ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2024): 0.7
Research article
Interdisciplinarity in modelling of biophysical processes; pp. 544–550
PDF | https://doi.org/10.3176/proc.2025.4.08

Authors
Jüri Engelbrecht, Kert Tamm ORCID Icon, Tanel Peets ORCID Icon
Abstract

In this article, the importance of interdisciplinary ideas for modelling and understanding signal propagation in nerve fibres is described as a fascinating problem of biophysics. A mathematical model involves the physical laws, assumptions, hypotheses, and finally, the governing equations. The analysis of this complex process is at the interface of physics, chemistry, and mathematics, together with experimental studies in electrophysiology. It is stressed that the mindsets of different communities may hinder cooperation.

References

1. Abbott, B. C., Hill, A. V. and Howarth, J. V. The positive and negative heat production associated with a nerve impulse. Proc. R. Soc. Lond. B, 1958, 148(931), 149–187. 
https://doi.org/10.1098/rspb.1958.0012   

2. Alvargonzález, D. Multidisciplinarity, interdisciplinarity, transdisciplinarity, and the sciences. Int. Stud. Philos. Sci., 2011, 25(4), 387–403. 
https://doi.org/10.1080/02698595.2011.623366  

3. Andersen, S. S. L., Jackson, A. D. and Heimburg, T. Towards a thermodynamic theory of nerve pulse propagation. Prog. Neurobiol., 2009, 88(2), 104–113. 
https://doi.org/10.1016/j.pneurobio.2009.03.002  

4. Bialek, W. Perspectives on theory at the interface of physics and biology. Rep. Prog. Phys., 2018, 81(1), 012601. 
https://doi.org/10.1088/1361-6633/aa995b  

5. Bressloff, P. C. Waves in Neural Media. From Single Neurons to Neural Fields. In Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, 2014. 
https://doi.org/10.1007/978-1-4614-8866-8  

6. Brohawn, S. G., Wang, W., Handler, A., Campbell, E. B., Schwarz, J. R. and MacKinnon, R. The mechanosensitive ion channel TRAAK is localized to the mammalian node of Ranvier. eLife, 2019, 8, e50403. 
https://doi.org/10.7554/eLife.50403  

7. Carrillo, N. and Martínez, S. Scientific inquiry: from metaphors to abstraction. Perspect. Sci., 2023, 31(2), 233–261. 
https://doi.org/10.1162/posc_a_00571  

8. Cartwright, N. How the Laws of Physics Lie. Oxford University Press, Oxford, 1983. 
https://doi.org/10.1093/0198247044.001.0001  

9. Cohen, J. E. Mathematics is biology’s next microscope, only better; biology is mathematics’ next physics, only better. PLOS Biol., 2004, 2(12), e439. 
https://doi.org/10.1371/journal.pbio.0020439  

10. Coombes, S. and Wedgwood, K. C. A. Neurodynamics. An Applied Mathematics Perspective. In Texts in Applied Math­ematics75. Springer, Cham, 2023. 
https://doi.org/10.1007/978-3-031-21916-0  

11. Coveney, P. V. and Fowler, P. W. Modelling biological complexity: a physical scientist’s perspective. J. R. Soc. Inter­face, 2005, 2(4), 267–280. 
https://doi.org/10.1098/rsif.2005.0045  

12. DeLanda, M. Intensive Science and Virtual Philosophy. Continuum, London, 2004.

13. Einstein, A. On the method of theoretical physics. Philos. Sci., 1934, 1(2), 163–169.
https://doi.org/10.1086/286316

14. Engelbrecht, J., Tamm, K. and Peets, T. Internal variables used for describing the signal propagation in axons. Continuum Mech. Thermodyn., 2020, 32(6), 1619–1627. 
https://doi.org/10.1007/s00161-020-00868-2  

15. Engelbrecht, J., Tamm, K. and Peets, T. Modeling of complex signals in nerve fibers. Med. Hypotheses, 2018, 120, 90–95. 
https://doi.org/10.1016/j.mehy.2018.08.021   

16. Engelbrecht, J., Tamm, K. and Peets, T. Modelling of Complex Signals in Nerves. Springer, Cham, 2021. 
https://doi.org/10.1007/978-3-030-75039-8  

17. Engelbrecht, J., Tamm, K. and Peets, T. On mathematical modelling of solitary pulses in cylindrical biomembranes. Biomech. Model. Mechanobiol., 2015, 14(1), 159–167. 
https://doi.org/10.1007/s10237-014-0596-2  

18. Engelbrecht, J., Tamm, K. and Peets, T. On the phenomenological modelling of physical phenomena. Proc. Estonian Acad. Sci., 2024, 73(3), 264‒278. 
https://doi.org/10.3176/proc.2024.3.10  

19. Ermentrout, G. B. and Terman, D. H. Mathematical Foundations of Neuroscience. In Interdisciplinary Applied Mathematics35. Springer, New York, 2010. 
https://doi.org/10.1007/978-0-387-87708-2  

20. National Academies. Facilitating Interdisciplinary Research. National Academies Press, Washington, D. C., 2004. 
https://doi.org/10.17226/11153  

