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Integrated mathematical models for describing complex biological processes

  • Biophysics of Complex Systems
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Abstract

This review describes integrated mathematical models of processes, such as calcium homeostasis, pathogen–host interaction (with hepatitis C virus as a pathogen), and the response of the human brain to a stimulating event. It is shown that integrated mathematical models provide a deeper insight into the mechanisms and conditions that lead to the development of diseases of different natures (musculoskeletal disorders, viral infections, and various impairments in brain function) and aid identification of the key targets and conditions for a directed effect of new generation drugs, as well as the interpretation of the results of state-of-theart CT imaging.

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Abbreviations

MAPK:

mitogen-activated protein kinase

TGF-ß:

transforming growth factor

HCV:

hepatitis C virus

PTH:

parathyroid hormone

RANK:

receptor activator of nuclear factor NF-κB

RANKL:

RANK ligand

OPG:

osteoprotegerin

IFN-a:

interferon a

fMRI:

functional magnetic resonance imaging

MRS:

magnetic resonance spectroscopy

BOLD signal:

blood oxygen level–dependent signal

ANLS:

astrocyte–neuron lactate shuttle

References

  1. C. K. Osborne, J. Shou, S. Massarweh, et al., Clin. Cancer Res. 11, 865s (2005).

    Google Scholar 

  2. D. Javelaud and A. Mauviel, Oncogene 24, 5742 (2005).

    Article  Google Scholar 

  3. J. Hiscott, H. Kwon, and P. Génin, J. Clin. Invest. 107, 143 (2001).

    Article  Google Scholar 

  4. M. T. Mc Auley, D. J. Wilkinson, J. J. Jones, et al., BMC Syst. Biol. 6, 130 (2012).

    Article  Google Scholar 

  5. M. Fribourg, B. Hartmann, M. Schmolke, et al., J. Theor. Biol. 351, 47 (2014).

    Article  Google Scholar 

  6. N. V. Ivanisenko, E. L. Mishchenko, I. R. Akberdin, et al., PLOS ONE 9, e91502 (2014).

    Article  ADS  Google Scholar 

  7. M. Baker, S. Denman-Johnson, B. S. Brook, et al., Math. Med. Biol. 30, 311 (2013).

    Article  MathSciNet  Google Scholar 

  8. M. Krupp, J. U. Marquardt, U. Sahin, et al., Bioinformatics 28, 1184 (2012).

    Article  Google Scholar 

  9. R. Leinonen, H. Sugawara, and M. Shumway, Nucleic Acids Res. 39, D19 (2011).

    Article  Google Scholar 

  10. O. V. Popik, E. D. Petrovskiy, E. L. Mishchenko, et al., Virus Res. 218, 71 (2016).

    Article  Google Scholar 

  11. G. Jones, S. A. Strugnell, and H. F. DeLuca, Physiol. Rev. 78, 1193 (1998).

    Article  Google Scholar 

  12. J. F. Raposo, L. G. Sobrinho, and H. G. Ferreira, J. Clin. Endocrinol. Metab. 87, 4330 (2002).

    Article  Google Scholar 

  13. V. Lemaire, F. L. Tobin, L. D. Greller, et al., J. Theor. Biol. 229, 293 (2004).

    Article  Google Scholar 

  14. S. Pozzi, M. Fulciniti, H. Yan, et al., Bone 53(2), 487 (2013).

    Article  Google Scholar 

  15. A. A. Ali., R. S. Weinstein, S. A. Stewart, et al., Endocrinology 146(3), 1226 (2005).

    Article  Google Scholar 

  16. M. C. Peterson and M. M. Riggs, Bone 46, 49 (2010).

    Article  Google Scholar 

  17. T. Bellido, A. A. Ali, L. I. Plotkin, et al., J. Biol. Chem. 278, 50259 (2003).

    Article  Google Scholar 

  18. M. R. McClung, E. M. Lewiecki, S. B. Cohen, et al., N. Engl. J. Med. 354, 821 (2006).

    Article  Google Scholar 

  19. P. Chen, J. H. Satterwhite, A. A. Licata, et al., J. Bone Miner. Res. 20, 962 (2005).

