OJAppS  Vol.2 No.1 , March 2012
A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism
ABSTRACT
When realistic mathematical models of whole body metabolism eventually become available, they are likely to add entirely new dimensions to the understanding of the integrated physiological function of the organism, in particular the mechanisms governing the regulation of transitions between different physiological states, like fed-fasted, exercise-rest and normal-diseased. So far the strategy for whole body modelling has primarily been a bottom-up approach where the central problem is an apparently insurmountable barrier of complexity involved in defining and optimising the huge number of parameters. Here we follow a top-down strategy and present a complete mathematical framework for realistic whole body model development. The approach proposed is modular and hierarchical and whole body metabolism is taken as the top level. Next are the organs, where the sum of the contributions from the individual organs must equal the top level metabolism. This hierarchy can be extended to lower levels of organisation, i.e. clusters of cells, individual cells, organelle and individual pathways. Exploiting this hierarchy, metabolism at each level forms an absolute constraint on the contributions from lower level. Importantly, these constraints can in many ways be defined experimentally through mass balance and flux data. Furthermore, the constrained approach allows the lower level models to be developed independently and subsequently adapted to the whole body model. The paper describes the process of whole body modelling in practical terms, centred on a mathematical framework, devised to allow whole-body models of any complexity to be developed. Furthermore, an example of sub-model incorporation in the whole-body framework is illustrated by adapting an existing erythrocyte model to the whole body constraints. Finally, we illustrate the operation of the system by including two sets of whole-body data from humans, reflecting two different physiological states.

Cite this paper
nullM. Madsen, S. Dano and B. Quistorff, "A Strategy for Development of Realistic Mathematical Models of Whole-Body Metabolism," Open Journal of Applied Sciences, Vol. 2 No. 1, 2012, pp. 11-27. doi: 10.4236/ojapps.2012.21002.
References
[1]   R. Gebhardt, “Heterogeneous Intrahepatic Distribution of Glutamine Synthetase,” Acta Histochemica, Supplement, Vol. 40, 1990, pp. 23-28.

[2]   C. Cori, “Mammalian Carbohydrate Metabolism,” Physo- logical Reviews, Vol. 11, No. 2, 1931, pp. 143-275.

[3]   N. Secher and B. Quistorff, “Brain Glucose and Lactate Uptake during Exhaustive Exercise,” Journal of Physi- ology, Vol. 568, 2005, p. 3. doi:10.1113/jphysiol.2005.095786

[4]   L. Sokoloff, “Metabolism of Ketone Bodies by the Brain,” Annual Review of Medicine, Vol. 24, No. 1, 1973, pp. 271-280. doi:10.1146/annurev.me.24.020173.001415

[5]   S. Hasselbalch, P. Madsen, L. Hageman, K. Olsen, N. Justesen, S. Holm, et al., “Changes in Cerebral Blood Flow and Carbohydrate Metabolism during Acute Hy- perketonemia,” Endocrinology and Metabolism, Vol. 270, No. 5, 1996, pp. 746-751.

[6]   S. Kahn, R. Hull and K. Utzschneider, “Mechanisms Linking Obesity to Insulin Resistance and Type 2 Diabetes,” Nature, Vol. 444, 2006, pp. 840-846. doi:10.1038/nature05482

[7]   E. Rosen and B. Spiegelman, “Adipocytes as Regulators of Energy Balance and Glucose Homeostasis,” Nature, Vol. 444, 2006, pp. 847-853. doi:10.1038/nature05483

[8]   C. Wang, C. Wang and Y. Wei, “Mitochondrial Dysfunction in Insulin Insensitivity: Implication of Mitochondrial Role in Type 2 Diabetes.” Annals of the New York Academy of Sciences, Vol. 1201, 2010, pp. 157-65. doi:10.1111/j.1749-6632.2010.05625.x

[9]   P. Mulquiney and P. Kuchel, “Model of 2,3-Bispho- sphoglycerate Metabolism in the Human Erythrocyte Based on Detailed Enzyme Kinetic Equations: Equations and Parameter Refinement,” Biochemical Journal, Vol. 342, 1999, pp. 567-580. doi:10.1042/0264-6021:3420567

