The Membrane BarrierThe fundamental role of membranes is as selective barriers in the formation of functional compartments. By and large, the selectivity is provided by proteins, which can have high specificity as well as allowing the coupling of material transport with other novel activities. The barrier aspect, on the other hand, is the provenance of the lipid and their great efficacy in this role is due to the almost universally ionic or dipolar nature of natural solutes. The apolar character of the lipid bilayer presents a large energetic barrier to entry by ionic and strongly polar molecules.

The rate at which net solute crosses a membrane depends on (1) the driving force, such as the concentration gradient or transmembrane electric potential, which is external to the membrane, and (2) the energetic barrier that the membrane presents, which depends on intrinsic bilayer properties and on the specific identity of the solute. For the barrier energetics, we can write the free energy of the solute-membrane interaction as the sum of work terms involved in bringing a solute into the membrane. This can be broken down to four contributions:

The first three terms on the right hand side represent all the electrostatic contributions, including interactions between the charge (or charge distribution) of the solute and the bulk dielectrics, dielectric interfaces and any intrinsic dipole potential of the membrane. These are mostly positive (unfavorable) contributions to the energy of the solute in the membrane. The "Neutral„ term includes all other contributions to the free energy, including van der Waals, hydrophobic, and specific chemical interactions. These are generally favorable contributions, depending on the chemical nature of the solute.

The Born energy of an ionWe can define the electric field and potential generated by a single charge, but what is its intrinsic electrostatic energy, and what does it mean? Normally, the energy of a charge is defined in the context of its interaction with a potential generated by another charge. However, clearly it is reasonable to expect that there is an energy associated with a charged particle, distinct from that of an otherwise identical but neutral one. In other words, we can ask what is the electrostatic work required to make it, i.e., to charge it up from zero? This is the self-energy of an ion, although this term is often restricted to the evaluation in vacuo. When the work is evaluated in a fluid dielectric (a solvent) it is commonly called the Born energy of the ion. This is an important parameter which determines the extent to which an ion will dissolve and partition in different solvents - including membranes. How do we calculate it?

The effect of the image charge interaction is to decrease the energetic penalty of an ion being in the membrane. This is because the image charge in the external medium (high dielectric) is of opposite sign and the energy of interaction is negative (favorable). Furthermore, when the ion is outside the membrane, the high dielectric medium on the "other side" of the membrane can be seen, which diminishes the magnitude of the unfavorable interaction with the image charge (of the same sign) inside the membrane. However, the correction to the Born energy in the center of the membrane is small, but it may knock off a few kT from the barrier height. Probably more importantly, because the image charge contribution increases as the ion approaches its image at the membrane surface, it significantly alters the shape of the potential energy profile for an ion in the membrane, giving it a more gradual shape rather than the step function that the Born energy alone would indicate.

Thus, the Born energy of a dipole is identical to that of a single ion with the same charge. Clearly, ion pairing is not very helpful in getting a charge into the membrane if the interaction between the charges is purely ionic. Covalent interaction would be different, as this essentiallyimplies discharge of the two ions, but would not be mechanistically simple or versatile.

Born energy of a dipole

A dipole possesses an electrostatic self-energy analogous to the Born energy of an ion. It is the sum of the Born energies of the two charges, ±q, at infinite separation, and the Coulomb energy of bringing them together. If the two charges have the same radius, a, and are at contact, so the separation r = 2a = l, the length of the dipole, we obtain:

Dispersion self energy of a molecule in a medium

The dispersion self energy is determined by the (positive) energy required to make a cavity -by breaking n solvent-solvent "bonds" (i.e., turning off the van der Waals forces), plus the (negative) energy of placing the molecule in the cavity - formation of n solute-solvent "bonds„ (turning the vdW forces back on). The result is that for a neutral, non-polar molecule, the favorable environment is that with the most similar dielectric properties. This is the underlying principle behind the "like dissolves like" rule. In fact, in the absence of polar interactions, it is always energetically favorable for a solute molecule to stay in its own environment. However, the effect is small and the entropy of mixing usually drives significant dissolution.

