Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Dynamic flux balance analysis of whole-body metabolism for type 1 diabetes

A preprint version of the article is available at bioRxiv.

Abstract

Type 1 diabetes (T1D) mellitus is a systemic disease triggered by a local autoimmune inflammatory reaction in insulin-producing cells that induce organ-wide, long-term metabolic effects. Mathematical modeling of the whole-body regulatory bihormonal system has helped to identify therapeutic interventions but is limited to a coarse-grained representation of metabolism. To extend the depiction of T1D, we developed a whole-body model of organ-specific regulation and metabolism that highlighted chronic inflammation as a hallmark of the disease, identified processes related to neurodegenerative disorders and suggested calcium channel blockers as adjuvants for diabetes control. In addition, whole-body modeling of a patient population allowed for the assessment of between-individual variability to insulin and suggested that peripheral glucose levels are degenerate biomarkers of the internal metabolic state. Taken together, the organ-resolved, dynamic modeling approach enables modeling and simulation of metabolic disease at greater levels of coverage and precision and the generation of hypothesis from a molecular level up to the population level.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Applied constraints from GIM model to WBM.
Fig. 2: Whole-body reaction flux dynamics classify T1D and healthy states.
Fig. 3: Multiscale whole-body model identified disrupted metabolic processes in T1D mellitus.
Fig. 4: Insulin metabolic indirect effects assessed by the probability density estimates of the reaction flux values.
Fig. 5: Interindividual variability in insulin response is reflected in key pathways of metabolism.
Fig. 6: Intraindividual variability is assessed through a sensitivity analysis of the integrated model.

Similar content being viewed by others

Data availability

The male whole-body metabolic model10 is available at the Virtual Metabolic Human48 database (http://vmh.life), the glucose–insulin model6 is available at https://github.com/Open-Systems-Pharmacology/Glucose-Insulin-Model. Source data for Figs. 26 are provided with this paper and in Zenodo64.

Code availability

All related code is available at https://github.com/ThieleLab/dwbm and in Zenodo64.

References

  1. Maahs, D. M., West, N. A., Lawrence, J. M. & Mayer-Davis, E. J. Epidemiology of type 1 diabetes. Endocrinol. Metab. Clin. North Am. 39, 481–497 (2010).

    Article  Google Scholar 

  2. Orchard, T. J., Costacou, T., Kretowski, A. & Nesto, R. W. Type 1 diabetes and coronary artery disease. Diabetes Care 29, 2528–2538 (2006).

    Article  Google Scholar 

  3. Thomas, N. J. et al. Frequency and phenotype of type 1 diabetes in the first six decades of life: a cross-sectional, genetically stratified survival analysis from UK Biobank. Lancet Diabetes Endocrinol. 6, 122–129 (2018).

    Article  Google Scholar 

  4. American Diabetes, A. Diagnosis and classification of diabetes mellitus. Diabetes Care 33, S62–S69 (2010).

    Article  Google Scholar 

  5. Heinemann, L. Variability of insulin absorption and insulin action. Diabetes Technol. Ther. 4, 673–682 (2002).

    Article  Google Scholar 

  6. Schaller, S. et al. A generic integrated physiologically based whole-body model of the glucose–insulin–glucagon regulatory system. CPT Pharmacomet. Syst. Pharm. 2, e65 (2013).

    Article  Google Scholar 

  7. Wadehn, F., Schaller, S., Eissing, T., Krauss, M. & Küpfer, L. A multiscale, model-based analysis of the multi-tissue interplay underlying blood glucose regulation in type I diabetes. In Proc. 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE, 2016).

  8. Schaller, S. et al. Robust PBPK/PD-based model predictive control of blood glucose. IEEE Trans. Biomed. Eng. 63, 1492–1504 (2016).

    Article  Google Scholar 

  9. Lahoz-Beneytez, J. et al. Physiologically based simulations of deuterated glucose for quantifying cell turnover in humans. Front. Immunol. 8, 474 (2017).

    Article  Google Scholar 

  10. Thiele, I. et al. Personalized whole-body models integrate metabolism, physiology, and the gut microbiome. Mol. Syst. Biol. 16, e8982 (2020).

    Article  Google Scholar 

  11. Brunk, E. et al. Recon3D enables a three-dimensional view of gene variation in human metabolism. Nat. Biotechnol. 36, 272–281 (2018).

    Article  Google Scholar 

  12. Karr, J. R. et al. A whole-cell computational model predicts phenotype from genotype. Cell 150, 389–401 (2012).

    Article  Google Scholar 

  13. Grafahrend-Belau, E. et al. Multiscale metabolic modeling: dynamic flux balance analysis on a whole-plant scale. Plant Physiol. 163, 637–647 (2013).