[10]   B. Hald, M. Madsen, S. Dan?, B. Quistorff and P. S?rensen, “Quantitative Evaluation of Respiration Induced Meta- bolic Oscillations in Erythrocytes,” Biophysical Chemistry, Vol. 141, No. 1, 2009, pp. 41-8. doi:10.1016/j.bpc.2008.12.008

[11]   J. Tyson and B. Novak, “Regulation of the Eukaryotic Cell Cycle: Molecular Antagonism, Hysteresis, and Irreversible Transitions,” Journal of Theoretical Biology, Vol. 210, 2001, pp. 249-263.

[12]   R. Hafner, G. Brown and M. Brand, “Analysis of the Control of Respiration Rate, Phosphorylation Rate, Proton Leak Rate and Protonmotive Force in Isolated Mitochondria Using the ‘Top-Down’ Approach of Metabolic Control Theory,” FEBS Journal, Vol. 188, No. 2, 1990, pp. 313-319.

[13]   J. Hofmeyr and A. Cornish-Bowden, “Regulating the Cel- lular Economy of Supply and Demand,” FEBS Letters, Vol. 476, No. 1, 2000, pp. 47-51. doi:10.1016/S0014-5793(00)01668-9

[14]   J. Ciapaite, G. Van Eikenhorst, S. Bakker, M. Diamant, R. Heine, M. Wagner, et al., “Modular Kinetic Analysis of the Adenine Nucleotide Translocator-Mediated Effects of Palmitoyl-CoA on the Oxidative Phosphorylation in Isolated Rat Liver Mitochondria,” Diabetes, Vol. 54, No. 4, 2005, p. 944. doi:10.2337/diabetes.54.4.944

[15]   D. Kahn and H. Westerhoff, “Control Theory of Regulatory Cascades,” Journal of Theoretical Biology, Vol. 153, No. 2, 1991, pp. 255-285. doi:10.1016/S0022-5193(05)80426-6

[16]   M. Brand, “Top Down Metabolic Control Analysis,” Jour- nal of Theoretical Biology, Vol. 182, No. 3, 1996, pp. 351-360. doi:10.1006/jtbi.1996.0174

[17]   S. Schuster, D. Kahn and H. Westerhoff, “Modular Analysis of the Control of Complex Metabolic Pathways,” Biophysical Chemistry, Vol. 48, No. 1, 1993, pp. 1-17. doi:10.1016/0301-4622(93)80037-J

[18]   C. Csajka and D. Verotta, “Pharmacokinetic-Pharmaco- dynamic Modelling: History and Perspectives,” Journal of Pharmacokinet and Pharmacodyn, Vol. 33, No. 3, 2006, pp. 227-279. doi:10.1007/s10928-005-9002-0

[19]   I. Nestorov, “Whole Body Pharmacokinetic Models,” Cli- nical Pharmacokinetics, Vol. 42, No. 10, 2003, pp. 883- 908. doi:10.2165/00003088-200342100-00002

[20]   A. Edginton, F. Theil, W. Schmitt and S. Willmann, “Whole Body Physiologically-Based Pharmacokinetic Models: Their Use in Clinical Drug Development,” Expert Opinion on Drug Metabolism and Toxicology, Vol. 4, No. 9, 2008, pp. 1143-52. doi:10.1517/17425255.4.9.1143

[21]   A. Kansal, “Modeling Approaches to Type 2 Diabetes,” Diabetes Technology & Therapeutics, Vol. 6, No. 1, 2004, pp. 39-47. doi:10.1089/152091504322783396

[22]   H. Kitano, K. Oda, T. Kimura, Y. Matsuoka, M. Csete, J. Doyle, et al., “Metabolic Syndrome and Robustness Tra- deoffs,” Diabetes, Vol. 53, No. 3, 2004, pp. 6-15. doi:10.2337/diabetes.53.suppl_3.S6

[23]   M. Hjelm and J. Seakins, “Modeling Amino Acid Metabolism,” Amino Acids, Vol. 3, No. 1, 1992, pp. 1-23. doi:10.1007/BF00806006

[24]   G. Cedersund and P. Str?lfors, “Putting the Pieces Together in Diabetes Research: Towards a Hierarchical Model of Whole-Body Glucose Homeostasis,” European Journal of Pharmaceutical Sciences, Vol. 36, No. 31, 2009, pp. 91-104.

