Mechanisms of Ion Transport across Cell Membranes

Ion transport across the cell membrane is essential to maintain the composition of the intracellular milieu . This chapter provides an introduction to ion transport processes in the cell membrane. The cell membrane is a thin sheet containing lipids (phospholipid bilayer) and proteins, many of which span its thickness (integral membrane proteins). Certain ions can permeate the membrane via proteins, but because of their electrical charge do not permeate the bilayer. Active and passive transport are defined based on their respective energy sources and explained at the mechanistic level, and includes basic mathematical treatments. Ion transport proteins (pores, channels, carriers, and pumps) are treated from both structural and functional viewpoints, with some of them covered in more detail because of their importance in body fluid homeostasis and renal function. The chapter closes with a discussion of the similarities and differences between the various classes of membrane proteins.


sodium; potassium; chloride; pore; ion channel; carrier; pump; diffusion; electrodiffusion


Ion transport by cell membranes serves two important purposes in pluricellular organisms, the maintenance of the volume and composition of the intracellular fluid, and the preservation and regulation of the volume and composition of the extracellular fluid. The first process involves fluxes between the cell interior and its surrounding medium (“homocellular” transport ), whereas the second one occurs because of transport across epithelial and endothelial cell layers (transcellular or “heterocellular” transport ). In addition, ion transport across intracellular membranes, which surround the nucleus and cytoplasmic organelles, is essential to generate and maintain ion concentration gradients between those organelles and the cytosol.

Needless to say, the narrowly regulated volume and ionic composition – inorganic cations (Na + , K + , H + , Ca 2+ , Mg 2+ ) and anions (Cl , phosphate, bicarbonate) – of the intracellular fluid is essential for cell survival, and for the cell’s normal functions. A similar argument can be made for the extracellular fluid compartments, that is, whole body balances of water and the ions listed above are essential for the survival, growth, and development of the organism.

Our main focus in this chapter will be on the molecular mechanisms of ion transport by the plasma membranes of cells. The cell membrane is a phospholipid bilayer doped with abundant proteins. This structure is both a barrier between the cytoplasm and the extracellular fluid, and the pathway for ion and water transport between the two compartments. For most ions, the lipid bilayer is the barrier and membrane transport proteins are the pathway for these fluxes.

The Cell Interior and Extracellular Fluid Have Different Ionic Compositions

A crucial property of living cells is their capacity to maintain an internal (intracellular or cytosolic) composition different from that of the surrounding (extracellular) medium. As with all other ionic solutions, the cytosol and the extracellular fluid obey the principle of macroscopic (or bulk) electroneutrality, that is, the sum of cationic and anionic charges are the same in each compartment. As discussed below, there is a microscopic deviation from this principle at the membrane surfaces when there is a difference in electrical potential across the membrane, but the actual differences between anion and cation concentrations are extremely small.

The maintenance of ionic asymmetry between intracellular and extracellular compartments is based on the existence of the cell membrane (or plasma membrane), which separates the cell interior from its surroundings. As shown schematically in Figure 2.1 , the membrane is a phospholipid bilayer, with high protein content. Membrane proteins can span the phospholipid bilayer (integral proteins, some of which span the membrane and are known as transmembrane proteins) or can be associated with the membrane surface (peripheral proteins). Transmembrane proteins perform many functions, including translocation of ions, nonelectrolytes, and water across the membrane (transport function, the main theme of this chapter); sensing and early transduction of extracellular events (signaling function); attachment to components of the cytoskeleton, the extracellular matrix or adjacent cells (adhesion function).

Figure 2.1

Structure of the plasma membrane.

This two-dimensional representation of the plasma membrane is based on the fluid-mosaic model modified according to recent observations. The membrane is a lipid bilayer that contains integral and peripheral membrane proteins. The bilayer is largely made of phospholipids that have polar heads and hydrophobic tails. The hydrophobic tails face each other, while the polar head groups face the adjacent aqueous solutions (extracellular fluid and cytosol). In addition, the membrane contains glycolipids and cholesterol. The phospholipid compositions of the two leaflets differ; e.g., phosphatidyl inositol is more abundant in the inner leaflet. Additionally, certain areas of the membrane form lipid rafts (see text). A small fraction of the membrane surface area is occupied by either strongly-bound proteins (integral membrane proteins), some crossing the membrane one or more times (transmembrane proteins) or loosely attached (peripheral) membrane proteins. Membrane proteins can be glycosylated or have other post-translational modifications (not shown). Some membrane proteins are attached to components of the cytoskeleton or the exoskeleton, directly or via other proteins. Integral membrane proteins can associate forming oligomers, as well as macromolecular complexes.

