Computer methods. Part A

Title Page\r......Page 0
Copyright Page......Page 2
Contributors......Page 3
Preface......Page 7
Methods in Enzymology......Page 8
Phase Response Curves: Elucidating the Dynamics of Coupled Oscillators......Page 35
An example-phase response curve of cellular circadian rhythms......Page 36
Self-sustained biological rhythms......Page 38
Coupled and entrained oscillators......Page 39
Phase response curves......Page 41
Entrainment zones and circle map......Page 42
Limit cycle in phase space and phase response curves......Page 44
Definitions......Page 45
A skeleton protocol-a minimal phase response curve recipe......Page 46
Nonlinear dynamics of the heart......Page 51
Classifications of neurons......Page 52
Consequences of entrainment for insect communication......Page 53
Discussion......Page 54
Appendix I......Page 55
Appendix II......Page 57
References......Page 58
Multiple Ion Binding Equilibria, Reaction Kinetics, and Thermodynamics in Dynamic Models of Biochemical Pathways......Page 62
The physicochemical basis of biology......Page 63
Basic principles of chemical thermodynamics......Page 64
Simulating biochemical systems......Page 65
Thermodynamics of biochemical reactions......Page 67
Enzyme kinetics and the Haldane constraint......Page 68
Multiple cation equilibria in solutions: Apparent equilibrium constant, buffering of cations, and computing time courses of cations as a consequence of biochemical reaction networks......Page 69
Calculation of proton binding fraction for each metabolite using multiple cation equilibria......Page 70
Reference and biochemical reactions and the flux through an enzyme catalyzed reaction......Page 74
Apparent equilibrium constant and the Haldane constraint......Page 75
Ion mass balance and the differential equations for ion concentrations......Page 76
Multiple cation equilibria in solutions: Proton, magnesium, and potassium ion binding in the creatine kinase reaction......Page 81
Example of detailed kinetics of a biochemical reaction: Citrate synthase......Page 86
pH dynamics and glycogenolysis in cell free reconstituted systems and in skeletal muscle......Page 90
Cardiac energetics......Page 91
The gibbs free energy of ATP hydrolysis in the heart......Page 92
Calculations of DeltarGprimeoATPase and DeltaGATPase in the heart in vivo......Page 93
Example 2: Calculating Deltar GATPase at basal work rate in the heart in vivo......Page 94
Effects of changes in ion concentrations on DeltarGprimeo of biochemical reactions in the mitochondrial matrix......Page 95
Physiological significance of multiple ion binding equilibria, reaction kinetics, and thermodynamics in cardiac energetics......Page 96
Integrating thermodynamic information in biochemical model building......Page 97
Databases of biochemical information......Page 98
References......Page 99
Analytical Methods for the Retrieval and Interpretation of Continuous Glucose Monitoring Data in Diabetes......Page 102
Introduction......Page 103
Decomposition of Sensor Errors......Page 106
Measures of Average Glycemia and Deviation from Target......Page 107
Risk and Variability Assessment......Page 109
Measures and Plots of System Stability......Page 113
Time-Series-Based Prediction of Future BG Values......Page 114
References......Page 117
Analysis of Heterogeneity in Molecular Weight and Shape by Analytical Ultracentrifugation Using Parallel Distributed Computing......Page 120
Introduction......Page 121
Methodology......Page 122
Job Submission......Page 130
Example 1: Simulated five-component system......Page 133
Sample preparation......Page 137
Experimental results......Page 138
Conclusions......Page 142
References......Page 144
Discrete Stochastic Simulation Methods for Chemically Reacting Systems......Page 147
Introduction......Page 148
The Chemical Master Equation......Page 149
The Stochastic Simulation Algorithm......Page 151
The Tau-Leaping Method......Page 154
The hybrid SSA/tau-leaping strategy......Page 157
The tau-selection formula......Page 159
Measurement of Simulation Error......Page 164
StochKit: A stochastic simulation toolkit......Page 166
The LacZ/LacY model......Page 168
Conclusion......Page 169
References......Page 171
Analyses for Physiological and Behavioral Rhythmicity......Page 173
Introduction......Page 174
Types of Biological Data and Their Acquisition......Page 175
Analysis in the Time Domain......Page 177
Analysis in the Frequency Domain......Page 183
Time/Frequency Analysis and the Wavelet Transform......Page 193
Signal Conditioning......Page 196
Strength and Regularity of a Signal......Page 201
References......Page 203
A Computational Approach for the Rational Design of Stable Proteins and Enzymes: Optimization of Surface Charge-Charge Interactions......Page 207
Introduction......Page 208
Calculating pair wise charge-charge interaction energies......Page 215
Optimization of surface charges using the genetic algorithm......Page 220
Experimental Verification of Computational Predictions......Page 222
Single site substitutions - proof of concept and test of robustness of the TK-SA model......Page 223
Rational design of surface charge-charge interactions using a genetic algorithm......Page 229
Effects of stabilization on enzymatic activity......Page 232
Closing Remarks......Page 234
References......Page 236
Efficient Computation of Confidence Intervals for Bayesian Model Predictions Based on Multidimensional Parameter Space......Page 244
Introduction......Page 245
Height of the Probability Density Function at the Boundary of the Smallest Multidimensional Confidence Region......Page 246
Approximating a One-Dimensional Slice of the Probability Density Function by Means of Normal Curve Spline Pieces......Page 248