    Article  Google Scholar 

  20. D. M. Slovik, R. M. Neer, and J. T. Potts, J. Clin. Invest. 68, 1261 (1981).

    Article  Google Scholar 

  21. S. J. Silverberg, E. Shane, T. P. Jacobs, et al., N. Engl. J. Med. 341, 1249 (1999).

    Article  Google Scholar 

  22. M. Rix, H. Andreassen, P. Eskildsen, et al., Kidney Int. 56, 1084 (1999).

    Article  Google Scholar 

  23. K. Kruse, U. Kracht, K. Wohlfart, et al., Eur. J. Pediatr. 148, 535 (1989).

    Article  Google Scholar 

  24. J. P. Messina, I. Humphreys, A. Flaxman, et al., Hepatology 61, 77 (2015).

    Article  Google Scholar 

  25. J. F. Perz, G. L. Armstrong, L. A. Farrington, et al., J. Hepatol. 45, 529 (2006).

    Article  Google Scholar 

  26. A. U. Neumann, N. P. Lam, H. Dahari, et al., Science 282, 103 (1998).

    Article  ADS  Google Scholar 

  27. H. Dahari, A. Lo, R. M. Ribeiro, et al., J. Theor. Biol. 247, 371 (2007).

    Article  Google Scholar 

  28. H. Dahari, R. M. Ribeiro, and A. S. Perelson, Hepatology 46, 16 (2007).

    Article  Google Scholar 

  29. L. Rong, H. Dahari, R. M. Ribeiro, et al., Sci. Transl. Med. 2, 30ra32 (2010).

    Article  Google Scholar 

  30. J. Guedj and A. S. Perelson, Hepatology 53, 1801 (2011).

    Article  Google Scholar 

  31. B. S. Adiwijaya, E. Herrmann, B. Hare, et al., PLoS Comput. Biol. 6, e1000745 (2010).

    Article  Google Scholar 

  32. B. S. Adiwijaya, T. L. Kieffer, J. Henshaw, et al., PLoS Comput. Biol. 8, e1002339 (2012).

    Article  Google Scholar 

  33. H. Dahari, R. M. Ribeiro, C. M. Rice, et al., J. Virol. 81, 750 (2007).

    Article  Google Scholar 

  34. M. Binder, N. Sulaimanov, D. Clausznitzer, et al., PLoS Pathog. 9, e1003561 (2013).

    Article  Google Scholar 

  35. E. L. Mishchenko, K. D. Bezmaternykh, V. A. Likhoshvai, et al., J. Bioinform. Comput. Biol. 5, 593 (2007).

    Article  Google Scholar 

  36. C. Laouénan, P. Marcellin, M. Lapalus, et al., Antimicrob. Agents Ch. 58, 5332 (2014).

    Article  Google Scholar 

  37. B. Roche, A. Coilly, A. M. Roque-Afonso, et al., Viruses 7, 5155 (2015).

    Article  Google Scholar 

  38. V. Belousova, A. A. Abd-Rabou, and S. A. Mousa, Pharmacol. Ther. 145, 92 (2015).

    Article  Google Scholar 

  39. B. S. Adiwijaya, B. Hare, P. R. Caron, et al., Antivir. Ther. 14, 591 (2009).

    Google Scholar 

  40. H. W. Reesink, G. C. Fanning, and K. A. Farha, Gastroenterology 138, 913 (2010).

    Article  Google Scholar 

  41. M. Gao, R. E. Nettles, M. Belema, et al., Nature 465, 96 (2010).

    Article  ADS  Google Scholar 

  42. N. Forestier, D. Larrey, D. Guyader, et al., J. Hepatol. 54, 1130 (2011).

    Article  Google Scholar 

  43. J. de Bruijne, A. van Vliet, C. J. Weegink, et al., Antivir. Ther. 17, 633 (2012).

    Article  Google Scholar 

  44. J. Guedj and A. U. Neumann, J. Theor. Biol. 267, 330 (2010).

    Article  Google Scholar 

  45. J. Guedj, H. Dahari, L. Rong, et al., Proc. Natl. Acad. Sci. U. S. A. 110, 3991 (2013).

    Article  ADS  Google Scholar 

  46. L. Rong, J. Guedj, H. Dahari, et al., PLoS Comput. 9, e1002959 (2013).

    Article  Google Scholar 

  47. D. Clausznitzer, J. Harnisch, and L. Kaderali, Virus Res. 218, 96 (2016).

    Article  Google Scholar 

  48. N. David, Y. Yaffe, L. Hagoel, et al., Virology 475, 139 (2015).

    Article  Google Scholar 

  49. N. Appel, M. Zayas, S. Miller, et al., PLoS Pathog. 4, e1000035 (2008).

    Article  Google Scholar 

  50. S. Yamauchi, K. Takeuchi, K. Chihara, et al., J. Biol. Chem. 290, 21857 (2015).

