Objectives
- 1.
Describe the nature of osmosis.
- 2.
Define osmotic pressure in terms of solute concentration through van’t Hoff’s law.
- 3.
Define the driving forces that control water movement across membranes.
- 4.
Explain how fluid movement across a capillary wall is determined by a balance of hydrostatic and osmotic pressures.
- 5.
Explain how cell volume changes in response to changing concentrations of permeant and impermeant solutes in the extracellular fluid.
Osmosis is the transport of solvent driven by a difference in solute concentration across a membrane that is impermeable to solute
Because of diffusion, a net movement of molecules occurs down concentration gradients, and substances tend to move in a way that abolishes concentration differences in different regions of a solution. Alternatively, it could be said that diffusion results in mixing . We now examine the consequences when a solute is prevented from diffusing down its concentration gradient. Fig. 3.1 A shows two aqueous compartments, 1 and 2, separated by a semipermeable membrane. Initially compartment 1 contains pure water and compartment 2 contains a solute dissolved in water. The membrane is permeable to water but impermeable to the solute. Because the solute concentration is higher in compartment 2 than in compartment 1, normally a net flux of solute molecules from 2 into 1 would occur. Because the membrane is impermeable to the solute, however, such a flux cannot take place; solute molecules cannot move from 2 into 1 to abolish the concentration difference between the two compartments.
The situation can be viewed from another perspective. When a solute is dissolved in water to form an aqueous solution, as the concentration of solute in the solution is increased, the concentration of water in the same solution must correspondingly decrease. In the two compartments shown in Fig. 3.1 A, whereas the solute concentration is higher in 2 than in 1, the water concentration is higher in 1 than in 2. Therefore, although the membrane does not permit the solute to move across from 2 into 1, it does allow water to move from 1 into 2. The difference in the water concentration allows us to predict, correctly, that a net flux of water will occur from 1 into 2. a
a This reasoning based on water concentration differences is heuristic but always gives the correct prediction.
The movement of water through a semipermeable membrane, from a region of higher water concentration to a region of lower water concentration, is called osmosis .Water transport during osmosis leads to volume changes
In light of the foregoing, we can think about simple diffusion again. Because an increase in solute concentration dictates a corresponding decrease in water concentration, when a solute concentration gradient exists, there must be a water concentration gradient running in the opposite direction. We can therefore view simple diffusion as a net flux of solute molecules down their concentration gradient occurring simultaneously with a net flux of water molecules down the water concentration gradient.
In osmosis, the membrane does not permit solute movement, so the only flux is that of water. Because the net flux of water in one direction is not balanced by a flux of solute in the opposite direction, the net movement of water would be expected to contribute to a change in volume: as water moves from compartment 1 to compartment 2, the volume of solution in 2 should increase, as shown in Fig. 3.1 B.
Osmotic pressure drives the net transport of water during osmosis
In the two-compartment situation depicted in Fig. 3.1 , as osmosis proceeds, the solution volume in 2 will increase and a “head” of solution will build up ( Fig. 3.1 B). The head of solution will exert hydrostatic pressure , which will tend to push the water across the membrane back to compartment 1, thus reducing the net flux of water from 1 into 2. As the solution volume in 2 increases, a point will be reached when the hydrostatic pressure from the solution head is sufficient to counteract exactly the net flow of water from 1 into 2.
This view suggests that we can also think of osmotic flow of water as being driven by some “pressure” that forces water to flow from 1 into 2. This pressure, arising from unequal solute concentrations across a semipermeable membrane, is termed osmotic pressure . From the earlier discussion, we expect that the larger the solute concentration difference between two solutions separated by a semipermeable membrane, the greater the osmotic pressure difference driving water transport. Therefore the osmotic pressure of a solution should be proportional to the concentration of solute. Indeed, the osmotic pressure can be described fairly accurately by van’t Hoff’s law a
a Derived by Jacobus Henricus van’t Hoff, who received the Nobel Prize in Chemistry in 1901.
