J . Phys. Chem. 1986, 90, 2787-2791
2787
Molecular Model of the Cooperative Amylose-I odlne-Trliodlde Complex Attilio CesQro,* Laboratory of Macromolecular Chemistry, BBMC Department, University of Trieste. I-341 27 Trieste, Italy
Julio C. Benegas, International Centre for Theoretical Physics, Trieste, Italy, and Instituto de Matematica Aplicada. Escuela de Fisica, Universidad Nacional de San Luis, Argentina
and Daniel R. Ripoll Instituto de Matematica Aplicada, Escuela de Fisica, Universidad Nacional de San Luis, Argentina (Received: September 1 1 , 1984)
A simple model has been presented which is based on some widely accepted characteristics of the amylose-iodine-triiodide complex and is capable of correlating a number of experimental features with molecular parameters. The proposed model assumes that sequences of bound species are initiated by triiodide ions and propagated (principally) by iodine. The theory is developed by using the matrix method of Zimm and Bragg and assuming that the cooperative interaction is of electrostatic origin, limiting the size of the polyiodine chain. The model reproduces most of the experimental data and, in particular, predicts an increase of the length of the bound polyiodine chain as a function of the degree of polymerization of the host polymer. The parameters obtained by fitting the data with the model suggest that, in the absence of complexing agents, the helical site of the amylosic chain is less favorable than the unordered site. Furthermore, despite the cooperativity of the iodine stacking with other triiodide and iodine units, end effects of the polymeric chain imply that 7-8 glucose units at the chain ends do not participate in iodine binding.
Introduction One of the best known examples of inclusion complexes in aqueous solution is the reaction of amylose with iodine in the presence of iodide to give a blue complex.' A full understanding of the aqueous complex has been elusive mainly because of the large number of independent variables that must be controlled and because the complex may exist in various states of aggregation, which depend upon kinetic as well as equilibrium Although a variety of helical structures have been derived from the solid state X-ray fiber diffraction analysis of the helical character is only weakly maintained in solution. In fact, in the absence of complexing agents, amylose behaves, above a given chain length, as a random coil.16 However, the local conformation of an amylose chain is also a matter of dispute. Differences in the models proposed for the conformation in solution can be ascribed to the extent to which crystalline helical conformation(s) is (are) retained in solution." Most recent studies have shown that, because the rotational angles of the glycosidic linkage can fluctuate in a rather large conformational ~ p a c e , ' ~ J ~ a configurational average is required to take account of the ma(1) Banks, w.; Greenwood, C. T. Starch and Its Components; Edinburgh University Press: Edinburgh, Scotland, 1975. (2) Pfannemueller, B. Carbohydr. Res. 1978, 61, 41. (3) Cesiro, A.; Brant, D. A. Biopolymers 1976, 16, 983. (4) Dintzis, F. R.; Beckwith, A. C.; Babcock, G. E.; Tobin, R. Macromolecules 1976, 9, 471, 478. (5) Senior, M. B.; and Hamori, E. Biopolymers 1973, 12, 65. (6) Tasumi, M. Chem. Lett. 1972, 75. (7) Heyde, M. E.; Rimai, L.; Kilponen, R. G.; Gill, D. J. Am. Chem. Soc.
1972, 94, 5222. (8) Teitelbaum, R. C.; Ruby, S.L.;Marks, T. J. J . Am. Chem. SOC.1978, 100, 3215. (9) Handa, T.; Yajima, H. Biopolymers 1979, 18, 873. (10) French, A. D.; Murphy, V. G. Polymer 1977, 18,489. (11) French, A. D.; Murphy, V. G. Carbohydr. Res. 1973, 27, 391. (12) Chu, S.S.C.; Jeffrey, G. A. Acta Crystallogr. 1967, 23, 1038. (13) Wu, H.-C.; Sarko, A. Biopolymers 1978, 61, 7. (14) Winter, W. T.; Sarko, A. Biopolymers 1974, 13, 1447. (15) Sarko, A.; Biloski, A. Carbohydr. Res. 1980, 79, 11. (16) Kcdama, M.; Noda, H.; Kamata, T. Biopolymers 1978, 17, 985. (17) Jordan, R. C.; Brant, D. A. Macromolecules 1980, 13, 491. (18) Jordan, R. C.; Brant, D. A.; Cesiro, A. Biopolymers 1978, 17,2617.