Two properties of the cell membrane are needed to generate and maintain the intracellular ion composition essential for life: the barrier function and the transport function. This distinction is didactically convenient, although both functions are clearly linked. By the barrier function, the cell membrane prevents the flux of certain molecules; by the transport function, it translocates certain molecules. These two functions bring about a steady-state in which cell volume and composition are kept constant and appropriate for cell survival. Relative to the extracellular fluid, some substances are maintained at high concentrations (e.g., K + and ATP), whereas others are maintained at low concentrations (e.g., Ca 2+ and Cl ) inside the cell.

The cell interior is not homogeneous, but is rather a complex medium including a highly structured cytoplasm (cytosol and cytoskeleton) and numerous organelles. The latter are separated from the cytosol by their membranes. Exchanges between each organelle and the cytosol occur by mechanisms similar to those present in the plasma membrane. In this chapter, we will not address organelle membrane function.

The Plasma Membrane: Structure Related to Function

The plasma membrane, which is 3–8 nm thick, is largely formed by phospholipids, organized in a bilayer, and proteins. The main phospholipids are phosphatidylcholine and phosphatidylethanolamine, with lower levels of phosphatidylinositol, phosphatidylserine, and phosphatidylglycerol, and sterols (cholesterol, ergosterol, zymosterol). The precise proportions vary among cells. Hydrophobic or amphipathic proteins are essential components of biological membranes. In most membranes, the w/w protein: lipid ratio is ca. 1, and therefore a membrane protein of ca. 40 kDa is surrounded by 50–55 lipid molecules.

Experimental work during the last two or three decades has ruled out the “fluid-mosaic” (Singer and Nicolson) model of membrane structure. In this model, biological membranes are considered two-dimensional viscous phospholipid bilayers in which integral membrane proteins are randomly distributed and free to rotate and diffuse laterally. A main objection is the demonstration of asymmetry in the lipid composition of the membrane. The current view is that the plasma membrane is a highly-organized and asymmetric structure composed of lipids and proteins. There are lateral differences in lipid composition within a monolayer; sphingolipids, sterols, and phosphatidylcholine predominate on the extracellular leaflet, whereas the cytoplasmic leaflet is enriched in phosphatidylinositol, phosphatidylethanolamine, phosphatidylserine, and phosphatidic acid, which results in a negative charge that facilitates binding of peripheral and transmembrane proteins. In addition, many membrane proteins cluster with others in microdomains, in which the lipid composition may differ from that of the bulk bilayer. These clusters are maintained by intramembrane lipid–lipid, protein–protein, and protein–lipid interactions, as well as interactions with intracellular molecules (cytoskeletal proteins) and extracellular components (extracellular matrix proteins and membrane proteins of adjacent cells). It is clear that the two monolayers also differ in composition. Lipid rafts are microdomains in the submicron range in which cholesterol and sphingolipids are enriched in the external leaflet, and cholesterol and phospholipids with saturated fatty acids in the internal leaflet of the plasma membrane. The surrounding bilayer is abundant in unsaturated fatty acids and contains more fluid than that in the raft. Lipid rafts exclude certain proteins and organize others in specific oligomeric structures. Rapid changes in composition and location in the membrane are essential for the role that lipid rafts play in signaling processes (e.g., receptor tyrosine kinases).

Phospholipids in the plasma membrane are not just a barrier and a “solvent” for membrane proteins, but play important roles in signaling processes. Inositol-1,4,5-triphosphate, diacylglycerol, and phosphatidylinositol-3,4,5-triphosphate (derived from phosphatidylinositol) are good examples. Phosphatidylinositol 4,5-bisphosphate (PIP 2 ) exerts regulatory effects on a number of ion channels and other transport proteins. Its effects can be stimulatory or inhibitory and appear to require PIP 2 binding. Other signaling molecules originating from plasma membrane phospholipids are arachidonic and docosahexaenoic acids, which are generated from phosphatidylethanolamine, phosphatidylcholine, and phosphatidylinositol by the action of phospholipase A 2 . Certainly, being a dielectric is not the only function of the phospholipid moiety of the cell membrane.

