The classification of ‘soft’ and ‘hard’ acids and bases given in Table 2.8 and Fig. 2.5 is for aqueous solutions as far as ions are concerned. It is therefore solvent-dependent, and depends not just on electron affinity but also ionic size. Free ions behave quite generally more as ‘a’-class (apparently hard) the lower the dielectric constant is, i.e. in organic solvents. However, when we consider systems of two immiscible solvents and the partition of complexes between them
M++ X– ƨ MX ƨ MX
aqueous aqueous organic solvent
it is usually the case that MX in the organic phase is relatively more strongly favoured the more ‘b’ class the anion and the cation. The electrostatic controls over these equilibria are obviously considerable. Now, the interior of a protein or of a membrane is more like an organic solvent than an aqueous solution and the anion, X, may be trapped there so that ‘b’ class behaviour of all metal elements may be more prominent in proteins than expected from aqueous solution equilibria. There is a selectivity term here too in that complexes of one metal ion can have a different partition coefficient, D, from others. Thus metal ions can be phase-separated.
Ligands too can be partitioned into different media, so that metal/ligand combinations can be found in membranes as well as in water. Again ligands and/or metals can be moved across membranes so as to be present only in certain compartments. Proteins have ‘leader’ sequences which direct them to selected places in cells.
2.10
Selection at surfaces and in precipitates
Cells possess many surface sites for binding metal ions and molecules gener- ally, where the binding depends on the concentration of the metal ion but the site has no concentration dependence though the number of sites employed is important. The major examples are membranes, large immobile particles of proteins, DNA/RNA, and polysaccharides. Here we include proteins in mem- branes such as pumps and channels. In these cases, which are undoubtedly of equal importance to those of free, soluble ligands, the binding equation can be readily deduced for sites of equal affinity since the problem is the same as for adsorption following the Langmuir isotherm where binding depends directly upon concentration of the material adsorbed, e.g. a metal ion, M. The binding constant is then given by the free metal ion concentration at 50 per cent satu- ration of the sites.
KB= 1/[M]50%
The variation in KBhas the same dependence upon the specific nature of the site and selected metal ion as for free ligand binding. Hence all the above sec- tions on selectivity are still applicable.
A further consideration follows when we treat conditions for simultaneous occupation of a surface site and binding by a free ligand. Consider, with the equation for surface binding, that for Kcthe binding constant for a freely soluble ligand, X, i.e.
Kc
MX | | M || X |
If we assume that both the surface and X need to be bound equally, then the requirement is [MX] ª [X] when K = 1/[M]50%.
[This condition can be deduced for solution equilibria alone if the system containing X is to respond optimally to [MX] and to [X] while reflecting changes in [M]. In fact this result is that commonly used in devising buffering solutions. For example, in the case of M = H+the best buffering by HX and X is where the pH = pKaof X, i.e. at [H+]
50%. Biological cells are held at around pH = 7 close to the pKaof phosphates, HCO–
3and histidine].
If the substance, metal ion plus anion or molecule, form a cooperative solid phase (see Section 2.18) such as a new liquid or a precipitate, then there is a single critical concentration, C, at which the new phase forms. This critical concentration is related to a binding constant in the new phase, KS= 1/C. For example—2.303 RT log C is the free energy difference between the material in the different phases which is given by 2.303 RT log Ks. Clearly, the formation of a new phase restricts the system to an absolute critical and constant concentration.
We believe these observations are crutial to the integrated functioning of cells (see Section 7.6 and in particular Chapter 20) since they have simultane- ously surface free solution and solid state binding agents. We turn to some examples of binding to surfaces such as pumps and channels.
2.11
The selectivity of channels
The existence of selective ion channels in the membranes is the basis of a special case of transport that is under thermodynamic control. To be selective a channel does not have to bind an element M; it is enough that it has the same radius as that of the (hydrated) ion, since being somewhat mobile and flexible molecules, proteins can simulate ‘holes’ of variable size and perform a ‘sieving’ action, allowing the free flow of certain ions while preventing that of others (Fig. 2.11). The sieving does not require that the interior of the channel is not hydrated and evidence suggests that the channel diameter for some ions is large, say 5–10 Å diameter, yet it still sieves (see Chapters 5 and 8). Selectivity, in this case, is shown by the fact that there are highly discrimina- tory potassium channels, sodium channels, calcium channels, and even proton channels (as well as various anion channels). Typical highly selective channels are the potassium channels of nerves, which show a selectivity Li < Na K > Rb > Cs, and the calcium channels which have selectivity Mg Ca > Sr > Ba (see Chapters 8 and 9). Since for these ions the energy at a site is a function of the inverse of the radius, it is clear that a channel hole can only match one ion closely for which there can be no real binding since it can pass unimpeded. This, in effect, is the same radius ratio effect that controls binding to chelating agents, but here there is a further problem, that of mobility, which requires a different process ensuring free movement in and out of the cell. Selection is based in part on repulsion, not on attraction: smaller ions do not cross the channels since they are too big to enter—they carry more water molecules and cannot be dehydrated except at the considerable expense of energy; larger ions cannot enter due to their size. Selection is then very effective and for these rea- sons Na+and Ca2+channels exclude K+, Li+, Mg2+, i.e. larger and smaller ions independently from charge considerations, by factors of, say, 10- to 100- fold. The lanthanides block the calcium channels, and barium blocks the potassium channels, showing that there is some interaction with channel sur- faces since La3+= Ca2+and Ba2+= K+in size. In practice many channels are
Fig. 2.11 A simplified view of a channel in a membrane. In real systems the channels can be in open or closed states and they are gated in various ways, e.g. electrically or conformationally, see Morowitz and Williams in further reading.
controlled by gates, kinetic devices allowing or preventing free flow. The ‘gates’ may be charge movements in the channels due to external electrostatic potentials.
The case of the proton is clearly different from that of other cations since it binds easily to several side-groups of proteins. A unique possibility is that of successive protonation-deprotonation of water molecules (or other OH groups) inside a protein channel (Fig. 2.12). The exact network of hydrogen is not confined to linked H2O; it could be any H-bond system which is continuous and can perform the necessary motions. Such channels are extremely impor- tant in energy capture devices (Chapter 5). Usually we do not think in terms of selectivity for protons, but biological systems have an outstanding need to make such a selection. The acidity of different biological compartments is an example of the result of such membrane selection.
Some channels act by exchanging ions both of the same and different charge types. Typical exchangers are H+/Na+, Na+/Ca2+, and Cl–/OH–.
2.12
Kinetic effects and control
The next step in our analysis of the uptake of metal ions will focus on the rate of movement of M from the external to the internal aqueous phase (see Figs 2.1 and 2.2). There are several possibilities which we consider in turn. These considerations could well oppose the thermodynamic assumptions made earlier (see Fig. 2.3), but we consider that it is more probable that they will act so as to enhance the thermodynamic selection within a steady state.