Ante Miličević

On reformulated Zagreb indices

Zagreb indices were reformulated in terms of the edge-degrees instead of the vertex-degrees as the original Zagreb indices. Three types of Zagreb indices were considered: original, modified and variable Zagreb indices. It is found that the optimum exponent of the variable reformulated Zagreb M2 index (v=−1/2) is identical with the exponent of the vertex-connectivity index, which is the most used topological index in QSPR and QSAR. The close relationship between the graph and its line graph is used to relate the original and reformulated indices.

Estimation of stability constants of coordination compounds using models based on topological indices.

Estimation of Stability Constants of Coordination Compounds using Models Based on Topological Indices The principal aim of our research was to develop theoretical models for estimating stability constants of coordination compounds, focusing on chelates of heavy metals, Cu(II) and Ni(II), with bioligands (amines, amino acids and peptides). We tried to solve the problem using graph-theoretical models. We also encountered a specific problem for coordination compounds - the choice of the constitutional formula, that is graph, of the complex species. Procjena konstanta stabilnosti koordinacijskih spojeva s pomoću modela temeljenih na topološkim indeksima Prikazani su načini rješavanja problema procjene konstanta stabilnosti bakrovih(II) i niklovih(II) kelata s aminima, aminokiselinama i peptidima primjenom graf-teorijskih modela. Osebujni problem za koordinacijske spojeve je izbor konstitucijske formule, tj. grafa kompleksnoga spoja, pa su stoga iskušani modeli temeljeni na formuli liganda i više oblika konstitucijske formule kompleksa. Pokazalo se da se najbolji rezultati postižu valencijskim indeksom povezanosti trećeg reda, 3χv. Iskušani su modeli temeljeni na kombinacijama indeksa izvedenih iz molekularnih segmenata. Takvi su se modeli pokazali osobito uspješnima za procjenu stabilnosti miješanih kompleksa.

Irving-Williams Order in the Framework of Connectivity Index 3χv Enables Simultaneous Prediction of Stability Constants of Bivalent Transition Metal Complexes

Logarithms of stability constants, log K1 and log β2, of the first transition series metal mono- and bis-complexes with any of four aliphatic amino acids (glycine, alanine, valine and leucine) decrease monotonously with third order valence connectivity index, 3χv, from Cu2+ to Mn2+. While stability of the complexes with the same metal is linearly dependent on 3χv, stability constants of Mn2+, Fe2+, Co2+, and Ni2+complexes with the same ligand show a quadratic dependence on 3χv. As Cu2+ complexes deviate significantly from quadratic functions, models for the simultaneous estimation of the stability constants, yielding r = 0.999 (S.E. = 0.05) and r = 0.998 (S.E. = 0.11), for log K1 and log β2, respectively, were developed only for Mn2+, Fe2+, Co2+, and Ni2+ complexes with amino acids.

On Use of the Variable Zagreb vM2 Index in QSPR: Boiling Points of Benzenoid Hydrocarbons

The variable Zagreb (v)M(2) index is introduced and applied to the structure-boiling point modeling of benzenoid hydrocarbons. The linear model obtained (the standard error of estimate for the fit model S(fit)=6.8 degrees C) is much better than the corresponding model based on the original Zagreb M2 index (S(fit)=16.4 degrees C). Surprisingly,the model based on the variable vertex-connectivity index (S(fit)=6.8 degrees C) is comparable to the model based on (v)M2 index. A comparative study with models based on the vertex-connectivity index, edge-connectivity index and several distance indices favours models based on the variable Zagreb (v)M2 index and variable vertex-connectivity index.However, the multivariate regression with two-, three- and four-descriptors gives improved models, the best being the model with four-descriptors (but (v)M2 index is not among them) with S(fit)=5 degrees C, though the four-descriptor model contaning (v)M2 index is only slightly inferior (S(fit)=5.3 degrees C).

Influence of Chelate Ring Interactions on Copper(II) Chelate Stability Studied by Connectivity Index Functions

Linear models for estimation of the first (K1), second (K2), and overall stability constant (beta2) based on the valence connectivity index of the third order ((3)chi(v)) were developed and checked on four sets of copper(II) chelates (with diamines, N-alkylated glycines, and naturally occurring amino acids, including their mixed complexes). Univariate models were valid when log K1 and log K2 values were linearly correlated, i.e., when there was no interaction between chelate rings. The univariate models proved applicable for estimation of all three stability constants of complexes with diamines and N-alkylated glycines, but for complexes with amino acids additional terms were needed (bivariate models). Models reproduced stability constants with an error usually less than 0.3 log K units.