This new notion of the structure of the plasma membrane is based on results of biophysical studies, including fluorescence recovery after photo-bleaching, single-particle tracking techniques, optical trapping by laser tweezers, and fluorescence correlation spectroscopy. These methods, applied to cell membranes, have yielded quantitative dynamic information on the distribution, mobility, and compartmentalization of membrane proteins. Biochemical, molecular, and physiological studies indicate that membrane transport proteins are not randomly distributed, but that they undergo homo- and hetero-associations, and that these associations may have functional significance. A case in point is the proposed proximity between plasma membrane Ca 2+ channels and Ca 2+ -sensitive proteins, including Ca 2+ -activated channels: Ca 2+ entry results in a large, but highly localized, increase in intracellular [Ca 2+ ], because of effective cytosolic buffering, and thus its signaling effects may be quite local.

In summary, the current view of the structure of the plasma membrane is that of a compartmentalized two-dimensional structure, mosaic-like, with less fluidity than proposed by the Singer–Nicolson model. The phospholipids have signaling functions in addition to previously recognized ones. The mobility of membrane proteins may be restricted by the structure of the lipid domain, interactions with cytoskeletal proteins or other cytoplasmic components, and/or homo- and hetero-associations with other integral membrane proteins. Future studies of membrane transport proteins along these lines are likely to reveal important aspects of their function and regulation in health and disease (see Chapter 14).

The Plasma Membrane is Selectively Permeable

The barrier and transport functions of the plasma membrane are determined by its composition, mostly regarding lipids and integral transmembrane proteins (for membrane structure, see references ; for a review of membrane proteins, see ). When the membrane is permeable to a specific molecule, then that molecule can cross the membrane. Permeability (cm s −1 ) is a property of a specific membrane for a specific molecule. The amount of substance that crosses the membrane per unit of time and membrane area is the flux . Using radioactive techniques, unidirectional fluxes can be measured (e.g., in case of a cell, influx and efflux); the net flux is the difference between the two unidirectional fluxes. A finite net flux denotes the presence of either a net driving force across the membrane or an active process.

Permeation of a specific molecule can take place through the lipid phase (i.e., solubility diffusion ) and/or through membrane proteins (i.e., mediated transport ). Solubility diffusion always results in equilibrating transport, dissipating differences in concentration or electrochemical potential (see the section “Diffusion and Electrodiffusion,” below). In contrast, mediated transport can either dissipate or generate differences in chemical or electrochemical potentials across the membrane. An example of mediated transport is the operation of the sodium pump, the Na + ,K + -ATPase.

The lipid phase of the plasma membrane is hydrophobic, and therefore has high permeability for lipophilic molecules and low permeability for hydrophilic molecules. Thus, a protein-free phospholipid membrane has a high permeability for nonpolar small molecules such as O 2 and CO 2 , a much lower permeability for uncharged small polar substances such as water, urea, and glycerol, and an extremely low permeability for ions and larger uncharged polar molecules, such as glucose. Most molecules are measurably permeable across plasma membranes. However, the diffusive permeability coefficients range over several orders of magnitude. It is thought that hydrophilic molecules permeate the membrane bilayer to some extent, because the thermal motion of the phospholipid molecules causes transient kinks in the bilayer structure.

Transport proteins can be classified in four groups, namely pores, channels, carriers (also referred to as transporters), and pumps (see next section). The expression of some transport proteins can be specific to tissue, cell, and sometimes membrane domain. Others are expressed in most, if not all, cell membranes. The functional significance of transport proteins is apparent in two realms. Some are primarily related to the establishment and maintenance of cellular composition (intracellular “homeostasis”), such as the Na + ,K + -ATPase and K + channels in most animal cells. Others are primarily related to specific cell functions, such as excitability (e.g., the tetrodotoxin-sensitive, voltage-activated Na + channel in nerve and muscle), and transepithelial Na + transport (e.g., the amiloride-sensitive, voltage-insensitive Na + channel in the apical membrane of certain epithelial cells).

A pore is an aqueous communication between both sides of the membrane, accessible to both sides at all times – that is, it is always “open” (permeable). A channel is also an aqueous communication between the two sides of the membrane, but it opens and closes stochastically by changes in conformation called gating ; when open, a channel is accessible from both sides of the membrane, when closed, it is impermeable. A carrier is a membrane transport protein whose permeation pathway is not simultaneously accessible to both sides of the membrane, but to one side at a time; changes in conformation change the orientation of the carrier, moving the transported ion to the other side; an appropriate simplified description is that a carrier has two gates and they are never open at the same time. Finally, a pump has the properties of a carrier, but in addition it is coupled to a metabolic energy source, in most cases hydrolysis of ATP.

