Physiology 5th Ed.

TRANSPORT ACROSS CELL MEMBRANES

Several types of mechanisms are responsible for transport of substances across cell membranes (Table 1-2).

Table 1–2 Summary of Membrane Transport

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*Na+ is transported downhill and one or more solutes are transported uphill.

Substances may be transported down an electrochemical gradient (downhill) or against an electrochemical gradient (uphill). Downhill transport occurs by diffusion, either simple or facilitated, and requires no input of metabolic energy. Uphill transport occurs by active transport, which may be primary or secondary. Primary and secondary active transport processes are distinguished by their energy source. Primary active transport requires a direct input of metabolic energy; secondary active transport utilizes an indirect input of metabolic energy.

Further distinctions among transport mechanisms are based on whether the process involves a protein carrier. Simple diffusion is the only form of transport that is not carrier mediated. Facilitated diffusion, primary active transport, and secondary active transport all involve integral membrane proteins and are called carrier-mediated transport. All forms of carrier-mediated transport share the following three features: saturation, stereospecificity, and competition.

image Saturation. Saturability is based on the concept that carrier proteins have a limited number of binding sites for the solute. Figure 1-4 shows the relationship between the rate of carrier-mediated transport and solute concentration. At low solute concentrations, many binding sites are available and the rate of transport increases steeply as the concentration increases. However, at high solute concentrations, the available binding sites become scarce and the rate of transport levels off. Finally, when all of the binding sites are occupied, saturation is achieved at a point called the transport maximum, or Tm. The kinetics of carrier-mediated transport are similar to Michaelis-Menten enzyme kinetics—both involve proteins with a limited number of binding sites. (The Tm is analogous to the Vmax of enzyme kinetics.) Tm-limited glucose transport in the proximal tubule of the kidney is an example of saturable transport.

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Figure 1–4 Kinetics of carrier-mediated transport. Tm, Transport maximum.

image Stereospecificity. The binding sites for solute on the transport proteins are stereospecific. For example, the transporter for glucose in the renal proximal tubule recognizes and transports the natural isomer D-glucose, but it does not recognize or transport the unnatural isomer L-glucose. In contrast, simple diffusion does not distinguish between the two glucose isomers because no protein carrier is involved.

image Competition. Although the binding sites for transported solutes are quite specific, they may recognize, bind, and even transport chemically related solutes. For example, the transporter for glucose is specific for D-glucose, but it also recognizes and transports a closely related sugar, D-galactose. Therefore, the presence of D-galactose inhibits the transport of D-glucose by occupying some of the binding sites and making them unavailable for glucose.

Simple Diffusion

Diffusion of Nonelectrolytes

Simple diffusion occurs as a result of the random thermal motion of molecules, as shown in Figure 1-5. Two solutions, A and B, are separated by a membrane that is permeable to the solute. The solute concentration in A is initially twice that of B. The solute molecules are in constant motion, with equal probability that a given molecule will cross the membrane to the other solution. However, because there are twice as many solute molecules in Solution A as in Solution B, there will be greater movement of molecules from A to B than from B to A. In other words, there will be net diffusion of the solute from A to B, which will continue until the solute concentrations of the two solutions become equal (although the random movement of molecules will go on forever).

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Figure 1–5 Simple diffusion. The two solutions, A and B, are separated by a membrane, which is permeable to the solute (circles). Solution A initially contains a higher concentration of the solute than does Solution B.

Net diffusion of the solute is called flux, or flow (J), and depends on the following variables: size of the concentration gradient, partition coefficient, diffusion coefficient, thickness of the membrane, and surface area available for diffusion.

CONCENTRATION GRADIENT (CA − CB)

The concentration gradient across the membrane is the driving force for net diffusion. The larger the difference in solute concentration between Solution A and Solution B, the greater the driving force and the greater the net diffusion. It also follows that, if the concentrations in the two solutions are equal, there is no driving force and no net diffusion.

