Ling's association-induction hypothesis is widely taught to the younger generation, we could have a much better chance to save life on earth". Last publication: Ling G. In: Water and the Cell. Pollack G. Springer, , p. Ling's bibliography Ling's like-minded scientists Criticism of Ling's theory.
LING "Ling offers no less than GERARD, University of Michigan "At a time when we look forward to the merging of the physical and biological sciences, this is a most stimulating book, distinguished by a bold and inquisitive attitude on the one hand, and careful experimental methods on the other. Ling's bibliography Ling's like-minded scientists Criticism of Ling's theory Home.
However, since such a term is clumsy, we have decided to preserve the term "fixed-charge system. Kritchevsky, D. A collection of 22 papers on the effects of deuterium oxide heavy water on various biochemical and physiological phenomena. The following reviews and articles deal with the elucidation of the amino-acid sequences in proteins; the second two review the recent advances which have been made in this area. Sanger, F. Advances in Protein Chern. A review covering the initial work in this field. Behrens, 0. Hill, R.
Pauling, L. Harvey Lectures, 49, Harvey Lectures, 50, Moore, S. Harvey Lectures, 52, In studying the motion of a macroscopic object, we learn that its energy exists in two forms: potential energy, determined by its location in space, and kinetic energy, determined by its velocity.
The laws of mechanics state that energy can be neither created de novo nor destroyed.
Conservation of energy may be demon- strated by an ideal frictionless pendulum; the sum of its kinetic and potential energies is constant during its motion. In reality, a pendulum eventually stops, indicating that the energy is not perfectly conserved. The discovery that this apparent loss of energy is due to its frictional conversion to heat led to the devel- opment of the science of thermodynamics which considers heat as a third form of energy, and introduces the concept of entropy.
Studies of the behavior of microscopic particles led to the establishment of three separate important conclusions: l just as macroscopic bodies possess potential and kinetic mechanical energy, so do atoms, molecules, and similar microscopic systems. In a discussion of the behavior of ions and molecules, the primary subject of the present volume, one never deals with just a few particles, but always with large collections of them of the order of 10 20 to 10 The mechanics of the motion of these tremendous populations must be treated statistically much like coin throwing.
If one tosses a coin once, he cannot be certain whether it will come up "heads" or "tails. Thus, we see that.
Figure l. The complexions which may be assumed by three identical localized particles when the total energy shared by all par- ticles is three units and energy levels, 0, l, 2, 3 are available to all of the particles. The behavior of ions and molecules in any physical system can be treated similarly. This is the subject matter of the science of statistical mechanics.
At a designated temperature, they share a total of three units of energy which may be passed from one molecule to another, but which cannot be increased or decreased. We shall refer to each of these distinguishable con- figurations as a complexion. Expressing the total number of complexions in an energy distribution as t no,nl,n2,na , where no, n1, n 2, n 3 are the number of par- ticles in the energy levels 0, I, 2, and 3, respectively, in this distribution we have: Nl 3!
In general,. If the total number of a priori equally probable complexions is designated by the symbol Q, then N! The entropy of the three water molecules in our ice crystal is thus determined by l the number of particles, 2 the thermal energy shared among them, and 3 the quantum-mechanically allowed energy levels. Suppose the molecules can assume an "alternate" state in which the number of allowed energy levels is larger, without a change in total- energy of the system.
The molecules will then have a larger Q, hence, a larger entropy in the "alternate" state than in the crystalline state. If there is no energy difference between the ground levels the energy at absolute zero of the crystalline and the "alter:o. This is analogous to the greater probability of getting a black side upper- most when tossing a die with four black sides and two red sides. The transforma- tion from ice to the "alternate" state entails an increase in Q and in entropy for this system. Thus, the concept of "entropy," which is somewhat abstruse in thermodynamics, has an explicit explanation in statistical mechanics.
The task of enumerating all the complexions for three water molecules in four energy levels is a relatively simple matter, but when we deal with 10 20 to 10 23 molecules, it is virtually impossible. Fortunately, in very large populations, there is only one distribution that makes an effective contribution to the entropy.
