Johnson Essential Numerical Computer Methods

1. Auflage 2010
ISBN: 978-0-12-384998-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 616 Seiten

Reihe: Reliable Lab Solutions

The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide a general progression from basic numerical methods to more specific biochemical and biomedical applications. - The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception - As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology - These chapters provide a general progression from basic numerical methods to more specific biochemical and biomedical applications

Autoren/Hrsg.

Johnson, Michael L.

Inhaltsverzeichnis

1;Front Cover;1
2;Essential Numerical Computer Methods;4
3;Copyright;5
4;Contents;6
5;Contributors;14
6;Preface;16
7;Chapter 1: Use of Least-Squares Techniques in Biochemistry;18
7.1;I. Update;18
7.2;II. Introduction;19
7.3;III. Nonlinear Least-Squares;21
7.4;IV. Why Use NLLS Analysis Procedures?;23
7.5;V. When to Use NLLS Analysis Procedures;24
7.6;VI. What Confidence Can Be Assigned to Results of NLLS Analysis?;31
7.7;VII. Conclusions;37
7.8;References;39
8;Chapter 2: Parameter Estimates from Nonlinear Models;40
8.1;I. Introduction;41
8.2;II. Discussion;52
8.3;Acknowledgments;53
8.4;References;53
9;Chapter 3: Analysis of Residuals: Criteria for Determining Goodness-of-Fit;54
9.1;I. Update;54
9.2;II. Introduction;55
9.3;III. Scatter Diagram Residual Plots;57
9.4;IV. Cumulative Probability Distributions of Residuals;58
9.5;V. ?2 Statistic: Quantifying Observed Versus Expected Frequencies of Residual Values;60
9.6;VI. Kolmogorov-Smirnov Test: An Alternative to the ?2 Statistic;61
9.7;VII. Runs Test: Quantifying Trends in Residuals;62
9.8;VIII. Serial Lagn Plots: Identifying Serial Correlation;64
9.9;IX. Durbin-Watson Test: Quantitative Testing for Serial Correlation;64
9.10;X. Autocorrelation: Detecting Serial Correlation in Time Series Experiments;66
9.11;XI. ?2 Test: Quantitation of Goodness-of-Fit;67
9.12;XII. Outliers: Identifying Bad Points;68
9.13;XIII. Identifying Influential Observations;69
9.14;XIV. Conclusions;70
9.15;Acknowledgments;70
9.16;References;71
10;Chapter 4: Monte Carlo Method for Determining Complete Confidence Probability Distributions of Estimated Model Parameters;72
10.1;I. Update;72
10.2;II. Introduction;73
10.3;III. Monte Carlo Method;75
10.4;IV. Generating Confidence Probability Distributions for Estimated Parameters;75
10.5;V. Implementation and Interpretation;77
10.6;VI. Conclusion;82
10.7;Acknowledgments;83
10.8;References;83
11;Chapter 5: Effects of Heteroscedasticity and Skewnesson Prediction in Regression: ModelingGrowth of the Human Heart;84
11.1;I. Introduction;84
11.2;II. Example from Modeling Growth of the Human Heart;85
11.3;III. Methods of Estimation;87
11.4;IV. Discussion;95
11.5;Acknowledgments;96
11.6;References;96
12;Chapter 6: Singular Value Decomposition: Application to Analysis of Experimental Data;98
12.1;I. Update;99
12.2;II. Introduction;100
12.3;III. Definition and Properties;108
12.4;IV. Singular Value Decomposition of Matrices Which Contain Noise;110
12.5;V. Application of Singular Value Decomposition to Analysis of Experimental Data;124
12.6;VI. Simulations for a Simple Example: The Reaction A B C;137
12.7;VII. Summary;150
12.8;Acknowledgments;151
12.9;Appendix: Transformation of SVD Vectors to Optimize Autocorrelations;152
12.10;References;155
13;Chapter 7: Irregularity and Asynchrony in Biologic Network Signals;158
13.1;I. Update;159
13.2;II. Introduction;159
13.3;III. Quantification of Regularity;163
13.4;IV. Implementation and Interpretation;165
13.5;V. Representative Biological Applications;169
13.6;VI. Relationship to Other Approaches;171
13.7;VII. Mechanistic Hypothesis for Altered Regularity;175
13.8;VIII. Cross-ApEn;175
13.9;IX. Toward More Faithful Network Modeling;183