    Article  Google Scholar 

  14. Krauss, M. et al. Integrating cellular metabolism into a multiscale whole-body model. PLoS Comput. Biol. 8, e1002750 (2012).

    Article  Google Scholar 

  15. Cordes, H., Thiel, C., Baier, V., Blank, L. M. & Kuepfer, L. Integration of genome-scale metabolic networks into whole-body PBPK models shows phenotype-specific cases of drug-induced metabolic perturbation. NPJ Syst. Biol. Appl 4, 10 (2018).

    Article  Google Scholar 

  16. Guebila, M. B. & Thiele, I. Model-based dietary optimization for late-stage, levodopa-treated, Parkinson’s disease patients. npj Syst. Biol. Appl. 2, 16013 (2016).

    Article  Google Scholar 

  17. Thiele, I., Clancy, C. M., Heinken, A. & Fleming, R. M. T. Quantitative systems pharmacology and the personalized drug–microbiota–diet axis. Curr. Opin. Syst. Biol. 4, 43–52 (2017).

    Article  Google Scholar 

  18. Yugi, K. et al. Reconstruction of insulin signal flow from phosphoproteome and metabolome data. Cell Rep. 8, 1171–1183 (2014).

    Article  Google Scholar 

  19. Atkinson, M. A., Eisenbarth, G. S. & Michels, A. W. Type 1 diabetes. Lancet 383, 69–82 (2014).

    Article  Google Scholar 

  20. Planas, R. et al. Gene expression profiles for the human pancreas and purified islets in type 1 diabetes: new findings at clinical onset and in long-standing diabetes. Clin. Exp. Immunol. 159, 23–44 (2010).

    Article  Google Scholar 

  21. Mahadevan, R. & Schilling, C. H. The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab. Eng. 5, 264–276 (2003).

    Article  Google Scholar 

  22. Subramanian, A. et al. A next generation connectivity map: L1000 platform and the first 1,000,000 profiles. Cell 171, 1437–1452 e1417 (2017).

    Article  Google Scholar 

  23. Banks, M. L., Hutsell, B. A., Blough, B. E., Poklis, J. L. & Negus, S. S. Preclinical assessment of lisdexamfetamine as an agonist medication candidate for cocaine addiction: effects in rhesus monkeys trained to discriminate cocaine or to self-administer cocaine in a cocaine versus food choice procedure. Int. J. Neuropsychopharmacol. https://doi.org/10.1093/ijnp/pyv009 (2015).

  24. Sarkar, A. X. & Sobie, E. A. Regression analysis for constraining free parameters in electrophysiological models of cardiac cells. PLoS Comput. Biol. 6, e1000914 (2010).

    Article  Google Scholar 

  25. Clayton, H. W. et al. Pancreatic inflammation redirects acinar to beta cell reprogramming. Cell Rep. 17, 2028–2041 (2016).

    Article  Google Scholar 

  26. McCall, A. L. & Farhy, L. S. Treating type 1 diabetes: from strategies for insulin delivery to dual hormonal control. Minerva Endocrinol. 38, 145–163 (2013).

    Google Scholar 

  27. Ma, G., Allen, T. J., Cooper, M. E. & Cao, Z. Calcium channel blockers, either amlodipine or mibefradil, ameliorate renal injury in experimental diabetes. Kidney Int. 66, 1090–1098 (2004).

    Article  Google Scholar 

  28. Lu, Y. et al. Mibefradil reduces blood glucose concentration in db/db mice. Clinics 69, 61–67 (2014).

    Article  Google Scholar 

  29. Massry, S. G. & Smogorzewski, M. Role of elevated cytosolic calcium in the pathogenesis of complications in diabetes mellitus. Min. Electrolyte Metab. 23, 253–260 (1997).

    Google Scholar 

  30. Almaas, E., Kovacs, B., Vicsek, T., Oltvai, Z. N. & Barabasi, A. L. Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature 427, 839–843 (2004).

    Article  Google Scholar 

  31. Sahoo, S., Franzson, L., Jonsson, J. J. & Thiele, I. A compendium of inborn errors of metabolism mapped onto the human metabolic network. Mol. Biosyst. 8, 2545–2558 (2012).

    Article  Google Scholar 

  32. Sargeant, R. J. & Paquet, M. R. Effect of insulin on the rates of synthesis and degradation of GLUT1 and GLUT4 glucose transporters in 3T3-L1 adipocytes. Biochem. J. 290, 913–919 (1993).

