Scientific paper
Estimation of Stability Constants of Cadmium(II) bis--Complexes with Amino Acids by Model Based on 3%v Connectivity Index
Ante Mili~evi}* and Nenad Raos
Institute for Medical Research and Occupational Health, Ksaverska c. 2, HR-10001 Zagreb, Croatia * Corresponding author: E-mail: antem@imi.hr
Received: 14-05-2010
Abstract
Linear model for estimation of the second, K2, and overall, P2, stability constant of cadmium(II) binary and ternary bis-complexes with five aliphatic a-amino acids based on valence connectivity index of the 3rd order (3%v) was developed. Set of amino acids included glycine, alanine, 2-aminobutanoic, 2-aminopentanoic (norvaline) and 2-aminohexanoic acid (norleucine), which by bonding to the cadmium(II) gave 25 K2 and 15 ¡52 values. For estimation of log P2, the model gave r = 0.940, and the S.E.cv = 0.10, and for the two subsets of log K2 constants the model yielded r = 0.936 and 0.842, and S.E.cv = 0.09. The complex CdGG was excluded from all regressions.
Keywords: Stability of coordination compounds, Theoretical models, Topological indices
1. Introduction
Cadmium is due to its high production and environmental pollution ubiquitous in the biosphere.1'2 It is toxic metal with deleterious effects on kidney, blood and blood vessels, liver, and bones, not to mention teratogenic effects.3 Cadmium(II) binds preferently to nucleic acids and their components,45 but its toxic effects are greatly modified by binding to metallothionein.67 Despite its significant biological and environmental role, not many papers were published on cadmium(II) complexes with amino acids.
From the viewpoint of coordination chemistry Cd2+ is very plastic cation, meaning that distorted coordination geometry is frequent for complexes of cadmium(II) which have coordination number in the range from 2 to 8.8910 Although cadmium(II) is considerably «softer» cation than Cu2+ and Zn2+, it binds oxalate and diamine with similar affinity as Zn2+, but substantially weaker than Cu2+.7 810 Consequently, cadmium(II) stability constants for complexes with amino acids and peptides are smaller than copper(II) constants and very close to the constants of zinc(II).1119 Despite poor stability, cadmium(II) complexes with amino acids show antimicrobial activity,20 and seem to participate in cadmium(II) toxicity.21,22
Because of biological and environmental significance of cadmium, we decided to check our models for
estimation of stability constants of coordination compounds, originally developed on copper(II) and nickel(II) chelates, on cadmium(II) complexes with amino acids. The main difficulties in applying topological indices for this purpose25 stem from the fact that the constitutional formula (i.e. molecular graph) of a coordination compound is not as well defined as of an organic compound, and that graph theory can not deal with conformers and »classical« stereoisomers. Thus, the valence connectivity index of the 3rd order (3£v) was calculated for different molecular species23,24 and correlated to log K1, log K2, and log /32 of copper(II) and nickel(II) chelates with amino acids and their derivatives, diamines, triamines, and pep-tides (dipeptides to pentapeptides).25 It was possible to obtain a good agreement between experiment and theory, and, moreover, to judge the quality of experimentally determined stability constants.26 Fair estimates of the stability constants were obtained even from the regression functions developed on different class of compounds.27,28 Also, by introduction of an indicator variable we succeeded to obtain a common model for estimation of the stability constants of copper(II) and nickel(II) chelates.29
In this paper we dealt with the estimation of the second, K2, and overall stability constants, ¡32, of cadmium(II) binary and ternary to-complexes with five aliphatic a-amino acids (glycine, alanine, 2-aminobutanoic, 2-aminopentanoic (norvaline) and 2-aminohexanoic acid