:π=RTCsolute
where π is the osmotic pressure, C solute is the solute concentration, T is the absolute temperature ( T = Celsius temperature +273.15, in absolute temperature units, i.e., Kelvins), and R is the universal gas constant (0.08205 liter·atmosphere·mole −1 ·Kelvin −1 ). The various units of measurement used in the study of osmosis are described in Box 3.1 .
Osmotic pressure is proportional to the total concentration of dissolved particles. Each mole of osmotically active particles is referred to as an osmole. One mole of glucose is equivalent to 1 osmole, because each molecule of glucose stays as an intact molecular particle when in solution. One mole of NaCl is equivalent to 2 osmoles, because when in solution, each mole of NaCl dissociates into 1 mole of Na + ions and 1 mole of Cl − ions, both of which are osmotically active.
One osmole in 1 liter of solution gives a 1 osmolar solution. Alternatively, one osmole in 1 kilogram of solution gives a 1 osmolal solution. Because osmolarity is defined in terms of solution volume, whereas osmolality is defined in terms of the weight of solution, osmolarity changes with temperature, whereas osmolality is independent of temperature. For simplicity, in this chapter all concentrations of osmotically active solutes are given in units of molar (M = mol/L) or millimolar (mM = 10 −3 mol/L).
With commonly used factors, van’t Hoff’s law ( Equation 3.1 ) gives the osmotic pressure in units of atmospheres. Physiological pressures are typically given in units of millimeters of mercury (mmHg). The conversion factor is 1 atmosphere = 760 mmHg.
Importantly, the osmotic pressure of a solution is a colligative property—that is, a property that depends only on the total concentration of dissolved particles and not on the detailed chemical nature of the particles. Therefore, in Equation 3.1 , C solute is the total concentration of all solute particles. For example, a nondissociable molecular solute such as glucose or mannitol at a concentration of 1 M gives C solute = 1 M. In contrast, a 1 M solution of an ionic solute such as NaCl, which can fully dissociate into equal numbers of Na + and Cl − ions, actually has a solute particle concentration of C solute = 2 M. Similarly, for a 1 M solution of MgCl 2 , which can dissociate into constituent Mg 2+ and Cl − ions, C solute = 3 M.
In Fig. 3.1 the osmotic pressure of the solution in compartment 1 is 0 ( C solute = 0), whereas the osmotic pressure of the solution in compartment 2 is equal to RTC solute . In practice, the magnitude of the osmotic pressure is also operationally equal to the amount of hydrostatic pressure that must be applied to the compartment with the higher solute concentration to stop the net flux of water into that compartment. The osmotic pressure of a physiological solution is typically very high ( Box 3.2 ).
All fluid compartments in the body contain dissolved solutes. Extracellular fluid is high in Na + and Cl − and low in K + , whereas intracellular fluid is high in K + and phosphate in various forms and low in Na + and Cl − . For cells in the body to maintain constant volume, the osmotic pressure arising from solutes inside cells must equal the osmotic pressure arising from solutes in the extracellular fluid. The total solute concentration in the fluids is typically close to 300 mM. The osmotic pressure resulting from this solute concentration at 37°C (310.15 Kelvin) can be estimated with van’t Hoff ‘s law:
π=RTC=0.08205[L⋅atmmol⋅K]×310.15[K]×300×10-3[molL]=7.63atm
At 7.63 atmospheres (atm), the osmotic pressure of intracellular and extracellular fluids is very high, especially in light of the fact that air pressure at sea level is just 1 atm. Indeed, to experience 7.63 atm, one needs to dive to a depth of approximately 67 m (∼220 ft) in the ocean. The high osmotic pressure of physiological solutions is the reason that red blood cells, which are much more permeable to water than to solutes, will swell very rapidly and burst (lyse) when they are placed into water or dilute solutions.
A note about units of measurement: 1 atm is equivalent to 760 mm of mercury (mmHg).
When impermeant solute is present on both sides of a semipermeable membrane, water flux across the membrane will depend on the osmotic pressure difference between the two compartments. In turn, the osmotic pressure difference depends on the difference of solute concentrations across the membrane:
Δπ=RTΔCsolute
where Δπ is the osmotic pressure difference across the membrane, Δ C solute is the difference in solute concentrations across the membrane, and R and T are as defined for Equation 3.1 .
