2.4—
Transport of Substances Across Membranes

In a healthy cell there is a continuous interchange of water, ions, uncharged solutes, metabolites and dissolved gases across the plasmalemma. As one might expect, not all of these substances move through the membrane in the same manner. Firstly, some substances diffuse into a cell down a gradient of potentia energy; such movement is spontaneous and is the thermodynamic equivalent 0¹ heat passing from a warmer to a cooler body. There are, however, many substances which are accumulated by cells against a gradient of potential hence their movement into the cell is 'uphill' and is equivalent to the flow of heat from a cooler to a warmer body. 'Uphill' transport requires work to be performed and thus consumes energy. 'Downhill' transport is frequently described as passive while 'uphill' transport is described as active and directly involves the participation of cellular metabolism.

In Fig. 2.11 some further sub-divisions of transport processes have been made. Thus, passive movements may occur by at least three types of pathway, whereas active movements must be linked to some energy-consuming mechanism, referred to as a 'pump', in the membrane. The third type of movement occurs because of the undulation and vesicularization of the membrane in endocytosis (see p. 61). Clearly this is a process which depends at some point on metabolism but, as is discussed below, the substances which move into the cell do not necessarily cross the membrane at all. In such circumstances the observed transport is not strictly active in a thermodynamic sense.

---

Figure 2.11
Types of active ('uphill') and passive ('downhill')
transport across a membrane. For discussion see text.

2.4.1—
Passive ('Downhill') Transport

Solute molecules in more concentrated solutions possess more free energy than those in lower concentrations; in other words they are at a higher potential. If two solutions of different concentration are mixed, solute molecules will diffuse from areas of high to areas of low potential. In any given situation the chemical potential of an uncharged solute is dependent on its activity as shown in equation 2.1.

---

For many practical purposes it is assumed that the activity of a solute moving freely in dilute solution is the same as its concentration so that the chemical potential is more frequently written

where C_s = the concentration in moles 1^–1 .

If the solute is charged, its movement from place to place can also be influenced by differences in electrical potential. An ion, therefore, has an electrochemical potential which is related to its concentration (strictly, its activity) and the electric potential of the medium in which it is moving. Thus,

where

and are the electrochemical potentials of the ion j in a given set of conditions and in a standard state respectively, C_j is the concentration of the ion j, Z_j is its algebraic valency (i.e. K⁺ would be + 1, and Cl^– , –1), F is the Faraday constant which defines the amount of electric charge (approx. 10⁵ coulombs) carried by 1 gram equivalent of the ion and y is the electric potential of the medium. It is important to appreciate that y is a property of the medium and not of the ion j in particular.

Because C_j and y can influence

independently it is easy to see that a difference in electrical potential across a membrane can promote the diffusion of an ion in the absence of any difference in concentration or even against a gradient of concentration. This situation is illustrated in Fig. 2.12 where we can see that the concentration of an ion within a membrane-bounded compartment may be much greater than in the surroundings and yet be at electrochemical equilibrium providing that a sufficiently large electric potential is maintained. It is wrong, therefore, to conclude, because an ion is more concentrated within a cell than in the outside solution, that it has been actively transported.

2.4.2—
Criteria For Active ('Uphill') Transport

To decide whether or not an ion or solute is actively transported across a membrane we need to know its activity or concentration in the two solutions separated by the membrane and for ions, in addition, we must know the electrical potential difference across the membrane. It is frequently difficult to measure the concentrations, and more difficult to measure the activity, of substances within cells with any accuracy, especially in those of higher plants.

In the giant cells of several sorts of algae, which may be 5,000 to 10,000 times the volume of a parenchyma cell in a root, such measurements are made

---

Figure 2.12
An explanation of the way in which a decrease in electrical potential, y , across a membrane
can result in the diffusion of an ion against a gradient of concentration. Note that, in the initial
situation, in spite of concentration of  j  being greater in B, the electrochemical. potential gradient is
still directed 'downhill' towards B. As B fills with ion  j,  µ_j  flattens out and, at equilibrium becomes zero—
at this point the 'uphill' concentration gradient and the 'downhill' electrical gradient are equal and opposite.

routinely. The electrical potential difference across membranes can be measured if a small glass micro-electrode, with a tip diameter of 1 to 3m m, can be inserted into the membrane-bounded compartment (see Clarkson, 1974).