It is the distribution in which the numbers of particles in the energy levels follow a geometric progression such that each energy level is less populated than the preceding lower level. Here e1 and e2 are the quantum-mechanically permissible energies at the two levels; kT, the product of the Boltzmann constant and the absolute temperature, is a measure of the average kinetic energy per particle and is approximately 0. For any ith or jth level,. It tells how the par- ticles are partitioned or distributed among the allowed energy levels.
Thus, in the example discussed, if the unit of energy corresponds to l. O kcaljmole, the partition function is p. N exp EjkT where E is the total energy of the collection. Structurally similar particles are distinguishable only by their location in space; thus, in non- localized systems like dilute water vapor where the motion of particles is not restricted, all the particles are indistinguishable from one another.
In a system of indistinguishable particles, each of the distributions 0,3,0,0 , 2,0,0,1 , and 1, 1,1,0 has only one possible complexion. For the nonlocalized system, equa- tions , , and take the forms:. N exp EjkT N! The opposite usually occurs, as the follow- ing considerations demonstrate. Actually, the energy of a multiatomic particle can be resolved into four independent components.
A particle moving with translational energy may simultaneously rotate with rotational energy and vibrate with vibrational energy. The complete partition function is written as a product of the several partition functions: translational, p. In the ice state, movement is almost entirely vibrational; each water molecule oscillates about a fixed locus. Freezing completely deprives the water molecules of translational movement. The H-bonds they form with neighboring molecules effectively prevent them from rotating.
At room temperature or below, there is insufficient energy to excite the water molecules electronically. Therefore, for most purposes, the total partition func- tion of ice, like that of other crystals, can be represented by its vibrational par- tition function. This process is usually too laborious to be feasible. But it is possible mathematically to derive equations that give the value of the partition function explicitly. Thus, the vibrational partition function for a crystal of ice is kT p.
When a water molecule leaves the surface of ice, it gains both translational and rotational freedom. The partition function of the water vapor must conse- quently consist largely of the product of the translational and rotational partition functions. Equation indicates that the number of allowed energy levels is directly proportional to the free volume. For a polyatomic nonlinear molecule that has three classical rotational degrees of freedom,.
Partition functions are useful for describing the distribution of particles over a set of energy levels; in Figure l. Partition func- tions offer a means of comparing the relative probability of two such states, but such a comparison is meaningless unless the two sets of levels refer to the same ground level. In general, a difference exists between the energies of the ground levels of associated and dissociated particles. It is these energy differences to which we refer when speaking of the energies of electrostatic, covalent, hydrogen, or other bonds. This difference in ground-level energy is a potential energy and its exact value is shared by all the particles in an assembly.
We need not consider it unless we are comparing assemblies that have different ground-energy levels. If the ground level of an assembly with partition function p. I and p. The sublimation of ice entails both the overcoming of the energy difference between the ground levels of the two states and the performance of work to expand the volume of the system against the pressure p.
Thermodynamically, this sum is called LlH, the change in heat content, or enthalpy. For the sublimation of water, -LlH is H represents the enthalpy change when both the reac- tant, water, and product, vapor, are in their respective standard states. For simplicity, we omit the superscript o from the conventional symbols t H0 , t Of course, sublimation does occur; thus, on a clear subzero wintry day, laundry dries in the open air.
Equations to also enable us to calculate the exact value of the entropy if we use the thermodynamic relationship. This great increase in entropy on sublimation arises from the large values of the translational and rotational partition function of water vapor as compared to the vibrational partition function of ice. The differ- ence is large enough to offset the otherwise prohibitively high llH opposing sublimation. On the other hand the heat of melting of ice is only 1.
This indicates that the gain of translational and rotational degrees of freedom for water mole- cules going from the solid to the liquid state must be much smaller than that for molecules going from the solid to the gaseous state. This is demonstrated by the fact that the total entropy of fusion of ice is only 5.
The following considerations explain this phenomenon: 1 The H-bonds between neighboring water molecules in the liquid greatly hinder rotation and thus diminish the rotational entropy gain on melting. Thus the increase of translational entropy on sublimation far exceeds the increase of translational entropy on fusion.