    Article  Google Scholar 

  51. M. Schliemann, E. Bullinger, S. Borchers, et al., BMC Syst. Biol. 5, 204 (2011).

    Article  Google Scholar 

  52. N. Papic, C. I. Maxwell, D. A. Delker, et al., Viruses 4, 581 (2012).

    Article  Google Scholar 

  53. N. Zhu, C. F. Ware, and M. M. Lai, Virology 283, 178 (2001).

    Article  Google Scholar 

  54. Y. M. Chung, K. J. Park, S. Y. Choi, et al., Biochem. Biophys. Res. Commun. 284, 15 (2001).

    Article  Google Scholar 

  55. A. Aubert, R. Costalat, and R. Valabrègue, Acta Biotheor. 49, 301 (2001).

    Article  Google Scholar 

  56. T. A. Rapoport and R. Heinrich, Biosystems 7, 120 (1975).

    Article  Google Scholar 

  57. R. Heinrich and S. Schuster, The regulation of Cellular Systems (Chapman & Hall, New York, 1996).

    Book  MATH  Google Scholar 

  58. M. S. Vafaee and A. Gjedde, J. Cereb. Blood Flow Metab. 20, 747 (2000).

    Article  Google Scholar 

  59. A. Aubert and R. Costalat, Neuroimage 17, 1162 (2002).

    Article  Google Scholar 

  60. R. B. Buxton, E. C. Wong, and L. R. Frank, Magn. Reson. Med. 39, 855 (1998).

    Article  Google Scholar 

  61. J. Frahm, G. Krüger, K. D. Merboldt, et al., Magn. Reson. Med. 35, 143 (1996).

    Article  Google Scholar 

  62. G. Krüger, A. Kastrup, A. Takahashi, et al., Neuroreport 10, 2939 (1999).

    Article  Google Scholar 

  63. A. Toglia, J. M. Kittelson, R. B. Roemer, et al., Int. J. Hyperthermia 2, 461 (1996).

    Article  Google Scholar 

  64. A. Aubert, R. Costalat, H. Duffau, et al., Acta Biotheor. 50, 281 (2002).

    Article  Google Scholar 

  65. A. Aubert and R. Costalat. J. Cereb. Blood Flow Metab. 25, 1476 (2005).

    Article  Google Scholar 

  66. A. Aubert, R. Costalat, P. J. Magistretti, et al., Proc. Natl. Acad. Sci. U. S. A. 102, 16448 (2005).

    Article  ADS  Google Scholar 

  67. R. Guillevin, C. Menuel, J. N. Vallée, et al., Compt. Rend. Biol. 334, 31 (2011).

    Article  Google Scholar 

  68. R. Costalat, J. P. Francoise, C. Menuel, et al., Acta Biotheor. 60, 99 (2012).

    Article  Google Scholar 

  69. M. Lahutte-Auboin, R. Guillevin, J. P. Françoise, et al., Acta Biotheor. 61, 79 (2013).

    Article  Google Scholar 

  70. T. Cakir, S. Alsan, H. Saybaşili, et al., Theor. Biol. Med. Model. 4, 48 (2007).

    Article  Google Scholar 

  71. L. Hertz, Neurochem. Int. 45, 285 (2004).

    Article  Google Scholar 

  72. J. Shen, K. F. Petersen, K. L. Behar, et al., Proc. Natl. Acad. Sci. U. S. A. 96, 8235 (1999).

    Article  ADS  Google Scholar 

  73. L. R. Drewes and D. D. Gilboe, J. Biol. Chem. 248, 2489 (1973).

    Google Scholar 

  74. S. I. Harik, R. A. Behmand, and J. C. LaManna, J. Appl. Physiol. 77, 896 (1994).

    Article  Google Scholar 

  75. N. J. Allen, R. Káradóttir, and D. Attwell, J. Neurosci. 25, 848 (2005).

    Article  Google Scholar 

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Correspondence to E. L. Mishchenko.

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Original Russian Text © E.L. Mishchenko, O.V. Petrovskaya, A.M. Mishchenko, E.D. Petrovskiy, N.V. Ivanisenko, V.A. Ivanisenko, 2017, published in Biofizika, 2017, Vol. 62, No. 5, pp. 949–968.

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Mishchenko, E.L., Petrovskaya, O.V., Mishchenko, A.M. et al. Integrated mathematical models for describing complex biological processes. BIOPHYSICS 62, 778–795 (2017). https://doi.org/10.1134/S0006350917050141

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