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Polyuronide interactions with polycoordinative metal ions
Food Hydrocolloids Vol.5 no.l /2 pp .75-85, 1991
Polyuronide interactions with polycoordinative metal ions E .E .Braudo A .N.Nesmeyanov Institute of Organoelement Compounds, USSR Academy of Sciences, Moscow, USSR
This paper is devoted to the interactions of polyuronides with cations whose coordination number exceeds unity . Such cations bind different polymer chains thus providing the formation of polymer networks and the gelation of polyuronide solutions. The systematic investigations of several research groups (1-4) resulted in the formation of a widely accepted conception. It includes as main features the idea about the multipoint ion-coordination binding of cations with sterically proper fragments of polyuronide chains ('nestling') and the notion about the cooperative nature of the binding process. These features result in the formation of extended sequences of bound cations (the 'egg-box' model , ref . 5). The analysis of the published data reveals , however, som e contradictions. Also some shortcoming in experimental corroborations of some important details is evident. Thus , although the cooperativity of Cu 2 + ion binding with polyuronides was proved experimentally (6), the isotherms of Ca 2 + ion binding with pectic substances point to a non-cooperative process (7,8) (see also 9). These results contradict many indirect but convincing observations. There are also no data presenting the distribution of bound cations along polyuronide chains. There is common agreement that the interactions of cations with polyuronides resulting in the network formation include both ion-ion or Coulombic interactions of cations with carboxylate groups and coordination interactions of cations with uncharged polar groups, such as hydroxyl and glycoside groups . Coordination interactions at least in the case of non-transitional metal ions appear to be of an ion-dipole nature. Thus, both types of interactions are electrostatic. A method of discriminating Coulombic and coordination components of a polyion-counterion interaction manifesting in the relative activity coefficient of the counterion is described in ref. 10. Our experimental results did not reveal coordination interactions of K+ or Na + ions with polyuronides; coordination interaction between Na+ ions and polyuronides was found by Seal et al. (11). As is seen from Figure 1, the pectate and the alginate bind Ca 2+ ions much stronger than if only Coulombic interactions were operative. This provides evidence for the coordination interactions of the two high-charged polyuronides with the Ca 2 + ions. The binding of the Ca 2 + ions with the high-esterified pectinate does not exceed substantially the predictions for Coulombic interactions. 75
E.E.Braudo
1200,.....-----------------------, ~
Ct 90
•
•1 600'
'.
-.
• •• •1
•
~D 12.5
•• • ·tt D!2J .~,.... 25
37.5
50
Fig. 1. The binding isotherms of Ca2+ ions with polyuronides. v = binding density; Cr = concentration of the free ligand. Ionic strength = 0.1. • sodium pectate (cone. 1.10- 3 to 6.10- 3 g-equiv/l); o sodium alginate (cone. 2.10- 3 g-equiv./l); x sodium pectinate, degree of esterification = 58%, (cone. 2.10- 3 g-equiv.ll); 0 calculated according to Manning for the pectate and the pectinate (calculation results for the alginate are indistinguishable). The composition of the alginate:the content of D-mannuronic acid rest blocks is 30%, that of L-guluronic acid rest blocks is 20%, that of the mixed composition blocks is 50%. Details of the experiments and of the calculations are presented in ref. 12.
It is common knowledge that ion-coordination interactions with metal ions are a prerequisite for the gelation of polyuronide solutions. Respectively it is worth trying to analyse those interactions by means of characteristics of the gelation process. Figure 2 presents the gelation boundaries by the interactions of an alginate and pectate with some divalent metal ions. The gelation boundary was determined by the registration of the minimal concentration of cross-linking agent sufficient for the gelation of a droplet of the polymer solution (14). It is seen that at large concentrations of cross-linking agent a constant, minimal value of the polymer concentration is attained. This polymer concentration was called the critical concentration of gelation. It corresponds to the saturation of the system with a cross-linking agent. As a rule the critical concentration of gelation does not depend on the nature of the cross-linking agent. It is governed by the molecular mass of the polymer and by its conformation. The critical concentration of gelation turned out to be equal to the concentration of coil overlap determined for polysaccharides by Morris et al. (15). By the lower concentrations of cross-linking agent the gelation boundary of a polymer is governed by the characteristics of the cross-linking reaction. Comparing the plots for the two polyuronides we see that the affinity series is reversed for alginate compared with pectate. The same holds for the affinity of
76
Polyuronide and polycoordinative metal ions
o Sodium alginate CuCl 2 > BoCI2 > SrCl 2 > CoCI2 o
•
•
•
.
'i....
>
:J
--~--.--
CT II
I CI
N
to
0.5
1.5
2.0
2 -1 Cs '10 ,mol- I
o....
8" 0.8 Sodium pectote
0.6 CoCI 2 > SrCl2 > BoCl 2 > CuCl2 •
•
•
: ,-'~~
';~O-O-O-._.6 __
0
0-
O'-------'-----~----'-----'------J
Q5
1.0
1.5
2D Cs '10~ mol, 1-1
Cp - concentroHon of a polymer; Cs -concenirotion of a crosslinking ogen+.