We have discussed four types of entropy: translational, rotational, vibra- tional, and electronic. For pure substances these include virtually all the com- plexions distinguishable on the basis of energy levels and spatial localization or. When we deal with a mixed population con- taining two or more types of molecule, we encounter a fifth form of entropy: configurational entropy. This is because a configuration in which A occupies. Thus there is only one distinguishable complexion, corresponding to Figure l.
But if there are three different species, there is a sixfold increase in the. If there are only two species, the increase is threefold Figure 1. The total number of complexions will be indicated as n. We then designate N! In Chapter 2, we shall demonstrate that both configurational entropy and thermal entropy play very important roles in determining the degree of asso- ciation of ions and molecules in various systems. The first three chapters of the book provide an extraordinarily clear summary of the subject matter of statistical mechanics.
The later chapters could perhaps be more profitably read after intensive study of a book like that of Rushbrooke below. Very little previous knowledge of mathematics or physics is required to read this book. Rushbrooke, G. Press Clarendon , London and New York, A remarkably well-written book, particularly for those who are not primarily physicists.
The subject, presented in a consistent framework, is at no point abstruse or obscure. The opening chapters of the book by Gurney above may be helpful in gaining a general orientation before beginning this more rigorous treatment. The symbols and terminology are the same as those used by Fowler and Guggenheim below ; this book may thus serve as an excellent introduction to the latter important work. Fowler, R. Press, London and New York, A more advanced and extremely valuable treatise. The effects of energy and entropy on dissociation phenomena 23 I The configurational entropy of dissociation in a fixed-charge system 25 2 The rotational entropy of dissociation in a :fixed-charge system 27 3 The effect of the adsorption energy on ionic association 29 B.
Nonliving three-dimensional fixed-charge systems 29 1 Exchange resins 29 2 Ion-selectivity properties of other nonliving fixed-charge systems 32 C. The living cell as a true :fixed-charge system 32 1 Components of cells as fixed-charge systems 32 a Cytological structures 34 b Vacuoles and similar cytological inclusions 34 ,c. The complex systems of protein, water, and ions that we call living matter are invariably found in environments of dilute aqueous salt solution, either as an external environment in the form of fresh or ocean water, or as an internal milieu in the form of tissue fluid.
In the introduction, we argued that biological inter- actions must be determined by specific short-range forces in conjunction with long-range forces, rather than by the latter alone. Yet the most notable achieve- ments in the understanding of dilute aqueous salt solutions Debye and Ruckel, ; Bjerrum, are consistent with, and in fact demand that the interactions between ions in dilute solution be almost entirely due to long-range Coulombic forces. In these theories, ionic association, which makes possible the interplay of short-range forces, is neglected.
Thus, there is apparently a conflict between the thesis of short-range interaction and the most important theories of salt solution. The resolution to this conflict lies in the fact that living protoplasm is not a simple dilute salt solution, but a three-dimensional lattice of protein, water, and salt in which the charge-bearing protein molecules are immobilized into a fixed- charge system.
Thus, the conditions that prevail in a dilute aqueous salt solution differ radically from those in protoplasm, and the conclusion that ions are not associated in the former is not applicable to the latter. To clarify this thesis we shall review theories and experiments which support the argument that increasing association follows increasing spatial fixation of one species of ion.
Thus, when charge fixation produces a sufficient degree of association, short-range interactions dominate and selectivity of counterions follows. Since the important theories of Debye and Hlickel and of Bjerrum were ad- vanced, the association of alkali-metal ions with simple anions in aqueous solution has been regarded as scant. Thus, in a dilute solution of alkali halides, for example, the activity coefficient-an inverse measure of ion-ion interaction-is determined only by the "ionic strength," which expresses the concentration and net charge of the ions but ignores their specific natures.
The Debye-Hlickel theory is a limiting law applicable to extremely dilute solutions only. Bjerrum's theory, however, does consider ion-ion association; defining the fraction of associated ion pairs a, he derived the equation. Bjerrum offered the interpretation that the sum of their ionic radii a is greater than the critical distance of separation q.