Note that for the transfer of a non-polar molecule from water to a low dielectric medium, this dispersion self energy is quite distinct from the hydrophobic effect, which is entirely dependent on the specific polar interactions between water molecules. The hydrophobic effect is much stronger and the dispersion terms for water are far less significant.

“The desolvation penalty”The interactions between polar solutes and solvent (water or membrane) are the summation of all the contributions, above, with the largest effect coming from the major electrostatic terms. Sequestering a polar molecule in a non-aqueous environment like a membrane, or protein interior, has a large energetic cost from breaking the very favorable interactions with water and replacing them by much weaker ones with the membrane solvent. This is also called the desolvation penalty. Since the dielectric constant of membrane lipid is very small, the difference in Born or self energies is similar to the total Born energy in water.The partitioning of the solute into the non-aqueous phase is determined by the extent towhich the desolvation penalty is repaid by equivalent interactions in the non-aqueousenvironment. In a protein, this is in the form of, for example, specific H-bonds and pre-oriented dipoles1. This can evidently be large, as proteins are capable of binding ions and polar cofactors with great affinity (and specificity). In low dielectric fluids there are few such opportunities, and ions and polar molecules are highly insoluble in the membrane bilayer, which is why they are generally of low permeability.1 Note that it is not correct to refer to the protein interior as having a high dielectric constant. The concept of dielectric implies freedom of orientation of dipoles in response to a charge or electric field, as in a fluid. Although exhibiting some (important) degree of overall flexibility, the buried side chains of proteins are highly restricted in motion and cannot reorient significantly. The dielectric constant is therefore low. On the other hand, the folded polypeptide provides a semi-rigid framework that can maintain dipoles in a fixed position, ready to accept a polar or ionic ligand. The energetic cost of this "pre-organization" is paid at the time of synthesis of the protein, by the free energy of peptide bond formation.

The dipole energy of the membraneMembrane bilayers and even monolayers have a large dipole field that is a significantinfluence on the energetics of ion transfer to the membrane. The origin of this potential is somewhat controversial, but appears to arise from the lipid ester carbonyls and/or (oriented) surface water molecules. The lipid headgroups, themselves, even though of dipolar character, are minor contributors, presumably because they are sufficiently mobile that their dipoles are averaged out. The field penetrates the membrane interior but goes to zero very quickly in the high dielectric of the surrounding water phase. However, it can be sensed and measured at macroscopic distances in the air (low dielectric) above a monolayer, e.g., on a Langmuir trough.

The polarity of the dipoles, whatever they are, is such that the membrane interior issignificantly positive. Estimates of several hundred millivolts have been given, with a typical value of 240 mV, equivalent to a "rule of thumb" for the energetic contribution to an ion in the center of the membrane of: WDipole ≈ 5.4 z kcal mol-1 (approx. 10 kBT). This makes for a significant difference in the barrier height for cations and anions, and it is well known that membranes are more permeable to anions than to cations. (This is not the only reason, however, as cations tend to be smaller than anions (due to electron loss rather than gain), so any 1/a dependence of other energetic terms (like the Born energy) also favors anions.)

Theoretical potential profiles for translocation of an ion across a

membrane. (A) Combined Born, image and neutral energy profiles are identical for ions differing only in the sign of the charge, while the dipole potentials differ. (B) Total potential profiles for hydrophobic ions with effective radius 4 Å. Noteadsorption sites just within the bilayer, a moderately high barrier for cation translocation and a relatively low barrier for anion translocation.

(C) Total potential profiles for 2 Å ions, showing much larger electrostatic barriers for translocation, although significantly less for anions than cations.

