Nonlinear Dynamics of Globular Proteins

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.