PARTITION COEFFICIENT (K)

The partition coefficient, by definition, describes the solubility of a solute in oil relative to its solubility in water. The greater the relative solubility in oil, the higher the partition coefficient and the more easily the solute can dissolve in the cell membrane’s lipid bilayer. Nonpolar solutes tend to be soluble in oil and have high values for partition coefficient, whereas polar solutes tend to be insoluble in oil and have low values for partition coefficient. The partition coefficient can be measured by adding the solute to a mixture of olive oil and water and then measuring its concentration in the oil phase relative to its concentration in the water phase. Thus,

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DIFFUSION COEFFICIENT (D)

The diffusion coefficient depends on such characteristics as size of the solute molecule and the viscosity of the medium. It is defined by the Stokes-Einstein equation (see later). The diffusion coefficient correlates inversely with the molecular radius of the solute and the viscosity of the medium. Thus, small solutes in nonviscous solutions have the largest diffusion coefficients and diffuse most readily; large solutes in viscous solutions have the smallest diffusion coefficients and diffuse least readily. Thus,

image

where

D

= Diffusion coefficient

K

= Boltzmann’s constant

T

= Absolute temperature (K)

r

= Molecular radius

η

= Viscosity of the medium

THICKNESS OF THE MEMBRANE (ΔX)

The thicker the cell membrane, the greater the distance the solute must diffuse and the lower the rate of diffusion.

SURFACE AREA (A)

The greater the surface area of membrane available, the higher the rate of diffusion. For example, lipid-soluble gases such as oxygen and carbon dioxide have particularly high rates of diffusion across cell membranes. These high rates can be attributed to the large surface area for diffusion provided by the lipid component of the membrane.

To simplify the description of diffusion, several of the previously cited characteristics can be combined into a single term called permeability (P). Permeability includes the partition coefficient, the diffusion coefficient, and the membrane thickness. Thus,

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By combining several variables into permeability, the rate of net diffusion is simplified to the following expression:

image

where

J

= Net rate of diffusion (mmol/sec)

P

= Permeability (cm/sec)

A

= Surface area for diffusion (cm2)

CA

= Concentration in Solution A (mmol/L)

CB

= Concentration in Solution B (mmol/L)

Diffusion of Electrolytes

Thus far, the discussion concerning diffusion has assumed that the solute is a nonelectrolyte (i.e., it is uncharged). However, if the diffusing solute is an ion or an electrolyte, there are two additional consequences of the presence of charge on the solute.

First, if there is a potential difference across the membrane, that potential difference will alter the net rate of diffusion of a charged solute. (A potential difference does not alter the rate of diffusion of a nonelectrolyte.) For example, the diffusion of K+ ions will be slowed if K+ is diffusing into an area of positive charge, and it will be accelerated if K+ is diffusing into an area of negative charge. This effect of potential difference can either add to or negate the effects of differences in concentrations, depending on the orientation of the potential difference and the charge on the diffusing ion. If the concentration gradient and the charge effect are oriented in the same direction across the membrane, they will combine; if they are oriented in opposite directions, they may cancel each other out.

SAMPLE PROBLEM. Solution A and Solution B are separated by a membrane whose permeability to urea is 2 × 10−5 cm/sec and whose surface area is 1 cm2. The concentration of urea in A is 10 mg/mL, and the concentration of urea in B is 1 mg/mL. The partition coefficient for urea is 10−3, as measured in an oil-water mixture. What are the initial rate and direction of net diffusion of urea?

SOLUTION. Note that the partition coefficient is extraneous information because the value for permeability, which already includes the partition coefficient, is given. Net flux can be calculated by substituting the following values in the equation for net diffusion: Assume that 1 mL of water = 1 cm3Thus,

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where

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The magnitude of net flux has been calculated as 1.8 × 10−4 mg/sec. The direction of net flux can be determined intuitively because net flux will occur from the area of high concentration (Solution A) to the area of low concentration (Solution B). Net diffusion will continue until the urea concentrations of the two solutions become equal, at which point the driving force will be zero.

Second, when a charged solute diffuses down a concentration gradient, that diffusion can itself generate a potential difference across a membrane called a diffusion potential. The concept of diffusion potential will be discussed more fully in a following section.

Facilitated Diffusion

Like simple diffusion, facilitated diffusion occurs down an electrochemical potential gradient; thus, it requires no input of metabolic energy. Unlike simple diffusion, however, facilitated diffusion uses a membrane carrier and exhibits all the characteristics of carrier-mediated transport: saturation, stereospecificity, and competition. At low solute concentration, facilitated diffusion typically proceeds faster than simple diffusion (i.e., is facilitated) because of the function of the carrier. However, at higher concentrations, the carriers will become saturated and facilitated diffusion will level off. (In contrast, simple diffusion will proceed as long as there is a concentration gradient for the solute.)