13.10;X. Spatial (Vector) ApEn;184
13.11;XI. Summary and Conclusion;186
13.12;References;187
14;Chapter 8: Distinguishing Models of Growth with Approximate Entropy;190
14.1;I. Update;190
14.2;II. Introduction;191
14.3;III. Definition and Calculation of ApEn;192
14.4;IV. Modifications of ApEn Calculation for this Application;193
14.5;V. Growth Models;194
14.6;VI. Expected Model-Dependent Distribution of ApEn;195
14.7;VII. Example of this Use of ApEn;196
14.8;VIII. Conclusion;199
14.9;Acknowledgments;201
14.10;References;201
15;Chapter 9: Application of the Kalman Filter to Computational Problems in Statistics;204
15.1;I. Introduction;204
15.2;II. Evaluating Gaussian Likelihood Using the Kalman Filter;206
15.3;III. Computing Posterior Densities for Bayesian Inference Using the Kalman Filter;209
15.4;IV. Missing Data Problems and the Kalman Filter;210
15.5;V. Extensions of the Kalman Filter Algorithm;213
15.6;References;213
16;Chapter 10: Bayesian Hierarchical Models;216
16.1;I. Introduction;216
16.2;II. The Gaussian Model;220
16.3;III. Computation;225
16.4;IV. Example: Meta-Regression;228
16.5;V. Example: Saltatory Model of Infant Growth;233
16.6;VI. Incorporation of Variance Components;236
16.7;VII. Model Checking;237
16.8;VIII. Conclusion;238
16.9;Acknowledgments;239
16.10;References;239
17;Chapter 11: Mixed-Model Regression Analysis and Dealing with Interindividual Differences;242
17.1;I. Introduction;243
17.2;II. Experiment and Data;244
17.3;III. Repeated-Measures ANOVA;245
17.4;IV. Mixed-Model Regression Analysis;252
17.5;V. An Alternative Linear Mixed-Effects Model;258
17.6;VI. Nonlinear Mixed-Model Regression Analysis;262
17.7;VII. Correlation Structures in Mixed-Model Regression Analysis;270
17.8;VIII. Conclusion;271
17.9;Acknowledgment;272
17.10;References;272
18;Chapter 12: Distribution Functions from Moments and the Maximum-Entropy Method;274
18.1;I. Introduction;274
18.2;II. Ligand Binding: Moments;276
18.3;III. Maximum-Entropy Distributions;282
18.4;IV. Ligand Binding: Distribution Functions;290
18.5;V. Enthalpy Distributions;296
18.6;VI. Self-Association Distributions;304
18.7;References;308
19;Chapter 13: The Mathematics of Biological Oscillators;310
19.1;I. Introduction;310
19.2;II. Oscillators and Excitability;311
19.3;III. Perturbations of Oscillators;316
19.4;IV. Coupled Oscillators;321
19.5;References;325
20;Chapter 14: Modeling of Oscillations in Endocrine Networks with Feedback;326
20.1;I. Introduction;326
20.2;II. General Principles in Endocrine Network Modeling;327
20.3;III. Simulating the Concentration Dynamics of a Single Hormone;329
20.4;IV. Oscillations Driven by a Single System Feedback Loop;332
20.5;V. Networks with Multiple Feedback Loops;347
20.6;VI. Summary and Discussion;350
20.7;Acknowledgments;352
20.8;References;353
21;Chapter 15: Boundary Analysis in Sedimentation Velocity Experiments;354
21.1;I. Update;355
21.2;II. Introduction;355
21.3;III. Methods of Data Acquisition;357
21.4;IV. Measurement of Transport in Analytical Ultracentrifuge;357
21.5;V. Traditional Methods of Analysis;358
21.6;VI. Transport Method;359
21.7;VII. Smoothing and Differentiating;361
21.8;VIII. Computation of Apparent Sedimentation Coefficient Distribution Functions;366
21.9;IX. Weight Average Sedimentation Coefficient from g(s*);371
21.10;X. Methods of Correcting Distribution Functions for Effects of Diffusion;374
21.11;XI. Discussion;375
21.12;References;375
22;Chapter 16: Statistical Error in Isothermal Titration Calorimetry;378
22.1;I. Update;378
22.2;II. Introduction;381
22.3;III. Variance-Covariance Matrix in Least Squares;383
22.4;IV. Monte Carlo Computational Methods;389
22.5;V. Van't Hoff Analysis of K(T): Least-Squares Demonstration;390
22.6;VI. Isothermal Titration Calorimetry;394
22.7;VII. Calorimetric Versus Van't HoffDeltaH from ITC;407