Fig. 2. Gelation boundaries in the systems polyuronide-divalent metal chloride-water. The composition of the alginate is shown in Figure 1. Taken from ref. 13.
those polyuronides to alkali metal ions, namely to Na+ and K+ ions (Figures 3, 4). Thus, the similarity in the relative affinity of a polyuronide to alkali metal ions and to alkali-earth metal ions is observed. The differences in the affinity of pectate and alginate to alkali metal ions can be explained by the differences in the tension of the electrostatic field in the 77
E.E.Braudo
__ No+ -0-
K+
0.80
0.60
OAO
1.0
1,.0 5.0 6.0 3.0 2 ~ Cp'10, g-eq.uiv.(kg of solvent ]
2.0
Fig. 3. Dependencies of the relative activity coefficient of a counterion on the concentration of an alginate in the aqueous solution. 'VI = the activity coefficient of a counterion; 'VI O = the activity coefficient of the common alkali metal ion in the chloride solution of the equal equivalent concentration. The composition of the alginate is shown in Figure 1.
lltr,o 1.00
0.90 0.80
0.70
0.60
~ b.
A
\,.
..
..
0.50 1.0
2.0 3.0 I,D 5.0 2 ~ Cp'10 • g-eCJuiv.(kg oC solvent)
6.0
Fig. 4. Dependencies of the relative activity coefficient of a counterion on the concentration of a pectate in the aqueous solution. See Figure 3.
78
Polyuronide and polycoordinative metal ions
vicinity of carboxylate groups . High tension favours the preferential binding of Na + ions in comparison to K+ ions. A measure of the electrostatic tension would be the pK a value (16). In fact , the polyuronides which have greater affinity to Na+ ions in comparison to K+ ions have greater pK a values . The similarity in the relative affinity of polyuronides to alkali metal ions and alka li-earth met al ions gives rise to the suggestion that it is a Coulombic component which governs the selectivity of ion-coordination interactions with polyuronides in the case of alkali-earth metal ions. One should bear in mind that ion selectivity series for a certain group of polyuronides are not universal. The acidity of carboxylic groups which seems to govern ion selectivity depends not only on the steric structure of a pyranosiduronate rest but also on other structural features of a macromolecule (Figure 5).
pK:PP
r-- - - - - -- - -- ----..,
4.4
3.8
3.2
2.6
005
0.10
0.15
020
0.25
!c ( )-1 m~ p • (g-equ·,v.)< . I
Reaction order with K, Critical concentration respect to the polymer (I2.mol- 2) of §e1ation (10 g-equiv.)
CaCI2 Sr02 BaCl 2 CuCl 2 LaCl 3 Nd(N03 h AgN03
2.4 2.3 1.8 2.1 2.2 1.7 1.4
1.04 1.20 1.38 0.80 1.04 0.99 1.13
7 13 30 45 73 49 5
± ± ± ± ± ±
0.9 2.1 3.6 2. 1 3.0 5.1
0.45 0.45 0.45 0.45 0.45 < 0.85 2.0
79
E.E.Braudo
A method of calculating the characteristics of the cross-linking reaction based on the Flory-Stockmayer theory is described in ref. 13. As is seen from Table I, the reaction order according to polymer in the alginate cross-linking is about two for both divalent and trivalent metal ions. This result confirms in particular the correctness of the use of lanthanoid metal ions as probes in model NMR investigations of the structure of divalent metals salts of polyuronic acids (17). Ag + ions, although univalent, do cross-link the alginate, giving rise to gelation. Thus, it is the coordination number not the charge which predetermines the cross-linking capacity of a cation. The critical concentration of alginate gelation under the action of Ag + ions is greater than in the cases of other polycoordinative ions studied. That can be explained by the contribution of cyclization processes due to the linear clusterization of Ag + ions. The method of quantitative characterization of a cross-linking reaction on the basis of the boundary conditions of gelation is simple and operative. However, by its use many important details are overlooked. Indeed, the method is based on Flory's postulate concerning the equal reactivity of all functional groups of a polymer. At the same time the maxima at the binding isotherms of Ca2+ ions with high-charged polyuronides (Figure 1) unequivocally provide evidence for the cooperativity of the interactions. A natural question appears: why did our precursors not observe the cooperativity as they determined Ca2+ ion binding isotherms? It seems that there are too low ionic strengths (0.01-0.02) which prevented the advance toward the region of low binding densities where the cooperativity is manifested. It is shown (13) that an increase in ionic strength can weaken the binding of Ca 2 + ions with a polyuronide, thus providing the increase of the concentration of unbound Ca2+ ions by the same binding density. The data presented in Figure 1 correspond to a relatively high ionic strength (0.1) which enabled the measurements by low binding densities. The maximum density of Ca2+ ion binding with pectate is 0.50. That means that all carboxylate groups can be involved in the interactions with Ca2+ ions. In the case of the alginate the maximum binding density is equal to 0.36, which coincides with the value obtained from the boundary conditions of gelation (13). In the last case the cyclization contribution was ignored, contrary to the determination of the binding isotherm. The coincidence of the results obtained by the two methods points to the absence of the cyclization by the interactions of Ca 2 + ions with the alginate. The constant values of the critical concentration of gelation (Table I) give rise to the suggestion that it holds for other polyvalent metal ions studied. These results confirm the viewpoint of Kohn et at. (2,18-21). The analysis of the isotherms of the cooperative binding is not a trivial matter. Generally we are dealing with a set of binding sites changing their affinity to the ligand in the course of the reaction. The set of respective functions cannot be derived from the isotherm. So, we need additional information or an a priori conception. According to the model proposed, all unoccupied sites of the macromolecule have the same binding constants, the last, however, being a function of the
