Search

An evaluation of the cooperativity effect in metal-ligand and protein-ligand complexes can be made by means of dimensionless parameters Kγ (homotropic), and Kγ′ (heterotropic). Starting from the relation n = ∂ ln ϵM/∂ ln [A] between formation function n and partition function ϵM = 1 + β1[A] + β2 [A]2 + …βi[A]i… + βt [A]t it is shown that on the Bjerrum plane n = f(ln [A]), the standard free-energy ▵G° and therefore the standard chemical potentials ▵μ°γ = RT ln Kγ and ▵μ°γ′= RT ln Kγ′ can be obtained exactly from a convoluted or saturation function FcM, which has the property of being 1 when ▵μ° = O, as do the equilibrium constants. The standard convoluted function FcM° for multi- step equilibria coincides with the maximum term, /gBt, of ϵM and can be calculated on the Bjerrum plane as balance between two integrals, one integral giving the contribution to free-energy of the ‘association’ partition function, ϵM, the other giving the contribution to free-energy of the ‘dissociation’ partition function, ϵDM. FcM can be calculated as the product of stepwise equilibrium constants K1,K2,…,Kt. Differences between areas on the Bjerrum plane measure ▵μ°γ/RT and ▵μ°γ′/RT. The statistical factors for homotropic and heterotropic complexes are equal. The chemical potential changes due to the cooperativity effect can be better evaluated from Kγ = βi1/i/(K1kst(γ)) (average cooperativity effect) rather than by Kγ = (βi/βi -2)1/2/(kst(γ)βi-1/βi-2) (stepwise cooperativity effect). The former is well correlated with the successive additions of ligands. The cooperativity effect is strongly influenced by changes in ionic strength, thus confirming the interpretation of the phenomenon as due to ligand-ligand external interactions. The cooperativity effect, although small (0 < ▵μ°γ▵ < 6 kJ/mol), is significantly greater than the experimental error. The cooperativity effect in homotropic and heterotropic metal complexes is of the same order of magnitude as the cooperativity effect in macromolecule-ligand equilibria.

The equilibria between metals or receptors and ligands are described by the formation function n = ligand bound/total receptor From the experimental formation function, the binding polynomial Σ M = 1 + β 1 [A] + … + β i [A] i + … + β t [A] t or formation (gran canonical) partition function is obtained as function of the cumulative constants β i . Σ M can be related to the stepwise equilibrium constants by introducing a dissociation partition function and a saturation function F c M = Σ M /Σ D . The standard value, F e⊝ M coincides with β t = K t = K 2 … K i … K t of the completely saturated receptor or metal. By calculating K γ =(β i 1/i / K 1 )(1/ k st( γ ) ) one obtains an average cooperativity effect between binding molecules. In nickel-ammonia system at 30 °C the cooperativity effect comes out to be Δμ° γ (i) = −0.752 + 0.621( i − 1) kJ/mol and in the system of bovine serum albumin (BSA) with copper(II) at 25 °C is Δμ° γ (i) = 0.034 + 0.123( i − 1) kJ/mol. By comparing the experimental binding polynomial with a model partition function for cooperative equal binding, Σ M.CE , e.g. for three site receptors or metals Σ M.CE = 1 + 3 k [A] + 3 γ 2 k 2 [A] 2 + γ 3 k 3 [A] 3 with k = equal intrinsic site constant, one obtains γ 2 = K γ 2 and γ 3 = K γ 3 . The values of γ 2 , γ 3 thus obtained are then introduced in a corrected formation function n corr which gives very good linear correlations on the Scatchard plot. From these plots the values of the intrinsic binding constant k are obtained which are k = 92.4 for nickel-ammonia at 30 °C and k = 1.3 × 10 3 for copper-BSA at 25 °C. These values correspond to values Δμ° k = − RT In k of −11.41 kJ/ mol and −17.8 kJ/mol, respectively. Also the equilibrium constants of the nickel-ammonia system at other temperatures and ionic strengths as well those of the cobalt(II)-ammonia system, have been analysed following the same procedure. In the nickel-hydrazine system the cooperativity is almost null and in the cadmium-ammonia system two different sets of sites are put in evidence. The strict parallelism and possible coupling of chemical and biochemical systems are discussed.