(norleucine). Both set of constants, K2 (N = 25) and /52 (N = 15), were determined at the same experimental conditions (T = 298 K, I (LiClO.) = 3 mol L1).101617
2. Methods
2. 1. Calculation of Topological Indices
We calculated topological indices using a program system E-DRAGON, developed by R. Todeschini and coworkers,30 which is capable of yielding 119 topological indices in a single run, along with many other molecular descriptors.31,32 Connectivity matrices were constructed with the aid of Online SMILES Translator and Structure File Generator.33
All models were developed by using 3%v index (the valence molecular connectivity index of the 3rd order), which was defined as:34-36
of cadmium(II) bis-complexes with glycine38 and ala
40,41,42
3Xv = 2[S(i) S(j) S(k) S(l)]-0-5
path
(1)
where 5(i), S(j), 5(k), and 5(l) are weights (valence values) of vertices (atoms) i, j, k, and l making up the path of length 3 (three consecutive chemical bonds) in a vertex-weighted molecular graph. Valence value, 5(i), of a vertex i is defined by:
S(i) = [Zv(i) - H(i)]/[Z(i) - Zv(i) - 1]
(2)
where Zv(i) is the number of valence electrons belonging to the atom corresponding to vertex i, Z(i) is its atomic number, and H(i) is the number of hydrogen atoms attached to it. For instance, 5 values for primary, secondary, tertiary and quaternary carbon atoms are 1, 2, 3, and 4, respectively; for oxygen in the OH group it equals 5, and for NH2 group 5(N) = 3. It has to be pointed out that 3xv is only a member of the family of valence connectivity indices nXv, which differ between each other by the path length, i.e. the number of 5 s in the summation term, Eq. 1.
The 3%v indices for cadmium(II) mono- and bis-complexes were calculated from the graph representations of the aqua complexes with two water molecules (Fig. 1), assuming that Cd(II) in mono-complexes is tetracoordinat-ed, and in bis-complexes hexacoordinated, as for cop-per(II) chelates.23,37 This is supported by X-ray structures
Figure 1. The graph representations for cadmium(II) mono- (CdL) and bis-complex (CdLA) with alanine. Heteroatoms are marked with O(Cd), *(N), and *(O).
nine,39 and some mixed Cd(II) bis-complexes. Moreover, the alternative assumption, that both, CdL and CdLA complexes are tetracoordinated yielded bad results.
2. 2. Regression Calculations
Regression calculations, including the leave-one-out procedure of cross validation, cv, were done using the CROMRsel program.43 The standard error of cross validation estimate is defined as:
(3)
where AX and N denotes cv residuals and the number of reference points, respectively.
3. Results and Discussion
3. 1. Estimation of the Overall Stability Constant P2
Firstly we estimated the overall stability constant, f}2:
A
M + L + A
MLA
(4)
where M denotes Cd2+, and L and A denote a-amino acids. Model was developed on 15 cadmium(II) binary and ternary bis-complexes with five aliphatic a-amino acids (Table 1). Beside naturally occurring glycine (G) and alanine (A), there were 2-aminobutanoic (B), 2-aminopentanoic (P) and 2-aminohexanoic acid (H) in the set.
Although at first it seemed there is no correlation between log /52 and 3xv(CdLA), after closer inspection of Fig. 2 we noticed some kind of the order. As /52 constant is independent on sequence of ligand bonding to the metal, complexes were such named that the first ligand (L) was always smaller or equal to the second ligand (A). Thus we were able to see from Fig. 2 that stability constant /52 of bis-complexes with identical second ligand (A) depends on the first ligand (L), i.e. log /52 linearly decreases along the homologous series of the first amino acid (with an exception of PH in the hexanoate series). Also, for the mixed complexes with identical first ligand, log /52 linearly increases along the homologous series of the second amino acid, with an exception of GG and GA in the glycine series. From Fig. 2 it is evident that slopes of the descending lines drop and the slopes of the ascending lines rise along the homologous series.