80
Polyuronide and polycoordinative metal ions
binding density. This approach enables calculation of the affinity profile of the cross-linking reaction , that is, the dependence of the apparent binding constant on the binding density (22). Figure 6 presents the reaction profile of the cooperativity parameter for the pectate. This parameter is the ratio of the constants of the sequential binding of two Ca 2 + ions. The profile has a peculiar form. It manifests that the binding process includes at least two cooperative stages . The first one presumably is caused by a conformation change on the binding of Ca 2 + ions or by the favourable mutual orientation of polyuronide chains . The second cooperative stage appears to be a result of a certain structurizing process at supramolecular level. Similar peculiarities are characteristic of alginates. The cooperativity parameter is a product of two factors. A statistical factor is governed by the number of microstates (23). The number diminishes as the binding density increases, giving rise to the anticooperative effect. The second factor is governed by the interactions of the bound ligands with one another and with the polymer chains. Thus, this factor characterizes the cooperative effects proper. As is seen from Figure 7, the cooperativity of the interactions mainly manifests on the first stage of the cross-linking process; however, the secondary cooperativity effect is also evident. The characteristics of the Ca 2 + ion binding with the pectate and the alginate are summarized in the Table II. The data include the intrinsic binding constants and the characteristics of the first cooperative stage of the binding process. The following assertions can be stated: 1. The intrinsic constants of Ca 2+ ion binding with highl y-charged polyuronides are much in excess of those calculated for Coulombic interactions. G.
1.15.-----------------------,
1.075
1.0
-
-
-
-
-0 -
-
-
-
-
-
-
o o
o 0
-0 0
'
-
-
-
-
-
-
---
0
o o 0
0
0
0
0.925
0
0
0
'00
0 000
0.85 0
12.5
25
37.5 10
2
~
50
Fig. 6. Dependence of the cooperativity parameter on the density of the Ca 2 + ion binding with the pectatc. Taken from ref. 22.
81
E.E.Braudo
QC
26.--------------------------, o o
22
0
o
18
0
o o
14
o o o
o
0
0
o
~o
o
125
o
.... 0
0
25
0
0
.0
Ql)oooo
n.
50
Fig. 7. Dependence of the cooperativity parameter component controlled by the interactions of bound ligands on the density of the Ca 2 + ion binding with the pectate. Taken from ref. 22.
Thus, the ability for coordination binding of Ca 2 + ions does not result from the formation of a proper intermolecular structure at primary binding steps but it is inherent in polyuronides. Naturally one should bear in mind that this statement is based on the results of extrapolation. Presumably the associates of uncrosslinked macromolecules presenting in semidiluted polyuronide solutions (24) enable the intermolecular ion-coordination binding of the Ca2+ ions just at the initial stages of the cross-linking process. The zero order with respect to the polymer of the pectate-Ca/" ion reaction (12) confirms this suggestion. 2. The intervals of variation of the cooperativity parameter are the same for both pectate and alginate. Hence, the differences in the affinity of the two polyuronides to Ca 2 + ions stem from the differences in their intrinsic binding constants. Knowing the values of the cooperativity parameter we can calculate the distribution of the bound ions along the polyuronide chains (22). This enables, in particular, one to test the validity of the egg-box model. The results we obtained were rather disappointing, which is evidently predetermined by the low values of the cooperativity parameters. So, at binding densities not greater than 0.1 the fraction of bound ligands forming the diads or the triads does not exceed 17% or 3% respectively. With increasing length of sequences, the fraction of the ligands involved shows a rapid decrease. Nearly 80% of bound ligands would have no 'neighbours'. Figure 8 depicts the fraction of bound ligands forming diads or triads ratioed to the respective values of the non-cooperative binding. It can be seen that the probability of the formation of diads or triads exceeds the random value by no
82
Table II. Effective thermodynamic characteristics of Ca 2 + binding by polyuronides Variation range of a characteristic Polyuronide
Experimental
According to Manning
Pectate
1360
54
1475-2515 (Vi';;; 0.11)
Alginate
165
44
220-540 (Vi';;; 0.18)
OJ = cooperativity parameter; -.1.(.1.GO)
1.028-1. 071 (Vj ,;;; 0.067)
70-170
1.024-1.070 (Vj ,;;; 0.12)
60-170
= increase of the standard Gibbs energy on each successive binding stage.
