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access icon free Modular bond-graph modelling and analysis of biomolecular systems

Bond graphs can be used to build thermodynamically-compliant hierarchical models of biomolecular systems. As bond graphs have been widely used to model, analyse and synthesise engineering systems, this study suggests that they can play the same rôle in the modelling, analysis and synthesis of biomolecular systems. The particular structure of bond graphs arising from biomolecular systems is established and used to elucidate the relation between thermodynamically closed and open systems. Block diagram representations of the dynamics implied by these bond graphs are used to reveal implicit feedback structures and are linearised to allow the application of control-theoretical methods. Two concepts of modularity are examined: computational modularity where physical correctness is retained and behavioural modularity where module behaviour (such as ultrasensitivity) is retained. As well as providing computational modularity, bond graphs provide a natural formulation of behavioural modularity and reveal the sources of retroactivity. A bond graph approach to reducing retroactivity, and thus inter-module interaction, is shown to require a power supply such as that provided by the ATP ⇌ ADP + Pi reaction. The mitogen-activated protein kinase cascade (Raf–MEK–ERK pathway) is used as an illustrative example.

References

    1. 1)
    2. 2)
    3. 3)
      • 60. Sauro, H.M., Ingalls, B.: ‘MAPK cascades as feedback amplifiers’, arXiv preprint arXiv:0710.5195, 2007.
    4. 4)
    5. 5)
    6. 6)
      • 11. Thoma, J.U., Mocellin, G.: ‘Simulation with entropy thermodynamics: understanding matter and systems with bondgraphs’ (Springer, 2006).
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
    17. 17)
      • 14. Gawthrop, P.J., Cursons, J., Crampin, E.J.: ‘Hierarchical bond graph modelling of biochemical networks’, Proc. R. Soc. A, Math. Phys. Eng. Sci., 2015, 471, (2184), pp. 123, doi: 10.1098/rspa.2015.0642. Available at arXiv:1503.01814.
    18. 18)
    19. 19)
    20. 20)
    21. 21)
    22. 22)
      • 29. Maxwell, J.C.: ‘Remarks on the mathematical classification of physical quantities’. Proc. London Mathematical Society, 1871, pp. 224233.
    23. 23)
    24. 24)
    25. 25)
    26. 26)
      • 38. Ingalls, B.P.: ‘Mathematical modelling in systems biology’ (MIT Press, 2013).
    27. 27)
    28. 28)
      • 63. Savageau, M.A.: ‘Biochemical systems analysis. A study of function and design in molecular biology’ (Addison-Wesley, Reading, Mass, 2009, 40th anniversary issue edition).
    29. 29)
      • 20. Vecchio, D.D., Murray, R.M.: ‘Biomolecular feedback systems’ (Princeton University Press, 2014)..
    30. 30)
      • 66. Keener, J.P., Sneyd, J.: ‘Mathematical physiology: I: cellular physiology’ (Springer, 2009, 2nd edn.), vol. 1. 21.
    31. 31)
    32. 32)
      • 55. Barton, J., Sontag, E.D.: ‘The energy costs of biological insulators’, arXiv preprint arXiv:1210.3809, 2012.
    33. 33)
    34. 34)
      • 2. Paynter, H.M.: ‘Analysis and design of engineering systems’ (MIT Press, Cambridge, Mass, 1961).
    35. 35)
      • 25. Goodwin, G.C., Graebe, S.F., Salgado, M.E.: ‘Control system design’ (Prentice-Hall, Englewood Cliffs, New Jersey, 2001).
    36. 36)
    37. 37)
    38. 38)
    39. 39)
      • 65. Cornish-Bowden, A.: ‘Fundamentals of enzyme kinetics’ (Wiley-Blackwell, London, 2013, 4th edn.).
    40. 40)
      • 33. Palsson, B.: ‘Systems biology: properties of reconstructed networks’ (Cambridge University Press, 2006)..
    41. 41)
    42. 42)