[25]   R. Bergman, L. Philips and C. Cobelli, “Physiologic Evaluation of Factors Controlling Glucose Tolerance in Man,” Journal of Clinical Investigation, Vol. 68, No. 6, 1981, pp.1456-1467. doi:10.1172/JCI110398

[26]   R. Basu, B. Camillo, G. Toffolo, A. Basu, P. Shah, A. Vella, et al., “Use of a Novel Triple-Tracer Approach to Assess Postprandial Glucose Metabolism,” American Journal of Physiology-Endocrinology and Metabolism, Vol. 284, No. 1, 2003, pp. 55-69.

[27]   C. Man, R. Rizza and C. Cobelli, “Meal Simulation Model of the Glucose-Insulin System,” IEEE Transactions on Biomedical Engineering, Vol. 54, No. 10, 2007, pp. 1740-1749. doi:10.1109/TBME.2007.893506

[28]   J. Kim, G. Saidel and M. Cabrera, “Multi-Scale Computational Model of Fuel Homeostasis during Exercise: Effect of Hormonal Control,” Annals of Biomedical Engineering, Vol. 35, No. 1, 2007, pp. 69-90. doi:10.1007/s10439-006-9201-x

[29]   D. Noble, “Modeling the Heart—From Genes to Cells to the Whole Organ,” Science, Vol. 295, No. 5560, 2002, pp. 1678-1682. doi:10.1126/science.1069881

[30]   S. Yeo, J. Kim, S. Lee, F. Park, W. Park, J. Kim, et al., “A Modular Object-Oriented Framework for Hierarchical Multi-Resolution Robot Simulation,” Robotica, Vol. 22, No. 2, 2004, pp. 141-154. doi:10.1017/S0263574703005435

[31]   C. Barwell and B. Hess, “Application of Kinetics of Yeast Pyruvate Kinase in Vitro to Calculation of Glycolytic Flux in the Anaerobic Yeast Cell,” Hoppe-Seyler’s Zeitschrift für Physiologische Chemie, Vol. 353, No. 2, 1972, pp. 1178-1184. doi:10.1515/bchm2.1972.353.2.1178

[32]   B. Wright and P. Kelly, “Kinetic Models of Metabolism in Intact Cells, Tissues, and Organisms,” Current Topics in Cellular Regulation, Vol. 19, 1981, pp. 103-158.

[33]   B. Teusink, J. Passarge, C. A. Reijenga, E. Esgalhado, C. C. van der Weijden, M. Schepper, et al., “Can Yeast Glycolysis be Understood in Terms of in Vitro Kinetics of the Constituent Enzymes? Testing Biochemistry,” European Journal of Biochemistry, Vol. 267, No. 17, 2000, pp. 5313-5329.

[34]   I. Famili, R. Mahadevan and B. Palsson, “k-Cone Analysis: Determining All Candidate Values for Kinetic Parameters on a Network Scale,” Biophysical Journal, Vol. 88, No. 3, 2005, pp. 1616-1625. doi:10.1529/biophysj.104.050385

[35]   P. A. Srere, “Macromolecular Interactions: Tracing the Roots,” Trends in Biochemical Sciences, Vol. 25, No. 3, 2000, pp. 150-153. doi:10.1016/S0968-0004(00)01550-4

[36]   J. Ovadi and V. Saks, “On the Origin of Intracellular Compartmentation and Organized Metabolic Systems,” Molecular and Cellular Biochemistry, Vol. 256-257, No. 1-2, 2004, pp. 5-12.