Crossing the Barrier Membrane Transport Mechanisms

Notwithstanding certain life forms encountered on the voyages of the starship Enterprise, life, as we know it, is inevitably associated with a localized "in" and an extensive "out", thereby necessitating the essential transport functions associated with the intake of food and the excretion of waste products. The boundary is a membrane that is an exquisitely selective barrier, with properties commensurate with its composition. By virtue of the hydrophobic nature of the lipid bilayer, it is intrinsically highly impermeable to charged and even to quite small, neutral polar species. Nevertheless, natural membranes do have a great deal of selective permeability and,compared to pure lipid bilayers, they have a very low electrical resistance - a factor of 106 – 108 lower than pure lipid. Essentially all of the natural transport functions of biological membranes are performed by membrane proteins.

The many transport functions of membranes fulfill one of four basic purposes:i. uptake of nutrients and excretion of waste productsii. regulation of cell volume, internal pH, ionic composition, etciii. generation of ionic and electrical gradientsiv. energy transduction - interconversion of free energy forms

Transport of small ions and moleculesBiological membranes are specifically permeable to many things, including some small ions and even very large molecules2. We have seen that moving charges and dipoles from water to a low dielectric medium is energetically expensive, so how is this achieved? In essence, the energetic cost must be avoided or, equivalently, the desolvation penalty must be paid back. The specific movement of small molecules across a membrane is assisted in one of three ways, all of which effect the essential action of screening the charge from the low dielectric of the membrane interior.

1. “True (diffusive) carriers” - molecules or ions are bound to a carrier which diffuses across the bilayer. Since the Born energy of an ion (which is the major contribution to the desolvation penalty) is inversely proportional to the radius, one way to enhance ion penetration into a membrane is to increase its diameter. This might be achieved by wrapping it in a high dielectric shell and allowing this package to enter and diffuse across the membrane - a “true carrier” mechanism. In fact, the best result would be to wrap it in conducting material, simply making the ion bigger - spreading the charge out so the charge density is not so great. The maximal effect, from just making the ion larger, can be easily calculated from the Born equation.

2 Transport of small molecules and ions is quite different, mechanistically, from that of macromolecules, and only the former will be dealt with here.

For K+, with an ionic radius of 1.35 Å, the Born energy difference for transfer from water to lipid would be: U = 81/1.35 = 60 kcal/mol. If the ion were enlarged 5-fold, by enveloping it in some highly polarizable material, the Born energy would decrease 5-fold, to 12 kcal/mol. Although still a significant barrier, this would make an enormous difference to the rate of passage across the membrane. For example, we can calculate the relative concentration of K+ in the membrane since the partition coefficient will be dominated by the very large electrostatic energy component. For the bare K+ ion, C(in)/C(out) = exp(-60/RT) ≈ 10-43. I think we can agree this is a very small number! One can put it in perspective by saying that only a few naked K+ would enter a membrane in the history of the universe, let alone actually cross one. In contrast, for theexpanded ion, C(in)/C(out) = exp(-12/RT) ≈ 10-9. This is 1034 times larger and, although this is an unrealistic “best case” scenario, it seems like this may be a workable general approach3.3 One might want to consider that the Born energies should be calculated for solvated K+ ion - it would then be larger, and the Born energy smaller. The primary hydration shell of 4-6 water molecules would make it about 3Å radius, which would bring down the Born energy to less than 30 kcal/mol. But we must remember that to remove the hydration waters from the bulk water would involve breaking hydrogen bonds - at least one per water molecule - at a cost of about 3-4 kcal/mol for each one. This would add at least 15 - 25 kcal/mol back to the net desolvationpenalty and little would be gained. In fact, the hydration state of ions in passive equilibrium with lipid is not generally known, but, for biologically facilitated transport processes, ions are usually fully desolvated at some point in the process, especially when high ion specificity is exhibited.

There are no known examples of a membrane protein working in this simple diffusive manner4, but there are several small antibiotic agents known as ionophores ("ion carriers") that do work like this. These are produced by bacteria and fungi as defensive and offensive agents, to the detriment of another organism's health. A well known example is valinomycin, a neutral molecule that facilitates the non-neutral movement of K+ ions across otherwise impermeable membranes. It is a cyclic "depsipeptide" - a mixed polymer of twelve L- and D-amino and other acids, linked in a (ABCD)3 motif - which wraps around a K+ ion like the seam of a tennis ball, with an overall diameter of 15-18 Å. In fact, the nature of these simple agents points to the most important principle underlying actual solutions to the ion transport problem – thedesolvation penalty is “pre-paid” by the synthesis of a molecular structure designed to accommodate the charge.