    Article  Google Scholar 

  33. Bonora, E. & Tuomilehto, J. The pros and cons of diagnosing diabetes with A1C. Diabetes Care 34, S184–S190 (2011).

    Article  Google Scholar 

  34. Gilarranz, L. J., Rayfield, B., Linan-Cembrano, G., Bascompte, J. & Gonzalez, A. Effects of network modularity on the spread of perturbation impact in experimental metapopulations. Science 357, 199–201 (2017).

    Article  Google Scholar 

  35. Dromms, R. A., Lee, J. Y. & Styczynski, M. P. LK-DFBA: a linear programming-based modeling strategy for capturing dynamics and metabolite-dependent regulation in metabolism. BMC Bioinformatics 21, 93 (2020).

    Article  Google Scholar 

  36. Goldenberg, J. Z. et al. Efficacy and safety of low and very low carbohydrate diets for type 2 diabetes remission: systematic review and meta-analysis of published and unpublished randomized trial data. BMJ 372, m4743 (2021).

    Article  Google Scholar 

  37. Lennerz, B. S., Koutnik, A. P., Azova, S., Wolfsdorf, J. I. & Ludwig, D. S. Carbohydrate restriction for diabetes: rediscovering centuries-old wisdom. J. Clin. Invest. https://doi.org/10.1172/JCI142246 (2021).

  38. Akirov, A., Diker-Cohen, T., Masri-Iraqi, H. & Shimon, I. High glucose variability increases mortality risk in hospitalized patients. J. Clin. Endocrinol. Metab. 102, 2230–2241 (2017).

    Article  Google Scholar 

  39. Tomkin, G. H. & Owens, D. Obesity diabetes and the role of bile acids in metabolism. J. Transl. Int. Med. 4, 73–80 (2016).

    Article  Google Scholar 

  40. Correa-Giannella, M. L. & Machado, U. F. SLC2A4gene: a promising target for pharmacogenomics of insulin resistance. Pharmacogenomics 14, 847–850 (2013).

    Article  Google Scholar 

  41. Sands, A. T. et al. Sotagliflozin, a dual SGLT1 and SGLT2 inhibitor, as adjunct therapy to insulin in type 1 diabetes. Diabetes Care 38, 1181–1188 (2015).

    Article  Google Scholar 

  42. Verma, S., McMurray, J. J. V. & Cherney, D. Z. I. The metabolodiuretic promise of sodium-dependent glucose cotransporter 2 inhibition: the search for the sweet spot in heart failure. JAMA Cardiol. 2, 939–940 (2017).

    Article  Google Scholar 

  43. Gaster, M., Staehr, P., Beck-Nielsen, H., Schroder, H. D. & Handberg, A. GLUT4 is reduced in slow muscle fibers of type 2 diabetic patients: is insulin resistance in type 2 diabetes a slow, type 1 fiber disease? Diabetes 50, 1324–1329 (2001).

    Article  Google Scholar 

  44. Shan, W. F., Chen, B. Q., Zhu, S. J., Jiang, L. & Zhou, Y. F. Effects of GLUT4 expression on insulin resistance in patients with advanced liver cirrhosis. J. Zhejiang Univ. Sci. B 12, 677–682 (2011).

    Article  Google Scholar 

  45. Richter, E. A. & Hargreaves, M. Exercise, GLUT4, and skeletal muscle glucose uptake. Physiol. Rev. 93, 993–1017 (2013).

    Article  Google Scholar 

  46. Chen, E. Y. et al. Enrichr: interactive and collaborative HTML5 gene list enrichment analysis tool. BMC Bioinformatics 14, 128 (2013).

    Article  Google Scholar 

  47. Mauri, M., Elli, T., Caviglia, G., Uboldi, G. & Azzi, M. RAWGraphs: a visualisation platform to create open outputs. In Proc. 12th Biannual Conference on Italian SIGCHI Ch. 28 (ACM, 2017).

  48. Noronha, A. et al. The Virtual Metabolic Human database: integrating human and gut microbiome metabolism with nutrition and disease. Nucleic Acids Res. 47, D614–D624 (2019).

    Article  Google Scholar 

  49. Covert, M. W., Xiao, N., Chen, T. J. & Karr, J. R. Integrating metabolic, transcriptional regulatory and signal transduction models in Escherichia coli. Bioinformatics 24, 2044–2050 (2008).

    Article  Google Scholar 

  50. Regittnig, W. et al. Plasma and interstitial glucose dynamics after intravenous glucose injection: evaluation of the single-compartment glucose distribution assumption in the minimal models. Diabetes 48, 1070–1081 (1999).

    Article  Google Scholar 

  51. Sorensen, J. T. A Physiologic Model of Glucose Metabolism in Man and Its Use to Design and Assess Improved Insulin Therapies for Diabetes (Massachusetts Institute of Technology, 1985).