An excellent example of facilitated diffusion is the transport of D-glucose into skeletal muscle and adipose cells by the GLUT4 transporter. Glucose transport can proceed as long as the blood concentration of glucose is higher than the intracellular concentration of glucose and as long as the carriers are not saturated. Other monosaccharides such as D-galactose, 3-O- methyl glucose, and phlorizin competitively inhibit the transport of glucose because they bind to transport sites on the carrier. The competitive solute may itself be transported (e.g., D-galactose), or it may simply occupy the binding sites and prevent the attachment of glucose (e.g., phlorizin). As noted previously, the nonphysiologic stereoisomer, L-glucose, is not recognized by the carrier for facilitated diffusion and, therefore, is not bound or transported.

Primary Active Transport

In active transport, one or more solutes are moved against an electrochemical potential gradient (uphill). In other words, solute is moved from an area of low concentration (or low electrochemical potential) to an area of high concentration (or high electrochemical potential). Because movement of a solute uphill is work, metabolic energy in the form of ATP must be provided. In the process, ATP is hydrolyzed to adenosine diphosphate (ADP) and inorganic phosphate (Pi), releasing energy from the terminal high-energy phosphate bond of ATP. When the terminal phosphate is released, it is transferred to the transport protein, initiating a cycle of phosphorylation and dephosphorylation. When the ATP energy source is directly coupled to the transport process, it is called primary active transport. Three examples of primary active transport in physiologic systems are the Na+-K+ ATPase present in all cell membranes, the Ca2+ ATPase present in sarcoplasmic and endoplasmic reticulum, and the H+-K+ ATPase present in gastric parietal cells.

Na+-K+ ATPase (Na+-K+ Pump)

Na+-K+ ATPase is present in the membranes of all cells. It pumps Na+ from ICF to ECF and K+ from ECF to ICF (Fig. 1-6). Each ion moves against its respective electrochemical gradient. The stoichiometry can vary but, typically, for every three Na+ ions pumped out of the cell, two K+ ions are pumped into the cell. This stoichiometry of three Na+ ions per two K+ ions means that, for each cycle of the Na+-K+ATPase, more positive charge is pumped out of the cell than is pumped into the cell. Thus, the process is termed electrogenic because it creates a charge separation and a potential difference. The Na+-K+ATPase is responsible for maintaining concentration gradients for both Na+ and K+ across cell membranes, keeping the intracellular Na+ concentration low and the intracellular K+ concentration high.

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Figure 1–6 Na+-K+ pump of cell membranes. ADP, Adenosine diphosphate; ATP, adenosine triphosphate; E, Na+-K+ ATPase; E ~ P, phosphorylated Na+-K+ ATPase; Pi, inorganic phosphate.

The Na+-K+ ATPase consists of α and β subunits. The α subunit contains the ATPase activity, as well as the binding sites for the transported ions, Na+ and K+. The Na+-K+ ATPase switches between two major conformational states, E1 and E2. In the E1 state, the binding sites for Na+ and K+ face the intracellular fluid and the enzyme has a high affinity for Na+. In the E2 state, the binding sites for Na+ and K+ face the extracellular fluid and the enzyme has a high affinity for K+. The enzyme’s ion-transporting function (i.e., pumping Na+ out of the cell and K+ into the cell) is based on cycling between the E1 and E2 states and is powered by ATP hydrolysis.

The transport cycle is illustrated in Figure 1-6. The cycle begins with the enzyme in the E1 state, bound to ATP. In the E1 state, the ion-binding sites face the intracellular fluid, and the enzyme has a high affinity for Na+; three Na+ions bind, ATP is hydrolyzed, and the terminal phosphate of ATP is transferred to the enzyme, producing a high-energy state, E1~P. Now, a major conformational change occurs, and the enzyme switches from E1~P to E2~P. In the E2state, the ion-binding sites face the extracellular fluid, the affinity for Na+ is low, and the affinity for K+ is high. The three Na+ ions are released from the enzyme to extracellular fluid, two K+ ions are bound, and inorganic phosphate is released from E2. The enzyme now binds intracellular ATP, and another major conformational change occurs that returns the enzyme to the E1 state; the two K+ ions are released to intracellular fluid, and the enzyme is ready for another cycle.