Subsequently, we developed a linear function based on the ascending lines:
log ß2 = a/XXCdLA)] + a2[3Xv(CdL)] + a3[ 3Xv(CdA)/3xv(CdL)] + b
Table 1. Experimental overall, fl2, and the second, K2, stability constants and 3%" indices calculated for Cd(II) aminoaci-dates
(Complexes (CdLA or CdAL)*	log ß2	log K	Y(CdLA)	3X(CdL)	3X(CdA)
CdGG	7.49	3.48	6.933	2.436	2.436
CdGAa	7.47	3.46	7.292	2.436	2.921
CdGBa	7.34	3.33	7.496	2.436	3.125
CdGPa	7.41	3.40	7.656	2.436	3.285
CdGHa	7.43	3.42	7.925	2.436	3.554
CdAAab	6.93	3.24	7.651	2.921	2.921
CdABa	7.13	3.44	7.855	2.921	3.125
CdAPa	7.15	3.46	8.015	2.921	3.285
CdAHa	7.24	3.55	8.284	2.921	3.554
CdBBab	6.88	3.24	8.059	3.125	3.125
CdBPa	7.05	3.41	8.219	3.125	3.285
CdBHa	7.2	3.56	8.488	3.125	3.554
CdPPab	7.01	3.29	8.379	3.285	3.285
CdPHa	7.31	3.59	8.648	3.285	3.554
CdHHab	7.03	3.29	8.917	3.554	3.554
CdAGb		3.78	7.292	2.436	2.921
CdBGb		3.70	7.496	2.436	3.125
CdBAb		3.49	7.855	2.921	3.125
CdPGb		3.69	7.656	2.436	3.285
CdPAb		3.43	8.015	2.921	3.285
CdPBb		3.33	8.219	3.125	3.285
CdHGb		3.69	7.925	2.436	3.554
CdHAb		3.50	8.284	2.921	3.554
CdHBb		3.46	8.488	3.125	3.554
CdHPb		3.57	8.648	3.285	3.554
* L always denotes smaller ligand and A the bigger one. a Complexes in the set for estimation of p2, and in the second
subset for estimation of K2. b Complexes in the first subset for estimation of K2.
The regression gave r = 0.940, and the S.E.cv = 0.10 (Table 2, Fig. 3). The complex CdGG was not included into regression because it does not belong to any family of lines.
The 3xv(CdA) index was included in the function because ascending lines show linear dependence of ¡32 on the variation of the second ligand. Also, 3£v(CdA) was divided with 3£v(CdL) to compensate different slope of the lines, which depends on the first ligand (Fig. 2). On the other hand, the second term of Eq. 5, 3£v(CdL), was introduced as a compensation for difference in intercepts of the ascending lines (Fig. 2). They decrease in the homologous series of the first ligand.
01)
O 7.1
go • . . ^^ ga\ \<ipx? jx^ (jk		
/^ra \	tph	
\ \ / \ \ \c byv \ \ab/4\ / r \»/ap\ / /		
\ b1x J x \ / xpp		ikjh
/AAa x \ / / \ 'bbx		
Y(CdLA)
Figure 2. Plot of log fi2 vs. 3^v(CdLA) reveals sequences of linear dependences. The ligand and the line that indicate linear dependence of that ligand series are coloured with the same colour.
Table 2. Linear regressions (Eq. 5) for the estimation of the overall, p2, and second, K2, stability constants
Regr.	N	Dependent	Slope (S.E.)		Intercept	r	S.E.	S.E.cv
No.		variable	Independent variable		(S.E.)			
			(MLA) 3X (ML)	X (MA)				
				3x (ML)				
1	14	log ß2	3.33(89) -6.6(18)	-8.0(24)	8.85(92)	0.940	0.06	0.10
2	14	log K2	3.08(89) -7.7(24)	-6.3(18)	5.71(93)	0.936	0.06	0.09
3	14	log K2	3.50(86) -6.8(17)	-8.9(23)	5.06(89)	0.842	0.06	0.09
Figure 3. Experimental vs. calculated values of log ¡2 for cadmi-um(II) complexes with five aliphatic a-amino acids (N = 14), Table 2, No. 1; r = 0.940, S.E.cv = 0.10.
