Application of Morse potential in nonlinear dynamics of microtubules

We here present a model of nonlinear dynamics of microtubules using modified extended tanh-function method as a mathematical tool. Interaction between neighbouring dimers belonging to a single protofilament is commonly modelled by a harmonic potential. In this paper, we introduce a more realistic Morse potential energy instead. We obtained three solitary waves as before, when the harmonic potential was used. However, the Morse potential allows transition from the state when elastic term in the expression for total energy is bigger than the inertial one to the state when the inertial potential is bigger. Also, three new solutions were obtained

Why are Biological Systems Nonlinear?

Biological systems are nonlinear due to existence of weak interactions between its constituent parts. In this short review we deal with two very important biological systems, DNA molecule and microtubule. We show how different nonlinear terms in their Hamiltonians, together with different mathematical procedures, yield to different final results. In case of DNA, nonlinearity is modeled by Morse potential and the final result is nonlinear wave called breather moving along its chain. On the other hand, nonlinearity existing in microtubule is modeled by W-potential, which brings about kink soliton as the final result

Generation of Optical-Terahertz Solitons in Quadratically Nonlinear Media

The possibility of generation of new type of optical-terahertz solitons by resonant optical rectification in quadratically nonlinear media is examined. The existence of various types of solitons is analyzed. Bound solitonic state of an optical laser pulse and a terahertz few cycle pulse becomes possible under condition of equality of the group velocity vg of optical pulse to the phase velocity vph of terahertz pulse. The conditions of soliton stability in bulk medium are discussed

Why are Biological Systems Nonlinear?

Biological systems are nonlinear due to existence of weak interactions between its constituent parts. In this short review we deal with two very important biological systems, DNA molecule and microtubule. We show how different nonlinear terms in their Hamiltonians, together with different mathematical procedures, yield to different final results. In case of DNA, nonlinearity is modeled by Morse potential and the final result is nonlinear wave called breather moving along its chain. On the other hand, nonlinearity existing in microtubule is modeled by W-potential, which brings about kink soliton as the final result

Generation of Optical-Terahertz Solitons in Quadratically Nonlinear Media

The possibility of generation of new type of optical-terahertz solitons by resonant optical rectification in quadratically nonlinear media is examined. The existence of various types of solitons is analyzed. Bound solitonic state of an optical laser pulse and a terahertz few cycle pulse becomes possible under condition of equality of the group velocity vg of optical pulse to the phase velocity vph of terahertz pulse. The conditions of soliton stability in bulk medium are discussed

Demodulated standing solitary wave and DNA-RNA transcription

Nonlinear dynamics of DNA molecule at segments where DNA-RNA transcription occurs is studied. Our basic idea is that the solitary wave, moving along the chain, transforms into a demodulated one at these segments. The second idea is that the wave becomes a standing one due to interaction with DNA surrounding, e.g., RNA polymerase molecules. We explain why this is biologically convenient and show that our results match the experimental ones. In addition, we suggest how to experimentally determine crucial constant describing covalent bonds within DNA. © 2018 Author(s)

Monte Carlo track structure simulation in studies of biological effects induced by accelerated charged particles in the central nervous system

Simulating the biological damage induced by charged particles trajectories (tracks) in the central nervous system (CNS) at different levels of its organization (molecular, cellular, and tissue) is a challenge of modern radiobiology studies. According to the recent experimental studies at particle accelerators, the most radiation-sensitive area of the CNS is the hippocampus. In this regards, the development of measurement-based Monte Carlo simulation of radiation-induced alterations in the hippocampus is of great interest to understand the radiobiological effects on the CNS. The present work investigates the influence of charged particles on the hippocampal cells of the rat brain using the Geant4 Monte Carlo radiation transport code. The applied computer simulation provides a method to simulate physics processes and chemical reactions in the developed model of the rat hippocampus, which contains different types of neural cells - pyramidal cells, mature and immature granular cells, mossy cells, and neural stem cells. The distribution of stochastic energy depositions has been obtained and analyzed in critical structures of the hippocampal neurons after irradiation with 600 MeV/u iron particles. The computed energy deposition in irradiated hippocampal neurons following a track of iron ion suggests that most of the energy is accumulated by granular cells. The obtained quantities at the level of molecular targets also assume that NMDA and GABA receptors belong to the most probable targets in the irradiated neural cells

Monte Carlo track structure simulation in studies of biological effects induced by accelerated charged particles in the central nervous system

Simulating the biological damage induced by charged particles trajectories (tracks) in the central nervous system (CNS) at different levels of its organization (molecular, cellular, and tissue) is a challenge of modern radiobiology studies. According to the recent experimental studies at particle accelerators, the most radiation-sensitive area of the CNS is the hippocampus. In this regards, the development of measurement-based Monte Carlo simulation of radiation-induced alterations in the hippocampus is of great interest to understand the radiobiological effects on the CNS. The present work investigates the influence of charged particles on the hippocampal cells of the rat brain using the Geant4 Monte Carlo radiation transport code. The applied computer simulation provides a method to simulate physics processes and chemical reactions in the developed model of the rat hippocampus, which contains different types of neural cells - pyramidal cells, mature and immature granular cells, mossy cells, and neural stem cells. The distribution of stochastic energy depositions has been obtained and analyzed in critical structures of the hippocampal neurons after irradiation with 600 MeV/u iron particles. The computed energy deposition in irradiated hippocampal neurons following a track of iron ion suggests that most of the energy is accumulated by granular cells. The obtained quantities at the level of molecular targets also assume that NMDA and GABA receptors belong to the most probable targets in the irradiated neural cells

Stationary solitary and kink solutions in the helicoidal Peyrard-Bishop model of DNA molecule

We study nonlinear dynamics of the DNA molecule relying on a helicoidal Peyrard-Bishop model. We look for traveling wave solutions and show that a continuum approximation brings about kink solitons moving along the chain. This statement is supported by the numerical solution of a relevant dynamical equation of motion. Finally, we argue that an existence of both kinks and localized modulated solitons (breathers) could be a useful tool to describe DNA-RNA transcription. © 2019 Author(s)

Localized modulated waves and longitudinal model of microtubules

We here study nonlinear dynamics of microtubule (MT). A so-called u - model is explained in detail. A single longitudinal degree of freedom per MT subunits is assumed. It is known that a continuum approximation of a basic discrete dynamical equation of motion enables existence of kink and antikink solitons along MT. In this paper we use semi- discrete approximation for this equation and show that modulated solitonic waves could propagate as well. We suggest possible biological implications of these waves. Also, a detailed parameter analysis is performed. (C) 2016 Elsevier Inc. All rights reserved