Cardiac glycosides (e.g., ouabain and digitalis) are a class of drugs that inhibits Na+-K+ ATPase. Treatment with this class of drugs causes certain predictable changes in intracellular ionic concentration: The intracellular Na+concentration will increase, and the intracellular K+ concentration will decrease. Cardiac glycosides inhibit the Na+-K+ATPase by binding to the E2~P form near the K+-binding site on the extracellular side, thereby preventing the conversion of E2~P back to E1. By disrupting the cycle of phosphorylation-dephosphorylation, these drugs disrupt the entire enzyme cycle and its transport functions.

Ca2+ ATPase (Ca2+ Pump)

Most cell (plasmamembranes contain a Ca2+ ATPase, or plasma-membrane Ca2+ ATPase (PMCA), whose function is to extrude Ca2+ from the cell against an electrochemical gradient; one Ca2+ ion is extruded for each ATP hydrolyzed. PMCA is responsible, in part, for maintaining the very low intracellular Ca2+ concentration. In addition, the sarcoplasmic reticulum of muscle cells and the endoplasmic reticulum of other cells contain variants of Ca2+ATPase that pump two Ca2+ ions (for each ATP hydrolyzed) from intracellular fluid into the interior of the sarcoplasmic or endoplasmic reticulum (i.e., Ca2+sequestration). These variants are called sarcoplasmic and endoplasmic reticulum Ca2+ ATPase (SERCA). Ca2+ ATPase functions similarly to Na+-K+ ATPase, with E1 and E2 states that have, respectively, high and low affinities for Ca2+. For PMCA, the E1 state binds Ca2+ on the intracellular side, a conformational change to the E2 state occurs, and the E2 state releases Ca2+ to extracellular fluid. For SERCA, the E1 state binds Ca2+ on the intracellular side and the E2 state releases Ca2+ to the lumen of the sarcoplasmic or endoplasmic reticulum.

H+-K+ ATPase (H+-K+ Pump)

H+-K+ ATPase is found in the parietal cells of the gastric mucosa and in the α-intercalated cells of the renal collecting duct. In the stomach, it pumps H+ from the ICF of the parietal cells into the lumen of the stomach, where it acidifies the gastric contents. Omeprazole, an inhibitor of gastric H+-K+ ATPase, can be used therapeutically to reduce the secretion of H+ in the treatment of some types of peptic ulcer disease.

Secondary Active Transport

Secondary active transport processes are those in which the transport of two or more solutes is coupled. One of the solutes, usually Na+, moves down its electrochemical gradient (downhill), and the other solute moves against its electrochemical gradient (uphill). The downhill movement of Na+ provides energy for the uphill movement of the other solute. Thus, metabolic energy, as ATP, is not used directly, but it is supplied indirectly in the Na+ concentration gradient across the cell membrane. (The Na+-K+ ATPase, utilizing ATP, creates and maintains this Na+ gradient.) The name secondary active transport, therefore, refers to the indirect utilization of ATP as an energy source.

Inhibition of the Na+-K+ ATPase (e.g., by treatment with ouabain) diminishes the transport of Na+ from ICF to ECF, causing the intracellular Na+ concentration to increase and thereby decreasing the size of the transmembrane Na+gradient. Thus, indirectly, all secondary active transport processes are diminished by inhibitors of the Na+-K+ ATPase because their energy source, the Na+ gradient, is diminished.

There are two types of secondary active transport, distinguishable by the direction of movement of the uphill solute. If the uphill solute moves in the same direction as Na+, it is called cotransport, or symport. If the uphill solute moves in the opposite direction of Na+, it is called countertransport, antiport, or exchange.

Cotransport

Cotransport (symport) is a form of secondary active transport in which all solutes are transported in the same direction across the cell membrane. Na+ moves into the cell on the carrier down its electrochemical gradient; the solutes, cotransported with Na+, also move into the cell. Cotransport is involved in several critical physiologic processes, particularly in the absorbing epithelia of the small intestine and the renal tubule. For example, Na+-glucose cotransport (SGLT) and Na+-amino acid cotransport are present in the luminal membranes of the epithelial cells of both small intestine and renal proximal tubule. Another example of cotransport involving the renal tubule is Na+-K+-2Cl cotransport, which is present in the luminal membrane of epithelial cells of the thick ascending limb. In each example, the Na+ gradient established by the Na+-K+ ATPase is used to transport solutes such as glucose, amino acids, K+, or Cl against electrochemical gradients.