E.E.Braudo
1.1
m:: 3
_. ••••• 1.0
_~ l2..
CT -
-
o
0 0
-
-
e_ -e
_
m=2 0.9
.o.• 0
0.
o 0.8 "--_-'-_ _L..-_-L.-_--'L..!!._--'-_----'_ _--' 5 10 15 o
Fig. 8. Dependencies of the ratio between the probability of the formation of the sequences of m bound ligands to the random value on the density of the Ca 2 + ion binding with the pectate. Taken from ref. 22.
more than 2% or 3% respectively. The ratios show a rapid drop with increase of the binding density. The deviations from the random values increase with the length of the sequence but the probability itself of the appearance of the sequences longer than triads at small binding densities is negligible. The results presented do not confirm the zipper mechanism of the ioncoordination binding of metal ions with polyuronides. One can show that for the successive binding of 90 or 99% of the bound Ca2+ ions at the initial upgrading portion of the affinity profile, i.e. of the dependence of the apparent binding constant on the binding density, the increase of the standard Gibbs energy change on each successive binding stage should be 7.52 or 10.72 kJ/mol respectively. In effect, this value does not exceed 0.17 kJ/mol. Thus, we have shown the cooperativity of the Ca 2 + ion binding with highly charged polyuronides. However, the degree of cooperativity occurred was insufficient for formation by the low binding densities of extended sequences of bound ligands as suggested by the egg-box model. References 1. Smidsroed,O. (1973) Some physical properties of alginates in solution and in the gel state. Norwegian Institute of Seaweed Research. Report N34. Trondheim. 2. Kohn,R. (1975) Pure Appl. Chem., 42,371. 3. Rees,D.A. and Welsh,E.J. (1977) Angew. Chern. Int. Ed. in Engl., 16, 214. 4. Morris,E.R. and Norton.Ll. (1983) In Wyn-Jones,E. and Gormaly,J. (eds), Aggregation Processes in Solution. Elsevier, Amsterdam, p. 549.
84
Polyuronide and polycoordinative metal ions
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
Grant,J.T., Morris,E.R., Rees,D.A., Smith,P.J.C. and Thom,D. (1973) FEBS Lett., 32, 195. Cesaro,A., Delben,F. and Paoletti.S, (1988) J. Chem. Soc. Far. Trans. 1.,84,2573. Kohn.R, and Furda.I. (1967) Coli. Czechosl. Chem. Commun., 32, 4470. Kohn,R. and Lovfska.J, (1967) Listy cukrovasrnicke, 83, N1, 17. Mattai,J. and Kwak,J.C.T. (1986) Macromol., 19, 1663. Yuryev,V.P., Braudo,E.E. and Tolstoguzov,V.B. (1983) Coli. Polym. Sci., 261, 210. Seale,R., Morris,E.R. and Rees,D.A. (1982) Carbohydr. Res., 110, 101. Braudo,E.E., Soshinsky,A.A., Yuryev,V.P. and Tolstoguzov,V.B. (1991) Carbohydr. Polym. (in press). Braudo,E.E. and Yuryev,V.P. (1991) Makromol. Chem. (in press). Yuryev,V.P., Grinberg,N.V., Braudo,E.E. and Tolstoguzov,V.B. (1979) Starch/Staerke, 31, 121. Morris,E.R., Culter,AN., Ross-Murphy,S.B. and Rees,D.A. (1981) Carbohydr. Polym., 1,5. Eisenrnan.G. (1961) In Kleinzeller,A. and Kotyk.A. (eds), Symposium on Membrane Transport and Metabolism. Publishing House of the Czechoslovak Academy of Sciences, Praha, p. 163. Anthonsen,T., Larsen.B, and Srnidsroed.O. (1972) Acta Chem. Scand., 26, 2988. Kohn.R. and Luknar.O. (1977) Coli. Czechosl. Chem. Comm., 42, 731. Kohn,R. and Malovikova.A. (1978) Ibid, 43, 1709. Kohn,R. and Malovikova.A. (1981) Ibid, 46, 1701. Kohn,R. (1982) Carbohydr. Polym., 2, 273. Braudo,E.E., Yuryev,V.P., Dotdayev,S.Kh. and Tolstoguzov,V.B. (1991) Ibid (in press). Cantor,C.R. and Schimmel,P.T. (1980) Biophysical Chemistry, Part 3. The Behaviour of Biological Macromolecules. W.H.Freeman, San Francisco, Ch, 15.5. Yuryev,V.P., Plashchina,I.G., Braudo,E.E. and Tolstoguzov,V.B. (1981) Carbohydr. Polym., 1, 139.