22.8;VIII. Conclusion;411
22.9;References;414
23;Chapter 17: Physiological Modeling with Virtual Cell Framework;416
23.1;I. Update;417
23.2;II. Introduction;418
23.3;III. Modeling Abstractions for Cellular Physiology;419
23.4;IV. Application to Existing Model;429
23.5;V. Conclusions;435
23.6;Acknowledgments;435
23.7;Appendix 1:. Physiological Model Description;435
23.8;Appendix 2:. Mathematical Description;438
23.9;References;441
24;Chapter 18: Fractal Applications in Biology: Scaling Time in Biochemical Networks;442
24.1;I. Update;443
24.2;II. Introduction;444
24.3;III. Fractal Morphology in Mammals: Some Branchings;447
24.4;IV. Chaos in Enzyme Reactions;454
24.5;V. Practical Guide to Identification of Chaos and Fractals in Biochemical Reactions;455
24.6;VI. Summary, or What Does It All Mean?;457
24.7;VII. Glossary;459
24.8;References;475
25;Chapter 19: Analytical Methods for the Retrieval and Interpretation of Continuous Glucose Monitoring Data in Diabetes;478
25.1;I. 2010 Update of Developments in the Field;479
25.2;II. Introduction;480
25.3;III. Decomposition of Sensor Errors;483
25.4;IV. Measures of Average Glycemia and Deviation from Target;484
25.5;V. Risk and Variability Assessment;486
25.6;VI. Measures and Plots of System Stability;489
25.7;VII. Time-Series-Based Prediction of Future BG Values;490
25.8;VIII. Conclusions;493
25.9;Acknowledgments;493
25.10;References;493
26;Chapter 20: Analyses for Physiological and Behavioral Rhythmicity;496
26.1;I. Introduction;496
26.2;II. Types of Biological Data and Their Acquisition;497
26.3;III. Analysis in the Time Domain;499
26.4;IV. Analysis in the Frequency Domain;505
26.5;V. Time/Frequency Analysis and the Wavelet Transform;513
26.6;VI. Signal Conditioning;519
26.7;VII. Strength and Regularity of a Signal;522
26.8;VIII. Some Practical Considerations on Statistical Comparisons ofAnalytical Results;523
26.9;IX. Conclusions;524
26.10;References;525
27;Chapter 21: Evaluation and Comparison of Computational Models;528
27.1;I. Update;529
27.2;II. Introduction;530
27.3;III. Conceptual Overview of Model Evaluation and Comparison;530
27.4;IV. Model Comparison Methods;533
27.5;V. Model Comparison at Work: Choosing Between Protein Folding Models;538
27.6;VI. Conclusions;542
27.7;Acknowledgments;543
27.8;References;543
28;Chapter 22: Algebraic Models of Biochemical Networks;546
28.1;I. Introduction;547
28.2;II. Computational Systems Biology;548
28.3;Example 1;551
28.4;Definition 1;555
28.5;Definition 2;556
28.6;Example 2;556
28.7;III. Network Inference;558
28.8;IV. Reverse-Engineering of Discrete Models: An Example;562
28.9;Definition 3;563
28.10;Definition 4;563
28.11;Example 3;563
28.12;V. Discussion;570
28.13;References;573
29;Chapter 23: Monte Carlo Simulation in Establishing Analytical Quality Requirements for Clinical Laboratory Tests: Meeting Clinical Needs;578
29.1;I. Update;579
29.2;II. Introduction;580
29.3;III. Modeling Approach;583
29.4;IV. Methods for Simulation Study;584
29.5;V. Results;585
29.6;VI. Discussion;597
29.7;References;599
30;Chapter 24: Pancreatic Network Control of Glucagon Secretion and Counterregulation;602
30.1;I. Update;603
30.2;II. Introduction;605
30.3;III. Mechanisms of Glucagon Counterregulation (GCR) Dysregulation in Diabetes;606
30.4;IV. Interdisciplinary Approach to Investigating the Defects in the GCR;608
30.5;V. Initial Qualitative Analysis of the GCR Control Axis;609
30.6;VI. Mathematical Models of the GCR Control Mechanisms in STZ-Treated Rats;612
30.7;VII. Approximation of the Normal Endocrine Pancreas by a Minimal Control Network (MCN) and Analysis of the GCR Abnormalities in the Insulin-Deficient Pancreas;615
30.8;VIII. Advantages and Limitations of the Interdisciplinary Approach;626
30.9;IX. Conclusions;629
30.10;Acknowledgment;629
30.11;References;629
31;Index;636