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The complexation of metal ions with various organic ligands in water: prediction of stability constants by QSPR ensemble modelling

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Abstract

Quantitative structure–property relationship modelling of the stability constants (log K) for the 1:1 (M:L) complexes of metal ions (M = Li+, Na+, K+, Be2+, Al3+, Ga3+, In3+, VO2+, Fe3+, Th4+, NpO2 +, Am3+) with structurally diverse organic ligands in aqueous solution was performed using ensemble multiple linear regression (eMLR) analysis, support vector machines, associative neural networks and substructural molecular fragments’ descriptors. The models were validated with cross-validation procedures and with complementary external test set. For eMLR in the 5-fold cross-validation, root-mean squared error of log K varies from 0.49 (Li+) to 2.30 (In3+), and it is comparable with the systematic errors in experimental data. Designed predictor for end users implements consensus models together with the estimation of their applicability domain.

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Abbreviations

AD:

Applicability domain

ASNN:

Associative neural networks

CM:

Consensus model

5CV:

5-Fold cross-validation

eMLR:

Ensemble multiple linear regression

FMF:

Forecast by molecular fragments

FVS:

Forward variable selection

ISIDA:

In SIlico design and data analysis

L:

Organic ligand

LOO:

Leave-one-out

M:

Metal ion

MAE :

Mean absolute error

Q :

Leave-one-out cross–validation correlation coefficient

QSPR:

Quantitative structure–property relationships

R 2 det :

Squared coefficient of determination

RMSE :

Root-mean squared error

SDF:

Structure data file

SMF:

Substructural molecular fragments

SVM:

Support vector machines

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Acknowledgments

We gratefully acknowledge Prof. L. Pettit for the English language improvement of the paper. V.S. thanks Dr. G. Pettit and Prof. L. Pettit from Academic Software for providing new version of the IUPAC Stability Constants Database.

Supporting Information

1). Structure data file Li_Na_K_Be_Al_Ga_In_V_Fe_Th_Np_Am.SDF contains the 2D structures of the organic ligands (L) and the experimental stability constant values (log K) for the equilibrium M + L = ML (M = Li+, Na+, K+, Be2+, Al3+, Ga3+, In3+, VO2+, Fe3+, Th4+, NpO2 + and Am3+) in water at 298 K and an ionic strength 0.1 M. 2). Predictive performances of the eMLR consensus models in 5CV (Table SI 1). 3). Predictive performances of the SVM models in 5CV (Table SI 2). 4). Predictive performances of the ASNN models in 5CV (Table SI 3). 5). The statistical parameters of the best individual eMLR models and optimal descriptor types according to the training subsets of the 5CV procedure (Table SI 4).

Author information

Authors and Affiliations

  1. Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninskiy Prospect, 31, 119071, Moscow, Russian

    Vitaly Solov’ev, Natalia Kireeva, Svetlana Ovchinnikova & Aslan Tsivadze

  2. Moscow Institute of Physics and Technology, Institutsky Per. 9, 141700, Dolgoprudny, Russia

    Natalia Kireeva & Svetlana Ovchinnikova

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  1. Vitaly Solov’ev
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Correspondence to Vitaly Solov’ev.

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Solov’ev, V., Kireeva, N., Ovchinnikova, S. et al. The complexation of metal ions with various organic ligands in water: prediction of stability constants by QSPR ensemble modelling. J Incl Phenom Macrocycl Chem 83, 89–101 (2015). https://doi.org/10.1007/s10847-015-0543-6

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  • DOI: https://doi.org/10.1007/s10847-015-0543-6

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