| Contributors | p. xi |
| Preface | p. xv |
| Volumes in Series | p. xvii |
| Phase Response Curves: Elucidating the Dynamics of Coupled Oscillators | p. 1 |
| Introduction | p. 2 |
| Estimation of Phase Response Curves | p. 11 |
| Specific Applications | p. 17 |
| Discussion | p. 20 |
| p. 21 |
| p. 23 |
| Acknowledgments | p. 24 |
| References | p. 24 |
| Multiple Ion Binding Equilibria, Reaction Kinetics, and Thermodynamics in Dynamic Models of Biochemical Pathways | p. 29 |
| Introduction | p. 30 |
| Biochemical Conventions and Calculations | p. 34 |
| Application to Physiological Systems | p. 57 |
| Discussion | p. 64 |
| Acknowledgment | p. 66 |
| References | p. 66 |
| Analytical Methods for the Retrieval and Interpretation of Continuous Glucose Monitoring Data in Diabetes | p. 69 |
| Introduction | p. 70 |
| Decomposition of Sensor Errors | p. 73 |
| Measures of Average Glycemia and Deviation from Target | p. 74 |
| Risk and Variability Assessment | p. 76 |
| Measures and Plots of System Stability | p. 80 |
| Time-Series-Based Prediction of Future BG Values | p. 81 |
| Conclusions | p. 84 |
| Acknowledgments | p. 84 |
| References | p. 84 |
| Analysis of Heterogeneity in Molecular Weight and Shape by Analytical Ultracentrifugation Using Parallel Distributed Computing | p. 87 |
| Introduction | p. 88 |
| Methodology | p. 89 |
| Job Submission | p. 97 |
| Results | p. 100 |
| Conclusions | p. 109 |
| Acknowledgments | p. 111 |
| References | p. 111 |
| Discrete Stochastic Simulation Methods for Chemically Reacting Systems | p. 115 |
| Introduction | p. 116 |
| The Chemical Master Equation | p. 117 |
| The Stochastic Simulation Algorithm | p. 119 |
| The Tau-Leaping Method | p. 122 |
| Measurement of Simulation Error | p. 132 |
| Software and Two Numerical Experiments | p. 134 |
| Conclusion | p. 137 |
| Acknowledgments | p. 139 |
| References | p. 139 |
| Analyses for Physiological and Behavioral Rhythmicity | p. 141 |
| Introduction | p. 142 |
| Types of Biological Data and Their Acquisition | p. 143 |
| Analysis in the Time Domain | p. 145 |
| Analysis in the Frequency Domain | p. 151 |
| Time/Frequency Analysis and the Wavelet Transform | p. 161 |
| Signal Conditioning | p. 164 |
| Strength and Regularity of a Signal | p. 169 |
| Conclusions | p. 171 |
| References | p. 171 |
| A Computational Approach for the Rational Design of Stable Proteins and Enzymes: Optimization of Surface Charge-Charge Interactions | p. 175 |
| Introduction | p. 176 |
| Computational Design of Surface Charge-Charge Interactions | p. 183 |
| Experimental Verification of Computational Predictions | p. 190 |
| Closing Remarks | p. 202 |
| Acknowledgments | p. 204 |
| References | p. 204 |
| Efficient Computation of Confidence Intervals for Bayesian Model Predictions Based on Multidimensional Parameter Space | p. 213 |
| Introduction | p. 214 |
| Height of the Probability Density Function at the Boundary of the Smallest Multidimensional Confidence Region | p. 215 |
| Approximating a One-Dimensional Slice of the Probability Density Function by Means of Normal Curve Spline Pieces | p. 217 |
| Locating the Boundary of the Smallest Multidimensional Confidence Region | p. 219 |
| Finding the Minimum and Maximum of the Prediction Model over the Confidence Region | p. 220 |
| An Application: Bayesian Forecasting of Cognitive Performance Impairment during Sleep Deprivation | p. 221 |
| 95% Confidence Intervals for Bayesian Predictions of Cognitive Performance Impairment during Sleep Deprivation | p. 223 |