Stability prediction of Cu2+, Ni2+ and Zn2+ N-salicylidene-aminoacidato complexes by models based on connectivity index 3 χ v

AbstractThis paper presents models for the estimation of stability constants (K1 and β2) of nickel(II), copper(II) and zinc(II) mono- and bis-complexes with 5 Schiff bases (salicylideneglycine, salicylidenealanine, salicylideneserine, salicylidenephenylalanine, and salicylidenetyrosine). The models were based on the molecular-graph theory and valence molecular connectivity index of the 3rd order, 3χv, derived from it. Univariate linear models were developed for each metal separately, while in the common models for two and three metals, the indicator variable, In, was introduced. The standard error of models for the log K1 constant was less than 0.12, while for log β2 models, the S.E. did not exceed 0.14.

Comparison of Two Methods for the Estimation of Stability of Copper(II) bis-Complexes with Aromatic Ligands Relevant to Alzheimer's Disease

Abstract In order to compare the density functional theory (DFT) and the method with the molecular valence connectivity index of the 3rd order (3χv) in the estimation of stability constants log β2, we used copper(II) complexes with thioflavin-based intercalation compounds designed for application in Alzheimer’s disease. Correlation of ten log β2 values calculated by DFT with 3χv yielded r=0.988 and S.E.=0.85. The correlations of indices ING, HOMA and 3χv with log β2, and the intercorrelations between the indices revealed the crucial influence of 3χv on the prediction of the stability of these complexes. Sažetak Izabrali smo komplekse bakra(II) s interkalacijskim spojevima temeljenima na tioflavinu, koji su namijenjeni za liječenje Alzheimerove bolesti, kako bismo usporedili teoriju funkcionala gustoće (DFT) s metodom molekularnog valencijskog indeksa 3. reda (3χv) za procjenu vrijednosti konstanti stabilnosti log β2. Korelacija deset vrijednosti log β2 izračunatih metodom DFT s 3χv indeksom dala je r=0,988 i S.E.=0,85. Korelacije indeksa ING, HOMA i 3χv s vrijednostima log β2 te međukorelacije indeksa pokazuju bitan utjecaj 3χv na predviđanje stabilnosti istraživanih kompleksa.

A new, simplified model for the estimation of polyphenol oxidation potentials based on the number of OH groups

Abstract We present a new and simpler regression model for the estimation of the first oxidation potentials (Ep1) of flavonoids based on the number of phenolic, alcoholic, and carboxylic OH groups. In the regression we included the Ep1 of 12 polyphenols (mostly flavonols and catechins) that were measured in our laboratory at pH 3. The model yielded r=0.986 and SE=0.040. Later successive inclusions of previously reported Ep values into the regression model, 7 at pH 3, the model (N=19) yielded r=0.980, SE=0.046 and 19 at pH 7 the model (N=38), yielded r=0.985, SE=0.044.

Toxicity of Aliphatic Ethers: A Comparative Study

SummaryThe CROMRsel procedure was used to model the toxicity of aliphatic ethers against mice. The best model obtained is based on three molecular descriptors and is a better model than other QSAR models from the literature. The only comparable model is one by Ren, based on four descriptors.

Modelling of copper(II) binding to pentapeptides related to atrial natriuretic factor using the 3χv connectivity index

Abstract Using molecular graph theory we studied the binding of NSFRY-NH2 and 12 related pentapeptide amides to Cu(II) as a model system for atrial natriuretic factor (ANF) peptide interactions with copper. Linear regression models based on the valence connectivity index of the 3rd order (3χv) reproduced experimental stability constants (log β) for 1N, 2N, 3N, and 4N coordinated complexes with the standard error of 0.30-0.39 log β units. We developed separate models for seven tyrosinic (N=28) and five non-tyrosinic peptides (N=20), and a common model for both kinds of peptides (N=48) with an indicator (dummy) variable. The results indicate additional aromatic stabilisation in 4N complexes due to metal cation-π interactions with tyrosine but not with the phenylalanine residue. We have also amended the log K and log K* values to correct miscalculations published by Janicka-Klos et al. in 2013 Služeći se teorijom molekularnih grafova istraživali smo vezivanje NSFRY-NH2 i 12 srodnih pentapetidnih amida za Cu(II) kao modelnog sustava za interakciju bakra s peptidnom molekulom atrijalnog natriuretičkog faktora (ANF). Modeli linarne regresije temeljeni na valencijskom indeksu povezanosti trećega reda (3χv) reproducirali su eksperimentalnu konstantu stabilnosti (log β) za komplekse koordinacije 1N, 2N, 3N i 4N sa standardnom pogreškom u rasponu od 0,30 do 0,39 log β jedinica. Razvili smo odvojene modele za sedam tirozinskih (N=28) i pet netirozinskih (N=20) peptida te skupni model s indikatorskom varijablom za obje vrste peptida (N=48). Rezultati upućuju na dodatnu aromatsku stabilizaciju u kompleksima vrste 4N zbog interakcija kationa s π-orbitalama tirozinskog ostatka, ali ne i fenilalaninskoga. Ispravili smo i pogrešne vrijednosti log K i log K* nastale omaškom u radu Anne Janicka-Klos i sur. 2013.