In this chapter we discuss the pathways and mechanisms of water transport across cell membranes and epithelia. The concepts of diffusion and osmosis are presented at the biophysical level and applied to water transport phenomena across lipid bilayers and membrane-spanning pores. Water pores (“aquaporins”) are described from biophysical and molecular points of view. The mechanism of water transport across the cell membrane is osmosis and cell volume is determined by the intracellular solute content and the extracellular osmolality. Water permeates the cell membrane via aquaporins and/or the phospholipid bilayer; other pathways having minor importance. Water transport in the absence of a substantial osmolality difference between the adjacent solutions is most likely osmotically coupled to solute transport in the same direction (“near-isosmotic fluid transport”), without requirement for large standing osmotic gradients. Epithelia display a wide range of permeabilities to water, which has important physiological significance, in particular for kidney function.
aquaporin; pore; permeability; osmosis; isosmotic; unstirred layers
The main purpose of this chapter is to review the basic aspects of water transport mechanisms across cell membranes and epithelia. In the first section we will discuss biophysical principles and definitions, with the aim of providing a theoretical framework useful for the analysis of experimental observations. In the second section, we will address general issues pertaining to water transport across cell membranes, focusing on intracellular water, and the pathways and mechanism for osmotic water flow. In the third section, we will discuss water transport by epithelia, focusing on pathways and mechanisms, in particular the role of solute–solvent coupling. We intend this chapter to serve as both an overview and an introduction to chapters covering specific aspects of water transport (Chapters 5, 9, 41, 42, 43). The three sections of the chapter are to a certain extent independent from each other, and can be studied separately.
The field of water transport across biological membranes has made a recent major transition with the discovery and characterization of the aquaporins. Aquaporins are integral membrane proteins, most of which are highly specific water pores expressed in plants and animals from bacteria to humans. The discovery of the aquaporins confirmed a long-held prediction for the existence of these pores, emanating from biophysical studies in red blood cells and renal proximal tubules.
This section is largely based on the excellent water transport treaty by Finkelstein. Other sources are House, Reuss and Cotton, Dawson, Hallows and Knauf, and Macey and Moura. Derivations of the equations can be found in Finkelstein’s book. Deliberately, this section has been kept simple, and qualitative explanations have been superimposed on a succinct quantitative analysis.
The main mechanism of net water transport in animal cells is osmosis, that is, net water flow driven by differences in water chemical potential, in turn dependent on differences in solute concentrations. Concerning water flow across a cell membrane, an important issue is whether water moves through the phospholipid bilayer and/or through specialized water-conducting pores. The mechanisms involved in water permeation via these two pathways constitute the main content of this first section. Hence, we start with osmosis.
Osmotic Equilibrium is a Balance of Osmotic and Hydrostatic Forces
The principle of osmotic equilibrium can be illustrated by considering a simple system, that is, a semipermeable membrane separating two aqueous phases: pure water and a solution that contains a nondissociating solute ( Figure 4.1 ). The membrane is permeable to water and impermeable to the solute (hence the term semipermeable ). At thermodynamic equilibrium, the net water flow across the membrane is zero. (In the case of water, flow can be expressed in molar terms [moles of water per unit area and unit time] or volume terms [volume of water per unit area and unit time]. For conversion to volume flow, the molar flow must be multiplied by <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='V¯w’>𝑉⎯⎯⎯𝑤V¯w
V ¯ w
[partial molar volume, a constant equal to 18 cm 3 /mole].) The equilibrium of net flows is the result of the equality of two forces: an osmotic force favoring water flow into the solution; and an opposing hydrostatic force resulting, for instance, from the difference in height of the fluid compartments generated by the osmotic water flow. For dilute solutions, osmotic equilibrium is approximately described by Van’t Hoff’s law :
Δ P = π = R T C s
When the semipermeable membrane separates two solutions, equilibrium is described by a slightly different equation: Δ P= Δπ =RT Δ C s , where Δπ is the difference in osmotic pressure (π′−π″) and Δ C s is the solute concentration difference ( C s ′− C s ″).