4 However, cellular transport proteins - described in #3 as transporters or permeases - are often referred to as "carriers" even though they do not actually diffuse across the membrane.

Structures of two neutral ionophores. Valinomycin carries monovalent alkali metal cations, K+, Rb+, Cs+. The residues of the (ABCD)3 motif are (A) D-a-hydroxyisovaleric acid, (B) L-valine, (C) L-lactic acid, and (D) D-valine.Beauvericin carries divalent alkaline earth cations, including Mg2+. The motif is (AB)3, with (A) N-methyl-Lphenylalanine, (B) D-a-hydroxyisovaleric acid.

The valinomycin/K+ complex

The K+ is bound in the center by oxygen atoms from the peptide and ester bonds, and the side chains present a hydrophobic exterior to the membrane. The latter is important - it adds to the favorable neutral term of the transfer free energy and makes the overall energetics substantially more favorable, compensating for the fact that the valinomycin wrapping is obviously not a conducting sphere and the Born energy contribution is, therefore, still very significant.

Other examples of ionophores are: a) nigericin - neutral K+/H+ exchange; b) a group known as enniatins, including beauvericin, which variously transport monovalent and divalent cations;c) A23187 - neutral Mg2+/2H+ exchange.

2. Transporters/permeases, etc ("carriers") - substances to be transported are bound to membrane proteins which undergo conformational (structural) changes that effectively move theligand(s) from one side of the membrane to the other - a topological flip. These are not as fast as channels but are much more diverse in their chemical specificity and reaction capabilities, and they function with elementary ions and with complex organic molecules. They are essentially vectorial enzymes and can also couple the transport of one species with that of another, or the transport of a molecule with a chemical reaction.

Uniporters - transport molecules singly, e.g., the erythrocyte (red blood cell) glucose transporter, (c.f., ionophores like valinomycin - K+ uniport; see “True carriers”, above).Symporters - couple the transport of two (or possibly more) different molecules, in the same direction, e.g., bacterial lactose permease (lactose/H+), epithelial glucose/Na+ transporter. (See also Secondary active transport, below).Antiporters - couple the transport of two molecules or ions in opposite directions (exchange), e.g., Cl-/HCO3

- exchange by the anion transporter of erythrocytes (band 3), mitochondrial Ca2+/Na+ antiporter, dopamine+/2H+ antiporter of chromaffin granules, (c.f., ionophores likenigericin - K+/H+ exchange, see “True carriers”). (See also Secondary active transport, below).The terms co-transport and counter-transport are sometimes used as synonyms for symport and antiport, respectively. However, and perhaps more commonly, the term cotransport is also used as a general reference to both symport and antiport.

3. Channels - these allow diffusion of small molecules or ions through a pore, which may or may not be very selective. The channel provides a polarizable path that screens the ionic charge.Channels provide by far the fastest means of ion transport, and are crucial for the development of the electrical activity of nerves, etc. Selectivity can be imposed at various levels of the channel -by the pore itself, by the channel mouth, or by a gate in the pore, and the gate may be controlled by a various stimuli, e.g., voltage, ions (especially Ca2+), hormones, neurotransmitters, etc:

i. Unregulated - porin channel of bacterial cell walls and mitochondrial outer membranes;

gramicidin A - channel-type ionophore for monovalent cations.ii. Voltage regulated, e.g., Na+ channeliii. Ion-gated, e.g., Ca2+ gated K+ channeliv. Chemically regulated, e.g., nicotinic acetylcholine receptor

The figures below show the action of gramicidin A, an ionophore that forms channels. Gramicidin A is a linear polymer of 15 alternating D and L amino acids, which allows it to adopt an unusual, left-handed π helix structure, (this is essentially a helical β-(extended chain)-form).The helix has a wide bore which accommodates small cations, and gramicidin forms a transmembrane pore by forming a transient, head-to-head (N-terminus-to-N-terminus) dimer. Each monomer has 6 tryptophans at the C-terminal end, which form a collar that anchors this end just below the headgroup region of a phospholipid bilayer.

