Mathematical Modeling in Experimental Nutrition: Vitamins, Proteins, Methods (eBook)

Front Cover 1
Advances in Food and Nutrition Research, Volume 40 4
Copyright Page 5
Contents 6
Contributors to Volume 40 14
Preface 20
Editor's Note 22
PART I: VITAMIN METABOLISM 24
Chapter 1. Quantitative and Conceptual Contributions of Mathematical Modeling to Current Views on Vitamin A Metabolism, Biochemistry, and Nutrition 26
I. Introduction 26
II. Historical Perspective and Early Studies 27
III. Experimental Considerations 28
IV. Whole-Body Models for Vitamin A Metabolism 31
V. Empirical Compartmental Analysis of Vitamin A Metabolism 34
VI. Liver Vitamin A Metabolism 37
VII. Other Tissues 42
VIII. Vitamin A Disposal Rate 44
References 45
Chapter 2. Mathematical Modeling in Nutrition: Constructing a Physiologic Compartmental Model of the Dynamics of ß-Carotene Metabolism 48
I. Introduction and Background 49
II. Materials, Methods, and Model Constraints 52
III. The Process of Constructing a Compartmental Model 55
IV. Intermediate Models 58
V. Statistical Considerations 63
VI. The Final Model 66
VII. System Behavior Proposed by the Model 66
VIII. Unobservable System Behavior Proposed by the Model 68
IX. Empirical Description of the Experimental Observations 72
X. Final Encouraging Words 74
References 75
Chapter 3. Experimental Approaches to the Study of ß-Carotene Metabolism: Potential of a 13C Tracer Approach to Modeling ß-Carotene Kinetics in Humans 78
I. Introduction 79
II. Methods 88
Ill. Results and Discussion 91
IV. Conclusions 97
References 98
Chapter 4. Modeling of Folate Metabolism 104
I. Introduction 104
II. Key Elements of Folate Metabolism Relevant to Modeling 106
III. Stable-Isotopic Studies in Humans 109
IV. Summary and Conclusions 114
References 114
Chapter 5. Molecular Biology in Nutrition Research: Modeling of Folate Metabolism 118
I. General Approaches 118
II. Modeling of Folate Metabolism 119
References 128
Chapter 6. Modeling Vitamin B6 Metabolism 130
I. Metabolism 130
II. Kinetics 136
III . Refining Models of Vitamin B6 Kinetics 140
IV. Conclusions 150
References 150
PART II: PROTEIN AND AMINO ACID METABOLISM 156
Chapter 7. Interrelationships between Metabolism of Glycogen Phosphorylase and Pyridoxal Phosphate—Implications in McArdle’s Disease 158
I. Introduction 159
II. Role of Cofactor in Phosphorylase Turnover 159
III. Labeling Methods to Monitor Phosphorylase Turnover 160
IV. Model Systems for Phosphorylase Expression 163
V. Vitamin B6 and McArdle’s Disease 165
References 169
Chapter 8. Metabolism of Normal and Met30 Transthyretin 172
I. Introduction 173
II. Methods 173
III. Results 175
IV. Discussion 177
References 178
Chapter 9. Use of a Four Parameter Logistic Equation and Parameter Sharing to Evaluate Animal Responses to Graded Levels of Nitrogen or Amino Acids 180
I. Diminishing Returns and Dose–Response Relationships 180
II.Diminishing Returns and Protein Quality 183
III. Response of Rats to Each Indispensable Amino Acid 185
References 189
PART III: ENERGY METABOLISM 192
Chapter 10. Total Energy Expenditure of Free-Living Humans Can Be Estimated with the Doubly Labeled Water Method 194
I. Introduction 194
II. Theory of the 2H218O Method 195
III. Analytical Methods 198
IV. Validations of the 2H218O Method 201
V. Conclusion 202
References 202
PART IV: METHODS FOR OBTAINING KINETIC DATA 204
Chapter 11. Microdialysis and Ultrafiltration 206
I. Introduction 206
II. Comparison of Microdialysis and Ultrafiltration 207
III. Examples of Studies Using Microdialysis and Ultrafiltration 214
IV. Summary 218
References 218
Chapter 12. Membrane Vesicles 220
I. Introduction 220
II. Methods 221
III. Discussion 226
References 227
Chapter 13. Culture of Mammary Tissue: Glucose Transport Processes 230
I. Introduction 230
II. Materials and Methods 231
III. Results and Discussion 232
IV. Conclusions 235
References 236
PART V: SIMULATING COMPLEX METABOLIC PROCESSES 238
Chapter 14. Analysis of Bioperiodicity in Physiological Responses 240
I. Bioperiodicity 240
II. Characterization of Biological Rhythms 241
III. Experimental Conditions 243
IV. Evaluation of Results 243
V. Discussion 247
References 249
Chapter 15. Nutrient–Response: A “Top Down” Approach to Metabolic Control 250
I. Introduction 250
II. Mathematical Treatment 251
III. Analysis of Data on Three Dietary Proteins 261
IV. Conclusions 263
References 264
Chapter 16. Modeling Membrane Transport 266
I. Introduction 266
II. A Multiregion, Distributed Exchange Model 268
III. Passive Diffusion 271
IV. Carrier-Mediated Transport 274
V. Building Complex Models 281
VI. Summary 283
References 284
PART VI: COMPUTATIONAL ASPECTS OF MODELING 286
Chapter 17. Estimation and Use of Kinetic Parameter Distributions in Metabolism and Nutrition 288
I. Introduction 288
II. Definitions and Theory 289
III. Uses for Prior Parameter Distributions 292
IV. Applications to Metabolism and Nutrition 294
V. Estimation of Prior Parameter Distributions 296
VI. Identifiability Issues 299
VII. Conclusions 301
References 301
Chapter 18. Essential Numerical Supports for Kinetic Modeling Software: Linear Integrators 304
I. Introduction 304
II. Linear Systems of Differential Equations 306
III. Modeling Software and Linear Integrators 313
IV. Conclusion 323
References 326
Chapter 19. Identifiability 328
I. Introduction 328
II. Examples 330
III. Classification of Parameters 333
IV. Parameter Identifiability and Estimation 334
V. Identifiability: Definitions 336
VI. Methods of Checking Identifiability 337
VII. Local Identifiability at a Point 341
VIII. Conclusion 343
References 344
Chapter 20. Dynamic Systems and Neural Networks: Modeling in Physiology and Medicine 346
I. Introduction 346
II. Linear Systems Modeling 347
III. Nonlinear Systems, Chaos, and Fractional Dimensions 347
VI. Geometric Interpretation of Models and Dynamical Systems 351
V. Neural Networks 356
VI. Conclusion 360
References 360
Chapter 21. Graph Theoretical Methods for Physiologically Based Modeling 362
I. Introduction 362
II. The Graph Model 363
III. Computer Implementation 371
IV. Analysis of Models 371
References 374
Index 376