The osmotic pressure depends on the molar concentration ( C s ) and on the degree of dissociation of the solute, that is, the number of particles that each molecule yields in solution (n). Ideally, the osmolality of a solution, in osmol/kg of water, is given by Osm =n C s , where C s is in mol l −1 . However, the effect of solute on the activity of the solvent is generally nonideal, that is, it may depend on the nature of the solute. The correction term for this effect is the osmotic coefficient, φ s , where the subscript denotes the solute. For physiological concentration ranges, the osmotic coefficient is closer to unity than the activity coefficient, but it can be significantly greater than 1 for macromolecules. For the sake of simplicity, the osmotic coefficient will be neglected in this discussion.
A 1 Osm solution at room temperature exerts an osmotic pressure of about 24.6 atm, which is equivalent to about 18,700 mm Hg. In a mammal, a 1% change in extracellular fluid osmolality (<3 mosmol/kg) is equivalent, as a driving force for water flow, to a hydrostatic pressure of 56 mm Hg. In animal cells, changes in osmolality cause large water fluxes across the plasma membrane, whereas hydrostatic pressure changes do not. Osmolality is a measure of concentration of particles, not of osmotic pressure, but it is frequently used to denote the latter.
The generation of Δ P in the presence of impermeant solute on one side can be explained on the basis of changes in the water chemical potential (μ w ), which is given by:
μ w = μ w o + R T ln X w + P V ¯ w
V ¯ w
is the partial molar volume of water. A solute addition to one side (at constant total volume) reduces the water chemical potential in that side (μ′ w ) because the water is “diluted” by the solute (and X w falls). The difference in water chemical potential thus generated (Δμ′ w = μ′ w − μ″ w ) is the “driving force” for water flow toward the side of higher osmolality (and lower μ w ). If both compartments are open and of appropriate dimensions, then a Δ P will result from changes in height ( Figure 4.1 ). If a compartment is closed, then its pressure will change in proportion to the water flux, with a proportionality constant dependent on compliance of the compartment.
Osmotic Water Flows Across Lipid and Porous Membranes have Different Properties
Near equilibrium, the volume flow is linearly related to the driving force:
J v = L p ( Δ P − Δ π )
V ¯ w
The above discussion underscores the fact that Δ P and Δπ are equivalent as “driving forces” in causing osmotic water flow. The mechanism of this equivalence can be understood if one considers the nature of the membrane and the mechanism of osmotic water transport, as explained below.
Osmotic Water Flow Across Lipid Membranes
Osmotic water flow across lipid membranes occurs by solubility diffusion . Water molecules move from one aqueous solution into the lipid and then into the other solution by independent, random motion. When Δ P =Δπ (0 net driving force) there are two diffusive water fluxes of equal magnitude and opposite direction, with no net water flow across the membrane. In the presence of a net driving force (Δ P −Δπ ≠ 0), a net flux arises. To examine the mechanism of water flow, let us consider the effects of Δ C s and Δ P on the water chemical potential in the two compartments.
A net diffusive water flow requires a difference in water chemical potential across the membrane. In a homogeneous membrane, a steady flux denotes a constant chemical potential gradient throughout the membrane thickness. If there is a difference in osmotic pressure between the two solutions, then the water mole fractions (and therefore the water concentrations) at the two sides, just inside the membrane must differ. It is commonly assumed that water transport across the membrane–solution interface is faster than water diffusion in the membrane itself. It follows that the water chemical potential just inside the membrane is very close to that in the adjacent layer of solution; therefore, water is near equilibrium across the interfaces. Finally, since μ w is inversely related to C s , a gradient of water concentration must exist across the membrane. This intramembrane gradient is the direct consequence of the differences in impermeant solute concentrations in the adjacent aqueous phases.
