Related papers: Modified extended tanh-function method and nonline…
In the present paper we describe a model of nonlinear dynamics of microtubules (MT) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the…
In the present paper we deal with nonlinear dynamics of microtubules (MTs). The structure and role of MTs in cells are explained. One model explaining MT dynamics is explained. Solutions of the crucial nonlinear differential equation depend…
A novel theoretical model of dynamic instability of a system of linear (1D) microtubules (MTs) in a bounded domain is introduced for studying the role of a cell edge in vivo and analyzing the effect of competition for a limited amount of…
Microtubules (MTs) represent basic components of a cytoskeleton. The present work studies nonlinear dynamics of MTs assuming tangential oscillations of the dimers. We introduce a two component model and show that the dynamics of MTs can be…
Microtubules (MTs) are the most important part of cytoskeleton. In this paper we deal with two basic nonlinear differential equations coming from the two known models describing nonlinear dynamics of MTs. These equations are solved using…
In this paper we propose a microscopic model to study the polymerization of microtubules (MTs). Starting from fundamental reactions during MT's assembly and disassembly processes, we systematically derive a nonlinear system of equations…
In this work we study a microtubule (MT) model, whose length is regulated by the action of processive kinesin motors. We treat the case of infinite processivity, i.e. particle exchange in the bulk is neglected. The exact results can be…
Microtubules (MTs) are dynamic protein filaments essential for intracellular organization and transport, particularly in long-lived cells such as neurons. The plus and minus ends of neuronal MTs switch between growth and shrinking phases,…
We focus on potential mechanisms for `energy-loss-free' transport along the cell microtubules, which could be considered as realizations of Fr\"ohlich's ideas on the role of solitons for superconductivity and/or biological matter. In…
Nonlinear dynamics of two biomolecules is studied. These are a microtubule and DNA molecule. Two mathematical procedures are explained, yielding to three kinds of solitary waves moving through the systems. These waves are kinks, modulated…
The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh-Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling…
Length-regulation of microtubules (MTs) is essential for many cellular processes. Molecular motors like kinesin 8, which move along MTs and also act as depolymerases, are known as key players in MT dynamics. However, the regulatory…
The nonlinear evolution of the m=1 internal kink mode is studied numerically in a setting where the tokamak core plasma is surrounded by a turbulent region with low magnetic shear. As a starting point we choose configurations with three…
In this study, a two-state mechanochemical model is presented to describe the dynamic instability of microtubules (MTs) in cells. The MTs switches between two states, assembly state and disassembly state. In assembly state, the growth of…
This paper provides the phase transition analysis of a reaction diffusion equations system modeling dynamic instability of microtubules. For this purpose we have generalized the macroscopic model studied by Mour\~ao et all [MSS]. This model…
Microtubules (MTs) are filamentous protein polymers roughly 25 nm in diameter. Ubiquitous in eukaryotes, MTs are well known for their structural role but also act as actuators, sensors, and, in association with other proteins, checkpoint…
Starting from the hypothesis that the tubulin dimer is a conformationally bistable molecule - fluctuating between a curved and a straight configuration at room temperature - we develop a model for polymorphic dynamics of the microtubule…
We propose an approach that links density functional theory (DFT) and molecular dynamics (MD) simulation to study fluid behavior in nanopores in contact with bulk (macropores). It consists of two principal steps. First, the theoretical…
Reduced magnetohydrodynamic (MHD) equations are used to study the nonlinear dynamics of external kinks in a quasi-axisymmetric (QA) stellarator with varying fractions of external rotational transform. The large bootstrap currents associated…
Deep learning algorithms provide a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. Development of novel model reduction methods, coupled with detection of abnormal modes with plasma…