Kinks and bell-type solitons in microtubules

Abstract

In the present paper, we study the nonlinear dynamics of microtubules relying on the known u-model. As a mathematical procedure, we use the simplest equation method. We recover some solutions obtained earlier using less general methods. These are kink solitons. In addition, we show that the solution of the crucial differential equation, describing nonlinear dynamics of microtubules, can be a bell-type soliton. The discovery of this new solution is supported by numerical analysis.

Mechanical Models of Microtubules

“…It turns out that, instead of the three lines in Figure 2, that is, the three solutions, we obtain infinitely many lines corresponding to each of them [39]. However, they represent three groups of parallel lines, which means that all these solutions are only shifted functions and, consequently, have equal physical meaning.…”

“…It is very likely that the most general procedure is the simplest equation method (SEM) [39][40][41] and its simplified version called as modified simplest equation method (MSEM) [42]. According to SEM, the series expansion is [39][40][41].…”

“…This brings about a system of seven equations, which can be obtained using Mathematica or similar software [39]. One of them can be written as…”

“…Also, K should be real and these two requirements eliminate Ψ 2 and Ψ 3 [39], which means that Ψ and A 0 in Eq. (19) are Ψ 1 and A 01 .…”

Randomness in microtubule dynamics: an error that requires correction or an inherent plasticity required for normal cellular function?

“…MT dynamics are compromised in degenerative diseases, such as Alzheimer's disease (Dent, 2017). The nonlinear dynamics that MTs rely on have been described as bell-type (Zdravkovic and Gligoric, 2016). Nucleotide hydrolysis drives the dynamics that are controlled by proteins, such as MT-associated proteins.…”