[37]   S. Schnell and T. Turner, “Reaction Kinetics in Intracellular Environments with Macromolecular Crowding: Simulations and Rate Laws,” Progress in Biophysics and Molecular Biology, Vol. 85, No. 2-3, 2004, pp. 235-260.

[38]   G. Reichel, “Waste-Water—A Library for Modelling and Simulation of Wastewater Treatment Plants in Modelica,” Proceeding of the 3rd International Modelica Conference, Lindk?ping, 2003, pp. 171-176.

[39]   P. Fritzson, “Principles of Object-Oriented Modeling and Simulation with Modelica 2.1,” Wiley-IEEE Press, 2004. doi:10.1109/9780470545669

[40]   A. Fick, “Uber die Messung des Blutquantums in den Herzventrikeln,” Seitung der Physikalisches und Medicinisches Gesellschaft zu Würzburg, Vol. 2, 1870, pp. 290-291.

[41]   P. Rasmussen, P. Plomgaard, R. Krogh-Madsen, Y. Kim, N. Secher and B. Quistorff, “MCA Vmean and the Arterial Lactate-to-Pyruvate Ratio Correlate during Rhythmic Handgrip,” Journal of Applied Physiology, Vol. 101, No. 5, 2006, pp. 1406-1411. doi:10.1152/japplphysiol.00423.2006

[42]   P. Rasmussen, N. Nyberg, J. Jaroszewski, R. Krogh- Madsen, N. Secher and B. Quistorff, “Brain Nonoxidative Carbohydrate Consumption Is Not Explained by Export of an Unknown Carbon Source: Evaluation of the Arterial and Jugular Venous Metabolome,” Journal of Cerebral Blood Flow & Metabolism, Vol. 30, No. 6, 2010, pp. 1240-1246. doi:10.1038/jcbfm.2010.25

[43]   B. Quistorff, N. Secher and J. Van Lieshout, “Lactate Fuels the Human Brain during Exercise,” FASEB Journal, Vol. 22, No. 10, 2008, pp. 3443-3449. doi:10.1096/fj.08-106104

[44]   P. Rasmussen, C. Madsen, H. Nielsen, M. Zaar, A. Gjedde, N. Secher, et al., “Coupling between the Blood Lactate-to-Pytuvate Ratio and MCA Vmean at the Onset of Exercise in Humans,” Journal of Applied Physiology, Vol. 107, No. 6, 2009, pp. 1799-805. doi:10.1152/japplphysiol.00468.2009

[45]   G. Van Hall, M. Str?mstad, P. Rasmussen, O. Jans, M. Zaar, C. Gam, et al., “Blood Lactate Is an Important Energy Source for the Human Brain,” Journal of Cerebral Blood Flow & Metabolism, Vol. 29, No. 6, 2009, pp. 1121-9. doi:10.1038/jcbfm.2009.35

[46]   F. Hynne, S. Dan? and P. G. Sorensen, “Full-Scale Model of Glycolysis in Saccharomyces Cerevisiae,” Biophysical Chemistry, Vol. 94, No. 1-2, 2001, pp. 121-163. doi:10.1016/S0301-4622(01)00229-0

[47]   B. Clarke, “Stability of Complex Reaction Networks,” Advances in Chemical Physics, Vol. 43, 1980, pp. 1-215. doi:10.1002/9780470142622.ch1

[48]   M. Kozlov, S. Tarasov and L. Khachiyan, “Polynomial Solvability of Convex Quadratic Programming,” Soviet Mathematics Doklady, Vol. 20, 1979, pp. 1108-1111.

[49]   H. Sherali and C. H. Tuncbilek, “A Global Optimization Algorithm for Polynomial Programming Problems Using a Reformulation-Linearization Technique,” Journal of Global Optimization, Vol. 2, No. 1, 1992, pp. 101-112. doi:10.1007/BF00121304

[50]   Y.-J. Chang and B. W. Wah, “Polynomial Programming Using Groebner Bases,” Computer Software and Applications Conference, Taiwan, 9-11 November 1994, pp. 236- 241.