Having made the necessary measurements a simple test can be applied to see if a given ion or solute within the compartment is at a higher or lower potential than in the surrounding solution. The principal snag in this analysis is that the cell or compartment should be in a steady state and that no net movement of solute should be occurring. In nature this condition is infrequently met.

Let us suppose that the ion j is at electrochemical equilibrium between the two compartments i.e.:

re-writing equation 2.3 and cancelling out

we have

---

gathering the electrical terms to the left-hand side we get

yⁱⁿ —y ^out is the electrical potential difference across the membrane where the ion j is at equilibrium and is given a special name, the Nernst Potential, and is usually symbolized Ej^N . We now compare this calculated equilibrium potential with the potential difference which is actually measured by the electrodes on either side of the membrane. If the calculated and observed values coincide we would conclude that, in spite of any differences in C_j across the membrane, the system was at equilibrium. If, however, the observed potential was lower than the equilibrium potential we would conclude that the electrical driving force was not sufficiently large to support the observed asymmetry of C_j and we would suspect that active transport was occurring. The example worked out in Table 2.8 may make this clearer. For each ion the appropriate Nernst Potential has

been calculated from the observed concentrations on the outside and inside of the membrane using equation 2.5. The exact correspondence of the Nernst Potential for potassium,

, with the measured electric potential difference shows that potassium ions inside the cell are at electrochemical equilibrium with those outside. For sodium, however, is much less negative than E, hence Na⁺ is at a lower electrochemical potential inside; there is, therefore, a strong tendency for sodium to diffuse into the cell, and the fact that the observed

---

concentration is only 1/20 th of the equilibrium concentration strongly suggests that metabolic energy must be coupled to a Na⁺ -efflux pump. Chloride ions in the cell are a very long way indeed from being in electrochemical equilibrium with their surroundings, being more than 1,000 times greater than the equilibrium concentration, thus their movement into the cell is steeply uphill.

In theory this type of analysis can be applied to any ion, although it is difficult to apply to minor ionic constituents, e.g. trace elements, because they may be complexed with organic ligands within the cell so that their ionic activity may be very much lower than their concentration as measured by chemical analysis.

If an analysis of the kind described in Table 2.8 shows that the transport of an ion in a given direction is 'uphill', one should not conclude necessarily that the membrane is equipped with a special pumping mechanism for that ion. In some cases it may be, but in others the 'uphill' transport of the ion may be coupled with the 'downhill' transport of another via a common carrier; this latter possibility is described under the heading Co-transport on p.56.

2.4.3—
The Nature and Origin of the Membrane Potential

It is clear that electrical potential differences across membranes are of great importance in generating driving forces on ions. It is important, therefore, to try to understand how these potentials arise and how they are maintained.

An electric potential difference arises because positive and negative charges become separated. Since the cytoplasm of most cells is electrically negative relative to the surroundings it is very slightly enriched in anions relative to cations. This can be attributed to the differential permeability of the cell membrane and to the activity of ion pumps. First let us examine how differential permeability can create an electrical potential difference.