Locating the Boundary of the Smallest Multidimensional Confidence Region......Page 250
Finding the Minimum and Maximum of the Prediction Model over the Confidence Region......Page 251
An Application: Bayesian Forecasting of Cognitive Performance Impairment during Sleep Deprivation......Page 252
95% Confidence Intervals for Bayesian Predictions of Cognitive Performance Impairment during Sleep Deprivation......Page 254
Conclusion......Page 258
Appendix Proof That the Boundary of the Confidence Region for a Multidimensional, Continuous PDF is a Level Contour......Page 260
References......Page 261
Analyzing Enzymatic pH Activity Profiles and Protein Titration Curves Using Structure-Based pKa Calculations and Titration Curve Fitting......Page 263
Introduction......Page 264
Calculating the pH dependence of protein characteristics......Page 265
Equations describing protein ionization reactions......Page 266
Theory of protein pKa calculation methods......Page 267
Calculating electrostatic energies from protein structures......Page 269
Choosing a set of protein structures......Page 270
Crystal contacts......Page 271
Adapting the protein structure to the experimental conditions......Page 272
Modeling protein conformational change......Page 273
Extracting pKa values from calculated titration curves......Page 274
Accuracy of protein pKa calculation methods......Page 275
How Reliable are Calculated pKa Values?......Page 276
Sensitivity analysis......Page 277
Predicting pH Activity Profiles......Page 278
Decomposition Analysis......Page 279
Redesigning protein pKa values......Page 280
Predicting Protein Stability Profiles......Page 281
Fitting pH Titration Curves, pH Activity Profiles, and pH Stability Profiles......Page 282
Classic equations for fitting pH-dependent characteristics of proteins......Page 283
Conclusion......Page 285
References......Page 286
Least Squares in Calibration: Weights, Nonlinearity, and Other Nuisances......Page 289
Introduction......Page 290
Formal equations for linear least squares......Page 293
Simple illustrations......Page 296
Extensions and practical concerns......Page 298
Characterizing a nonlinear response function......Page 299
Uncertainty in the unknown......Page 304
Should I try a data transformation?......Page 306
Variance function estimation......Page 307
When chi2 is too large......Page 311
Conclusion......Page 312
References......Page 313
Evaluation and Comparison of Computational Models......Page 316
Conceptual Overview of Model Evaluation and Comparison......Page 317
Akaike Information Criterion and Bayesian Information Criterion......Page 321
Cross-Validation and Accumulative Prediction Error......Page 322
Bayesian Model Selection and Stochastic Complexity......Page 324
Model Comparison at Work: Choosing between Protein Folding Models......Page 326
Conclusions......Page 330
References......Page 332
Desegregating Undergraduate Mathematics and Biology-Interdisciplinary Instruction with Emphasis on Ongoing Biomedical Research......Page 334
Introduction......Page 335
Institutional context......Page 338
Features of the course......Page 339
Course structure......Page 340
Population studies......Page 341
Genetics......Page 342
Endocrinology......Page 343
Circadian rhythms......Page 345
Discussion......Page 346
References......Page 349
Mathematical Algorithms for High-Resolution DNA Melting Analysis......Page 351
Introduction......Page 352
Extracting Melting Curves from Raw Fluorescence......Page 353
Methods Used for Clustering and Classifying Melting Curves by Genotype......Page 360
Methods Used for Modeling Melting Curves......Page 363
References......Page 370
Biomathematical Modeling of Pulsatile Hormone Secretion: A Historical Perspective......Page 372
Introduction......Page 373
Early Attempts to Identify and Characterize Pulsatile Hormone Release......Page 375
Impact of Sampling Protocol and Pulse Detection Algorithm on Hormone Pulse Detection......Page 376
Application of Deconvolution Procedures for the Identification and Characterization of Hormone Secretory Bursts......Page 378
Limitations and Subsequent Improvements in Deconvolution Procedures......Page 379
Evaluation of Pulsatile and Basal Hormone Secretion Using a Stochastic Differential Equations Model......Page 380
Characterization of Regulation of Signal and Response Elements: Estimation of Approximate Entropy......Page 382
Evaluation of Coupled Systems......Page 383
Evaluation of Hormonal Networks with Feedback Interactions......Page 387
Acknowledgments......Page 389
References......Page 390
AutoDecon: A Robust Numerical Method for the Quantification of Pulsatile Events......Page 394
Introduction......Page 395
Overview of deconvolution method......Page 397
AutoDecon insertion module......Page 399
AutoDecon triage module......Page 400
AutoDecon combined modules......Page 401
Variation on the theme......Page 403
Weighting factors......Page 405
Experimental data......Page 406
Data simulation......Page 407
Algorithm operating characteristics......Page 409
Concordant secretion events......Page 410
Typical AutoDecon output......Page 411
Experimental data analysis......Page 412
Comparison between AutoDecon and other algorithms......Page 417
Optimal sampling paradigms for AutoDecon......Page 424
Discussion......Page 426
References......Page 430
Modeling Fatigue over Sleep Deprivation, Circadian Rhythm,and Caffeine with a Minimal Performance Inhibitor Model......Page 432
Introduction......Page 433
The Walter Reed Army Institute of Research Stay Alert caffeine gum study......Page 434
Data processing......Page 435
Caffeine modeling......Page 436
Performance inhibitor model......Page 437
Results......Page 439
Discussion......Page 441
References......Page 446
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