Figure 1-7 illustrates the principles of cotransport using the example of Na+-glucose cotransport (SGLT1, or Na-glucose transport protein 1) in intestinal epithelial cells. The cotransporter is present in the luminal membrane of these cells and can be visualized as having two specific recognition sites, one for Na+ ions and the other for glucose. When both Na+ and glucose are present in the lumen of the small intestine, they bind to the transporter. In this configuration, the cotransport protein rotates and releases both Na+ and glucose to the interior of the cell. (Subsequently, both solutes are transported out of the cell across the basolateral membrane—Na+ by the Na+-K+ ATPase and glucose by facilitated diffusion.) If either Na+ or glucose is missing from the intestinal lumen, the cotransporter cannot rotate. Thus, both solutes are required, and neither can be transported in the absence of the other (Box 1-1).

image

Figure 1–7 Na+-glucose cotransport in an intestinal epithelial cell. ATP, Adenosine triphosphate; SGLT1, Na+-glucose transport protein 1.

BOX 1–1 Clinical Physiology: Glucosuria Due to Diabetes Mellitus

DESCRIPTION OF CASE. At his annual physical examination, a 14-year-old boy reports symptoms of frequent urination and severe thirst. A dipstick test of his urine shows elevated levels of glucose. The physician orders a glucose tolerance test, which indicates that the boy has type I diabetes mellitus. He is treated with insulin by injection, and his dipstick test is subsequently normal.

EXPLANATION OF CASE. Although type I diabetes mellitus is a complex disease, this discussion is limited to the symptom of frequent urination and the finding of glucosuria (glucose in the urine). Glucose is normally handled by the kidney in the following manner: Glucose in the blood is filtered across the glomerular capillaries. The epithelial cells, which line the renal proximal tubule, then reabsorb all of the filtered glucose so that no glucose is excreted in the urine. Thus, a normal dipstick test would show no glucose in the urine. If the epithelial cells in the proximal tubule do not reabsorb all of the filtered glucose back into the blood, the glucose that escapes reabsorption is excreted. The cellular mechanism for this glucose reabsorption is the Na+-glucose cotransporter in the luminal membrane of the proximal tubule cells. Because this is a carrier-mediated transporter, there are a finite number of binding sites for glucose. Once these binding sites are fully occupied, saturation of transport occurs (transport maximum).

In this patient with type I diabetes mellitus, the hormone insulin is not produced in sufficient amounts by the pancreatic β cells. Insulin is required for normal uptake of glucose into liver, muscle, and other cells. Without insulin, the blood glucose concentration increases because glucose is not taken up by the cells. When the blood glucose concentration increases to high levels, more glucose is filtered by the renal glomeruli and the amount of glucose filtered exceeds the capacity of the Na+-glucose cotransporter. The glucose that cannot be reabsorbed because of saturation of this transporter is then “spilled” in the urine.

TREATMENT. Treatment of the patient with type I diabetes mellitus consists of administering exogenous insulin by injection. Whether secreted normally from the pancreatic β cells or administered by injection, insulin lowers the blood glucose concentration by promoting glucose uptake into cells. When this patient received insulin, his blood glucose concentration was reduced; thus, the amount of glucose filtered was reduced, and the Na+-glucose cotransporters were no longer saturated. All of the filtered glucose could be reabsorbed, and therefore, no glucose was excreted, or “spilled,” in the urine.

Finally, the role of the intestinal Na+-glucose cotransport process can be understood in the context of overall intestinal absorption of carbohydrates. Dietary carbohydrates are digested by gastrointestinal enzymes to an absorbable form, the monosaccharides. One of these monosaccharides is glucose, which is absorbed across the intestinal epithelial cells by a combination of Na+-glucose cotransport in the luminal membrane and facilitated diffusion of glucose in the basolateral membrane. Na+-glucose cotransport is the active step, allowing glucose to be absorbed into the blood against an electrochemical gradient.

Countertransport

Countertransport (antiport or exchange) is a form of secondary active transport in which solutes move in opposite directions across the cell membrane. Na+ moves into the cell on the carrier down its electrochemical gradient; the solutes that are countertransported or exchanged for Na+ move out of the cell. Countertransport is illustrated by Ca2+-Na+ exchange (Fig. 1-8) and by Na+-H+ exchange. As with cotransport, each process uses the Na+ gradient established by the Na+-K+ ATPase as an energy source; Na+ moves downhill and Ca2+ or H+ moves uphill.

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Figure 1–8 Ca2+-Na+ countertransport (exchange) in a muscle cell. ATP, Adenosine triphosphate.