4. Active transport This term implies the movement of something "uphill" - against itsthermodynamic gradient. Obviously this cannot be energetically uphill in a real sense, so something else must be proceeding "downhill" to at least an equivalent extent. Movement of solutes from one solution phase to another is conveniently referred to as an "osmotic" process, and the free energy of solute transport is osmotic free energy. Active transport can be divided into mechanisms that exchange one osmotic component for another - secondary active transport, in which no change in the nature of the free energy occurs - and mechanisms which utilize a non-osmotic free energy source to effect uphill transport - primary active transport.

Secondary active transport is essentially the same as co-transport as described above, and is based on 'carriers' or permeases. Symporters and antiporters can both move ions or molecules against an electrochemical activity gradient at the expense of another gradient; when both gradients are equal, net transport stops (see below). This is called secondary active transport because the free energy of the driving reaction and the driven reaction are of the same type – both are osmotic, i.e., concentration or (electro)chemical activity gradients. Obviously the ultimate energy source must be provided in a different, mechanism with a primary energy source (food, light, etc). Interconversion of different forms of free energy is commonly described as energy transduction.

Primary active transport uses a non-osmotic type of free energy (bond energy, oxidation reduction (redox) energy, light energy, etc) to drive transport, e.g.:A. ATP hydrolases (ATPases) - There are two very different mechanistic types:(i) in P type the coupling between transport and chemistry (ATP hydrolysis) is through a covalent phosphorylated protein intermediate, e.g., Na+/K+-ATPase (all eukaryotic cell membranes), Ca2+-ATPase (muscle).(ii) in F and V type the coupling is mechanical, in which a rotary motion is induced by ionic interactions with a protein “machine”, e.g., F-type: H+-ATPase (bacteria, mitochondria, chloroplasts), Na+-ATPase (bacteria, Archaea); V-type: H+-ATPase (eukaryotic organelles, esp., plant vacuoles; Archaea).B. Redox-linked - the "electron transport chains" of respiration (mitochondria and bacteria - mostly H+, but some examples of Na+) and photosynthesis (chloroplasts and bacteria – only H+ known so far)C. Conformationally-coupled: (i) redox "driven" - cytochrome oxidase (H+)(ii) light "driven" - bacteriorhodopsin (H+), halorhodopsin (Cl-)D. Methanogenesis - the primary energy source of a large group of Archaea, the methanogens, is the reduction of CO2 by H2 forming CH4. The chemistry is unique to this group of organisms, although it electron transfer in principle. The energy transduction steps transport H+ and Na+.E. Decarboxylation enzymes - a few prokaryotic examples are known of membrane-bound decarboxylases that pump Na+ ions, coupled to the catalytic cycle. This can be the primary energy source for these organisms.

Modes of Membrane Transport for Small Molecules and Ions1. Simple diffusion - Just through lipid bilayer (not generally physiologically significant)2. Facilitated diffusion - Special proteins required; passive* Channels (binding site is always accessible)* Carriers (binding site changes accessibility)3. Active transport - energy-coupled; special proteins* Primary - coupled to other (non-transport) free energy sources* Secondary - coupled to another transport processSimple vs. Facilitated Transport1. Substrate specificity - binding site (can also have inhibitors)2. Substrate saturation3. Competitive inhibition4. Counter flow induced by alternative substratesFacilitated diffusion - Channels vs. Carriers1. Speed (dangerous to use as criterion)2. Evidence of conformational change, e.g., changes in binding site asymmetry and accessibility

Comparison of transport rates for selected systems