In real life, membranes are never completely impermeable to solute. What happens when the membrane is only partially impermeable to solute? We can deduce the answer by considering the two extreme cases we already know: (1) If the membrane allows the solute molecules to pass through as freely as water molecules can, the flux of water is counterbalanced by the flux of solute in the opposite direction and the situation is no different from free diffusion—there would be no osmotic pressure difference; and (2) if the membrane is completely impermeable to solute but completely permeable to water, the maximum osmotic pressure that can be achieved is given by Equation 3.2 . The behavior of real-life membranes must lie somewhere between these two extremes. Because the relative permeability of the membrane to solute and water determines the actual behavior, we can define a parameter, called the reflection coefficient , represented by the symbol σ:
σ =1-PsolutePwater
where P solute and P water are the membrane permeabilities to solute and water, respectively. When the membrane is absolutely impermeable to solute, P solute = 0, and σ = 1—the membrane “reflects” all solute molecules and does not allow them to pass through, and full osmotic pressure should develop. When the solute molecules permeate the membrane as readily as do water molecules, P solute / P water = 1, and σ = 0. In this case the membrane allows free passage of both water and solute, and the osmotic pressure should be 0. By incorporating the reflection coefficient into the osmotic pressure equation, we can describe membrane behavior more accurately:
Δπ = σRTΔCsolute
where Δπ is the effective osmotic pressure difference across a membrane.
The fact that, even at the same concentration, solutes with different reflection coefficients can generate different osmotic pressures gives rise to a distinction between osmolarity and tonicity , which is explained in Box 3.3 .
Each mole of dissolved solute particles contributes 1 osmole to the solution; therefore any dissolved solute contributes to the osmolarity of a solution. With regard to the ability to drive water flow by osmosis, not all solutes are equal. Solutes with low membrane permeability (σ close to 1) have far greater osmotic effect than those with high membrane permeability (σ close to 0). Therefore two solutions of equal osmolarity can have different osmotic effects on cells. As an example, take a cell initially equilibrated with extracellular fluid (ECF). When a solute is added to the ECF, the ECF becomes hyperosmolar with respect to the intracellular fluid (ICF). If the added solute has σ = 1 (is impermeant), the cell will lose water and shrink; the ECF is then said to be hypertonic with respect to the cell. If the added solute has σ = 0 (is completely membrane-permeant), the osmotic pressure of the ECF will not change and neither will the cell volume. In this case the ECF is said to be isotonic with respect to the cell. Similarly, a solution that causes the cell to gain water and swell is said to be hypotonic .
The direction of fluid flow through the capillary wall is determined by the balance of hydrostatic and osmotic pressures, as described by the starling equation
In the previous section we noted that hydrostatic pressure can counteract water movement driven by osmotic pressure. This suggests that hydrostatic and osmotic pressures can both drive water movement through a membrane. We can also conclude that the direction of net fluid flow must be determined by the balance of osmotic and hydrostatic pressures across a membrane barrier. This principle governs the movement of fluid into and out of capillaries and is thus fundamental to circulatory physiology.
In analyzing fluid movement across capillary walls, we only need to identify the forces that drive fluid out of the capillary into the fluid space of the surrounding tissue (the interstitium) and the forces that drive fluid from the interstitium into the capillary. Fig. 3.2 shows the four pressures that are in play; the direction of water movement driven by each pressure component is indicated by an arrow associated with that pressure. These pressures are commonly referred to as the Starling forces . a
a Named after Ernest Starling, a 19th-century physiologist who first investigated fluid movement driven by osmotic and hydrostatic forces and who is also known for the Frank-Starling law of heart function.