Ca2+-Na+ exchange is one of the transport mechanisms, along with the Ca2+ ATPase, that helps maintain the intracellular Ca2+ concentration at very low levels (≈10−7 molar). To accomplish Ca2+-Na+exchange, active transport must be involved because Ca2+ moves out of the cell against its electrochemical gradient. Figure 1-8 illustrates the concept of Ca2+-Na+ exchange in a muscle cell membrane. The exchange protein has recognition sites for both Ca2+and Na+. The protein must bind Ca2+ on the intracellular side of the membrane and, simultaneously, bind Na+ on the extracellular side. In this configuration, the exchange protein rotates and delivers Ca2+ to the exterior of the cell and Na+ to the interior of the cell.

The stoichiometry of Ca2+-Na+ exchange varies between different cell types and may even vary for a single cell type under different conditions. Usually, however, three Na+ ions enter the cell for each Ca2+ion extruded from the cell. With this stoichiometry of three Na+ ions per one Ca2+ ion, three positive charges move into the cell in exchange for two positive charges leaving the cell, making the Ca2+-Na+exchanger electrogenic.

Osmosis

Osmosis is the flow of water across a semipermeable membrane because of differences in solute concentration. Concentration differences of impermeant solutes establish osmotic pressure differences, and this osmotic pressure difference causes water to flow by osmosis. Osmosis of water is not diffusion of water: Osmosis occurs because of a pressure difference, whereas diffusion occurs because of a concentration (or activity) difference of water.

Osmolarity

The osmolarity of a solution is its concentration of osmotically active particles, expressed as osmoles per liter or milliosmoles per liter. To calculate osmolarity, it is necessary to know the concentration of solute and whether the solute dissociates in solution. For example, glucose does not dissociate in solution; theoretically, NaCl dissociates into two particles and CaCl2 dissociates into three particles. The symbol “g” gives the number of particles in solution and also takes into account whether there is complete or only partial dissociation. Thus, if NaCl is completely dissociated into two particles, g equals 2.0; if NaCl dissociates only partially, then g falls between 1.0 and 2.0. Osmolarity is calculated as follows:

image

where

Osmolarity

= Concentration of particles (mOsm/L)

g

= Number of particles per mole in solution (Osm/mol)

C

= Concentration (mmol/L)

If two solutions have the same calculated osmolarity, they are called isosmotic. If two solutions have different calculated osmolarities, the solution with the higher osmolarity is called hyperosmotic and the solution with the lower osmolarity is called hyposmotic.

Osmolality

Osmolality is similar to osmolarity, except that it is the concentration of osmotically active particles, expressed as osmoles (or milliosmoles) per kg of water. Because 1 kg of water is approximately equivalent to 1 L of water, osmolarity and osmolality will have essentially the same numerical value.

SAMPLE PROBLEM. Solution A is 2 mmol/L urea, and Solution B is 1 mmol/L NaCl. Assume that gNaCl = 1.85. Are the two solutions isosmotic?

SOLUTION. Calculate the osmolarities of both solutions to compare them. Solution A contains urea, which does not dissociate in solution. Solution B contains NaCl, which dissociates partially in solution but not completely (i.e., g < 2.0). Thus,

image

image

The two solutions do not have the same calculated osmolarity; therefore, they are not isosmotic. Solution A has a higher osmolarity than Solution B and is hyperosmotic; Solution B is hyposmotic.

Osmotic Pressure

Osmosis is the flow of water across a semipermeable membrane due to a difference in solute concentration. The difference in solute concentration creates an osmotic pressure difference across the membrane and that pressure difference is the driving force for osmotic water flow.

Figure 1-9 illustrates the concept of osmosis. Two aqueous solutions, open to the atmosphere, are shown in Figure 1-9A. The membrane separating the solutions is permeable to water but is impermeable to the solute. Initially, solute is present only in Solution 1. The solute in Solution 1 produces an osmotic pressure and causes, by the interaction of solute with pores in the membrane, a reduction in hydrostatic pressure of Solution 1. The resulting hydrostatic pressure difference across the membrane then causes water to flow from Solution 2 into Solution 1. With time, water flow causes the volume of Solution 1 to increase and the volume of Solution 2 to decrease.

Figure 1-9B shows a similar pair of solutions; however, the preparation has been modified so that water flow into Solution 1 is prevented by applying pressure to a piston. The pressure required to stop the flow of water is the osmotic pressure of Solution 1.