Mechanisms of ion TRANSPORT

Ion Transport can be Active or Passive

The definitions of active and passive transport are thermodynamic. Passive transport occurs in the direction expected for the existing driving force, which in the case of ions involves the chemical gradient (given by the difference in concentration between the two sides of the membrane) and the electrical gradient (given by the transmembrane electrical potential difference or membrane voltage). In other words, passive transport is energetically downhill. In contrast, active transport takes place in the absence of or against the prevailing electrochemical gradient. In other words, active transport is energetically uphill, and therefore requires an energy input. Depending on the origin of this energy, one can distinguish two types of active transport.

Primary active transport is characterized by the direct use of metabolic energy, supplied by light, redox potential or ATP hydrolysis. In most cases of plasma membrane primary active transport in eukaryotic organisms, the energy is provided by the hydrolysis of ATP, a process catalyzed by the same molecule that performs the transport. Hence, in this case the transporter is also an ATP hydrolase (ATPase). Transporters responsible for primary active transport are referred to as pumps. In plasma membranes of most animal cells there can be expression of one or more of four ion-transporting ATPases. These are the Na + ,K + -ATPase, H + -ATPase, H + ,K + -ATPase, and Ca 2+ -ATPase.

Secondary active transport is characterized by the indirect use of metabolic energy. The energy stored in the electrochemical gradient of one substrate is utilized to transport actively another species (ion or molecule). In animal cells, including those from epithelia, secondary active transport is most frequently linked to Na + transport. The Na + ,K + -ATPase establishes an electrochemical potential gradient for Na + across the plasma membrane, which includes chemical (high extracellular and low intracellular [Na + ]) and electrical components (cell electrically negative to the extracellular compartment), both contributing to a net driving force favoring Na + entry into the cell. This gradient is then utilized by carriers to actively transport other substrates, by coupling their translocation to that of Na + at the molecular level.

Depending on the directions of the fluxes, there are two kinds of secondary active transport: One is co-transport (or symport ) in which the substrates move in the same direction, such as downhill for Na + and uphill for the co-transported substrate (e.g., Na + -glucose co-transport). The other one is countertransport (also antiport or exchange ), in which the fluxes are in opposite directions (e.g., Na + –H + exchange). In most instances, secondary active transport involves only two species (Na + and another substrate), but in some cases there are three: an example is the Na + -K + -2Cl co-transporter, an electroneutral symporter that is expressed principally in epithelial cells. This transporter accounts for uphill Cl uptake, a step necessary for Cl absorption (e.g., in the apical membrane of cells of the thick ascending limb of the loop of Henle) or Cl secretion (e.g., in the basolateral membrane of crypt cells in the intestine and epithelial cells in the airway). For quantitative analyses of membrane transport processes, see Läuger, Macey and Moura, and Stein.

Active and Passive Transport Processes can be Evaluated by Considering Direction of Electrochemical Potential Difference (Driving Force)

As stated above, passive transport is energetically downhill, driven by the pre-existing driving force; this force depends on the chemical or electrochemical gradient, for uncharged and charged solutes, respectively. Under isothermal conditions the driving force encompasses differences in concentration, electrical potential, and/or pressure across the membrane. Under these conditions, the electrochemical potential difference ( <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Δμ¯j’>???Δμ¯j
Δ μ ¯ j
) for the j th ion is given by Eq. (2.1) :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='Δμ¯j=zjVmF+RTln(CjiCjo)+ΔPV¯j’>???=?????+??ln(??????)+????Δμ¯j=zjVmF+RTln(CjiCjo)+ΔPV¯j
Δ μ ¯ j = z j V m F + R T ln ( C j i C j o ) + Δ P V ¯ j
where z is the valence, V m is the membrane voltage, F is the Faraday constant, R is the gas constant, T is the absolute temperature, C is the concentration, i and o refer to the two sides of the membrane (inside and outside, respectively), Δ P is the transmembrane hydrostatic pressure difference, and <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='V¯j’>??V¯j
V ¯ j
is the ion’s partial molar volume. The electrochemical potential has the three components defined above, given by the three terms on the right side of the equation. Across animal cell membranes, steady-state hydrostatic or osmotic pressure differences are small or nil (see Chapter 4), and therefore the third term of Eq. (2.1) is eliminated, yielding:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='Δμ¯j=zjVmF+RTln(CjiCjo)’>???=?????+??ln(??????)Δμ¯j=zjVmF+RTln(CjiCjo)
Δ μ ¯ j = z j V m F + R T ln ( C j i C j o )

