eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
On mechanisms of electromechanophysiological interactions between the components of signals in axons; pp. 81–96

Jüri Engelbrecht, Kert Tamm, Tanel Peets

Recent studies have revealed the complex structure of nerve signals in axons. There is experimental evidence that the propagation of an electrical signal (action potential) is accompanied by mechanical and thermal effects. In this paper, first, an overview is presented on experimental results and possible mechanisms of electromechanophysiological couplings which govern the signal formation in axons. This forms a basis for building up a mathematical model describing an ensemble of waves. Three basic physical mechanisms responsible for coupling are (i) electric-lipid bi-layer interaction resulting in the mechanical wave in biomembrane; (ii) electric-fluid interaction resulting in the mechanical wave in the axoplasm; (iii) electric-fluid interaction resulting in the temperature change in axoplasm. The influence of possible changes in variables which could have a role for interactions are analysed and the concept of internal variables introduced for describing the endothermic processes. The previously proposed mathematical model is modified reflecting the possible physical explanation of these interactions.

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. B Biol. Sci., 1958, 148(931), 149-187.
2. 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.
3. Appali, R., Petersen, S., and van Rienen, U. A comparision of Hodgkin-Huxley and soliton neural theories. Adv. Radio Sci., 2010, 8, 75-79.
4. Barz, H., Schreiber, A., and Barz, U. Impulses and pressure waves cause excitement and conduction in the nervous system. Med. Hypotheses, 2013, 81(5), 768-772.
5. Bean, B. P. The action potential in mammalian central neurons. Nat. Rev. Neurosci., 2007, 8(6), 451-465.
6. Berezovski, A. and Va ́n, P. Internal Variables in Thermoelasticity. Springer, Cham, 2017.
7. Bishop, G. H. Natural history of the nerve impulse. Physiol. Rev., 1956, 36(3), 376-399.
8. Chen, H., Garcia-Gonzalez, D., and Jerusalem, A. Computational model of the mechanoelectrophysiological coupling in axons with application to neuromodulation. Phys. Rev. E, 2019, 99(3), 032406.
9. Christov, C. I. and Velarde, M. G. Dissipative solitons. Physica D, 1995, 86(1-2), 323-347.
10. Clay, J. R. Axonal excitability revisited. Prog. Biophys. Mol. Biol., 2005, 88(1), 59-90.
11. Courtemanche, M., Ramirez, R. J., and Nattel, S. Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol., 1998, 275(1), 301-321.
12. Debanne, D., Campanac, E., Bialowas, A., Carlier, E., and Alcaraz, G. Axon physiology. Physiol. Rev., 2011, 91(2), 555-602.
13. Drukarch, B., Holland, H. A., Velichkov, M., Geurts, J. J. G., Voorn, P., Glas, G., and de Regt, H. W. Thinking about the nerve impulse: a critical analysis of the electricity-centered conception of nerve excitability. Prog. Neurobiol., 2018, 169, 172-185.
14. Einstein, A. On the method of theoretical physics. Philos. Sci., 1934, 1(2), 163-169.
15. El Hady, A. and Machta, B. B. Mechanical surface waves accompany action potential propagation. Nat. Commun., 2015, 6, 6697.
16. Engelbrecht, J. Questions About Elastic Waves. Springer International Publishing, Cham, 2015.
17. Engelbrecht, J., Peets, T., and Tamm, K. Electromechanical coupling of waves in nerve fibres. Biomech. Model. Mechanobiol., 2018, 17(6), 1771-1783.
18. Engelbrecht, J., Peets, T., and Tamm, K. Soliton trains in dispersive media. Low Temp. Phys., 2018, 44(7), 696-700.
19. Engelbrecht, J., Peets, T., Tamm, K., Laasmaa, M., and Vendelin, M. On the complexity of signal propagation in nerve fibres. Proc. Estonian Acad. Sci., 2018, 67(1), 28-38.