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Figure 1–9 Osmosis across a semipermeable membrane. A, Solute (circles) is present on one side of a semipermeable membrane; with time, the osmotic pressure created by the solute causes water to flow from Solution 2 to Solution 1. The resulting volume changes are shown. B, The solutions are closed to the atmosphere, and a piston is applied to stop the flow of water into Solution 1. The pressure needed to stop the flow of water is the effective osmotic pressure of Solution 1. Atm, Atmosphere.

The osmotic pressure (π) of Solution 1 depends on two factors: the concentration of osmotically active particles and whether the solute remains in Solution 1 (i.e., whether the solute can cross the membrane or not). Osmotic pressure is calculated by the van’t Hoff equation (as follows), which converts the concentration of particles to a pressure, taking into account whether the solute is retained in the original solution.

Thus,

image

where

π

= Osmotic pressure (atm or mm Hg)

g

= Number of particles per mole in solution (Osm/mol)

C

= Concentration (mmol/L)

σ

= Reflection coefficient (varies from 0 to 1)

R

= Gas constant (0.082 L – atm/mol – K)

T

= Absolute temperature (K)

The reflection coefficient (σ) is a dimensionless number ranging between 0 and 1 that describes the ease with which a solute crosses a membrane. Reflection coefficients can be described for the following three conditions (Fig. 1-10):

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Figure 1–10 Reflection coefficient (σ).

image σ 1.0 (see Fig. 1-10A). If the membrane is impermeable to the solute, σ is 1.0, and the solute will be retained in the original solution and exert its full osmotic effect. In this case, the effective osmotic pressure will be maximal and will cause maximal water flow. For example, serum albumin and intracellular proteins are solutes where σ = 1.

image σ 0 (see Fig. 1-10C). If the membrane is freely permeable to the solute, σ is 0, and the solute will diffuse across the membrane down its concentration gradient until the solute concentrations of the two solutions are equal. In other words, the solute behaves as if it were water. In this case, there will be no effective osmotic pressure difference across the membrane and, therefore, no driving force for osmotic water flow. Refer again to the van’t Hoff equation and notice that, when σ = 0, the calculated effective osmotic pressure becomes zero. Urea is an example of a solute where σ = 0 (or nearly 0).

image σ = a value between 0 and 1 (see Fig. 1-10B). Most solutes are neither impermeant (σ = 1) nor freely permeant (σ = 0) across membranes, but the reflection coefficient falls somewhere between 0 and 1. In such cases, the effective osmotic pressure lies between its maximal possible value (when the solute is completely impermeable) and zero (when the solute is freely permeable). Refer once again to the van’t Hoff equation and notice that, when σ is between 0 and 1, the calculated effective osmotic pressure will be less than its maximal possible value, but greater than zero.

When two solutions separated by a semipermeable membrane have the same effective osmotic pressure, they are isotonic; that is, no water will flow between them because there is no effective osmotic pressure difference across the membrane. When two solutions have different effective osmotic pressures, the solution with the lower effective osmotic pressure is hypotonic and the solution with the higher effective osmotic pressure is hypertonic. Water will flow from the hypotonic solution into the hypertonic solution.

SAMPLE PROBLEM. A solution of 1 mol/L NaCl is separated from a solution of 2 mol/L urea by a semipermeable membrane. Assume that NaCl is completely dissociated, that σNaCl = 0.3, and σurea = 0.05. Are the two solutions isosmotic and/or isotonic? Is there net water flow, and what is its direction?

SOLUTION. STEP 1. To determine whether the solutions are isosmotic, simply calculate the osmolarity of each solution (g × C) and compare the two values. It was stated that NaCl is completely dissociated (i.e., separated into two particles); thus, for NaCl, g = 2.0. Urea does not dissociate in solution; thus, for urea, g = 1.0.

image

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Each solution has an osmolarity of 2 Osm/L—they are indeed isosmotic.

Step 2. To determine whether the solutions are isotonic, the effective osmotic pressure of each solution must be determined. Assume that at 37°C (310 K), RT = 25.45 L-atm/mol. Thus,

image

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Although the two solutions have the same calculated osmolarities and are isosmotic (Step 1), they have different effective osmotic pressures and they are not isotonic (Step 2). This difference occurs because the reflection coefficient for NaCl is much higher than the reflection coefficient for urea and, thus, NaCl creates the greater effective osmotic pressure. Water will flow from the urea solution into the NaCl solution, from the hypotonic solution to the hypertonic solution.