2.4.3.1—
Diffusion Potential

Imagine a simple system of two compartments separated by a membrane which has a much higher permeability to K⁺ than to Cl^– (Fig. 2.13). If the compartments are filled with potassium chloride solutions of different concentration, initially K⁺ will move through the membrane out of the more concentrated compartment, and for a very brief period, the more concentrated cell will lose K⁺ faster than Cl^– leaving it enriched in negative charge. The negative diffusion potential thus created slows down the further escape of K⁺ by attracting it back into the more concentrated compartment. When the potential has developed, a large concentration difference can be maintained between the compartments. Since the membrane has a finite permeability to Cl^– , albeit a low one, over a long period of time both the electrical potential difference (the diffusion potential) and the concentration difference would run down as Cl^– leaked through the membrane. If the membrane were completely impermeable to Cl^– , the

---

potential, once established, would be maintained indefinitely. In nature, membrane permeability to anions is a tenth to one hundredth of that for the monovalent cations; thus, the maintenance of a potential of the kind just considered depends on topping up the cell with anions at a rate comparable with their leakage into the surroundings. This is an 'uphill' transport and therefore requires the mediation of some ion pumping mechanism. Active transport is, therefore, necessary to maintain a diffusion potential.

Figure 2.13
Development of charge separation and a diffusion potential
in a model system containing a membrane selectively
permeable to cations. For further explanation see text.
(From Clarkson. 1974.)

In nature it is frequently possible to find cells where the electrical potential difference across the plasmalemma is, indeed, a diffusion potential of the kind just described which depends very closely on the concentration of either K⁺ or H⁺ in the medium and in the cytoplasm. In such circumstances its value can be predicted from the Goldman equation (2.6) which relates the concentration ratios of ions across the membrane and their permeabilities (P_K , P_Na , P_Cl etc.).

---

This relationship will apply strictly only to situations where the cell and the surroundings are in a steady state and hence limits its application to mature and non-growing cells. The last pair of terms in equation 2.6 has been put in to emphasize that other diffusing ions can be added to the equation; clearly H⁺ has an important effect on the membrane potential in some instances (Kitasato, 1968). Since the concentration ratio is multiplied by the permeability coefficient, the value of E will be most strongly influenced by the ionic asymmetry of the most rapidly diffusing ion. In the system considered above the value of E would have been given by

and be governed almost entirely by K⁺ since P_Cl was very small compared with P_K . Notice that the ratio of the chloride terms is inverted relative to the cationic terms. This is explained because the chloride concentration differential will tend to reduce any negative electrical potential set up by the asymmetric distribution of the cations.

2.4.4—
Membrane Pumps

Pumping mechanisms which allow cells to accumulate solutes up gradients of potential can contribute to the membrane potential in both an indirect and a direct way. The former type are referred to as neutral exchange pumps in which the cell dumps an unwanted ion of equal and like charge into the external environment in a one-to-one exchange for an ion which is more useful, e.g. there are well known exchanges of cellular Na⁺ or H⁺ for K⁺ from the surroundings. The second type transports an ion in one direction only without coupled exchange and is known as electrogenic since charge is separated. They can, therefore add to, or subtract from the diffusion potential, described above, depending on which ion is carried. These two types of mechanisms are outlined in Fig. 2.11.

2.4.4.1—
Neutral Ion Pumps

Neutral ion pumps are present in the plasmalemma of all cells and by their activity they create the ionic asymmetry necessary to set up the diffusion potential described above. As a much simplified illustration of this, consider a cell which, because of its synthetic and respiratory activity, is generating H⁺ and HCO₃^– internally. A pair of exchange pumps could swap H⁺ and HCO₃^– for K⁺ and Cl^– from the surroundings quickly enriching the interior in these ions and thus setting up the conditions in which the differential rates of diffusion

---

of K⁺ and Cl^– out of the cell give rise to a membrane potential. But how does such a pump actually work? There are fewer detailed examples than one would like but the best known is of the membrane-bound ATPase which exchanges intracellular Na⁺ for extracellular K⁺ in many animal and plant cells (see Hall, 1971; Hodges et al., 1972). In the red blood cell it is known that Na⁺ is one of the cofactors which is essential for the binding of ATP to the ATP-ase enzyme. In vivo the active centre of the enzyme is accessible only from the cytoplasm, so that the ATP and the Na⁺ must be inside the cell (Fig. 2.14). Once bound, the ATP

