Abstract
The general opinion and knowledge about nonlinear phenomena in the physical sciences has grown quite remarkably within the last 20 years. The prevalence of nonlinear processes in nature has been recognized for a long time — but until recently — also often neglected when dealing with specific problems. This approach was necessary in order to get tractable models which could be handled with the well proven linear mathematical tools, such as Fourier analysis and superposition principles. The fruitful collaboration over the last two decades between applied mathematicians, physicists, and engineers - has however brought about new mathematical tools which makes it possible to deal with certain nonlinear problems in a more systematic way. In particular, there are systems in which nonlinear and dispersive effects coexist and compete — this competition is often relieved by formation of a stable pulselike object — it is in such systems that the concept of the soliton plays a useful role. Especially when viewed as a paradigm for a new nonlinear “normal” mode. This approach has already been applied with success in a number of areas of physics where dispersive and nonlinear effects are important, i.e. condensed matter, plasmas, and optics.1 So it is with some optimism that we are now facing the similar but much more complicated problems in biological systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
See for example: “Physics in One Dimension,” Eds. J. Bernasconi and T. Schneider, Springer Series in Solid-State Sciences, vol. 23, Springer-Verlag, New York (1981).
A. S. Davydov and N. I. Kislukha, Phys. Status Solidi (b), 59, 465 (1973) and Sov. Phys. JETP 44, 571 (1976).
A. S. Davydov, “Biology and Quantum Mechanics,” Pergammon Press (1982).
T. Holstein, Mol. Cryst. Liq. Cryst. 77, 235 (1981).
G. Careri, U. Buontempo, F. Carta, E. Gratton, and A. C. Scott, Phys. Rev. Lett. (in press), see also A. C. Scott’s contribution to these proceedings.
Yu. N. Chirgadze and N. A. Nevskaya, Biopolymers 15, 607 (1976).
W. H. Moore and S. Krimm, Biopolymers 15, 2439 (1976).
N. B. Abbott and A. Elliott, Proc. Roy. Soc. (London) A 234, 247 (1956).
J. M. Hyman in “Nonlinear problems: Present and Future,” Eds. A. R. Bishop, D. K. Campbell, B. Nicolaenko, North Holland Publishing Company (1982) p. 91.
C. J. Brown and D. E. C. Carbridge, Acta Cryst. 7, 711 (1954). I thank L. MacNeil for pointing this reference out to me.
The coordinates used here were kindly supplied by F. Poulsen at the Carlsberg Lab., Copenhagen.
D. J. Thouless, Phys. Rep. 13, 93 (1973).
M. Karplus and J. A. McCammon, C. R. C. Crit. Rev. Biochem. 9, 293 (1981).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 Plenum Press, New York
About this chapter
Cite this chapter
Lomdahl, P.S. (1984). Nonlinear Dynamics of Globular Proteins. In: Adey, W.R., Lawrence, A.F. (eds) Nonlinear Electrodynamics in Biological Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2789-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2789-9_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4612-9720-8
Online ISBN: 978-1-4613-2789-9
eBook Packages: Springer Book Archive