The capillary hydrostatic pressure (blood pressure) is P c ; the hydrostatic pressure in the interstitium is P i . The principal contributors to the osmotic pressure difference across the capillary wall are proteins dissolved in the plasma, which are too large to pass through the capillary walls ( Box 3.4 ). Osmotic pressure arising from dissolved proteins is commonly referred to as colloid osmotic pressure (COP) , or oncotic pressure . Plasma COP in the capillary is symbolized as π c ; the COP of the interstitial fluid is symbolized as π i . The capillary hydrostatic pressure pushes water out of the capillary into the interstitium, whereas any interstitial hydrostatic pressure pushes interstitial water into the capillary. The osmotic components operate in the opposite way: the capillary COP pulls interstitial water into the capillary, whereas interstitial COP pulls water out of the capillary into the interstitium. Movement of fluid out of the capillary is called filtration, and movement of fluid into the capillary is called absorption. As blood passes through a capillary, the balance of these four pressures determines whether filtration or absorption occurs:Net fluid movement∝(Pressures that drive fluid out)-(Pressures that drive fluid in).
By far the most abundant solutes in blood plasma are low-molecular-weight ions and molecules (e.g., Na + , Cl − ). The total concentration of such small solutes is close to 300 mM. If a membrane barrier were completely impermeable to these solutes, an osmotic pressure close to 6000 mmHg (i.e., ∼7.6 atm; see Box 3.1 ) would develop. In reality, the wall of a typical capillary is quite permeable to small solutes (reflection coefficient, σ ≈ 0). Thus with respect to small solutes, the interstitial fluid has approximately the same composition as plasma, with the consequence that small solutes exert very little net osmotic effect across the capillary wall. It is reasonable that the walls of most capillaries are quite permeable to low-molecular-weight solutes, because the circulating blood brings small nutrient molecules (e.g., glucose, amino acids) that must leave the capillaries to nourish the cells in tissue. These cells, in turn, generate metabolic waste (e.g., carbon dioxide) that must enter the capillaries and be borne away by the blood.
Two types of proteins are found in significant amounts in the plasma. Albumin, with a molecular weight of approximately 69,000, is present at approximately 4.5 g/dL (grams/deciliter, same as grams/100 milliliters), or approximately 0.65 mM. Globulins, with a molecular weight of approximately 150,000, are present at approximately 2.5 g/dL, or approximately 0.17 mM. These proteins, being macromolecules, do not readily pass through the capillary wall (σ ≥ 0.9); therefore the plasma is protein-rich, whereas the interstitial fluid is low in proteins. Because the total protein concentration in plasma is close to 0.82 mM, we expect the osmotic pressure contributed by the proteins to be:
π=σRTC=0.9×0.08205[L⋅atmmol⋅K]×310.15[K]×0.82×10-3[molL]=0.0216atm
or 15.8 mmHg, which is quite a bit less than the π c = 25 mmHg that is typically measured. This suggests that each protein molecule exists in solution not as a single particle, but rather as an ionic macromolecule with some associated small ions. Because the proteins cannot leave the capillary, the population of small “counterions” that are associated with them must also remain within the capillary (see Box 4.4 ), thereby increasing the total amount of effectively impermeant solute. In other words, by ignoring the fact that proteins can dissociate into more than one ionic particle, we underestimate the osmotic contribution of proteins.
The most important point is that proteins, because they do not readily pass through the capillary wall, are the predominant contributor to osmotic forces across the capillary wall.
We know that
(Pressures that drive fluid out)=Pc+πi
and
(Pressures that drive fluid in)=Pi+πc,
so net fluid movement can be represented more formally and quantitatively as
Jv=LpS[(Pc+πi)-(Pi+πc)],
where J v is the volume of fluid filtered through the capillary wall and is known as volume flow ; L p is the hydraulic conductivity , which characterizes the ease with which a membrane barrier allows water to pass through; and S is the area of membrane through which water flows. We can see from Equation 3.5 that when the pressures driving fluid out ( P c + π i ) exceed the pressures driving fluid in ( P i + π c ), J v is a positive number and there is net fluid flow out of the capillary into the interstitium—i.e., filtration. Conversely, J v being negative corresponds to absorption of fluid into the capillary. The terms enclosed in square brackets in Equation 3.5 can be rearranged:
Jv=LpS[(Pc-Pi)-(πc-πi)]
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