Figure 2.14
A highly simplified illustration of the working of a sodium-potassium exchange pump based on a
membrane-bound ATPase. The cross hatched area on the ATPase is its active centre. The large
re-orientation of the molecule is for illustrative purposes only—quite subtle molecular re-arrangement
may be all that is necessary to expose the Na⁺ - binding site to the outside and for the step called relaxation.

is hydrolysed, ADP is released into the cytoplasm leaving the cleaved terminal phosphorus atom attached to the active centre to form a phosphoenzyme. These reactions result in some molecular re-orientation of the phosphoenzyme and its attached Na⁺ which exposes the ion-binding site to the different chemical environment of the external medium. It is proposed that this change of environment alters the ion-specificity of the binding site so that K⁺ is favoured; K⁺ thus replaces Na⁺ . This done, there is a second re-orientation (referred to as 'relaxation' in Fig. 2.14) which carries the bound K⁺ to the inside. The phosphorus is released from the active centre and Na⁺ , which is preferentially bound on the cytoplasmic side exchanges for K⁺ and the pump is ready for a second cycle. The pump has used the free energy released on hydrolysis of ATP as fuel to exchange K⁺ and Na⁺ against their respective electrochemical potential gradients. The two ions in the appropriate orientations are essential cofactors in the enzyme reaction; in vitro, ATPase of this kind will not hydrolyse ATP unless Na⁺ and K⁺ are both present.

In theory many pumps based on ATPase are possible with only subtle modifications of the ATPase molecule to provide binding sites of varying field

---

strength which will select various ions, e.g. a Ca²⁺ transporting ATPase is found in mitochondria and in sarcoplasmic reticulum (Racker, 1972).

2.4.4.2—
Electrogenic Pumps

The unidirectional transport of an ion across a membrane separates charges and in so doing provides a driving force for the passive diffusion of a similarly charged ion in the opposite direction or an oppositely charged ion in the same direction. The molecular details of exactly how an electrogenic pump is put together remain uncertain although in one instance it is highly likely that an electrogenic H⁺ -efflux pump is based on an ATPase (Slayman et al., 1973). It is possible, nevertheless, to deduce certain general consequences of their operation. If, for instance, there was an outwardly directed pump at the plasmalemma which actively pumped hydrogen ions (protons) out of the cell thus making the interior electrically negative, this could contribute to the electrical driving force on the diffusion of K⁺ from the external medium. Indeed the rate at which charge is extruded and the rate at which it leaks back into the cell must be very nearly in balance unless a dangerously large potential is to accumulate. Examples of both proton extrusion pumps and anion influx pumps of the electrogenic kind are well documented from research on plant tissues (Higinbotham & Anderson, 1974; Spanswick, 1972). In the giant alga, Acetabularia, an electrogenic chloride influx pump contributes more than half of the potential of –170mV found across the plasmalemma when the cell is kept in the light. Almost immediately the cell is put in the dark the pump stops working (since it is closely linked with photosynthesis) and the membrane potential abruptly depolarizes to –80mV (Saddler, 1970). A similar light-dependent electrogenic pump is found in Nitella translucens (Spanswick, 1972, 1974). Electrogenic pumps are not, however, restricted to green tissues but have been reported in plant roots (Higinbotham et al., 1970) and fungal hyphae (Slayman, 1970). In every instance, however, inhibition of the pump caused an immediate depolarization of the membrane potential, indeed this is often used to detect the activity of such a pump. The inhibition of a neutral ion pump gives rise to gradual depolarization as the ionic asymmetry runs down (see equation 2.6).

2.4.5—
Membrane Carriers

Many ions and uncharged solutes cross membranes more rapidly than could be expected if they passed through the membrane lipids without some assistance. Since pores in membranes are too narrow to accommodate many substances which are transported, it is widely believed that membranes contain carrier molecules which, in combination with the solute, facilitate diffusion. The ion pumps considered above are carriers of a special kind since they are linked to

---

the metabolic activity of the cell; the carriers we shall now consider promote net movements of solutes only down the prevailing potential gradient and are not capable of 'uphill' transport even if in some instances (see p. 57) they appear to be doing so.