Chelate and cooperativity effects both in the field of complexes formed in solution by metal ion with ligands and in the field of binding between protein and ligands were examined on the basis of thermodynamic arguments. The analysis was carried out by means of the formation function n = ∂ ln ΣM/∂ ln[A] where ΣM is a partition function having free metal or macro-molecule as basis reference level and A is a ligand. The chemical potential changes due to cooperativity and chelation are calculated from differences between areas of the diagram n = f(ln[A]). The chemical potentials are: Δμ°γ = -RT ln Kγ (homotropic co-operativity), Δμ°γ′ = -RT ln Kγ′ (heterotropic co-operativity), Δμ°ϵ = -RT ln Kϵ (homotropic chelation), Δμ°ϵ′ = -RT ln Kϵ′ (heterotropic chelation). The cooperativity and chelation parameters Kγ, Kγ′, Kϵ, Kϵ′ are related to each other by other parameters Kη = Kϵ·Kγ and Kη′= Kϵ′·Kγ′. All these dimensionless parameters are derived as ratios of experimental equilibrium constants. Therefore a corresponding consistent chemical potential scale can be obtained from experimental data for all these effects, leading to quantitative comparisons between cooperative and chelate effects, either homotropic or heterotropic. Thermodynamic function changes in metal-ligand complexes can also be compared on this same scale with the energetic changes in protein-ligand complexes.

The crystals of calcium diiodate(V) hexahydrate, Ca(IO3)2. 6H2O are orthorhombic, space group Fdd2 with 8 molecules in the unit cell. The structure consists of pyramidal anions joined to one another in chains by intermolecular I ... O interactions. The chains are held together by calcium ions and by hydrogen bonds between water molecules and anions. The coordination polyhedron around calcium can be described as a square antiprism, with distances Ca- O=2.43-2.57 A. In the pyramidal anion the distances between oxygen and iodine atoms are I-O=1.78, 1.90, 1.85 A. The environment of the iodine atom is approximately octahedral: the coordination is completed by two water molecules and by one oxygen atom of another anion.

The crystals of thiocarbohydrazide dihydrochloride dihydrate, SC(NH-NH3)2Cl2. 2H2O are monoclinic, space group C2/c. The structure has been determined from three-dimensional data measured by automatic diffractometer. The final agreement factor was R = 3.8% with hydrogen atoms contribution. In the crystal structure, the cation possess a binary symmetry axis. Its trans, trans, conformation is different from the cis, trans conformation of the neutral molecules. Other relevant differences between diprotonated and neutral form concern the displacement of the terminal groups - N + H3 with respect to the plane of the thioureide group, NCSN, and the distribution of the single-double bond character between the bonds CN and SC. In the cation, in fact, the double bond character of S-C=1.645(3) A is more, and that of CN(1)=1.363(5) A less pronounced than in the neutral molecule. These results agree with the behaviour of thiocarbohydrazide in acidic or in alkaline solutions. The anion-cation, water-anion and water-cations interactions correspond to hydrogen bonds.

The crystals of bis(thiocarbohydrazideN,S)cadmium dichloride, Cd(SC(NHNH 2 ) 2 ) 2 Cl 2 , belong to monoclinic space group P2 1 /c. The structure of the compound, determined from three-dimensional data, consists of trans -octahedral complexes where the ligand molecule forms pentatomic chelate rings with N,S as donor atoms. The chlorine atoms lie along the normal to the plane containing metal and organic molecules. The distances CdN=2.34(3) and CdS=2.59(1) A are slightly shorter than those found in non-chelate cadmium complexes; CdCl=2.73(1) A is very close to the sum of ionic radii. The configuration of the ligand, with on -NH 2 group turned towards SC, repeats that of crystallized thiocarbohydrazide. Some differences, however, in distances, planarity, and angles between complexed or free ligand can be detected. The complexes are held together in layers parallel to (102) by weak hydrogen bonds NH⋯Cl.

The proton ionisation constants of DL-4,4′-dithiobis-(2-aminobutyric acid), (abbrev. DIENK) and of S,S′-methylene-di-L-cisteine,(abbrev. HOMC) have been determined potentiometrically at different temperatures and ionic strengths, μ. The constants at 25.0°C and μ = 0.1 M KCl are for DIENK: −log K1=8.954(8), −log K12 = 8.158(11), −log K13 = 2.200(13), −log K14∼1.50; and for HOMC: −log K1 = 9.413(10), −log K12 = 8.676(13), −log K13 = 2.523(14), −log K14 ∼ 1.60. All the ionisation constants are larger than the corresponding ones of α-aminoacids without sulphur atoms in the chain. The capacity to increase the acidic character or to lower the basic character of any group seems to be a general property of sulphur atoms. The thermodynamic functions ΔH and ΔS have been calculated from data of ionisation constants at temperatures between 5° and 30δC. The ionisation constants at different ionic strengths up to 2 M (KCl) have been determined.