20. Engelbrecht, J., Tamm, K., and Peets, T. On solutions of a Boussinesq-type equation with displacement-dependent nonlinearities: the case of biomembranes. Philos. Mag., 2017, 97(12), 967-987.
21. Engelbrecht, J., Tamm, K., and Peets, T. Modeling of complex signals in nerve fibers. Med. Hypotheses, 2018, 120, 90-95.
22. Engelbrecht, J., Tamm, K., and Peets, T. Primary and secondary components of nerve signals. arXiv:1812.05335, 2018.
23. Engelbrecht, J., Tamm, K., and Peets, T. Modelling of processes in nerve fibres at the interface of physiology and mathematics. arXiv 1906.01261, 2019.
24. Engelbrecht, J., Tamm, K., and Peets, T. Internal variables used for describing the signal propagation in axons. Continuum Mech. Thermodyn., 2020. doi:10.1007/s00161-020-00868-2
25. Eringen, A. C. Nonlinear Theory of Continuous Media. McGraw-Hill Book Company, New York, 1962.
26. Fillafer, C., Mussel, M., Muchowski, J., and Schneider, M. F. Cell surface deformation during an action potential. Biophys. J., 2018, 114(2), 410-418.
27. Gonzalez-Perez, A., Mosgaard, L. D., Budvytyte, R., Villagran-Vargas, E., Jackson, A. D., and Heimburg, T. Solitary electromechanical pulses in lobster neurons. Biophys. Chem., 2016, 216, 51-59.
28. Gross, D., Williams, W. S., and Connor, J. A. Theory of electromechanical effects in nerve. Cell. Mol. Neurobiol., 1983, 3(2), 89-111.
29. Hall, C. W. Laws and Models: Science, Engineering, and Technology. CRC Press, Boca Raton, 1999.
30. Heimburg, T. and Jackson, A. D. On the action potential as a propagating density pulse and the role of anesthetics. Biophys. Rev. Lett., 2007, 02(01), 57-78.
31. Heimburg, T. and Jackson, A. D. On soliton propagation in biomembranes and nerves. Proc. Natl. Acad. Sci. USA, 2005, 102(28), 9790-9795.
32. Heimburg, T. and Jackson, A. D. Thermodynamics of the nervous impulse. In Structure and Dynamics of Membranous Inter- faces (Nag, K., ed.). John Wiley & Sons, 2008, 18-337.
33. Hodgkin, A. L. The Conduction of the Nervous Impulse. Liverpool University Press, 1964.
34. 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.
35. Holland, L., de Regt, H. W., and Drukarch, B. Thinking about the nerve impulse: the prospects for the development of a comprehensive account of nerve impulse propagation. Front. Cell. Neurosci., 2019, 13, 208.
36. Howarth, J. V., Keynes, R. D., and Ritchie, J. M. The origin of the initial heat associated with a single impulse in mammalian non-myelinated nerve fibres. J. Physiol., 1968, 194(3), 745-793.
37. Iwasa, K., Tasaki, I., and Gibbons, R. C. Swelling of nerve fibers associated with action potentials. Science, 1980, 210(4467), 338-339.
38. Kang, K. H. and Schneider, M. F. Nonlinear pulses at the interface and its relation to state and temperature. Eur. Phys. J. E., 2020, 43, 8.
39. Kaufmann, K. Action Potentials and Electromechanical Coupling in the Macroscopic Chiral Phospholipid Bilayer. Caruaru, 1989.
40. Lundström, I. Mechanical wave propagation on nerve axons. J. Theor. Biol.,1974, 45, 487-499.
41. Martinac, B. and Poole, K. Mechanically activated ion channels. Int. J. Biochem. Cell Biol., 2018, 97, 104-107.
42. Maugin, G. A. and Engelbrecht, J. A thermodynamical viewpoint on nerve pulse dynamics. J. Non-Equilib. Thermodyn., 1994, 19(1), 9-23.