2.4.5.1—
Evidence from Kinetics

One widely used approach to gather information about carriers has been the application of kinetics first derived from enzyme reactions. The evidence for these carriers is obtained by placing a cell or tissue in a range of solute concentrations and measuring the initial rate of uptake. As illustrated in Fig. 2. 15 the uptake rate shows a tendency to saturate at higher concentrations and can thus be used to calculate the maximum velocity, V_max , possible under the conditions used in the experiment. By making a double reciprocal plot of the data (Fig. 2.15) the concentration of solute at which half maximal velocity is achieved can

Figure 2.15
Saturation kinetics of solute uptake versus concentration. Such results are used
as evidence for the association of the solute and a carrier. The double reciprocal plot of
the data gives a more accurate estimate of  V_max  and K_m  when the number of points is limited.

be estimated. This is known as the Michaelis Constant, K_m . The K_m measures the affinity of the carrier for the solute it carries; if the affinity is high then the concentration, K_m will be low and vice versa. For most ions in plant tissue K_m is quite low, concentrations ranging from 5–100 mM , but for sugars and other metabolites K_m values are usually greater than 300 mM . Much work of this kind is summarized by Epstein (1972) who shows that at concentrations less than 0.1 mM , the uptake of a given ion is not subject to serious interference from other

---

common ions in solution. There is, however, competitive inhibition between related ions of similar molecular dimensions, e.g. K⁺ uptake is inhibited competitively by Rb⁺ but not by Na⁺ ; Ca²⁺ is inhibited by Sr²⁺ but not by Mg²⁺ . Thus the carriers which bind the major nutrient ions at low concentrations appear to be highly ion-selective. At higher concentrations (more than 1.0–10.0 mM ) this selectivity begins to decline. The interpretation of this observation is contentious and beyond the scope of this chapter but can be pursued in Epstein (1972), Laties (1969) and Clarkson (1974).

The limitation of the kinetic approach is that it can tell us nothing about the nature of the carrier. One can observe similar uptake kinetics for ions whose transport into the cell must be mediated by ion pumps e.g. H₂ PO₄ ^– and Cl^– (see p. 48) as for ions which probably diffuse into the cell passively e.g. Na⁺ and Ca²⁺ and for those which are completely exotic and toxic, e.g. Tl⁴⁺ (Barber, 1974). Indeed, it has been pointed out that saturation kinetics of this kind would also be found if salt movement was observed across a synthetic membrane containing nothing but pores (Stein & Danielli, 1956), where the system would saturate when all of the pores were filled with solute at any moment in time; V_max is, after all, merely a measurement of capacity to react or transport and K_m is derived from it (Fig. 2.15).

2.4.5.2—
Ionophores as Lipophilic Carriers

A more illuminating approach to the nature of carriers has come from studies on the ionic conductance of synthetic membranes which have been modified in various ways. A bilayer of pure phospholipids has a very low conductance to ions, usually only 10^–7 to 10^–8 ohm^–1 cm^–2 . The addition of very small amounts of ionophores (i.e. ion-carrying antibiotics) like monactin or valinomycin to the solutions bathing the synthetic bilayer causes a huge increase in the conductance. Figure 2.16 shows that 10^–6M monactin changes the membrane conductance to K⁺ nearly a million-fold and that even at 10^–10 M its effect is quite strong. The conductance change for a given monactin concentration is greatest for K⁺ and for Rb⁺ and is much less for Na⁺ , Cs⁺ and Li⁺ . Monactin is, therefore, acting as a selective carrier of K⁺ and Rb⁺ and valinomycin, another bacterial product, behaves similarly. Since these two compounds differ chemically it is instructive to see what they have in common. Both of them are amphipathic ring-structured molecules which have their non-polar groups on the outside of the ring and their polar groups directed towards the space at the centre of the molecule. The outside of the ring interacts favourably with lipid while the hydrophilic core, 0.7 nm in diameter, provides room for several hydrated potassium ions to be bound. Evidence from a variety of sources shows that this complex diffuses across the membrane so that the ions never leave a polar environment (Eisenman et al., 1968).