When Δπ=0, but Δ P ≠ 0, the chemical potentials of water in the two solutions differ (see Eq. (4.2) ). If P ′> P″ , then the water flux from side ′ is greater than that from side ″, creating an intramembrane gradient of water concentration and chemical potential.
The osmotic water permeability coefficient of a lipid membrane is given by:
P o s = D w m β w V ¯ w δ m V ¯ o i l
V ¯ o i l
is the partial molar volume of the membrane lipid.
Osmotic Water Flow Across a Porous Membrane
Let us consider a membrane made of a rigid, water-impermeable material. The pore density (number of pores per unit area) is n . Each pore is a water-filled cylinder of length L and radius r , and cannot be penetrated by the solute. The mechanism of water flow in this situation depends mostly on the pore radius. In large pores there is viscous water flow that can be described by Newtonian mechanics. In pores of molecular dimensions there is no appropriate theoretical treatment, but if the pores are so small that there is single file water transport (i.e., water molecules in the pore cannot slip past each other), then there is a surprisingly simple solution.
In large pores water flow driven by a hydrostatic pressure is described by Poiseuille’s law, which was derived for water flow in thin capillaries:
J v = n ( Π ) r 4 8 L η Δ P
If the only driving force is osmotic, then the mechanism of water flow involves the development of a hydrostatic pressure gradient within the pore. Initially, the water concentrations in the pore and in the water-filled compartment are the same, but at the other interface the solution has lower water concentration than the pore. If water transport across the membrane interfaces is faster than within the membrane, then the water chemical potentials just inside the pore are equal to those in the adjacent solutions. At the pore end facing the water compartment there is no difference in hydrostatic pressure, but at the end facing the solution compartment the pressure inside the pore falls, because the lower water concentration in the solution elicits a water efflux from the pore. If Δμ w is zero across the opening, then the difference in water concentration between solution and pore is exactly balanced by a drop in the pore pressure. In the steady-state, the pressure gradient in the pore is constant ( Figure 4.2 , top right).
The analysis presented above holds for pores of r equal to or greater than 15 nm. For pores smaller than 15 nm, several corrections have been attempted, but the underlying assumptions are questionable. Regardless of the lack of a satisfactory theory, it has been suggested that Poiseuille’s law is a reasonable approximation for water diffusion and convection in small pores.
The P os of a single-file pore is given by :
P o s = n v ¯ w k T N γ L 2
v ¯ w
is the volume of a water molecule, k is the Boltzmann constant (gas constant/molecule, equal to R / N A where N A is Avogadro’s number), N is the number of water molecules inside the pore, and γ is the friction coefficient per water molecule. Assuming that the water densities in the pore and in the bulk solution are equal, and recalling that kT /γ= D w :
P o s = n ( Π ) r 2 D w L
Comparison of Diffusion and Osmotic Permeability Coefficients Reveals Whether Water Permeates Lipid Bilayer or Pores
Now we consider a membrane exposed to solutions of identical composition, except that water is partially replaced with tracer water at a concentration C w ( Figure 4.3 ). There are no other differences in composition or pressure between the two compartments. Both contain solutions of infinite volume and ideally mixed ( C w at the membrane surface= C w in the bulk solution). The tracer water flux is given by:
J w * = P d w Δ C w *
Δ C w *
is the difference in concentration of tracer water ( C w *′−C w *″). In the case of a lipid membrane, the tracer–water flux is by solubility diffusion; hence:
P d w = D w m β w V ¯ w ∂ m V ¯ o i l
This expression is identical to that for P f (or P os ) for a lipid membrane ( Eq. (4.7) ). Therefore, for a lipid membrane, P os =P dw .
The case of a porous membrane is discussed below.
If the pores obey Poiseuille’s law, the diffusive water flux via the pores is:
J w * = n ( Π ) r 2 D w L Δ C w *