This equation is used to evaluate the driving force for ion transport under isobaric conditions. In the case of nonelectrolytes, z =0 and the first term of Eq. (2.2) can also be eliminated, yielding:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='Δμj=RTln(CjiCjo)’>???=??ln(??????)Δμj=RTln(CjiCjo)
Δ μ j = R T ln ( C j i C j o )
where Δ μ j denotes the chemical potential difference. This equation describes the driving force for nonelectrolyte transport.

From Eq. (2.2) (under isobaric and isothermal conditions), Ussing derived the flux-ratio equation, a fundamental expression which provides a thermodynamic test for active or passive transport:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='Jin/Jout=(Ci/Co)exp(zVmF/RT)’>???/????=(??/??)exp(????/??)Jin/Jout=(Ci/Co)exp(zVmF/RT)
J i n / J o u t = ( C i / C o ) exp ( z V m F / R T )
where J is flux (the subscripts denote influx and efflux, respectively). The test proceeds as follows: the ratio of unidirectional fluxes ( J in /J out ) is determined experimentally, and the driving forces are measured; if the ratio deviates from the prediction given by Eq. (2.4) , which evaluates the passive driving forces, then active transport is suspected. Deviations from the flux-ratio equation can also result from the presence of exchange diffusion and single-file diffusion, as discussed by Schultz.

Pathways and Mechanisms of Passive Transport

Passive transport can be via the lipid bilayer (solubility diffusion) or via transmembrane proteins (mediated). Solubility diffusion is a permeation process that involves the movement of a molecule dissolved in the aqueous solution bathing one side of the membrane into the lipid phase of the membrane, then across the membrane, and then from the membrane lipid into the solution bathing the opposite side. Clearly, two processes are involved. The first one (“solubility”) governs the fluxes at the solution–membrane interface, and depends on the relative solubility of the molecule in lipid and water, which can be quantified by the oil–water partition coefficient, β, a coefficient equal to the ratio of the molecule’s steady-state concentrations in lipid and water. The second process (“diffusion”) governs the solute translocation within the membrane lipid, which depends largely on the mass and shape of solute molecules. The lipid solubility of the molecule is the main factor determining its permeability via the lipid moiety of the membrane.

Mediated transport is the mode of transmembrane transport of substances with very low solubility in phospholipids, that is, charged and polar substances. The transport proteins provide a hydrophilic path across the membrane, through which the solute permeates or a narrow pore in which amino acid charges replace the water molecules surrounding the ion or polar molecule in free solution.

Diffusion and Electrodiffusion

Diffusion and electrodiffusion are the main processes of passive solute transport across homogeneous phases (e.g., lipid membranes or aqueous pores) by independent motion of the solute molecules. Diffusion applies to uncharged particles and electrodiffusion to ions. Although diffusion does not strictly apply to ion transport, its analysis is simpler and helps in understanding electrodiffusion.

Diffusion of a solute in aqueous solution is the result of the random thermal motion of solute molecules. In the absence of convection, if there are differences in concentration between different sectors of the solution, then random solute motion will tend to make its distribution homogeneous (equilibrating transport). All solute particles move randomly at uniform average velocities, dependent on the solution temperature. Hence, more particles will tend to move from regions of high concentration to sectors of low concentration than in the opposite direction, simply because there are more particles per unit volume in the high concentration regions. In other words, differences in concentration cause unequal unidirectional fluxes in a regime of diffusion because of differences in the number of particles flowing in each direction per unit of time, not because of different velocities of individual particles flowing in one direction or the other. In diffusion, the molecules move independently of each other and of other particles present in the solution, that is, there is no flux coupling. This is the independence principle .

Diffusion of a nonelectrolyte in solution is described by Fick’s first law :

<SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='Js=−DsdCsdx’>??=???????Js=−DsdCsdx
J s = − D s d C s d x
where J s is the solute flux (moles cm 2 sec −1 ), D s is the solute diffusion coefficient (cm 2 sec −1 ) and dC s /d x is the concentration gradient. The negative sign denotes the direction of the flux.