croscopic equilibrium, and dynamic, proper tie^.'^
Structure and Energetics of the Dissolved Complex In the dissolved amylose-iodine complex, there seems now little doubt that iodine resides within the annular cavity of a more or less regular helical amylose chain (Figure l ) , as emerged early from the work of Rundle and co-workers on the crystalline20 and dissolvedz1complex. The helical character of the dissolved complex does not imply that the complexed polymer adopts a rigid, rodlike conformation; indeed, the hydrodynamic volume of the polymer decreases upon the complexation with i ~ d i n e . ' * ~ , ~ Although all the spectroscopic properties of the dissolved complex suggest that iodine species are arrayed in linear sequences within the cavity, neither the distribution of iodine chain lengths nor even the mean chain length has been unambiguously established. The complex presents strong absorption and circular of these dichroic bands near 600 nm;22-24the wavelength A, bands is a strong function of the mean degree of polymerization x of the amylose chains and reaches an asymptotic upper limit near 640 nm for x > 100. These changes have been related to the changes in chain length of the polyiodine array^,^^^^^ in analogy with the Kuhn model for the polyenes.25 The value of A, also depends on the degree of saturation of the complex and moreover on the concentration of iodide ion.' The stoichiometry of the complex continues to be a matter of debate. It has now been repeatedly confirmed that the ratio of bound triiodide to total bound iodine, R = [13-]/([12] + [I)]), cannot be zero.' Iodide (or other negative) ions are mandatory (19) Braga, D.; Ferracini, E.; Ferrero, A.; Ripamonti, A.; Brant, D. A.; Buliga, G.; Cesiro, A. Int. J. Biol. Macromol. 1985, 7, 161. (20) Rundle, R. E. J . Am. Chem. SOC.1947, 69, 1769. (21) Rundle, R. E.; Baldwin, R. R. J . Am. Chem. SOC.1943, 65, 554. (22) Bailey, J. M.; Whelan, W. J. J . Biol. Chem. 1961, 236, 969. (23) Pfannemueller, B.; Mayerhoefer, H.; Schulz, R. C. Makromol. Chem. 1969, 121, 147. (24) Banks, W.; Greenwood, C. T.; Kahn, K. M. Carbohydr. Res. 1971, 1
7
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(25) Kuhn, H. J . Chem. Phys. 1949, 17, 1198. (26) Ono,S.;Tsuchihashi, S.;Kuge, T. J. Am. Chem. SOC.1953, 75,3601.
0022-3654/86/2090-2787$01.50/0 0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 12, 1986
2788
Cesdro et al.
complex which follows the approach of for the development of the blue color, but, at least in s o l ~ t i o n ’ ~ ~ ~ amylose-iodine-triiodide -~~ Cesdro, Konic, and Brant,40 using a generalization of the Zimm the existing data reveal no evidence for a complex saturated with and Bragg4*matrix model for the helix-coil transition in polyI,- ions ( R = 1). The most recent works on the subject, using peptides. In the present paper the assumption is made that the a variety of techniques, favor R = 0.330or R = 0.5,8q3’suggesting cooperative (or stacking) interaction is of a limited effective range; that it may depend somewhat on such variables as mean polymer the interaction is further assumed to be electrostatic in nature. chain length, iodide and/or salt concentration, and the physical Since the presence of charged species is mandatory for the inistate of the complex (i.e., crystalline or dissolved). The coopertiation of the complex, it is postulated that the process begins with ativity of the iodine binding process has been accepted for many the binding of Is- to some helical conformational sites of amylose. year^.^'^^^ The original proposals of a direct charge-transfer The initial ion induces locally some helical conformation which interaction between iodine and the oxygen atoms of the polyleads to the growth of the complex by further condensation of saccharide a n n ~ l u s ~have , ~ ~not . ~been ~ successfully corroborated ~ ’ on polarizable neutral I2 molecules driven by electrostatic ion-induced by studies on the a-cyclodextrin-pentaiodide s t r ~ c t u r e ,and a-cyclodextrin crystallized with I2 in the absence of I-.36 dipole interaction. This hypothesis is substantiated by the strong intermolecular forces existing between iodine molecules giving, The enthalpy of complexation is found to be constant in the for example, a heat of sublimation of 65.5 kJ/mol which is 43% range of reaction conditions which leave A,, unchanged,30and of the dissociation energy of the gaseous diatomic iodine molecule it varies with amylose chain length in a way that mimics the at 0 K.42 The distance dependence of this interaction follows also ~~ depencence of A, on the degree of p ~ l y m e r i z a t i o n .Therefore the requirement of short effective range. According to the the rather large