Similarly, experimental observations on other strong electrolytes such as KCl and alkylammonium chlorides agree with this theory see Harned and Owen, But, when we investigate the alkylammonium fluorides, even in fairly dilute solution, we detect ion-pair formation. Fuoss and Kraus presented theoretical arguments along Bjerrum's line of reasoning and experimental observations to show that triple and quadruple associated ionic clusters form at high ionic con- centrations. The state of complete association for salt ions is clearly reached in the ionic crystal; theoretically, we can crystallize all strong electrolytes from their aqueous solutions by lowering the temperature and increasing the concentration.
Thus, complete dissociation of alkali-metal-ion salts occurs only under specific conditions determined by the nature of variables such as the anion, ionic concen- tration, and the dielectric constant of the medium; no ion pair may be said never to associate. The change of the value of Z2 in equation from 1, for NaCl, to 2, for multi- valent salts such as Li2SO, and Na2S04, indicates a higher degree of ionic associa- tion at low ionic concentrations. Both conductance, as in Table 2. Contrasting these results with the smaller degree of association in the strong electrolytes, one sees the simplest example of the effects of fixation; the fixation of two negative charges together to form a divalent anion increases the degree of association.
In this case, the two charges happen to be in very close proximity. Although the two carboxyl groups on this divalent acid are physically indistinguishable, they have very different dissociation constants. Li,SO, 0. Na,SO, 0. KzSO, 0. Ag,SO, 0. Table 2. These data, calculated from the conductivities, indicate a con- siderable degree of ionic association at low ionic strength.
Data from Righellato and Davies, For the first associa- tion, there are also two choices, thus favoring the association of the second proton. Measured in 20 per cent methanol in water, the pK values of the two equivalent carboxyl groups are, respectively, 5. After correction for the entropy factor, an energy difference of some 0. We may conclude that the fixation of two charged groups together makes dis- sociation from the second group more difficult than it would be if the groups were not fixed.
In other words, an increase in the average association follows this most simple type of ionic-site fixation. The effect in question occurs also when many charged groups are fixed together either by covalent bonds or through micellar aggregation resulting from the action of short-range van der Waals' forces.
A very sharp drop in equivalent conductance is associated with further increase of concentration. This phenomenon has been explained as a result of micelle formation J. McBain, ; G. Hartley, The equivalent conductance is the sum of the con- ductances due to the anion and the cation. McBain reasoned that the mobility of the long-chain electrolyte increases with micellar aggregation. The experimental results shown in Figure 2. Hartley et al. Hartley's explanation is most convincing: In this condition, "more bromine is being carried toward the cathode than is migrating.
McBain, The long-chain cations aggregate into a semifixed-charge system while the bromide ion shifts from an essentially dis- sociated condition to a high degree of association; see Figure 2. The strong. Figure 2. The in- flection 1 marks the critical point for micelle formation with its associated charge fixation. Cationic transfer numbers were determined by the moving boundary method. Figure after G. Y" I'-- ::l - "01 Q 'E-.
These data show both that the individual conductances of these polyelectrolyte solutions are much lower than those of equivalent solutions of N aBr and that the sum of the conductances of the Na-SPA and the Br-PVBB solution is lower than the conductance of NaBr. The simplest explanation for these observations is. The curves demonstrate the significance of the specific nature of counterions in determining micellar aggregation. Figure after Grieger, The behavior of linear poly- electrolytes is thus similar to that of micellar aggregates.
The experimental facts show that, as more and more charged groups are fixed together, the over-all degree of association between ions of opposite charge increases. Two points are worth mentioning: l In dicarboxylic acids, the disso- ciation of the first cation affects the dissociation of only one other cation. In polyelectrolytes, the dissociation of the first cation influences more than one subsequent dissociation. The average association thus increases with the total.
When the fixed-charge system assumes macroscopic dimensions, very few ions can diffuse away; this is usually understood in terms of the maintenance of macroscopic electroneutrality.
