Quantum nanochemistry. Volume V, Quantum structure-activity relationships (Qu-SAR)

608 Pages·2016·92.734 MB·English

by  Putz, Mihai V

QUANTUM
NANOCHEMISTRY
(A Five-Volume Set)
Volume V:
Quantum Structure–Activity Relationships
(Qu-SAR)
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
QUANTUM
NANOCHEMISTRY
(A Five-Volume Set)
Volume V:
Quantum Structure–Activity Relationships
(Qu-SAR)
Mihai V. Putz
Assoc. Prof. Dr. Dr.-Habil. Acad. Math. Chem.
West University of Timişoara,
Laboratory of Structural and Computational Physical-Chemistry
for Nanosciences and QSAR, Department of Biology-Chemistry,
Faculty of Chemistry, Biology, Geography,
Str. Pestalozzi, No. 16, RO-300115, Timişoara, ROMANIA
Tel: [phone]; Fax: [phone]
&
Principal Investigator of First Rank, PI1/CS1
Institute of Research-Development for Electrochemistry
and Condensed Matter (INCEMC) Timisoara,
Str. Aurel Paunescu Podeanu No. 144 ,
RO-300569 Timişoara, ROMANIA
Tel: [phone]; Fax: [phone]
E-mail: [email protected]
URL: www.mvputz.iqstorm.ro
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[The] natural tendency of the mind [is] to give to the shape of a graph
some intrinsic value…to its ultimate consequences…because qualitative
and empirical deduction already gives them sufficient framework for
experiment and prediction.
(Thom, 1975)
To XXI Scholars
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
CONTENTS
List of Abbreviations ...................................................................................xi
Preface to Five-Volume Set .........................................................................xv
About the Author .......................................................................................xxi
Foreword to Volume V: Quantum Structure–Activity
Relationships (Qu-SAR) ..........................................................................xxiii
Preface to Volume V: Quantum Structure–Activity
Relationships (Qu-SAR) ..........................................................................xxvii
Chapter 1. Logistic Enzyme Kinetics ................................................................1
Abstract .................................................................................................................2
1.1 Introduction ................................................................................................3
1.2 Michaelis-Menten Enzyme Kinetics and Limited
W-Lambert Solution ...................................................................................5
1.3 Logistic Formulation and Explicit Enzyme Kinetics’ Solution .................10
1.4 Reliability of the Logistic Enzyme Kinetic .............................................13
1.4.1 Quasi Steady-State Approximation Analysis ..............................13
1.4.2 Full Time Course Analysis ..........................................................15
1.4.3 Analysis of Fitting Curves ...........................................................20
1.5 Multiple Alternative Enzyme-Substrate Reactions ..................................22
1.6 Application on Competitive Inhibition ....................................................26
1.7 Application on Reversible Kinetics .........................................................31
1.8 Logistic Approach of Haldane-Radić Enzyme Kinetics ..........................39
1.8.1 Haldane-Radić Equation..............................................................41
1.8.2 Probabilistic form of the Haldane-Radić Equation .....................43
1.8.3 W-Lambert Solution of Haldane-Radić Equation .......................44
1.8.4 Logistic Solution of Haldane-Radić Equation.............................47
1.9 Quantum Enzyme Kinetics ......................................................................53
1.9.1 Quantum Enzyme Catalysis ........................................................57
1.9.2 Application to Mixed Inhibition ..................................................62
1.10 Conclusion ...............................................................................................68
Keywords ............................................................................................................71
viii Contents
References ...........................................................................................................71
Author’s Main References .........................................................................71
Specific References ...................................................................................72
Chapter 2. Statistical Space for Multivariate Correlations ..........................77
Abstract ...............................................................................................................78
2.1 Introduction ................................................................................................78
2.2 Statistical Correlation Analysis ..................................................................82
2.2.1 Correlation Coefficient ..................................................................82
2.2.2 Mono-Linear Regression ...............................................................86
2.2.3 Multi-Linear Regression..............................................................101
2.3 Inferential Analysis of Statistical Samples ..............................................108
2.3.1 Z-Statistics ...................................................................................108
2.3.2 The Selection Theory ..................................................................118
2.3.2.1 From Global (Collectivity) to
Local (Sample) Statistics.............................................118
2.3.2.2 The A-Consequence: The Chi-Square Statistics .........122
2.3.2.3 The B-Consequence: The t-Student Statistics .............129
2.3.2.4 The C-consequence: The Fisher Statistics ..................134
2.4 Robustness of Correlations: Confidence Intervals ...................................138
2.4.1 Validation of Statistical Information ...........................................138
2.4.1.1 Synopsis of Statistical Concepts .................................138
2.4.1.2 Validation of Statistical Hypothesis for
Median Value in Bilateral Case ...................................142
2.4.1.3 Validation of Statistical Hypothesis for the
Difference Between the Median Values ......................147
2.4.1.4 Validation of Statistical Hypothesis
By Testing the Similitude of Dispersions ....................152
2.4.2 Confidence Intervals....................................................................154
2.4.2.1 Chi-square Statistics ....................................................154
2.4.2.2 The Chi-Square-Test for
Normal Concordance ..................................................159
2.4.2.3 The Chi-Square Test for the Parametrical
Concordances and Likelihood .....................................166
2.4.3 Robustness of Regression: Multi-Regression
Analysis of Variance (ANOVA) ..................................................170
2.5 Conclusion ...............................................................................................182
Keywords ..........................................................................................................186
Contents ix
References .........................................................................................................186
Author’s Main References .......................................................................186
Specific References .................................................................................187
Further Readings .....................................................................................191
Chapter 3. Chemical Orthogonal Spaces for Structure–Activity
Relationship (COS-SAR) .......................................................................193
Abstract .............................................................................................................194
3.1 Introduction ..............................................................................................195
3.2 Spectral Regressions’ Models on Chemical Orthogonal Space ...............197
3.2.1 Introducing SPECTRAL-SAR ....................................................197
3.2.2 SPECTRAL-Diagonal-SAR ........................................................209
3.2.3 Algebraic Correlation Factor .......................................................217
3.2.4 Algebraic vs. Statistic Correlations .............................................219
3.2.5 Projective QSAR .........................................................................221
3.2.6 Non-linear Catastrophe QSAR ....................................................229
3.2.7 QSAR by Quantum Amplitude (Qua-SAR) ................................243
3.2.8 From Residual to Structural Alerts’ QSAR
(Res/SA-SAR)......................................................................................248
3.2.9 QSAR by SMILES’ Structure and Chemical Reactivity
Principles .....................................................................................254
3.2.9.1 Electronegativity and Its Minimum Principle .............260
3.2.9.2 Chemical Hardness and Its Maximum Principle .............262
3.2.9.3 Chemical Power and Its Double Minimum
Principle ......................................................................264
3.2.9.4 Electrophilicity and Its Triple Minimum
Principle ......................................................................265
3.2.10 Topo-Reactive QSAR ..................................................................274
3.2.10.1 A Historical Perspective on Topology and
Link to Chemical Graphs ..........................................276
3.2.10.2 Common Construct of Topological Indices ..............280
3.2.10.3 Introducing SuTIs: Super-Topological Indices .............282
3.2.10.4 Topo-Reactivity by Timişoara-Parma Rule ...............290
3.2.11 Logistic QSAR ............................................................................300
3.3 Qu-SAR Case Studies on Chemical Orthogonal Space ...........................300
3.3.1 SPECTRAL-SAR Ecotoxicology (on T. pyriformis) ..................300
3.3.2 Algebraic vs. Statistic Correlation (for Aliphatic
Amines’ Toxicity) ........................................................................312