85
Polyuronide interactions with polycoordinative metal ions E .E .Braudo A .N.Nesmeyanov Institute of Organoelement Compounds, USSR Academy of Sciences, Moscow, USSR
This paper is devoted to the interactions of polyuronides with cations whose coordination number exceeds unity . Such cations bind different polymer chains thus providing the formation of polymer networks and the gelation of polyuronide solutions. The systematic investigations of several research groups (1-4) resulted in the formation of a widely accepted conception. It includes as main features the idea about the multipoint ion-coordination binding of cations with sterically proper fragments of polyuronide chains ('nestling') and the notion about the cooperative nature of the binding process. These features result in the formation of extended sequences of bound cations (the 'egg-box' model , ref . 5). The analysis of the published data reveals , however, som e contradictions. Also some shortcoming in experimental corroborations of some important details is evident. Thus , although the cooperativity of Cu 2 + ion binding with polyuronides was proved experimentally (6), the isotherms of Ca 2 + ion binding with pectic substances point to a non-cooperative process (7,8) (see also 9). These results contradict many indirect but convincing observations. There are also no data presenting the distribution of bound cations along polyuronide chains. There is common agreement that the interactions of cations with polyuronides resulting in the network formation include both ion-ion or Coulombic interactions of cations with carboxylate groups and coordination interactions of cations with uncharged polar groups, such as hydroxyl and glycoside groups . Coordination interactions at least in the case of non-transitional metal ions appear to be of an ion-dipole nature. Thus, both types of interactions are electrostatic. A method of discriminating Coulombic and coordination components of a polyion-counterion interaction manifesting in the relative activity coefficient of the counterion is described in ref. 10. Our experimental results did not reveal coordination interactions of K+ or Na + ions with polyuronides; coordination interaction between Na+ ions and polyuronides was found by Seal et al. (11). As is seen from Figure 1, the pectate and the alginate bind Ca 2+ ions much stronger than if only Coulombic interactions were operative. This provides evidence for the coordination interactions of the two high-charged polyuronides with the Ca 2 + ions. The binding of the Ca 2 + ions with the high-esterified pectinate does not exceed substantially the predictions for Coulombic interactions. 75
E.E.Braudo
1200,.....-----------------------, ~
Ct 90
•
•1 600'
'.
-.
• •• •1
•
~D 12.5
•• • ·tt D!2J .~,.... 25
37.5
50
Fig. 1. The binding isotherms of Ca2+ ions with polyuronides. v = binding density; Cr = concentration of the free ligand. Ionic strength = 0.1. • sodium pectate (cone. 1.10- 3 to 6.10- 3 g-equiv/l); o sodium alginate (cone. 2.10- 3 g-equiv./l); x sodium pectinate, degree of esterification = 58%, (cone. 2.10- 3 g-equiv.ll); 0 calculated according to Manning for the pectate and the pectinate (calculation results for the alginate are indistinguishable). The composition of the alginate:the content of D-mannuronic acid rest blocks is 30%, that of L-guluronic acid rest blocks is 20%, that of the mixed composition blocks is 50%. Details of the experiments and of the calculations are presented in ref. 12.
It is common knowledge that ion-coordination interactions with metal ions are a prerequisite for the gelation of polyuronide solutions. Respectively it is worth trying to analyse those interactions by means of characteristics of the gelation process. Figure 2 presents the gelation boundaries by the interactions of an alginate and pectate with some divalent metal ions. The gelation boundary was determined by the registration of the minimal concentration of cross-linking agent sufficient for the gelation of a droplet of the polymer solution (14). It is seen that at large concentrations of cross-linking agent a constant, minimal value of the polymer concentration is attained. This polymer concentration was called the critical concentration of gelation. It corresponds to the saturation of the system with a cross-linking agent. As a rule the critical concentration of gelation does not depend on the nature of the cross-linking agent. It is governed by the molecular mass of the polymer and by its conformation. The critical concentration of gelation turned out to be equal to the concentration of coil overlap determined for polysaccharides by Morris et al. (15). By the lower concentrations of cross-linking agent the gelation boundary of a polymer is governed by the characteristics of the cross-linking reaction. Comparing the plots for the two polyuronides we see that the affinity series is reversed for alginate compared with pectate. The same holds for the affinity of
76
Polyuronide and polycoordinative metal ions
o Sodium alginate CuCl 2 > BoCI2 > SrCl 2 > CoCI2 o
•
•
•
.
'i....
>
:J
--~--.--
CT II
I CI
N
to
0.5
1.5
2.0
2 -1 Cs '10 ,mol- I
o....
8" 0.8 Sodium pectote
0.6 CoCI 2 > SrCl2 > BoCl 2 > CuCl2 •
•
•
: ,-'~~
';~O-O-O-._.6 __
0
0-
O'-------'-----~----'-----'------J
Q5
1.0
1.5
2D Cs '10~ mol, 1-1
Cp - concentroHon of a polymer; Cs -concenirotion of a crosslinking ogen+.
