Chapter 1: Use of Least-Squares Techniques in Biochemistry

I. Update

II. Introduction

III. Nonlinear Least-Squares

IV. Why Use NLLS Analysis Procedures?

V. When to Use NLLS Analysis Procedures

VI. What Confidence Can Be Assigned to Results of NLLS Analysis?

VII. Conclusions

References

Chapter 2: Parameter Estimates from Nonlinear Models

I. Introduction

II. Discussion

Acknowledgments

References

Chapter 3: Analysis of Residuals: Criteria for Determining Goodness-of-Fit

I. Update

II. Introduction

III. Scatter Diagram Residual Plots

IV. Cumulative Probability Distributions of Residuals

V. χ2 Statistic: Quantifying Observed Versus Expected Frequencies of Residual Values

VI. Kolmogorov-Smirnov Test: An Alternative to the χ2 Statistic

VII. Runs Test: Quantifying Trends in Residuals

VIII. Serial Lagn Plots: Identifying Serial Correlation

IX. Durbin-Watson Test: Quantitative Testing for Serial Correlation

X. Autocorrelation: Detecting Serial Correlation in Time Series Experiments

XI. χ2 Test: Quantitation of Goodness-of-Fit

XII. Outliers: Identifying Bad Points

XIII. Identifying Influential Observations

XIV. Conclusions

Acknowledgments

References

Chapter 4: Monte Carlo Method for Determining Complete Confidence Probability Distributions of Estim

I. Update

II. Introduction

III. Monte Carlo Method

IV. Generating Confidence Probability Distributions for Estimated Parameters

V. Implementation and Interpretation

VI. Conclusion

Acknowledgments

References

Chapter 5: Effects of Heteroscedasticity and Skewnesson Prediction in Regression: ModelingGrowth of

I. Introduction

II. Example from Modeling Growth of the Human Heart

III. Methods of Estimation

IV. Discussion

Acknowledgments

References

Chapter 6: Singular Value Decomposition: Application to Analysis of Experimental Data

I. Update

II. Introduction

III. Definition and Properties

IV. Singular Value Decomposition of Matrices Which Contain Noise

V. Application of Singular Value Decomposition to Analysis of Experimental Data

VI. Simulations for a Simple Example: The Reaction A B C

VII. Summary

Acknowledgments

Appendix: Transformation of SVD Vectors to Optimize Autocorrelations

References

Chapter 7: Irregularity and Asynchrony in Biologic Network Signals

I. Update

II. Introduction

III. Quantification of Regularity

IV. Implementation and Interpretation

V. Representative Biological Applications

VI. Relationship to Other Approaches

VII. Mechanistic Hypothesis for Altered Regularity

VIII. Cross-ApEn

IX. Toward More Faithful Network Modeling

X. Spatial (Vector) ApEn

XI. Summary and Conclusion

References

Chapter 8: Distinguishing Models of Growth with Approximate Entropy

I. Update

II. Introduction

III. Definition and Calculation of ApEn

IV. Modifications of ApEn Calculation for this Application

V. Growth Models

VI. Expected Model-Dependent Distribution of ApEn

VII. Example of this Use of ApEn

VIII. Conclusion

Acknowledgments

References

Chapter 9: Application of the Kalman Filter to Computational Problems in Statistics

I. Introduction

II. Evaluating Gaussian Likelihood Using the Kalman Filter

III. Computing Posterior Densities for Bayesian Inference Using the Kalman Filter

IV. Missing Data Problems and the Kalman Filter

V. Extensions of the Kalman Filter Algorithm

References

Chapter 10: Bayesian Hierarchical Models

I. Introduction

II. The Gaussian Model

III. Computation

IV. Example: Meta-Regression

V. Example: Saltatory Model of Infant Growth

VI. Incorporation of Variance Components

VII. Model Checking

VIII. Conclusion

Acknowledgments

References

Chapter 11: Mixed-Model Regression Analysis and Dealing with Interindividual Differences