The protonation constant of oxamic acid, H2NCOCOOH, was determined potentiometrically and resulted to be log K1 = 1.836 in 0.1 M KCl at 25.0 °C. No protonation or deprotonation is detectable in alkaline media. The calculation of the protonation constant has been carried out by a computer program based on the Sillen method. The estimated standard deviation of log K1 has been determined from the statistical analysis of the distribution diagram of Δp[H] = p[Ho] -p[Hc] against p[Ho]. This method can detect systematic errors affecting the data. Effects of (i) ionic strength (up to 2 M, (ii) temperature (in the range 5 ÷ 30 °C, (iii) solvent (in the mixture H2O (40%)-tetrahydrofuran(THF) (60%)) on the equilibrium have been investigated. The effects of ionic strength and temperature are those typical for monocarboxylic acids. The protonation constant increases up to log K1 = 2.897 in the mixture H2OTHF. This variation is compared with the variations of log K1 for other acids in water and in the same mixture; the possible influence of the dielectric constant of the solvent is considered. The coordinating power of oxamic acid toward divalent ions is very low and it is not enhanced by the changing of solvent.

The equilibria in aqueous solutions of thiocarbohydrazide have been potentiometrically at 25.0±0.1°C and compared with those found in solutions of thiosemicarbazide. In acidic media a two-step protonation equilibrium has been found for thiocarbohydrazide and a one-step protonation equilibrium for thiosemicarbazide; this corresponds to the number of hydrazinic radicals of the two molecules, thus suggesting that the protons are attached to the -NH-NH 2 group also in thiosemicarbazide. The dependence of the cumulative protonation constants β n upon the ionic strength up to μ = 2 M is that typical for cation acids for both compounds. In alkaline media both compounds present a two-step protonation equilibrium. The dependence on the ionic strength of the protonation constants β n * in alkaline media is that typical for anions bases. These anions derive from thio-enolic forms of the molecules. The existence of cation acids and anion bases in the solutions has been checked also by electrophoretic tests. The stepwise constants for both compounds show a regular decreases as expected for polyprotic acids.

Equilibria in aqueous solutions of S-methylisothiocarbohydrazide (S-tcaz) with protons and divalent metals have been studied by potentiometric method. The dissociation constants of the acids formed by S-tcaz and the formation constants of its complexes with divalent metals have been calculated by means of computer programs. The dissociation constants of the cation acids formed with protons are pK1 = 7.708(2) and pK12 = 1.364(7) at 25°C and ionic strength μ = 0.5M KCl. Dependance of dissociation constants upon temperature between 5° and 35° has been determined and the thermodynamic functions ΔG, δDH, Δ S calculated. The dependance upon ionic strength between μ = 0.01 and μ = 2.0 M KCl shows the trend typical for cation acids. The determination of the formation constants of complexes formed by S-tcaz with divalent metals Mn2+, Co2+, Ni2+, Zn2+, and Cd2+ has demonstrated that there are in solution the species: Mn(S−tcaz)2+; Co(S−tcaz)2+, Co(S−tcaz)22+; Ni(S−tcaz)2+, Ni(S−tcaz)22+, Ni(S−tcaz)32+; Zn(S−tcaz)2+, Zn(S−tcaz22+; Cd(S−tcaz)2+, Cd(S−tcaz)22+. The complexes follow the same pattern as those formed by the parent compound thiocarbohydrazide, but complexes of S-tcaz are stronger than the latter. Structures with pentatomic chelate rings with N, S as donor atoms are suggested for these complexes.

The association equilibria of thiocarbohydrazide, SC (NHNH2)2, with divalent ions Co2+, Ni2+, Zn2+ have been determined potentiometrically at 25.0±0.1°C in 0.5 M KCl solution. The following stability constants have been obtained: for Co2+, log K1 = 2.969(18), log K2 = 2.689(18); for Ni2+, log K1 = 4.404(8), log K2 = 3.700(8), log K3 = 3.113(8); for Zn2+, log K1 = 2.526(23). A method for the calculation of the estimated standard deviations is given. The stability constants obtained are comparable, for number of steps as well as values, with the stability constants of carbohydrazide, O=C(NHNH2)2, with the same metals. For both ligands, complexes with five-membered ring chelates can be postulated, the donor atoms being N,S and N,O respectively. The constants for thiocarbohydrazide are slightly higher than the corresponding constants of the oxygenated analog, except for zinc where the reverse occurs. Therefore, in agreement with the classification of Ahrland, ZnII confirms to be an (A)-acceptor, and NiII a (B)-acceptor.

The equilibrium constants of DL-2-amino-4-hydroxybutyric acid (homoserine=hoser) have been determined potentiometrically; at 25°C±0.1 and μ=0.1 M KCl, they are log K 1 =9.257 (1), log K 12 =2.265 (1). The dependence upon ionic strength in the range 0.1–2 M KCl and upon temperature in the range 5–30°C have been also determined. The thermodynamic functions ΔH 1 =10.9 (4) kcal . mole −1 , ΔS 1 =5.9 (15) cal. mole −1 . degree −1 and ΔH 12 =0.3(4) kal . mole −1 , ΔS 12 =11.4 (13) cal . mole −1 . degree −1 are comparable with those of serine and threonine. The ligand forms with metals the complexes: Mn(hoser) + ; Co(hoser) + , Co(hoser) 2 ; Ni(hoser) + , Ni(hoser) 2 , Ni(hoser) − 3 ; Cu (hoser) + , Cu(hoser) 2 ; Zn(hoser) + , Zn(hoser) 2 , Cd(hoser) + . The equilibrium constants follow the Irving-Williams series. All the complexes contain very likely pentatomic chelate rings. By comparison with crystal structures of solid complexes and by considering the values of log K n /K n+1 some hypotheses are put forward on the structures of the complexes.