3. 2. Estimation of the Second Stability Constant K2
The values of the second stability constant, K2:
A
ML(A) + A(L)
MLA(MAL)
(6)
of the cadmium(II) complexes (Table 1), with the same ligands as in the case of the ¡¡2 constant, were also estimated by the Eq. 5. However, because of the dependence of K2 on the sequence of ligand bonding to the Cd(II), there were 25 K2 values which we divided into two subsets (Table 1). The dependence of log K2 on 3^v(CdLA) (Fig. 4) shows that for every first ligand series of bis-complexes the binary complex has the minimum K2 value. The exception was again the glycine series. Thus we
divided the data to make the first subset consisted of complexes preceding the minimum and the second subset consisted of complexes to go after the minimum (Fig. 4). In the second subset were complexes with the first ligand smaller or equal to second, same as in the case of ¡ 2 constant, and the opposite was true for the first subset (Table 1). For both subsets the pattern similar to log ¡2 pattern (Fig. 2) was observed, although with somewhat larger deviations for the second set. Consequently, Eq. 5 was also used to estimate log K2. The only difference was that for K2 constant, L denoted the smaller and A the bigger lig-and, regardless the order of their bonding to the cadmi-um(II) (Eq. 6).
For the first subset (N = 14) the regression gave r = 0.936, and S.E.cv = 0.09 (Table 2, Fig. 5), and for the second subset (N = 14) r = 0.842, and S.E.cv = 0.09
Figure 5. Experimental vs. calculated values of log K2 for the first subset of cadmium(II) complexes (Table 1) with five aliphatic a-amino acids (N = 14), Table 2, No. 2; r = 0.936, S.E.cv = 0.09.
	\G		
	\ bg \ T\	pg ♦	hg
			\ hp
			\ ah bh îttt,
			\ a Ahp
gg •—_	_.GA \	baî	XAF^// \
	\ \ \ \	GPX?	/ H? \ \p A w / \
	\ \ \ )	—y	/ \
	•		\ / \
	gb		\ / pb > ■
			\/ pp hh
		aa	bb
6.8 7.0 7.2 7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0
V(MLA)
Figure 4. Plot of log K2 vs. 3^v(CdLA). The ligand and the curve that connect the complexes of that ligand series are coloured with the same colour.
Figure 6. Experimental vs. calculated values of log K2 for the second subset of cadmium(II) complexes (Table 1) with five aliphatic a-amino acids (N = 14), Table 2, No. 3; r = 0.842, S.E.cv = 0.09
(Table 2, Fig. 6) were yielded. From both subsets, as for the estimation of ß2, the complex CdGG was excluded because it does not belong to any series of lines.
4. Conclusion
In this paper, for the first time we developed the regression model for the estimation of stability constants of cadmium(II) complexes. The model is valid for the estimation of second, K2, and overall, ß2, stability constant of cadmium(II) bis-complexes with aliphatic amino acids. It is based on the observation that stability constants of bis-complexes with the same smaller ligand linearly increase along the homologuos series of the bigger ligand, and that stability constants of bis-complexes with the same bigger ligand linearly decrease along the homologuos series of the smaller ligand.
In further research, we will try to apply this model to other metal complexes to see if it is generally valid.
5. Acknowledgement
This work was supported by Croatian Ministry of Science, Technology, Education and Sport (project 0221770495-2901).
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Povzetek
Razvili smo linearni model za oceno druge in splošne konstante stabilnosti, K2 in P2 za kadmijeve(II) binarne in ternar-ne te-komplekse s petimi alifatskimi a-amino kislinami; model je osnovan na valenčnem indeksu povezanosti tretjega reda (3%v). Niz aminokislin je vseboval glicin, alanin, 2-aminobutanoično, 2-aminopentanoično (norvalin) in 2-amino-heksanoično kislino (norlevcin), ki se vežejo na kadmij(II) in tako določimo 25 K2 and 15 P2 vrednosti. Napovedi modela za log P2 so ocenjene z r = 0.940 in S.E.cv = 0.10, medtem ko so statistični parametri ocene modela za log K2 dveh delnih nizov r = 0.936 in 0.842, in S.E.cv = 0.09. Kompleks CdGG je bil izločen iz vseh regresijskih modelov.