21. Gavaghan, D., Garny, A., Maini, P. K. and Kohl, P. Mathematical models in physiology. Phil. Trans. R. Soc. A, 2006, 364(1842), 1099–1106. 
https://doi.org/10.1098/rsta.2006.1757  

22. Heimburg, T. and Jackson, A. D. On soliton propagation in biomembranes and nerves. Proc. Natl. Acad. Sci. U. S. A., 2005, 102(28), 9790–9795. 
https://doi.org/10.1073/pnas.0503823102  

23. Hodgkin, A. L. and Huxley, A. F. A quantitative description of membrane current and its application to conduction and ex­citation in nerve. J. Physiol., 1952, 117(4), 500–544. 
https://doi.org/10.1113/jphysiol.1952.sp004764  

24. Hodgkin, A. L. The Conduction of the Nervous Impulse. Liverpool University Press, 1964.

25. Hopfield, J. J. Two cultures? Experiences at the physics-biology interface. Phys. Biol., 2014, 11(5), 053002. 
https://doi.org/10.1088/1478-3975/11/5/053002  

26. Izhikevich, E. M. Dynamical Systems in Neuroscience. The Geometry of Excitability and Bursting. The MIT Press, London, 2006. 
https://doi.org/10.7551/mitpress/2526.001.0001  

27. Kaplan, D. M. and Craver, C. F. The explanatory force of dynamical and mathematical models in neuroscience: a mech­anistic perspective. Philos. Sci., 2011, 78(4), 601–627. 
https://doi.org/10.1086/661755  

28. Kohl, P., Crampin, E. J., Quinn, T. A. and Noble, D. Systems biology: an approach. Clin. Pharmacol. Ther., 2010, 88(1), 25–33. 
https://doi.org/10.1038/clpt.2010.92  

29. Lieberstein, H. M. On the Hodgkin-Huxley partial differential equation. Math. Biosci., 1967, 1(1), 45–69. 
https://doi.org/10.1016/0025-5564(67)90026-0  

30. Ling, T., Boyle, K. C., Zuckerman, V., Flores, T., Ramakrishnan, C., Deisseroth, K. et al. High-speed interferometric imaging reveals dynamics of neuronal deformation during the action potential. Proc. Natl. Acad. Sci. U. S. A., 2020, 117(19), 10278–10285. 
https://doi.org/10.1073/pnas.1920039117  

31. Maugin, G. A. Internal variables and dissipative structures. J. Non-Equilib. Thermodyn., 1990, 15(2), 173‒192. 
https://doi.org/10.1515/jnet.1990.15.2.173   

32. McCulloch, A. D. and Huber, G. Integrative biological modelling in silico. In In Silico’ Simulation of Biological Processes: Novartis Foundation Symposium (Bock, G. and Goode, J. A., eds), 247, 4–25. John Wiley & Sons, Chichester, 2002. 
https://doi.org/10.1002/0470857897.ch2  

33. Mueller, J. K. and Tyler, W. J. A quantitative overview of biophysical forces impinging on neural function. Phys. Biol., 2014, 11(5), 051001. 
https://doi.org/10.1088/1478-3975/11/5/051001   

34. Nagumo, J., Arimoto, S. and Yoshizawa, S. An active pulse transmission line simulating nerve axon. Proc. IRE, 1962, 50(10), 2061–2070. 
https://doi.org/10.1109/JRPROC.1962.288235  

35. National Research Council. Catalyzing Inquiry at the Interface of Computing and Biology. National Academies Press, Washington, D. C., 2005. 
https://doi.org/10.17226/11480  

36. Nelson, P. Biological Physics: Energy, Information, Life. W. H. Freeman, New York, 2003.

37. Noble, D. The rise of computational biology. Nat. Rev. Mol. Cell Biol., 2002, 3(6), 459–463. 
https://doi.org/10.1038/nrm810  

38. Nolte, D. D. Introduction to Modern Dynamics: Chaos, Networks, Space and Time. Oxford University Press, Oxford, 2015.

39. Porubov, A. V. Amplification of Nonlinear Strain Waves in Solids. World Scientific, Singapore, 2003.
https://doi.org/10.1142/9789812794291

40. Rovelli, C. Helgoland. Penguin Random House, London, 2022.

41. Scott, A. Neuroscience: A Mathematical Primer. Springer, New York, 2002.

42. Shrivastava, S. and Schneider, M. F. Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling. J. R. Soc. Interface, 2014, 11(97), 20140098. 
https://doi.org/10.1098/rsif.2014.0098  

43. Slattery, J. C. Momentum, Energy, and Mass Transfer in Continua. McGraw-Hill, New York, 1971.

44. Tasaki, I. A macromolecular approach to excitation phenomena: mechanical and thermal changes in nerve during excitation. Physiol. Chem. Phys. Med. NMR, 1988, 20(4), 251–268.

45. Terakawa, S. Potential-dependent variations of the intracellular pressure in the intracellularly perfused squid giant axon. J. Physiol., 1985, 369(1), 229–248. 
https://doi.org/10.1113/jphysiol.1985.sp015898  

46. Torres, N. V. and Santos, G. The (mathematical) modeling process in biosciences. Front. Genet., 2015, 6, 1–9. 
https://doi.org/10.3389/fgene.2015.00354

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