43. Maugin, G. A. and Muschik, W. Thermodynamics with internal variables. Part I. General concepts. J. Non-Equilib. Thermodyn., 1994, 19(3), 217-249.
44. Meissner, S. T. Proposed tests of the soliton wave model of action potentials, and of inducible lipid pores, and how non-electrical phenomena might be consistent with the Hodgkin-Huxley model. arXiv:1808.07193, 2018.
45. Mueller, J. K. and Tyler, W. J. A quantitative overview of biophysical forces impinging on neural function. Phys. Biol., 2014, 11(5), 051001.
46. Mussel, M. and Schneider, M. F. It sounds like an action potential: unification of electrical, chemical and mechanical aspects of acoustic pulses in lipids. arXiv:1806.08551, 2018.
47. Nagumo, J., Arimoto, S., and Yoshizawa, S. An active pulse transmission line simulating nerve axon. Proc. IRE, 1962, 50(10), 2061-2070.
48. National Research Council. Catalyzing Inquiry at the Interface of Computing and Biology. The National Academies Press, Washington, 2005.
49. Nelson, P. C., Radosavljevic ́, M., and Bromberg, S. Biological physics: Energy, Information, Life. W. H. Freeman & Co, New York, 2004.
50. Noble, D. Biophysics and systems biology. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci., 2010, 368(1914), 1125-1139.
51. Perez-Camacho, M. I. and Ruiz-Suárez, J. C. Propagation of a thermo-mechanical perturbation on a lipid membrane. Soft Matter, 2017, 13(37), 6555-6561.
52. Petrov, A. G. Electricity and mechanics of biomembrane systems: flexoelectricity in living membranes. Anal. Chim. Acta, 2006, 568(1-2), 70-83.
53. Porubov, A. V. Amplification of Nonlinear Strain Waves in Solids. World Scientific, Singapore, 2003.
54. Ranade, S. S., Syeda, R., and Patapoutian, A. Mechanically activated ion channels. Neuron, 2015, 87(6), 1162-1179.
55. Richie, J. M. Energetic aspects of nerve conduction: the relationships between heat production, electrical activity and metabolism. Prog. Biophys. Mol. Biol., 1973, 26, 147-187.
56. Ritchie, J. M. and Keynes, R. D. The production and absorption of heat associated with electrical activity in nerve and electric organ. Q. Rev. Biophys., 1985, 18(4), 451-476.
57. Rvachev, M. M. On axoplasmic pressure waves and their possible role in nerve impulse propagation. Biophys. Rev. Lett., 2010, 5(2), 73-88.
58. Tamm, K., Engelbrecht, J., and Peets, T. Temperature changes accompanying signal propagation in axons. J. Non-Equilib. Thermodyn., 2019, 44(3), 277-284.
59. 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.
60. Tasaki, I. and Byrne, P. M. Heat production associated with a propagated impulse in bullfrog myelinated nerve fibers. Jpn. J. Physiol., 1992, 42(5), 805-813.
61. Tasaki, I., Kusano, K., and Byrne, P. M. Rapid mechanical and thermal changes in the garfish olfactory nerve associated with a propagated impulse. Biophys. J., 1989, 55(6), 1033-1040.
62. Terakawa, S. Potential-dependent variations of the intracellular pressure in the intracellularly perfused squid giant axon. J. Physiol., 1985, 369(1), 229-248.
63. Ván, P., Berezovski, A., and Engelbrecht, J. Internal variables and dynamic degrees of freedom. J. Non-Equilib. Thermodyn., 2008, 33(3), 235-254.
64. Watanabe, A. Mechanical, thermal, and optical changes of the nerve membrane associated with excitation. Jpn. J. Physiol., 1986, 36(4), 625-643.
65. Yang, Y., Liu, X.-W., Wang, H., Yu, H., Guan, Y., Wang, S., and Tao, N. Imaging action potential in single mammalian neurons by tracking the accompanying sub-nanometer mechanical motion. ACS Nano, 2018, 12(5), 4186-4193.


Back to Issue