[51]   H. Nielsen, M. Febbraio, P. Ott, P. Krustrup and N. Secher, “Hepatic Lactate Uptake versus Leg Lactate Output during Exercise in Humans,” Journal of Applied Physiology, Vol. 103, No. 4, 2007, pp. 1227-33. doi:10.1152/japplphysiol.00027.2007

[52]   H. Nielsen, N. Secher, O. Clemmesen and P. Ott, “Maintained Cerebral and Skeletal Muscle Oxygenation during Maximal Exercise in Patients with Liver Cirrhosis,” Journal of Hepatology, Vol. 43, No. 2, 2005, pp. 266-271. doi:10.1016/j.jhep.2005.02.039

[53]   U. Sauer, “Metabolic Networks in Motion: 13C-Based Flux Analysis,” Molecular Systems Biology, Vol. 2, No. 14, 2006, p. 62. doi:10.1038/msb4100109

[54]   L. Nybo, M. Dalsgaard, A. Steensberg, K. Moller and N. Secher, “Cerebral Ammonia Uptake and Accumulation during Prolonged Exercise in Humans,” Journal of Physiology, Vol. 563, Pt. 1, 2005, pp. 285-290. doi:10.1113/jphysiol.2004.075838

[55]   M. Dalsgaard, B. Quistorff, E. Danielsen, C. Selmer, T. Vogelsang and N. Secher, “A Reduced Cerebral Metabolic Ratio in Exercise Reflects Metabolism and Not Accumulation of Lactate within the Human Brain,” Journal of Physiology, Vol. 554, Pt. 2, 2004, pp. 571-578. doi:10.1113/jphysiol.2003.055053

[56]   M. Dalsgaard, F. Madsen, N. Secher, H. Laursen and B. Quistorff, “High Glycogen Levels in the Hippocampus of Patients with Epilepsy,” Journal of Cerebral Blood Flow & Metabolism, Vol. 27, 2007, pp. 1137-41. doi:10.1038/sj.jcbfm.9600426

[57]   R. Shulman and D. Rothman, “13C NMR of Intermediary Metabolism: Implications for Systemic Physiology,” Annual Review of Physiology, Vol. 63, 2001, pp. 15-48. doi:10.1146/annurev.physiol.63.1.15

[58]   M. Hucka, A. Finney, H. M. Sauro, H. Bolouri, J. C. Doyle, H. Kitano, et al., “The Systems Biology Markup Language (SBML): A Medium for Representation and Exchange of Biochemical Network Models,” Bioinformatics, Vol. 19, No. 4, 2003, pp. 524-531. doi:10.1093/bioinformatics/btg015

[59]   H. Schmidt and M. Jirstrand, “Systems Biology Toolbox for MATLAB: A Computational Platform for Research in Systems Biology,” Bioinformatics, Vol. 22, No. 4, 2006, pp. 514-515. doi:10.1093/bioinformatics/bti799

[60]   K. Frayn, “Metabolic Regulation: A Human Perspective,” Portland Press, Portland, 2001.

[61]   T. Devlin, “Textbook of Biochemistry,” Wiley-Liss Incorporated, Wilmington, 1997.

[62]   E. Newsholme and A. Leech, “Biochemistry for the Medical Sciences,” John Wiley & Sons, New York, 1984.

[63]   L. Williams and R. Leggett, “Reference Values for Resting Blood Flow to Organs of Man,” Clinical Physics and Physiological Measurement, Vol. 10, No. 3, 1989, pp. 187-217. doi:10.1088/0143-0815/10/3/001

[64]   W. Boron and E. Boulpaep, “Medical Physiology,” Saunders Press, Philadelphia, 2003.

[65]   A. C. Guyton, C. E. Jones and T. G. Coleman, “Circulatory Physiology: Cardiac Output and Its Regulation,” 2nd Edition, W. B. Saunders Company, Philadelphia, 1973.

 
 
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