Fig. 2. Gelation boundaries in the systems polyuronide-divalent metal chloride-water. The composition of the alginate is shown in Figure 1. Taken from ref. 13.
those polyuronides to alkali metal ions, namely to Na+ and K+ ions (Figures 3, 4). Thus, the similarity in the relative affinity of a polyuronide to alkali metal ions and to alkali-earth metal ions is observed. The differences in the affinity of pectate and alginate to alkali metal ions can be explained by the differences in the tension of the electrostatic field in the 77
E.E.Braudo
__ No+ -0-
K+
0.80
0.60
OAO
1.0
1,.0 5.0 6.0 3.0 2 ~ Cp'10, g-eq.uiv.(kg of solvent ]
2.0
Fig. 3. Dependencies of the relative activity coefficient of a counterion on the concentration of an alginate in the aqueous solution. 'VI = the activity coefficient of a counterion; 'VI O = the activity coefficient of the common alkali metal ion in the chloride solution of the equal equivalent concentration. The composition of the alginate is shown in Figure 1.
lltr,o 1.00
0.90 0.80
0.70
0.60
~ b.
A
\,.
..
..
0.50 1.0
2.0 3.0 I,D 5.0 2 ~ Cp'10 • g-eCJuiv.(kg oC solvent)
6.0
Fig. 4. Dependencies of the relative activity coefficient of a counterion on the concentration of a pectate in the aqueous solution. See Figure 3.
78
Polyuronide and polycoordinative metal ions
vicinity of carboxylate groups . High tension favours the preferential binding of Na + ions in comparison to K+ ions. A measure of the electrostatic tension would be the pK a value (16). In fact , the polyuronides which have greater affinity to Na+ ions in comparison to K+ ions have greater pK a values . The similarity in the relative affinity of polyuronides to alkali metal ions and alka li-earth met al ions gives rise to the suggestion that it is a Coulombic component which governs the selectivity of ion-coordination interactions with polyuronides in the case of alkali-earth metal ions. One should bear in mind that ion selectivity series for a certain group of polyuronides are not universal. The acidity of carboxylic groups which seems to govern ion selectivity depends not only on the steric structure of a pyranosiduronate rest but also on other structural features of a macromolecule (Figure 5).
pK:PP
r-- - - - - -- - -- ----..,
4.4
3.8
3.2
2.6
005
0.10
0.15
020
0.25
!c ( )-1 m~ p • (g-equ·,v.)< . I
Reaction order with K, Critical concentration respect to the polymer (I2.mol- 2) of §e1ation (10 g-equiv.)
CaCI2 Sr02 BaCl 2 CuCl 2 LaCl 3 Nd(N03 h AgN03
2.4 2.3 1.8 2.1 2.2 1.7 1.4
1.04 1.20 1.38 0.80 1.04 0.99 1.13
7 13 30 45 73 49 5
± ± ± ± ± ±
0.9 2.1 3.6 2. 1 3.0 5.1
0.45 0.45 0.45 0.45 0.45 < 0.85 2.0
79
E.E.Braudo
A method of calculating the characteristics of the cross-linking reaction based on the Flory-Stockmayer theory is described in ref. 13. As is seen from Table I, the reaction order according to polymer in the alginate cross-linking is about two for both divalent and trivalent metal ions. This result confirms in particular the correctness of the use of lanthanoid metal ions as probes in model NMR investigations of the structure of divalent metals salts of polyuronic acids (17). Ag + ions, although univalent, do cross-link the alginate, giving rise to gelation. Thus, it is the coordination number not the charge which predetermines the cross-linking capacity of a cation. The critical concentration of alginate gelation under the action of Ag + ions is greater than in the cases of other polycoordinative ions studied. That can be explained by the contribution of cyclization processes due to the linear clusterization of Ag + ions. The method of quantitative characterization of a cross-linking reaction on the basis of the boundary conditions of gelation is simple and operative. However, by its use many important details are overlooked. Indeed, the method is based on Flory's postulate concerning the equal reactivity of all functional groups of a polymer. At the same time the maxima at the binding isotherms of Ca2+ ions with high-charged polyuronides (Figure 1) unequivocally provide evidence for the cooperativity of the interactions. A natural question appears: why did our precursors not observe the cooperativity as they determined Ca2+ ion binding isotherms? It seems that there are too low ionic strengths (0.01-0.02) which prevented the advance toward the region of low binding densities where the cooperativity is manifested. It is shown (13) that an increase in ionic strength can weaken the binding of Ca 2 + ions with a polyuronide, thus providing the increase of the concentration of unbound Ca2+ ions by the same binding density. The data presented in Figure 1 correspond to a relatively high ionic strength (0.1) which enabled the measurements by low binding densities. The maximum density of Ca2+ ion binding with pectate is 0.50. That means that all carboxylate groups can be involved in the interactions with Ca2+ ions. In the case of the alginate the maximum binding density is equal to 0.36, which coincides with the value obtained from the boundary conditions of gelation (13). In the last case the cyclization contribution was ignored, contrary to the determination of the binding isotherm. The coincidence of the results obtained by the two methods points to the absence of the cyclization by the interactions of Ca 2 + ions with the alginate. The constant values of the critical concentration of gelation (Table I) give rise to the suggestion that it holds for other polyvalent metal ions studied. These results confirm the viewpoint of Kohn et at. (2,18-21). The analysis of the isotherms of the cooperative binding is not a trivial matter. Generally we are dealing with a set of binding sites changing their affinity to the ligand in the course of the reaction. The set of respective functions cannot be derived from the isotherm. So, we need additional information or an a priori conception. According to the model proposed, all unoccupied sites of the macromolecule have the same binding constants, the last, however, being a function of the