Other substances are known which select for divalent cations, e.g. the unnamed compound A23187 which is a carboxylic acid antibiotic found in

---

Figure 2.16
Influence of the ionophore, monactin, on the electrolytic conductance of a
phospholipid bilayer in the presence of single salt solutions of alkali cations.
(Redrawn from Eiseman et al.,  1968.)

cultures of Streptomyces chartreusensis (Reed & Lardy, 1972). This compound carries Ca²⁺ and Mg²⁺ across bilayers and natural membranes but has no effect on monovalent cations.

Apart from a few synthetic analogues all of the ion-carrying antibiotics are natural products of bacteria and fungi. There are many who believe that compounds of a similar kind may act as ion carriers in all membranes but the technical difficulty of isolating what are probably minute quantities of such compounds from tissues appears to be formidable and so the belief may rest on faith for some time yet.

2.4.5.3—
Co-transport

As suggested earlier, carrier-assisted diffusion can sometimes appear to go in an 'uphill' direction, thus giving the impression of active transport. In many animal tissues and micro-organisms, sugars, amino acids, organic acids and vitamins move into the cell up a concentration gradient. This transport is, however, almost completely dependent on having Na⁺ or H⁺ in the external medium; other ions such as K⁺ , Rb⁺ or Li⁺ cannot be substituted. It has been

---

found that the metabolite is carried into the cell along with an ion-carrier complex which is diffusing 'downhill' (Fig. 2.17). In both Chlorella and Neurospora, glucose is transported in this way along with protons, H⁺ (Komor & Tanner, 1974; Slayman & Slayman, 1974).

Figure 2.17
Scheme to illustrate co-transport of protons and sugar. The proton extrusion pump is electrogenic
and thus makes the inside electrically negative. Protons diffuse back into the cell passively  via  the
carrier which also binds a sugar molecule. The protonated carrier plus sugar diffuses towards the
inner face of the membrane where it dissociates and releases the sugar molecule.

Co-transport depends on active transport in an indirect way (as indeed does all diffusion, see p. 50) because energy-dependent extrusion pumps ensure that the cytoplasm is kept well below its equilibrium concentration in H⁺ and Na⁺ . These ions tend to diffuse back into the cell and, in doing so, decrease their free energy. The energy they give up is coupled, via the carrier, to the co-transport of the solute whose free energy is increased as it moves into the cell.

Co-transport may also assist the 'uphill' movement of inorganic ions into the cell; it may be a more common process than is generally realized. Recent

---

evidence by Lowendorf et al., (1974) suggests that the active transport of phosphate into the hyphae of Neurospora depends on (a) the activity of a proton extrusion pump at the plasmalemma which is sensitive to the pH of the external medium, and (b) the formation of a ternary complex between a proton and a phosphate ion from the external medium with a membrane carrier. The protonated phosphate carrier diffuses to the cytoplasmic side of the membrane down the electrochemical gradient of the proton, releasing the proton and phosphate ion into the cytoplasm. This, and other examples of inorganic ion co-transport (see Raven & Smith, 1974) suggest a reason why so little progress has been made in elucidating the molecular details of certain 'pumps' particularly of those which transport anions. Put most simply, it may be that these influx pumps do not exist and that the uphill transport is driven by a combination of active extrusion and re-entry by diffusion of protons or perhaps sodium ions.

Co-transport illustrates the ingenious way in which nature can turn necessity to its own advantage. The active excretion of H⁺ and Na⁺ is essential to maintain pH control and osmo-regulation in the cell, but the energy expended is partly recovered in the transport of essential metabolites and ions into the cell.