  52. El-Khatib, F. H., Russell, S. J., Nathan, D. M., Sutherlin, R. G. & Damiano, E. R. A bihormonal closed-loop artificial pancreas for type 1 diabetes. Sci. Transl. Med. 2, 27ra27 (2010).

    Article  Google Scholar 

  53. Lewis, N. E. et al. Omic data from evolved E. coli are consistent with computed optimal growth from genome‐scale models. Mol. Syst. Biol. 6, 390 (2010).

    Article  Google Scholar 

  54. Toroghi, M. K., Cluett, W. R. & Mahadevan, R. A multi-scale model of the whole human body based on dynamic parsimonious flux balance analysis. IFAC-PapersOnLine 49, 937–942 (2016).

    Article  Google Scholar 

  55. Segre, D., Vitkup, D. & Church, G. M. Analysis of optimality in natural and perturbed metabolic networks. Proc. Natl Acad. Sci. USA 99, 15112–15117 (2002).

    Article  Google Scholar 

  56. Heirendt, L. et al. Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0. Nat. Protoc. 14, 639–702 (2019).

    Article  Google Scholar 

  57. Sobie, E. A. Parameter sensitivity analysis in electrophysiological models using multivariable regression. Biophys. J. 96, 1264–1274 (2009).

    Article  Google Scholar 

  58. Gudmundsson, S. & Thiele, I. Computationally efficient flux variability analysis. BMC Bioinformatics 11, 489 (2010).

    Article  Google Scholar 

  59. Thiele, I. & Palsson, B. Ø. A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat. Protoc. 5, 93–121 (2010).

    Article  Google Scholar 

  60. Duan, Q. et al. LINCS Canvas Browser: interactive web app to query, browse and interrogate LINCS L1000 gene expression signatures. Nucleic Acids Res. 42, W449–W460 (2014).

    Article  Google Scholar 

  61. Mahadevan, R., Edwards, J. S. & Doyle, F. J. III Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys. J. 83, 1331–1340 (2002).

    Article  Google Scholar 

  62. Heinemann, A., Wischhusen, F., Puschel, K. & Rogiers, X. Standard liver volume in the Caucasian population. Liver Transpl. Surg. 5, 366–368 (1999).

    Article  Google Scholar 

  63. Bordbar, A. et al. Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics. Sci. Rep. 7, 46249 (2017).

    Article  Google Scholar 

  64. Guebila, M. B. & Thiele, I. Dynamic flux balance analysis on whole-body metabolism for type 1 diabetes (version 0.2). Zenodo https://doi.org/10.5281/zenodo.4670413 (2021).

Download references

Acknowledgements

We acknowledge Bayer Technology Services for providing an academic version of the PK-SIM/MOBI software suite and the source file for the GIM model, K. Yugi from the University of Tokyo for providing the insulin model, and the Molecular Systems Physiology lab members at the University of Luxembourg for reviewing the manuscript and valuable discussions. Vector elements for Figs. 1, 4 and 6 were taken from vecteezy.com and freepik.com. This study was funded by Luxembourg National Research Fund (FNR) through the ATTRACT programme grant (FNR/A12/01, awarded to I.T.) and by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 757922, awarded to I.T.). The funders had no role in study design, data collection, data analysis, or interpretation.

Author information

Authors and Affiliations

Authors

Contributions

M.B.G. and I.T. conceived the study. M.B.G. developed the framework and carried out the simulations and analysis. M.B.G. and I.T. wrote and edited the manuscript.

Corresponding author

Correspondence to Ines Thiele.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Computational Science thanks Thomas Eissing, Laurence Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Handling editor: Ananya Rastogi, in collaboration with the Nature Computational Science team.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Methods, figures and tables.

Source data

Source Data Fig. 2

GIM simulation results from 0 to 600 min at 5 min intervals for 14 glucose and insulin challenges.

Source Data Fig. 3

Minimum and maximum bounds of healthy and T1D whole-body model with irreversible reactions.

Source Data Fig. 4

FVA solutions for the T1D model.

Source Data Fig. 5

Simulation results of 30 patients + 1 average patient for 600 min at 5 min time step.

Source Data Fig. 6

CRONICS simulation results for 30 patients from 16 min after insulin injection to 600 min at a time step of 2.5 min.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ben Guebila, M., Thiele, I. Dynamic flux balance analysis of whole-body metabolism for type 1 diabetes. Nat Comput Sci 1, 348–361 (2021). https://doi.org/10.1038/s43588-021-00074-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s43588-021-00074-3

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing