Scientific paper
Prediction of Stability Constants of Zinc(II) Complexes with 2-aminobenzamide and Amino Acids
Ante Mili~evi} and Nenad Raos
Institute for Medical Research and Occupational Health, 10001 Zagreb, P.O.B. 291, Croatia
* Corresponding author: E-mail: antem@imi.hr Tel.:+385 14682524; Fax: +385 14673303
Received: 02-03-2015
Abstract
We developed a model for the stability (log ßZnLB) of Zn2+ mixed complexes (N = 16) with 2-aminobenzamide (L) and four amino acids (B) glycine, alanine, valine, and phenylalanine at 300, 310, 320, and 330 K. The model based on the quadratic regression function of the molecular valence connectivity index of the third order, 3^v, yielded S.E. = 0.02. We also developed an overall model for K1, K2 and ßZnLB of the same system at all of the four temperatures (N = 48). This model yielded S.E. = 0.05.	"
Keywords: coordination compounds, stability constants, graph-theoretical indices, regression models, models in chemistry
1. Introduction
Although models based on graph theoretical indices rely on somewhat vague concepts, as do other models based on topological approaches in theoretical chemistry,1,2 they have proved quite successful in many applications. Graph theoretical indices correlate well with many physi-cochemical parameters3-6 and biological activities (QSAR).7,8 Our efforts to use topological indices, especially the valence connectivity index of the 3rd order, 3^v, in order to build regression models for the prediction of stability constants of coordination compounds9 ended with varying success, depending on the nature of coordination compounds as well as on the quality of experimental data. Stability constants of copper(II) complexes with a-amino acids were reproduced with such a precision that it was even possible to evaluate the results of two electroa-nalytical methods (GEP and SWV) used for their measurement.10 For copper(II) complexes with derivatives of thioflavin T and clioqiunol, used as model compounds for the study of Alzheimer's disease, we obtained even better results11 than those achieved by the more demanding DFT method.12 In some cases, our method, despite being strictly empirical, enabled the analysis of coordination, i.e. it gave insight into the structure of the complex.13,14 However, in other cases additional variables15 and unusual forms of regression functions16 had to be introduced in or-
der to obtain an acceptable agreement between theory and experiment.
The topic of this contribution are mixed zinc(II) complexes of 2-aminobenzamide (2-AB) with amino acids. These complexes have already been studied by pH-metric and spectrophotometric methods,17 because 2-aminobenza-mide and its derivatives have desirable pharmacological properties,18 and are also used as analytical reagents.19 On the other hand, zinc(II) participates in many biological pro-cesses,20 so the study of the above mentioned complexes should lead to a better understanding of the pharmacokine-tics of 2-aminobenzamide and its derivatives.
Besides the model for stability (ßZnLB) of mixed complexes of 2-aminobenzamide (L) with Zn2+ and four amino acids (B) glycine, alanine, valine, and phenylalani-ne at different temperatures (300, 310, 320, and 330 K):
(1)
we developed an overall model for ßZnLB, K1 and K2, defined as:
length 3 (three consecutive chemical bonds) in a vertex-(3) weighted molecular graph. The valence value, 8(f), of a vertex i is defined by:
2. Methods
2. 1. Calculation of Topological Indices
We calculated topological indices using the E-DRAG-ON program system, developed by R. Todeschini and co-workers, capable of yielding 119 topological indices in a single run, along with many other molecular descriptors.21'22 Connectivity matrices were constructed with the aid of the Online SMILES Translator and Structure File Generator.23 The valence molecular connectivity index of the 3rd order, 3£v, was defined as:24-27
8i) = [Z'(i) - H(i)]/[Z(i) - Zv(i) - 1]
(5)
Y = E [5(i) 8(j) 5(k) 8(l)]-°-5
path
(4)
where 8(i), 5j), 5(k), and 8(l) are weights (valence values) of vertices (atoms) i, j, k, and l making up the path of
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.
The 3xv index for all mono- and mixed complexes was calculated from the graph representations of aqua-complexes (Fig. 1), assuming that the metal in the mono-complexes is tetracoordinated and in mixed complexes hexacoordinated.
2. 2. Regression Calculations
Regression calculations, including the leave-one-out procedure (LOO) of cross validation were done using the CROMRsel program.28 The standard error of the cross-validation estimate was defined as:
Figure 1. Constitutional formulas of Zn(II) tetracoordinated mo-nocomplexes with glycine (B) and hexacoordinated mixed complex with 2-aminobenzamide (L) and glycine (B)
(6)
where AX and N denotes cv residuals and the number of reference points, respectively.
3. Results
In order to model the logarithm of stability constant, log ^ZnLB, (Eq. 1, Table 1) of mixed Zn2+complexes with 2-aminobenzamide and amino acids (ZnLB), we used the quadratic function of 3£v (Figure 2):
Table 1. Experimental stability constants log K1; log K2 and log ßZnLB [17] and ъуХ index of Zn(II) complexes with 2-aminobenzamide (L) and amino acids (B)
Temperature (K)	Amino acid (B)	log K1	log K2	log #ZnLB	(ZnB)	(ZnLB)
3°°	Gly	4.96	5.29	9.13	1.748	5.77°
	Ala	4.89	5.13	8.97	2.148	6.°82
	Val	4.59	4.83	8.67	2.599	6.533
	Phe	4.46	4.68	8.52	3.581	7.195
31°	Gly	4.84	5.22	8.95	1.748	5.77°
	Ala	4.76	5.°6	8.79	2.148	6.°82
	Val	4.46	4.8°	8.53	2.599	6.533
	Phe	4.33	4.66	8.39	3.581	7.195
32°	Gly	4.73	5.18	8.81	1.748	5.77°
	Ala	4.65	5.°1	8.64	2.148	6.°82
	Val	4.36	4.73	8.36	2.599	6.533
	Phe	4.24	4.59	8.22	3.581	7.195
33°	Gly	4.61	5.°8	8.63	1.748	5.77°
	Ala	4.56	4.94	8.49	2.148	6.°82
	Val	4.23	4.67	8.22	2.599	6.533
	Phe	4.13	4.54	8.°9	3.581	7.195
log ßznLB = a1[3^v(ZnLB)] + a2[3/(ZnLB)]2 + b (7)
because it proved better than the linear function (e.g. at 300 K, S.E. = 0.04 and 0.06 for quadratic and linear function, respectively; N = 4).
ding stability constants of a referent complexes (either with glycine, alanine, valine, or phenylalanine); 3xv denotes 3xv(ZnB) in the case of K1 constant and for K2 and ßZnLB it corresponds to 3£v(ZnLB) normalized on 3£v(Zn-Gly):
3Xv = 3Xv(ZnLB) - [3xv(ZnLGly) - 3/(ZnGly)] 10)
Figure 2. Quadratic dependence of log ßZnLB of mixed Zn2+comple-xes with 2-aminobenzamide and amino acids (ZnLB) on their ъуХ index, at four temperatures.
As the dependence of log ßZnLB on temperature in the range 300-330 K is linear,17 we proposed the model for all four of the temperatures (N = 16) simply by including temperature into Eq. (7):
log ßZnLB = a1[3xv(ZnLB)] + a2[3xv(ZnLB)]2+
+ a3T + b
(8)
where T is the absolute temperature at which constants, log ßZnLB, were measured. The model yielded S.E.cv = 0.03 (Model 1, Table 2).
The values of log K1 and log K2 (Eqs. 2 and 3) show the same quadratic dependence on 3£v (Figure 3). This enabled the development of the model (N = 12) for all of the constants at a given temperature:
log K = a13xv + a2[3xv]2 + a3[log K0] + b
(9)
where K denotes K1, K2 and ßZnLB; K0 are the correspon-
Figure 3. The dependence of log K (log Kp log K2 and log ßZnLB) on ЪХ at 300 K; ъуХ denotes Xv(ZnB) in the case of K1 constant and for K2 and ßZnLB constants Ъ%Х is Xv(ZnLB) normalized on Xv(Zn-B), Eq. (10).
Taking glycine complexes as referent, the model gave S.E.cv = 0.09 (Model 2, Table 2).
The same function, Eq. (9), can be applied to K1, K2 and ßZnLB at all four of the temperatures (N = 48). In this case, K0 denotes the corresponding stability constants of a referent complexes at all of the temperatures. Taking glycine complexes as referent, the model gave S.E.cv = 0.06 (Model 3, Table 2).
