Data Analysis in Biochemistry and Biophysics

Data Analysis in Biochemistry and Biophysics describes the techniques how to derive the most amount of quantitative and statistical information from data gathered in enzyme kinetics, protein-ligand equilibria, optical rotatory dispersion, chemical relaxation methods. This book focuses on the determination and analysis of parameters in different models that are used in biochemistry, biophysics, and molecular biology. The Michaelis-Menten equation can explain the process to obtain the maximum amount of information by determining the parameters of the model. This text also explains the fundamentals present in hypothesis testing, and the equation that represents the statistical aspects of a linear model occurring frequently in this field of testing. This book also analyzes the ultraviolet spectra of nucleic acids, particularly, to establish the composition of melting regions of nucleic acids. The investigator can use the matrix rank analysis to determine the spectra to substantiate systems whose functions are not known. This text also explains flow techniques and relaxation methods associated with rapid reactions to determine transient kinetic parameters. This book is suitable for molecular biologists, biophysicists, physiologists, biochemists, bio- mathematicians, statisticians, computer programmers, and investigators involved in related sciences

Table of Contents:
ForewordPreface Acknowledgments1. Scope of Problems Investigated 1. Introduction 2. A Problem from Absorption Spectroscopy 3. The Use of Function Minimization and Matrices 4. An Example from Concentration-Dependent Aggregating Systems 5. Linear and Nonlinear Models 6. The General Problem for Linear Models 7. The General Problem for Nonlinear Models 8. The Use of Statistics 9. The Problem of Constraining the Parameters 10. Determining Unknown Components: Matrix Rank Analysis 11. A Word of Caution References2. Matrices 1. Introduction 2. Matrices 3. Rules of Matrix Algebra 4. Special Matrices 5. Determinants of Square Matrices 6. Matrix Rank and Elementary Transformations 7. The Inverse of a Matrix 8. Vector Algebra 9. Linear Equations 10. Quadratic Forms 11. Eigenvalues and Eigenvectors 12. Partitioned Matrices 13. Application to Coordinate Geometry and Bilinear Forms References3. Analysis Pure Analysis 1. Sets 2. Functions and Their Properties 3. Functions of Several Real Variables Applied Analysis 4. Applications of Differentiation 5. Applications of Integration 6. Miscellaneous Topics References4. Minimization of Functions 1. Introduction 2. Functional Extrema 3. Least Squares 4. Minimax Curve Fitting or Chebyshev Minimization 5. Linear Programming 6. Determination of Parameters in Nonlinear Models 7. Application References5. Statistics I 1. Introduction 2. Sample Space and Elementary Consideration of Probability Distributions 3. Frequency Distributions 4. Probability 5. Standard Distributions with a Single Variable 6. Bivariate Distribution 7. Multivariate Distributions 8. Statistical Inference 9. Distributions of Quadratic Forms References6. Statistics II 1. Introduction 2. Hypothesis Testing 3. Formalizing Notions on Hypothesis Testing 4. The General Linear Model of Full Rank 5. Testing General Linear Model Hypotheses 6. Some Notes on Nonlinear Models References7. Absorption Spectra of Mixtures 1. Introduction 2. Absorption Spectra of Mixtures 3. Applications in Protein Modification to Determine Reactivity of Amino Acid Residues 4. Application to Solvent Perturbation 5. Binding Studies References8. Analysis of Nucleic Acid Spectra 1. Introduction 2. RNA Spectra 3. DNA Spectra References9. Matrix Rank Analysis 1. Introduction 2. The Matrix Rank Analysis Method 3. Application of Matrix Rank Analysis to the Optical Rotatory Dispersion Spectra of TMV RNA Taken at a Variety of Ionic Strengths and Temperatures 4. Application to Reaction Rates of Partially Oxidized Hemoglobin 5. Alternative Methods for Determining the Shape of the Spectra References10. Optical Rotary Dispersion and Circular Dichroism of Proteins 1. Introduction 2. Possible Structures of Proteins and Polypeptides (the Ramachandran Diagrams) 3. Methods for Determining the Secondary Structure of Proteins 4. Problems Involved in Optical Rotatory Dispersion Analysis of Proteins 5. Possible Methods for Determination of Side Chain Contributions 6. Circular Dichroism of Proteins 7. Fitting an Optical Rotatory Dispersion Curve with Drude Terms 8. Analysis of Circular Dichroism Spectra 9. Decomposition of Optical Rotatory Dispersion Curves into Their Contributing Circular Dichroic Bands References11. Optical Rotatory Dispersion and Circular Dichroism of Nucleic Acids and their Components 1. Introduction 2. ORD of RNA Components 3. Possible Sequence Determination and Distinguishing between Isomers 4. Calculation of ORD of Homopolymers and RNA 5. Testing Hypotheses about RNA Structure 6. Optical Rotatory Dispersion of RNA References12. Aggregating Systems 1. Introduction 2. Aggregation Schemes 3. Number Average Molecular Weights: Ideal Systems 4. Weight Average Molecular Weights 5. Gel Filtration Methods in the Determination of Molecular Weight Distributions 6. Mixed Aggregation References13. Allosteric Effects and Other Cooperative Phenomena in Protein-Ligand Equilibria 1. Introduction 2. Description of Some Models in the Literature 3. Sequential Binding or Adair's Equation-Proteins without Any Subunits 4. Models of Koshland, Nemethy, and Filmer 5. The Model of Monod, Wyman, and Changeux 6. Expansion of Models 7. Cases Considered by Frieden 8. Scatchard's Model 9. Distinguishing between Different Models 10. Comments on Procedures 11. Analysis of Data References14. Enzyme Kinetics 1. Introduction 2. Two Cases Treated by Wilkinson 3. The Effects of pH on Vmax 4. Cases Treated by Cleland 5. A Complex Case and Ways of Handling It References15. Rapid Reactions: Transient Enzyme Kinetics and Other Rapid Biological Reactions 1. Introduction 2. Techniques of Measuring Rapid Reactions 3. Combination of Hemoglobin with Ligands 4. A Potential Method for the Determination of Spectra of Intermediates 5. Determination of the Number of Intermediates and Rate Constants in Enzyme Catalyzed Reactions 6. Relaxation Methods 7. A Word of Caution References16. Tracer Techniques in Compartmentalized Systems 1. Introduction 2. Two-Compartment Systems 3. Closed Systems and Open Systems 4. Three-Compartment Systems 5. Problems with the Use of Simultaneous Linear Differential Equations 6. Multicompartment Systems 7. Simulation of Tracer Data 8. Modification of the Multicompartment System Model and Other Models ReferencesAppendix: Statistical TablesAuthor IndexSubject Index