I. Introduction

II. Experiment and Data

III. Repeated-Measures ANOVA

IV. Mixed-Model Regression Analysis

V. An Alternative Linear Mixed-Effects Model

VI. Nonlinear Mixed-Model Regression Analysis

VII. Correlation Structures in Mixed-Model Regression Analysis

VIII. Conclusion

Acknowledgment

References

Chapter 12: Distribution Functions from Moments and the Maximum-Entropy Method

I. Introduction

II. Ligand Binding: Moments

III. Maximum-Entropy Distributions

IV. Ligand Binding: Distribution Functions

V. Enthalpy Distributions

VI. Self-Association Distributions

References

Chapter 13: The Mathematics of Biological Oscillators

I. Introduction

II. Oscillators and Excitability

III. Perturbations of Oscillators

IV. Coupled Oscillators

References

Chapter 14: Modeling of Oscillations in Endocrine Networks with Feedback

I. Introduction

II. General Principles in Endocrine Network Modeling

III. Simulating the Concentration Dynamics of a Single Hormone

IV. Oscillations Driven by a Single System Feedback Loop

V. Networks with Multiple Feedback Loops

VI. Summary and Discussion

Acknowledgments

References

Chapter 15: Boundary Analysis in Sedimentation Velocity Experiments

I. Update

II. Introduction

III. Methods of Data Acquisition

IV. Measurement of Transport in Analytical Ultracentrifuge

V. Traditional Methods of Analysis

VI. Transport Method

VII. Smoothing and Differentiating

VIII. Computation of Apparent Sedimentation Coefficient Distribution Functions

IX. Weight Average Sedimentation Coefficient from g(s*)

X. Methods of Correcting Distribution Functions for Effects of Diffusion

XI. Discussion

References

Chapter 16: Statistical Error in Isothermal Titration Calorimetry

I. Update

II. Introduction

III. Variance-Covariance Matrix in Least Squares

IV. Monte Carlo Computational Methods

V. Van't Hoff Analysis of K(T): Least-Squares Demonstration

VI. Isothermal Titration Calorimetry

VII. Calorimetric Versus Van't HoffDeltaH from ITC

VIII. Conclusion

References

Chapter 17: Physiological Modeling with Virtual Cell Framework

I. Update

II. Introduction

III. Modeling Abstractions for Cellular Physiology

IV. Application to Existing Model

V. Conclusions

Acknowledgments

Appendix 1:. Physiological Model Description

Appendix 2:. Mathematical Description

References

Chapter 18: Fractal Applications in Biology: Scaling Time in Biochemical Networks

I. Update

II. Introduction

III. Fractal Morphology in Mammals: Some Branchings

IV. Chaos in Enzyme Reactions

V. Practical Guide to Identification of Chaos and Fractals in Biochemical Reactions

VI. Summary, or What Does It All Mean?

VII. Glossary

References

Chapter 19: Analytical Methods for the Retrieval and Interpretation of Continuous Glucose Monitoring

I. 2010 Update of Developments in the Field

II. Introduction

III. Decomposition of Sensor Errors

IV. Measures of Average Glycemia and Deviation from Target

V. Risk and Variability Assessment

VI. Measures and Plots of System Stability

VII. Time-Series-Based Prediction of Future BG Values

VIII. Conclusions

Acknowledgments

References

Chapter 20: Analyses for Physiological and Behavioral Rhythmicity

I. Introduction

II. Types of Biological Data and Their Acquisition

III. Analysis in the Time Domain

IV. Analysis in the Frequency Domain

V. Time/Frequency Analysis and the Wavelet Transform

VI. Signal Conditioning

VII. Strength and Regularity of a Signal

VIII. Some Practical Considerations on Statistical Comparisons ofAnalytical Results

IX. Conclusions

References

Chapter 21: Evaluation and Comparison of Computational Models

I. Update

II. Introduction

III. Conceptual Overview of Model Evaluation and Comparison

IV. Model Comparison Methods

V. Model Comparison at Work: Choosing Between Protein Folding Models

VI. Conclusions

Acknowledgments

References

Chapter 22: Algebraic Models of Biochemical Networks

I. Introduction

II. Computational Systems Biology

Example 1

Definition 1

Definition 2

Example 2

III. Network Inference

IV. Reverse-Engineering of Discrete Models: An Example

Definition 3

Definition 4

Example 3

V. Discussion

References

Chapter 23: Monte Carlo Simulation in Establishing Analytical Quality Requirements for Clinical Labo

I. Update

II. Introduction

III. Modeling Approach

IV. Methods for Simulation Study

V. Results

VI. Discussion

References

Chapter 24: Pancreatic Network Control of Glucagon Secretion and Counterregulation

I. Update

II. Introduction

III. Mechanisms of Glucagon Counterregulation (GCR) Dysregulation in Diabetes

IV. Interdisciplinary Approach to Investigating the Defects in the GCR

V. Initial Qualitative Analysis of the GCR Control Axis

VI. Mathematical Models of the GCR Control Mechanisms in STZ-Treated Rats

VII. Approximation of the Normal Endocrine Pancreas by a Minimal Control Network (MCN) and Analysis

VIII. Advantages and Limitations of the Interdisciplinary Approach

IX. Conclusions

Acknowledgment

References

Index