Furthermore, we have found that it is possible to make the model more predictive. To be more precise, it is enough to know the K0, i.e. K1, K2 and ßZnLB constants of a referent complex at only two temperatures. The K0 values at the other two temperatures can be then easily calculated from the linear dependence of K1, K2 and ßZnLB on T. This way, fewer experimental constants are needed for
Table 2. Regression models for the estimation of stability constants log Kp log K2 and log ßZnLB of Zn(II) complexes with 2-aminobenzamide (L) and amino acids (B)
Model (Eq.)	Stability constant	N	a1(S.E.)	Regression coefficients a2(S.E.) a3(S.E.)		6(S.E.)	r	S.E.	S.E.cv
1 (8)	ßZnLB	16	-3.22(41)	0.216(32)	-0.0155(6)	25.2(13)	0.9960	0.02	0.03
2 (9)	K1, K2, ßZnLB	12	-1.26(43)	0.171(87)	0.987(11)	1.78(52)	0.9995	0.06	0.08
3 (9)	K1, K2, ßZnLB	48	-1.22(17)	0.167(34)	0.9880(43)	1.72(20)	0.9996	0.05	0.06
Figure 4. Experimental vs. calculated values of K (K1, K2 and ßZn-LB) by Eq. (9), where K refer to the stability of glycine complexes at 300 and 310 K. The model yielded r = 0.9996, S.E. = 0.05,
calibration. Such a model, calibrated on K1, K2 and ß of glycine complexes at 300 and 310 K, yielded S.E.cv = 0.06 (Figure 4).
4.	Conclusion
We developed two kinds of models. A model for the prediction of stability (log ßZnLB) of Zn2+ mixed complexes with 2-aminobenzamide (L) and four amino acids (B) at four temperatures (N = 16), and a model for the prediction of K1, K2 and ßZnLB of the same system (N = 48). In both cases, the theoretical results showed excellent agreement with the experimental ones, yielding errors commensurable with the errors of measurements. Specifically, the maximal differences between the experimental and theoretical (cross-validated) values were 0.06 and 0.15 for the two models (Models 1 and 3, Table 2), respectively, while the declared standard error of measurements were 0.03-0.08 for log K1 and 0.03-0.09 for log ßZnLB.
It should also be pointed out that the log K1 function has the same form as the function for copper(Il) mono-complexes with amino acids.29
5.	References
1. P. L. Ayers, R. J. Boyd, P. Bultinck, M. Caffarel, R. Carbó-Dorca, M. Causa, J. Cioslowski, J. Contreras-Garcia, D. L. Cooper, P. Coppens, C. Gatti, S. Grabowski, P. Lazzeretti, P. Macchi, A. M. Pendas, P. L. A. Popelier, K. Ruedenberg, H. Rzepa, A. Savin, A. Sax, W. H. E. Schwarz, S. Shahbazian, B. Silvi, M. Solà, V. Tsirelson, Comput. Theor. Chem. 2015,
1053, 2-16. http://dx.doi.org/10.10167j.comptc.2014.09.028
2.	E. V. Babaev, Intuitive chemical topology concepts, in: D. Bonchev, R. Rouvray, (Eds.), Chemical Topology: Introductions and Fundamentals, Gordon and Breach, Reading, 1999, pp. 167-264.