      • 5. Mukherjee, A., Karmaker, R., Samantaray, A.K.: ‘Bond graph in modeling, simulation and fault indentification’ (I.K. International, New Delhi, 2006).
    43. 43)
      • 67. Voit, E.O.: ‘A first course in systems biology’ (Garland Science, New York and London, 2013).
    44. 44)
    45. 45)
    46. 46)
      • 49. Sontag, E.D.: ‘Modularity, retroactivity, and structural identification’, in Koeppl, H., Setti, G., di Bernardo, M., et al (Eds.): ‘Design and analysis of biomolecular circuits’ (Springer New York, 2011), pp. 183200. doi: 10.1007/978-1-4419-6766-4_9.
    47. 47)
    48. 48)
    49. 49)
    50. 50)
    51. 51)
    52. 52)
    53. 53)
    54. 54)
    55. 55)
    56. 56)
      • 64. Fell, D.: ‘Understanding the control of metabolism, volume 2 of Frontiers in Metabolism’ (Portland press, London, 1997)..
    57. 57)
      • 1. Wellstead, P., Bullinger, E., Kalamatianos, D., et al: ‘The role of control and system theory in systems biology’, Annu. Rev. Control, 2008, 32, (1), pp. 3347, ISSN 1367-5788. doi: 10.1016/j.arcontrol.2008.02.001.
    58. 58)
      • 4. Gawthrop, P.J., Smith, L.P.S.: ‘Metamodelling: bond graphs and dynamic systems’ (Prentice-Hall, Hemel Hempstead, Herts, England, 1996), ISBN 0-13-489824-9.
    59. 59)
    60. 60)
    61. 61)
      • 10. Cellier, F.E.: ‘Continuous system modelling’ (Springer-Verlag, 1991).
    62. 62)
      • 28. Borutzky, W.: ‘Incremental bond graphs’, in Borutzky, W. (Ed.): ‘Bond graph modelling of engineering systems’ (Springer New York, 2011), pp. 135176. doi: 10.1007/978-1-4419-9368-7_4.
    63. 63)
      • 37. Sauro, H.M.: ‘Network dynamics’, in Ireton, R., Montgomery, K., Bumgarner, R., et al (Eds.): ‘Computational Systems Biology, volume 541 of Methods in Molecular Biology’ (Humana Press, New York, 2009), pp. 269309. doi: 10.1007/978-1-59745-243-4-13.
    64. 64)
    65. 65)
      • 3. Wellstead, P.E.: ‘Introduction to physical system modelling’ (Academic Press, 1979).
    66. 66)
    67. 67)
      • 45. Kaltenbach, H.-M., Stelling, J.: ‘Modular analysis of biological networks’, in Goryanin, I.I., Goryachev, A.B. (Eds.): ‘Advances in systems biology, volume 736 of Advances in Experimental Medicine and Biology’ (Springer New York, 2012), pp. 317. doi: 10.1007/978-1-4419-7210-1_1.
    68. 68)
    69. 69)
    70. 70)
    71. 71)
    72. 72)
      • 6. Karnopp, D.C., Margolis, D.L., Rosenberg, R.C.: ‘System dynamics: modeling, simulation, and control of mechatronic systems’ (John Wiley & Sons, 2012, 5th edn.), ISBN 978-0470889084.
    73. 73)
    74. 74)
    75. 75)
    76. 76)
      • 30. Atkins, P., de Paula, J.: ‘Physical chemistry for the life sciences’ (Oxford University Press, 2011, 2nd edn.).
    77. 77)
    78. 78)
      • 44. Szallasi, Z., Periwal, V., Stelling, J.: ‘On modules and modularity’, in Szallasi, Z., Stelling, J., Periwal, V. (Eds.): ‘System modeling in cellular biology: from concepts to nuts and bolts’ (MIT press, 2010), pp. 1940.
    79. 79)
    80. 80)
      • 12. Greifeneder, J., Cellier, F.E.: ‘Modeling chemical reactions using bond graphs’. Proc. ICBGM12, 10th SCS Intl. Conf. on Bond Graph Modeling and Simulation, Genoa, Italy, 2012, pp. 110121.
    81. 81)
      • 17. Vecchio, D.D., Ninfa, A.J., Sontag, E.D.: ‘Modular cell biology: retroactivity and insulation’, Mol. Syst. Biol., 2008, 4, pp. 116, doi: 10.1038/msb4100204.
    82. 82)
    83. 83)
      • 78. Wellstead, P.: ‘A New Look at Disease: Parkinson's through the eyes of an engineer’ (Control Systems Principles, Stockport, UK, 2012).
    84. 84)
      • 61. Beard, D.A., Qian, H.: ‘Chemical biophysics: quantitative analysis of cellular systems’ (Cambridge University Press, 2010).
    85. 85)
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