80
Polyuronide and polycoordinative metal ions
binding density. This approach enables calculation of the affinity profile of the cross-linking reaction , that is, the dependence of the apparent binding constant on the binding density (22). Figure 6 presents the reaction profile of the cooperativity parameter for the pectate. This parameter is the ratio of the constants of the sequential binding of two Ca 2 + ions. The profile has a peculiar form. It manifests that the binding process includes at least two cooperative stages . The first one presumably is caused by a conformation change on the binding of Ca 2 + ions or by the favourable mutual orientation of polyuronide chains . The second cooperative stage appears to be a result of a certain structurizing process at supramolecular level. Similar peculiarities are characteristic of alginates. The cooperativity parameter is a product of two factors. A statistical factor is governed by the number of microstates (23). The number diminishes as the binding density increases, giving rise to the anticooperative effect. The second factor is governed by the interactions of the bound ligands with one another and with the polymer chains. Thus, this factor characterizes the cooperative effects proper. As is seen from Figure 7, the cooperativity of the interactions mainly manifests on the first stage of the cross-linking process; however, the secondary cooperativity effect is also evident. The characteristics of the Ca 2 + ion binding with the pectate and the alginate are summarized in the Table II. The data include the intrinsic binding constants and the characteristics of the first cooperative stage of the binding process. The following assertions can be stated: 1. The intrinsic constants of Ca 2+ ion binding with highl y-charged polyuronides are much in excess of those calculated for Coulombic interactions. G.
1.15.-----------------------,
1.075
1.0
-
-
-
-
-0 -
-
-
-
-
-
-
o o
o 0
-0 0
'
-
-
-
-
-
-
---
0
o o 0
0
0
0
0.925
0
0
0
'00
0 000
0.85 0
12.5
25
37.5 10
2
~
50
Fig. 6. Dependence of the cooperativity parameter on the density of the Ca 2 + ion binding with the pectatc. Taken from ref. 22.
81
E.E.Braudo
QC
26.--------------------------, o o
22
0
o
18
0
o o
14
o o o
o
0
0
o
~o
o
125
o
.... 0
0
25
0
0
.0
Ql)oooo
n.
50
Fig. 7. Dependence of the cooperativity parameter component controlled by the interactions of bound ligands on the density of the Ca 2 + ion binding with the pectate. Taken from ref. 22.
Thus, the ability for coordination binding of Ca 2 + ions does not result from the formation of a proper intermolecular structure at primary binding steps but it is inherent in polyuronides. Naturally one should bear in mind that this statement is based on the results of extrapolation. Presumably the associates of uncrosslinked macromolecules presenting in semidiluted polyuronide solutions (24) enable the intermolecular ion-coordination binding of the Ca2+ ions just at the initial stages of the cross-linking process. The zero order with respect to the polymer of the pectate-Ca/" ion reaction (12) confirms this suggestion. 2. The intervals of variation of the cooperativity parameter are the same for both pectate and alginate. Hence, the differences in the affinity of the two polyuronides to Ca 2 + ions stem from the differences in their intrinsic binding constants. Knowing the values of the cooperativity parameter we can calculate the distribution of the bound ions along the polyuronide chains (22). This enables, in particular, one to test the validity of the egg-box model. The results we obtained were rather disappointing, which is evidently predetermined by the low values of the cooperativity parameters. So, at binding densities not greater than 0.1 the fraction of bound ligands forming the diads or the triads does not exceed 17% or 3% respectively. With increasing length of sequences, the fraction of the ligands involved shows a rapid decrease. Nearly 80% of bound ligands would have no 'neighbours'. Figure 8 depicts the fraction of bound ligands forming diads or triads ratioed to the respective values of the non-cooperative binding. It can be seen that the probability of the formation of diads or triads exceeds the random value by no
82
Table II. Effective thermodynamic characteristics of Ca 2 + binding by polyuronides Variation range of a characteristic Polyuronide
Experimental
According to Manning
Pectate
1360
54
1475-2515 (Vi';;; 0.11)
Alginate
165
44
220-540 (Vi';;; 0.18)
OJ = cooperativity parameter; -.1.(.1.GO)
1.028-1. 071 (Vj ,;;; 0.067)
70-170
1.024-1.070 (Vj ,;;; 0.12)
60-170
= increase of the standard Gibbs energy on each successive binding stage.