3.	Z. Mihali}, N. Trinasti}, J. Chem. Educ. 1992, 69, 701-712. http://dx.doi.org/10.1021/ed069p701
4.	B. Luči}, S. Nikoli}, N. Trinajsti}, Croat. Chem. Acta 1995, 68, 417-434.
5.	E. V. Konstantinova, M. V. Diudea, Croat. Chem. Acta 2000, 73, 383-403.
6.	M. Randić, S. C. Basak, M. Pompe, M. Novič, Acta Chim. Slov. 2001, 48, 169-180.
7.	L. H. Hall, L. B. Kier, Eur. J. Med. Chem. 1981, 16, 399407.
8.	S. Bajaj, S. S. Sambi, A. K. Madan, Croat. Chem. Acta 2005, 78, 165-174.
9.	N. Raos, A. Miličevi}, Arh. Hig. Rada Toksikol. 2009, 60, 123-128.
http://dx.doi.org/10.2478/10004-1254-60-2009-1923
10.	N. Raos, G. Branica, A. Miličevi}, Croat. Chem. Acta 2008, 81, 511-517.
11.	A. Miličevi}, N. Raos, Arh. Hig. Rada Toksikol. 2013, 64, 539-545.
http://dx.doi.org/10.2478/10004-1254-64-2013-2418
12.	A. Rimola, J. Ali-Torres, C. Rodriguez- Rodriguez, J. Poater, E. Matito, M. Sola, M. Sodupe, J. Phys. Chem. A 2011, 115, 12659-12666. http://dx.doi.org/10.1021/jp203465h
13.	A. Miličevi}, N. Raos, Acta Chim. Slov. 2012, 59, 194-198.
14.	A. Miličevi}, N. Raos, General model based on connectivity index 3X for the prediction of stability constants of coppelli) complexes with a-amino acids, in: I. Gutman (Ed.), Topics in Chemical Graph Theory, Univ. Kragujevac, Kragu-jevac, 2014, pp. 193-204.
15.	A. Miličevi}, N. Raos, Acta Chim. Slov. 2014, 61, 904-908.
16.	A. Miličevi}, N. Raos, Croat. Chem. Acta 2009, 82, 633- 639.
17.	J. Dharmaraja, P. Subbaraj, T. Esakkidurai, S. Shobana, S. Raji, Acta Chim. Slov. 2014, 61, 803-812.
18.	D. Oltmanns, M. Eisenhut, W. Mier, U. Heberkorn, Curr. Med. Chem. 2009, 16, 2086-2094. http://dx.doi.org/10.2174/092986709788612684
19.	S. B. Katiyar, I. Bansal, J. K. Saxena, P. M. Chauhan, Bi-oorg. Med. Chem. Lett. 2005, 15, 47-50. http://dx.doi.org/10.1016/j.bmcl.2004.10.046
20.	B. L. Vallee, K. H. Falchuk, Physiol. Rev. 1993, 73, 79-118.
21.	I. V. Tetko, J. Gasteiger, R. Todeschini, A. Mauri, D. Livingstone, P. Ertl, V. A. Palyulin, E. V. Radchenko, N. S. Zefirov, A. S. Makarenko, V. Y. Tanchuk, V. V. Prokopenko, , J. Com-put. Aid. Mol. Des. 2005, 19, 453-63. http://dx.doi.org/10.1007/s10822-005-8694-y
22.	VCCLAB, Virtual Computational Chemistry Laboratory, http://www.vcclab.org, 2005.
23.	http://cactus.nci.nih.gov/services/translate/
24.	L. B. Kier, L. H. Hall, J. Pharm. Sci. 1976, 65, 1806-1809. http://dx.doi.org/10.1002/jps.2600651228
25.	L. B. Kier, L. H. Kall, Molecular Connectivity in Structure-
S.E. = 0.06.
Activity Analysis, Willey, New York, 1986.
26.	L. B. Kier, L. H. Hall, Molecular Connectivity in Chemistry and Drug Research, Academic Press, New York, 1976.
27.	M. Randić, MATCH Commun. Math. Comput. Chem. 2008, 59, 5-124.
28.	B. Lučić, N. Trinajsti}, J. Chem. Inf. Comput. Sci. 1999, 39, 121-132. http://dx.doi.org/10.1021/ci980090f
29.	A. Miličević, N. Raos, Chin. J. Chem. 2011, 29, 1800-1804. http://dx.doi.org/10.1002/cjoc.201180316
Povzetek
Razvili smo model za stabilnost (log ßZnLB) Zn2+ mešanih kompleksov (N = 16) z 2-aminobenzamidom (L) in štirimi amino kislinami (B): glicinom, alaninom, valinom in fenilalaninom pri 300, 310, 320 in 330 K. Model je osnovan na kvadratni regresijski funkciji molekularnega indeksa valenčne povezljivosti tretjega reda, 3^v. Za isti sistem smo postavili tudi splošni model za K1, K2 in ßZnLB pri vseh temperaturah.