Fick’s second law of diffusion considers the time course of the process:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='dCdt=Dsd2Csdx2′>????=???2????2dCdt=Dsd2Csdx2
d C d t = D s d 2 C s d x 2
where dC/dt is the rate of change in solute concentration, and x denotes distance.

The average time required by diffusing particles to cover a given distance is inversely proportional to the diffusion coefficient, and directly proportional to the square of the traveled distance. Einstein approximated the second law of diffusion with λ =( D s t ) ½ , where λ is the traveled distance in the x-axis. The dependence of t on the square of the distance makes diffusion a very slow transport process for long distances. For a typical D s =10 −5 cm 2 sec −1 , it takes 1 millisecond for the solute to diffuse 1 μm, but it takes 1000 seconds ( ca. 16.7 minutes) to diffuse 1 mm. Convective flow (see Chapter 9) is a much more effective mass transport mechanism for long distances.

Now we consider a thin lipid membrane of thickness δ m separating two aqueous compartments ( Figure 2.2 ). The solutions on both sides are well stirred, so that the solute concentrations are homogeneous in both. Inserting the solute partition coefficient (β s ) in Eq. (2.5) s denotes lipid solubility relative to water solubility), we obtain the following expression for the solute flux:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='Js=−DsβsδmΔCs’>??=?????????Js=−DsβsδmΔCs
J s = − D s β s δ m Δ C s
where Δ C s is the solute concentration difference between the two solutions. Defining the solute permeability ( P s ) as P s = D s β s m , Eq. (2.7) reduces to:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='Js=−PsΔCs’>??=?????Js=−PsΔCs
J s = − P s Δ C s

Figure 2.2

Diffusion across a membrane.

(a) A membrane separates two aqueous solutions (1 and 2). The dots represent molecules of a solute to which the membrane is permeable; the solute concentration ( C s ) is greater in solution 1. Solute molecules move randomly in each solution and collide with the membrane with a probability proportional to the concentration. Solutes collide, dissolve in, and diffuse across the membrane. The unidirectional fluxes (J 1→2 and J 2→1 ) are proportional to the solute concentrations in sides 1 and 2, respectively; the net flux (J net ) is proportional to the concentration difference. The concentration difference does not accelerate the molecules, and hence it is not a force, although it is usually referred to as the chemical driving force. Diffusion is a passive, equilibrating transport, i.e., net transport ceases when the concentrations on both sides of the membrane are equal. (b) Lines denote solute concentration profiles in the solutions and the membrane depending on the partition coefficient (β s ). When β s =1, solute concentration in the membrane boundaries are identical to those in the adjacent solutions; concentrations in the membrane are greater or smaller than those in the adjacent solution if β s is greater or smaller than unity, respectively. The membrane thickness is denoted by δ m .

The diffusive permeability coefficient of the membrane relates the flux to the driving force and denotes the ease with which the membrane permits mass transfer of a particular species. Its units are cm s −1 , those of velocity. In the simple case of a nonelectrolyte, under isothermal and isobaric conditions, the permeability ( P ) of solute s is given by a rearrangement of Eq. (2.8) : P s = J s C s . This is the phenomenological, experimentally determined permeability, calculated by dividing the steady-state solute flux by the difference between the solute concentrations of well-stirred bathing solutions. The other definition of diffusive permeability is mechanistic, and considers the factors involved in solubility diffusion, D s , β s , and δ m , as described above.

The preceding discussion considers the specific case of solubility diffusion, but the phenomenological definition of permeability can be applied in principle to any transport mechanism. Of course, its interpretation varies. An important case is that of the permeation of certain hydrophilic nonelectrolytes through aqueous pores in the membrane. If the lipid bilayer is impermeable to the solute, then diffusive transport is entirely via the pores. The permeable area of this membrane ( S p ) is only a fraction of the total membrane area, given (for 1 cm 2 of membrane) by S p = nπr 2 , where n is the density of homogeneous pores of radius r . The partition coefficient is unity (the solute is dissolved in water both inside and outside of the pore), and is hence eliminated from the equation:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='Ps=nπr2Ds/L’>??=???2??/?Ps=nπr2Ds/L
P s = n π r 2 D s / L

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Jun 6, 2019 | Posted by in NEPHROLOGY | Comments Off on Mechanisms of Ion Transport across Cell Membranes

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