enthalpy change (ca. -71 kJ/mol of bound 12) characteristics of the complex in the solid state,20-21 it is assumed must sustain its largest contribution from the cooperative interthat only helical conformations of amylose can bind iodine and actions between the atoms of the linear bound iodine chains and that approximately one helical turn constitutes a “binding site”. a much smaller contribution from interactions of the bound species For purposes of modelling, each “site” has the same average with the polymer chain. Direct calorimetric measurements have number of glucose units, no matter what the particular conforby Cesdro and Brant,3 been reported by Takahashi and 01-10,~’ mational state of each sugar residue may be, provided that the and by Cesdro et al.’O Other enthalpic data on complex formation overall chain trajectory is helical. Thus, the following states (and were derived from the van’t Hoff plot of the apparent equilibrium corresponding statistical weights) can be identified for a generic constant as a function of the temperature, AHvH, and range from site in the amylosic chain -42 to -87 kJ/mol (of bound molecular iodine).30 Given the cooperativity of the complex formation, one would also expect a dependence of the isosteric heat of binding on the degree of 1: free helical site complexation, 0, as well as on t e m p e r a t ~ r e . , ~The direct microcalorimetric determinations30 have indeed shown that the inbl: 1,- bound to helical site tegral heat of reaction from 6 = 0 to 0.2 (AH-,) is ca.13 kJ/mol more negative than the value of AHeI under the same experib2: I, bound to helical site, first neighbor to Ismental conditions, a fact which supports the occurrence of a cooperative process. Concerning the energetics of the complexb3: 1, bound to helical site, second neighbor to 13ation, a further aspect too often neglected is that the helical sequences of sites for the iodine binding cannot be considered preformed, as the helical character of the uncomplexed chain is in addition to the statistical weight, c, of a coil site and S which highly transitory and flexible. Therefore, a process which requires denotes the beginning of a helical sequence. Furthermore the chain segments arrayed in helical sequences, such as for the present stacking interaction is considered to be effective only up to the case, must involve a conformational transition with, at least, an second neighbor on both sides of the initiating 13-ion, since the entropy contribution which is not negligible a priori.39 strong distance dependence of the ion-induced dipole interaction The above summary of the known properties has been necessary makes this interaction very small for longer distances. Therefore in order to generate an understanding of the framework of facts the maximum size of the polyiodine chain is limited to five units. on which a theoretical model can be developed. The model correlates three consecutive sites, and for each site there are five statistical weights, giving a matrix of statistical The Model weights of size 25 X 25. By eliminating the redundancy43 it reduces to the following 9 X 9 matrix: A statistical-mechanical model has been developed for the
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(27) Gilbert, G. A.; Marriott, J. V. R. Trans. Faraday SOC.1948,44,84. (28) Knutson, C. A,; Cluskey, J. E.; Dintzis, F. R. Carbohydr. Res. 1982, 101, 117. (29) Cronan, C. L.; Schneider, F. W. J . Phys. Chem. 1969, 73, 3990. (30) Cesiro, A.; Jerian, E.; Saule, S. Biopolymers 1980, 19, 1491. (31) Noltemeyer, M.;Saenger, W. Nature 1976, 259, 629. (32) Rundle, R. E.; Foster, J. F.; Baldwin, R. R. J . Am. Chem. SOC.1944, 66, 21 16. (33) Stein, R.S.; Rundle, R. E. J. Chem. Phys. 1948, 16, 195. (34) Murakami, H. J . Chem. Phys. 1954, 22, 367. (35) Griffiths, D. W.; Bender, M. L. Adv. Catal. 1973, 23, 209.
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(36) McMullan, R. K.; Saenger, W.; Fayos, J.; Mootz, D. Carbohydr. Res. 1973, 31, 211.
(37) Takahashi, K.; Ono, S. J . Biochem. 1972, 72, 1041. (38) Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic: London, 1982; Chapter 5. (39) Brant, D. A. Q. Rev. Biophys. 1976, 9, 527. (40) Cesiro, A.; Konic,W.; Brant, D. A. In S o h i o n Properties of Polysaccharides; Brant, D. A., Ed.;ACS Symp. Ser. No. 150; American Chemical Society: Washington DC, 1981, Chapter 32. (41) Zimm, B. H.; Bragg, J. K. J . Chem. Phys. 1959, 31, 526. (42) Shirley, D. A.; Giarque, W. E. J. Am. Chem. SOC.1959, 81, 4778.
The Journal of Physical Chemistry, Vol. 90, No. 12, 1986 2789
The Cooperative Amylose-Iodine-Triiodide Complex The indices h,, h2, and h3 mean a helical site with an 13-ion, an I2first neighbor to I< and an I2second neighbor to I
