunits of F ₁ ). N5-15 If the H ⁺ gradient across the mitochondrial inner membrane reverses, the F _o F ₁ ATPase will actually function as an ATPase and use the energy of ATP hydrolysis to pump H ⁺ out of the mitochondrion. Similar F _o F ₁ ATPases are also present in bacteria and chloroplasts.

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ATP Molecules Synthesized per NADH

Glycolysis and the citric acid cycle generate the reducing equivalents NADH and FADH ₂ , and then the inner membrane of the mitochondria converts the energy of these reducing equivalents to ATP in two steps. First, the electron transport chain uses the energy from NADH and FADH ₂ to pump H ⁺ from the mitochondrial matrix into the intermembrane space between the mitochondrial inner and outer membranes, converting O ₂ to H ₂ O in the final step. Second, the ATP synthase uses the energy stored in the H ⁺ gradient to generate ATP from ATP plus inorganic phosphate.

Generation of the H ⁺ Gradient

For each NADH consumed in the inner matrix of the mitochondrion, it appears that complex I and complex III of the electron transport chain (see Fig. 5-9 ) each pump 4 H ⁺ from the matrix, across the inner membrane, and into the intermembrane space, and complex IV pumps out an additional 2 H ⁺ . Thus, for each NADH, the consensus is that the mitochondrion pumps 10 H ⁺ . The FADH ₂ from succinate feeds into the electron transport chain at complex II (which is actually succinate dehydrogenase), bypassing complex I. Thus, for each FADH ₂ , the consensus is that the mitochondrion pumps 6 H ⁺ .

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