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The conductance of NaBr in various concentrations of polyvinyl alcohol dotted lines a-d shows that no reasonable correction for viscosity can cause line l to coincide with line 2. Furthermore, extrapolation of lines 2, 3, or 4 to a concentration of zero, at which neither viscosity nor "chain interference" would surpass that of NaBr, cannot reasonably be expected to alter the conclusion that conductance is being reduced through ionic site fixation.
Figure after Edelson and Fuoss, Thus, if 10 charges are fixed together, dilution of the system with a very large volume of pure water will not change it much. But if these 10 charges are entirely separate, such dilution leads to the dispersion and dissociation of all the ions. These factors probably play a predominant role in producing a high degree of ionic association in linear polyelectrolytes or micellar aggregates to which we refer collectively as semifixed-charge systems. In the next section, we shall discuss how other statistical-mechanical considerations suggest other mechanisms, which are less important in semifixed-charge systems but become highly significant in true fixed-charge systems.
As the degree of ionic association is enhanced, short-range forces begin to play an important role in determining the dissociation energy between members of an ion pair. Thus we can expect differences between the dis- sociation energies of different ions to emerge. This, in turn, leads to ionic speci- ficity. An examination of experimental evidence confirms this expectation. If a fixed-charge system is either purely or effectively anionic or cationic, dissocia- tion of a counterion leaves a net charge that discourages the dissociation of a second otherwise equivalent counterion.
However, ionic dissociation in a three- dimensional macroscopic anionic or cationic fixed-charge system always has two components: 1 dissociation from the surface layer into the free solution, similar to dissociation from a linear polymer, and 2 dissociation in the bulk phase in which macroscopic electroneutrality is conserved and the great majority of counterions are confined within the fixed-charge system. The dissociation of counterions inside such a macroscopic fixed-charge system is thus not dissociation away from the fixed-charge system as a whole; rather it is a matter of how a population of counterions will distribute itself statistically among the possible positions within the system.
If such a fixed-charge system is a rigid three-dimensional lattice, charges borne on it will, like those in crystals, occupy specific positions in space. The sys- tem may then be represented as consisting of minute microcells, each enclosing one fixed ionic site, Figure 3. In this ideal case, the most probable distribution of ions is one in which they are distributed one to a microcell. Any other configura- tion entails multiple occupancies which are energetically unfavorable and there- fore improbable.
To aid in the visualization of this model, one may imagine that each volume containing 10 or 20 microcells is a large polyelectrolyte mole- cule. The detachment of one counterion will make it less probable that a second counterion will dissociate. Thus, a counterion must either remain in its "own" microcell or occupy an energetically unfavorable position.
Ionic association and dissociation in a true fixed-charge system thus becomes a question of the probabilities of either association or dissociation within the unit microcell. The earliest models of liquids were built on the assump- tion that the molecules were distributed randomly. We have chosen a statistical-mechanical model for the treatment of association phenomena; it treats aqueous solutions and fixed- charge systems as if they were crystals with a very large number of sites, each of which may be occupied by a solvent molecule or a solute ion.
Let us consider an aqueous salt solution; in such a solution, association phenomena are understood in terms of chemical equilibrium. B exp. E is the energy of association; R is the gas constant; and Tis the absolute temperature. AB then The partition-function ratio p. A typical value for!
E is kcaljmole. Substituting into equations and , we obtain a value of a equal to unity; there should be no dissociation of NaCl in water at all. Yet it is completely dissociated. Fowler and Guggenheim have shown that this error arises from ignoring the effect of hydration. Thus, these hydrated ions are effectively polyatomic particles.
A rigorous evaluation of the rotational partition function of such aggregates is difficult; but its important effect on ionic association is demonstrated by the following example. The dissociation of trimethylammonium nitrate, both ions of which are polyatomic, may be represented as.
Here the use of such estimated values leads to the conclusion that ions are dissociated in dilute aqueous solutions, a conclusion consistent with observations of real solutions.
