Wave patterns inα-helix proteins with interspine coupling

Abstract

Modulational instability is a direct way by which localized structures emerge in nonlinear systems. We investigate analytically, through the linear stability of plane wave solutions, the existence of localized structures in α-helix proteins with three spines. Through numerical simulations, trains of pulses are found and confirm our analytical predictions. The presence of higher-order interactions between adjacent spines tends to suppress the formed localized structures for erratic ones to emerge. These erratic structures are highly localized and rather reinforce the idea that the energy to be used in metabolic processes is rather confined to specific regions for its efficiency.

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

“…In chemistry, it appears as a continuous-limit model for mesoscopic molecular structures [46]. In protein folding and bending, in the propagation of Davydov's solitons, it is responsible for energy transport and storage along α-helix proteins [8,47,48], bubble propagation and energy localization for specific molecular processes such as DNA transcription and replication [49,50]. In laser propagation, the NLS equation describes the propagation of a laser beam in a medium whose index of reflection is sensitive to the wave amplitude [51][52][53].…”

Energy patterns in twist-opening models of DNA with solvent interactions

“…With some systematic differences, these equations are commonly found in nonlinear optics, biophysics, Bose-Einstein condensates and plasma physics [11,[25][26][27][28]30]. In the context of biomolecular dynamics, they have been shown to be of potential interest in the study of energy transfer and storage in DNA and proteins [11,12,29,30]. Only the stability of their plane-wave solutions will be studied here, while Eq.…”

Bright solitary waves as charge transport in DNA: A variational approximation

“…Solitons are localized solutions of integrable nonlinear partial differential equations which interact elastically, however, the term soliton is often used to refer to localized solutions of non integrable systems of partial differential equations which are indeed called solitary waves. Solitons and solitary waves have been proposed to explain energy transfer in Bose‐Einstein condensates, and energy and charge transfer in physical media like proteins, DNA and many others. A large number of works addressing solitons or solitary waves to explain charge transfer or propagation in DNA have been carried over the years, focusing on different aspects of the DNA molecule as well as many physical, biological and chemical processes that take place within DNA.…”

“…It was suggested in many works that energy and or charge transfer may be activated in different media by the modulational instability mechanism of plane waves . However, though the modulational instability mechanism allows the creation of many bright solitons (bell shape solitons), it fails to provide many important information about the bright solitons generated like their explicit close analytical form which may be used to predict the dynamics of the solitons for different applications.…”