The chelate effect occurs in the binding of a ligand, containing two or more donor atoms, with a metal ion [1] or a macromolecule [2]. The chelate effect causes an increase in the stability of the complexes with respect to those formed with the same number of donor atoms belonging to separate liganding molecules. The evaluation of the chelate effect has been done up to now calculating the constant Kchel = KML/βMA2, where M = metal or macromolecule, A = monodentate ligand, L = bidentate chelating ligand, KML = formation constant of the chelate ML, βMA2 = cumulative formation constant of the complex MA2. L (homotropic chelate) has two donor atoms equal to that of A. By an analysis of the binding polynomial [3] on the Bjerrum plane (n, −log L), it can shown how the correct equilibrium constant to evaluate the chelate effect is for bidentate chelating ligands and for n-dentate ligands. These adimensional constants are obtained as the ratio of two operational equilibrium constants, namely KML andeach of which is expressed in homogeneous reciprocal concentration units (conc.−1). If the donor atoms of the chelating ligand are different (heterotropic chelate), then the thermodynamic stability can be evaluated by , where MAB is a mixed ligand complex, and similar constants hold for higher complexes. Again the ratio is between two operational constants , each expressed in conc−1. With the same arguments it can be shown that the cooperativity effect, i.e the mutual repulsion or attraction between ligands, can be evaluated by and by for homotropic and heterotropic cooperativity, respectively. The chelate effect comprehends in itself the cooperativity effect and this can be taken into account in the constants Kη = Kϵ·Kγ and Kη′ = Kϵ′·Kγ′. The constants Kϵ, Kγ Kϵ′, and Kγ′ must be corrected for statistical effects. All these constants are expressed in the same units as the activity coefficients. From these constants, the corresponding changes in chemical potentials, Δμ° = −RTlnK can be calculated. These values expressed in kJ mol−1 allow the evaluation on the same scale of chelate and cooperativity effects, together with changes in the activity coefficients. The correctness of the choice of scale is shown by examining the chelate effect values obtained for copper(II) complexes of dicarboxylic acids at 25 °C [4]. Cu(II)/succinate 11 chelate would have been unstable according to Kchel. = 0.32 mol dm−3, whereas it comes out to be stable according to Kη = 11.4 mol−1 dm3 (Δμ°η = −6.03 kJ mol−1, in agreement with the experimental evidence [5]. The net chelate effect, Δμ°η, is linearly related both to the number of donor atoms and to the number of chelate rings. The enthalpy and entropy contributions to the chelate effect can also be calculated and critically analysed.

Researches in this laboratory have shown how in aqueous solution, the aminoacids, DL-4-amino-3-hydroxy-butanoic and DL-3-amino-2-hydorxypropanoic acid (isoserine) form complexes with divalent metals. The complexes contain the pentatomic chelate ring where the alcoholic group appears to be ionized even in acidic solution [1, 2]. On the other hand the corresponding isomers, threonine and serines bind the metal via the α-aminoacid moiety and only in alkaline solution the hydroxyl group dissociates and is involved in chelation to the metal [3]. In order to explain the different roles of aminoethanolate and aminocarboxylate moieties in complex formation, we have now undertaken the calorimetric determination of enthalpy changes in the reactions of DL-isoserine with Ni(II) and Cu(II) in aqueous solution at 25 °C and I = 0.1 mol dm−3 (KCl). The calorimetric measurements have been carried out by a modified LKB 8700-2 calorimeter. The values of the thermistor resistence in the reaction vessel were obtained by measuring the output voltage of the unbalanced Wheatstone bridge by a digital microvoltmeter HP 3455A. The e.m.f. values were printed at regular time intervals by a strip-printer HP 5150A with timer and converted to resistence values by an empirical relation. The ΔH0 values obtained for the protonation reaction of isoserine, H2NCH2CH(OH)COOH, H2L, are: The enthalpy changes of Ni(II) complexes are: The data for Cu(II) complexes are: The corresponding entropy changes are rather high, particularly in the copper complexes. This stands for a remarkable entropy contribution to the stability of the complexes, coming from redistribution of water molecules involved in the process. Some hypotheses on the structure of the complexes can be put forward. They will be tested by extending the calorimetric studies to other ligands containing the aminoethanol moiety.