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Assuming that there is no difference between the rotational-entropy gain on dissociation in a free solution and that in a fixed-charge system, we shall investi- gate the effects of configurational entropy on dissociation in a fixed-charge system. Then we shall incorporate the rotational entropy effect. Finally we shall discuss association energy within the fixed-charge system. Let p be the number of sites at which a counterion may he said to be associated, and u, the number of sites at which a counterion may be said to be dissociated.
Let a represent the fraction of ions that are associated; 1 - a , the fraction of ions that are dissociated; and define the relation, t. Equation then becomes. To evaluate a, we assume that, for thermal entropy, the conditions, a and h , hold. A is equal to the partition function of the associated ion pair p. Then p. If the counterion occupies a position in an outer shell with radii r 2 and r3, respectively, it is considered dissociated. The value of r2 is deter- mined by the limit of complete dielectric saturation. Assume that it has a value of 7A. This estimation suggests that a relatively high degree of ionic association may be expected on the basis of the theoretical model.
The value of r2 is crucial in this estimation. If r 2 is not 7A, but 2A, a will be only To understand this difference, we must consider the mechanism by which ionic association is in- creased due to the configurational entropy. In the fixed-charge system, the fixed sites are quite evenly distributed and have a unique configuration.
In free solution, the anions may have a very large number of configurations; one of these is shown in Figure 2. Comparing this with Figure 2. In the configuration shown in B, the total number of associated sites is considerably diminished due to overlap and the total number of dissociated sites is correspondingly increased. Since the average configuration in free solution is more like B than A, a higher degree of dissociation is predicted on the basis of configurational entropy alone. Yang at the Insti- tute for Advanced Studies, Princeton, suggested the mechanism by which the configurational entrop:y of dissociation is decreased in a fixed-charge system.
Space occupied by associated countercations Fixed anion A B Figure 2. Part A shows diagrammatically the relatively uniform distribution of ilxed ionic sites in a fixed-charge system. This creates a maximal ratio of the total associated sites shaded to the dissociated sites unshaded , leading to a higher degree of ion association.
Part B typifies a more probable configuration of the ion in a free solution. Here a smaller ratio results from the overlapping of associated sites and the consequent increase of dissociated sit. This leads to a lower degree of ion association. The large value of pis due to the existence of more than one configuration corresponding to the associated state see Chapter 4 and the sharp edge is due to the steep drop of dielectric constant as one approaches an ion see Figure 6, Ling, For ice and for solid ethyl alcohol, the latent heats of vaporization are The hydrogen bonds in ice and in solid alcohol determine this difference; vaporization is possible only when enough energy is absorbed to break these bonds Pauling, In melting, molecules are not completely dispersed.
It takes 0.
Thus, there is a reduction of the number of hydrogen bonds in the melting of ice. The entropy of ice is largely vibrational. The increase in rota- tional entropy also follows naturally: since H20 is asymmetrical, its full rotational entropy [see equation ] is attained only in the vapor state. Although water has the same molecular asymmetry in the ice state, the formation of hydrogen bonds effectively inhibits free rotation so that there is relatively little rotational entropy in ice. Let us now examine the entropies of melting of various substances: that of hydrogen is 2.
Most theories of the entropy of melting are built on the premise that a volume expansion accompanies melting. This leads to an increase of free volume and a consequent increase of translational communal and vibrational entropy see Slater, , p. In the case of water, melting is accompanied by a decrease of volume, not an increase. Yet the entropy of melting is considerably higher than the entropies of melting for many substances that occupy larger volumes in the liquid state than in the solid state.
Since this extra entropy cannot be translational, vibrational, or electronic, t we can conclude that melting of ice is accompanied by an increase of rotational entropy. The ice-liquid water transformation involves the breaking of permanent energy barriers; this allows the molecules to rotate. The fixed hydrogen bonds in the solid state thus restrict free rotation more than do the fluid energy barriers of the liquid state.
A fixed-charge system bears a relation to free solution similar to the relation of ice to liquid water. The proteinaceous fixed-charge system possesses a high density of permanently fixed hydrogen-bonding sites; these can inhibit the free rotation of dipolar molecules like water, and also of ions and polar molecules with their hydration shells of water.