| Conclusion | p. 227 |
| Acknowledgments | p. 229 |
| Appendix | p. 229 |
| References | p. 230 |
| Analyzing Enzymatic pH Activity Profiles and Protein Titration Curves Using Structure-Based pK<a/ Calculations and Titration Curve Fitting | p. 233 |
| Introduction | p. 234 |
| Calculating the pH Dependence of Protein Characteristics | p. 235 |
| Setting up and Running a pKa/ Calculation | p. 243 |
| Analyzing the Results of a pKa/ Calculation | p. 244 |
| How Reliable Are Calculated pKa/ Values? | p. 246 |
| Predicting pH Activity Profiles | p. 248 |
| Decomposition Analysis | p. 249 |
| Predicting Protein Stability Profiles | p. 251 |
| Fitting pH Titration Curves, pH Activity Profiles, and pH Stability Profiles | p. 252 |
| Conclusion | p. 255 |
| References | p. 256 |
| Least Squares in Calibration: Weights, Nonlinearity, and Other Nuisances | p. 259 |
| Introduction | p. 260 |
| Review of Least Squares | p. 263 |
| Experiment Design Using Vprior/-Numerical Illustrations | p. 269 |
| Conclusion | p. 282 |
| References | p. 283 |
| Evaluation and Comparison of Computational Models | p. 287 |
| Introduction | p. 288 |
| Conceptual Overview of Model Evaluation and Comparison | p. 288 |
| Model Comparison Methods | p. 292 |
| Model Comparison at Work: Choosing between Protein Folding Models | p. 297 |
| Conclusions | p. 301 |
| Acknowledgments | p. 303 |
| References | p. 303 |
| Desegregating Undergraduate Mathematics and Biology - Interdisciplinary Instruction with Emphasis on Ongoing Biomedical Research | p. 305 |
| Introduction | p. 306 |
| Course Description | p. 309 |
| Discussion | p. 317 |
| Acknowledgments | p. 320 |
| References | p. 320 |
| Mathematical Algorithms for High-Resolution DNA Melting Analysis | p. 323 |
| Introduction | p. 324 |
| Extracting Melting Curves from Raw Fluorescence | p. 325 |
| Methods Used for Clustering and Classifying Melting Curves by Genotype | p. 332 |
| Methods Used for Modeling Melting Curves | p. 335 |
| References | p. 342 |
| Biomathematical Modeling of Pulsatile Hormone Secretion: A Historical Perspective | p. 345 |
| Introduction | p. 346 |
| Early Attempts to Identify and Characterize Pulsatile Hormone Release | p. 348 |
| Impact of Sampling Protocol and Pulse Detection Algorithm on Hormone Pulse Detection | p. 349 |
| Application of Deconvolution Procedures for the Identification and Characterization of Hormone Secretory Bursts | p. 351 |
| Limitations and Subsequent Improvements in Deconvolution Procedures | p. 352 |
| Evaluation of Pulsatile and Basal Hormone Secretion Using a Stochastic Differential Equations Model | p. 353 |
| Characterization of Regulation of Signal and Response Elements: Estimation of Approximate Entropy | p. 355 |
| Evaluation of Coupled Systems | p. 356 |
| Evaluation of Hormonal Networks with Feedback Interactions | p. 360 |
| Future Directions | p. 362 |
| Acknowledgments | p. 362 |
| References | p. 363 |
| AutoDecon: A Robust Numerical Method for the Quantification of Pulsatile Events | p. 367 |
| Introduction | p. 368 |
| Methods | p. 370 |
| Results | p. 384 |
| Discussion | p. 399 |
| Acknowledgments | p. 403 |
| References | p. 403 |
| Modeling Fatigue over Sleep Deprivation, Circadian Rhythm, and Caffeine with a Minimal Performance Inhibitor Model | p. 405 |
| Introduction | p. 406 |
| Methods | p. 407 |
| Results | p. 412 |
| Discussion | p. 414 |
| Acknowledgments | p. 419 |
| References | p. 419 |
| Author Index | p. 423 |
| Subject Index | p. 437 |
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