E.E.Braudo
1.1
m:: 3
_. ••••• 1.0
_~ l2..
CT -
-
o
0 0
-
-
e_ -e
_
m=2 0.9
.o.• 0
0.
o 0.8 "--_-'-_ _L..-_-L.-_--'L..!!._--'-_----'_ _--' 5 10 15 o
Fig. 8. Dependencies of the ratio between the probability of the formation of the sequences of m bound ligands to the random value on the density of the Ca 2 + ion binding with the pectate. Taken from ref. 22.
more than 2% or 3% respectively. The ratios show a rapid drop with increase of the binding density. The deviations from the random values increase with the length of the sequence but the probability itself of the appearance of the sequences longer than triads at small binding densities is negligible. The results presented do not confirm the zipper mechanism of the ioncoordination binding of metal ions with polyuronides. One can show that for the successive binding of 90 or 99% of the bound Ca2+ ions at the initial upgrading portion of the affinity profile, i.e. of the dependence of the apparent binding constant on the binding density, the increase of the standard Gibbs energy change on each successive binding stage should be 7.52 or 10.72 kJ/mol respectively. In effect, this value does not exceed 0.17 kJ/mol. Thus, we have shown the cooperativity of the Ca 2 + ion binding with highly charged polyuronides. However, the degree of cooperativity occurred was insufficient for formation by the low binding densities of extended sequences of bound ligands as suggested by the egg-box model. References 1. Smidsroed,O. (1973) Some physical properties of alginates in solution and in the gel state. Norwegian Institute of Seaweed Research. Report N34. Trondheim. 2. Kohn,R. (1975) Pure Appl. Chem., 42,371. 3. Rees,D.A. and Welsh,E.J. (1977) Angew. Chern. Int. Ed. in Engl., 16, 214. 4. Morris,E.R. and Norton.Ll. (1983) In Wyn-Jones,E. and Gormaly,J. (eds), Aggregation Processes in Solution. Elsevier, Amsterdam, p. 549.
84
Polyuronide and polycoordinative metal ions
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.
Grant,J.T., Morris,E.R., Rees,D.A., Smith,P.J.C. and Thom,D. (1973) FEBS Lett., 32, 195. Cesaro,A., Delben,F. and Paoletti.S, (1988) J. Chem. Soc. Far. Trans. 1.,84,2573. Kohn.R, and Furda.I. (1967) Coli. Czechosl. Chem. Commun., 32, 4470. Kohn,R. and Lovfska.J, (1967) Listy cukrovasrnicke, 83, N1, 17. Mattai,J. and Kwak,J.C.T. (1986) Macromol., 19, 1663. Yuryev,V.P., Braudo,E.E. and Tolstoguzov,V.B. (1983) Coli. Polym. Sci., 261, 210. Seale,R., Morris,E.R. and Rees,D.A. (1982) Carbohydr. Res., 110, 101. Braudo,E.E., Soshinsky,A.A., Yuryev,V.P. and Tolstoguzov,V.B. (1991) Carbohydr. Polym. (in press). Braudo,E.E. and Yuryev,V.P. (1991) Makromol. Chem. (in press). Yuryev,V.P., Grinberg,N.V., Braudo,E.E. and Tolstoguzov,V.B. (1979) Starch/Staerke, 31, 121. Morris,E.R., Culter,AN., Ross-Murphy,S.B. and Rees,D.A. (1981) Carbohydr. Polym., 1,5. Eisenrnan.G. (1961) In Kleinzeller,A. and Kotyk.A. (eds), Symposium on Membrane Transport and Metabolism. Publishing House of the Czechoslovak Academy of Sciences, Praha, p. 163. Anthonsen,T., Larsen.B, and Srnidsroed.O. (1972) Acta Chem. Scand., 26, 2988. Kohn.R. and Luknar.O. (1977) Coli. Czechosl. Chem. Comm., 42, 731. Kohn,R. and Malovikova.A. (1978) Ibid, 43, 1709. Kohn,R. and Malovikova.A. (1981) Ibid, 46, 1701. Kohn,R. (1982) Carbohydr. Polym., 2, 273. Braudo,E.E., Yuryev,V.P., Dotdayev,S.Kh. and Tolstoguzov,V.B. (1991) Ibid (in press). Cantor,C.R. and Schimmel,P.T. (1980) Biophysical Chemistry, Part 3. The Behaviour of Biological Macromolecules. W.H.Freeman, San Francisco, Ch, 15.5. Yuryev,V.P., Plashchina,I.G., Braudo,E.E. and Tolstoguzov,V.B. (1981) Carbohydr. Polym., 1, 139.
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