Let us assume that this restriction of rotation in the dissociated state, within a fixed-charge system, reduces the partition function ratio p. E is as low as -5 kcaljmole. The exponential relation between association energy and ion association is such that if t:,. At low concentrations long-chain electrolytes are completely dissociated, but above a critical concentration when these molecules suddenly aggregate into micelles, they show a high degree of ionic association.
Similarly, the polymerization of simple monomeric ions into linear polymers leads to an increased association of their counterions. If a cross-linking agent such as. This is an example of an ion exchange resin:. To understand the high degree of association between fixed ions and their counterions and the attendant selective ionic accumulation, we must examine the decrease in entropy of dissociation within such systems.
Configurational entropy decreases have been discussed in Section 2. Under normal conditions Amberlite exchange resins contain 50 per cent or less water by weight see Rohm and Haas, Thus, in one liter of resin grams of carbon chains form a network consisting of basic C-C units. Given a C-C bond length of 1. Pauling, , Chapter 5 , sup- pose that each residue is a -CH 2- with an average weight of 14; if all the residues were joined into a single chain, it would be 4 X 6.
If it is divided into centimeter segments, there should be 3. Since a water molecule is about 2. Rotation of a sA mole- cule in a lattice with average interstices of SA must be greatly restricted. Thus the restriction of both configurational and rotational entropy gain on dissociation depends largely on the spatial fixation of the lattice. Since the degree of fixation in ion exchange resins varies directly with the percentage of cross-linking agent, one would expect an increasing degree of association and, therefore, of ionic selectivity to be exhibited sharply with an increasing percentage of cross-linking agent.
This concept is consistent with the findings of Gregor and Bonner : In the synthesis of an exchange resin, the ionic selectivity coefficient increases as the percentage of cross-linking agents in the polymer increases. See Figure 2. The degree of CfOSS linking varies with the per- centage of divinylbenzene present. Figure after Gregor, The selectivity coefficient K' is defined in Figure 2. DVB stands for divinylbenzene. Data from Bonner, Given the conditions of substantial charge fixation, ionic selectivity always follows.
K Eisenman et al. Typical examples are quoted in Table 2. Whether the system is crystalline as in minerals and zeolites, vitreous as in glass, or a dense aggregation of polymeric molecules as in dried oxidized collodion, each is a fixed-charge system. These examples show that ionic selectivity but not a particular sequential order of ion selectivity is independent of the nature of the fixed ionic groups. The only common features shown by all these systems are the possession of charged groups and the fixation of these in space. According to our hypothesis, living protoplasm consists of various types of fixed-charge systems, the universal constituents of which are proteins, water, and salt ions.
To clarify this we distinguish three classes of cellular components see Figure 2. Oxychromatin or linin. The cytoplasm is shown as a granular network in which various cytological particles are sus- pended. Data from Wilson, Thus, if the constituent material of these structures were not fixed, these solvents would extract and remove it. Since such cellular elements persist for microscopic observation they must be structurally rigid.
These rigid structures of protoplasm must be protein; thus the essential com- ponents, whatever their chemical composition, must be fixed onto a protein lattice. As the proteins of living cells, essential lipids, etc. Different structures and their diverse substructures must have fixed ionic groups of varied nature and density.
These subcellular compart- ments are obviously not fixed-charge systems. Not conspicuous in most animal cells, they are found in plant cells to be generally larger and to contain saps that have the physical consistency and chemical composition of true dilute salt solu- tions, and must be so regarded. The fundamental concepts developed in this thesis provide both an explanation for the ionic behavior of cytoplasm and an explanation for the ionic behavior of cells which contain a conspicuous vacuolar system.
In 1, karyotype analyses from different individuals, only eight of the cells had such a chromosome. It had a constriction in the short arm which was interpreted as a satellite stalk. Ferguson-Smith, M. Lancet , i , Cytogenetics , 2 , Moores, E. Human Genet. German, J. Emerit, I. McGavin, D. Heitz, E.