Kink solitons in DNA

We here examine the nonlinear dynamics of artificial homogeneous DNA chain relying on the plain-base rotator model. It is shown that such dynamics can exhibit kink and antikink solitons of sine-Gordon type. In that respect we propose possible experimental assays based on single molecule micromanipulation techniques. The aim of these experiments is to excite the rotational waves and to determine their speeds along excited DNA. We propose that these experiments should be conducted either for the case of double stranded (DS) or single stranded (SS) DNA. A key question is to compare the corresponding velocities of the rotational waves indicating which one is bigger. The ratio of these velocities appears to be related with the sign of the model parameter representing ratio of the hydrogen-bonding and the covalent-bonding interaction within the considered DNA chain.Comment: 15 pages, 5 figure

Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.Comment: 14 pages, 15 figures. The high resolution figure files are available by reques

The importance of quantum decoherence in brain processes

Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence timescales ~10^{-13}-10^{-20} seconds are typically much shorter than the relevant dynamical timescales (~0.001-0.1 seconds), both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.Comment: Minor changes to match accepted PRE version. 15 pages with 5 figs included. Color figures and links at http://www.physics.upenn.edu/~max/brain.html or from [email protected]. Physical Review E, in pres

Spectroscopic evidence for Davydov-like solitons in acetanilide

Detailed measurements of infrared absorption and Raman scattering on crystalline acetanilide [(CH3CONHC6H5)x] at low temperature show a new band close to the conventional amide I band. Equilibrium properties and spectroscopic data rule out explanations based on a conventional assignment, crystal defects, Fermi resonance, and upon frozen kinetics between two different subsystems. Thus we cannot account for this band using the concepts of conventional molecular spectroscopy, but a soliton model, similar to that proposed by Davydov for -helix in protein, is in satisfactory agreement with the experimental data. © 1984 The American Physical Society

Calcium signaling modulates the dynamics of cilia and flagella

To adapt to changing environments cells must signal and signaling requires messengers whose concentration varies with time in space. We here consider the messenger role of calcium ions implicated in regulation of the wave-like bending dynamics of cilia and flagella. The emphasis is on microtubules as polyelectrolytes serving as transmission lines for the flow of Ca2+ signals in the axoneme. This signaling is superimposed with a geometric clutch mechanism for the regulation of flagella bending dynamics and our modeling produces results in agreement with experimental data

Resonance mode in DNA dynamics

In this article we use Peyrard-Bishop-Dauxois model (PBD) to study the nonlinear oscillations of DNA nucleotides of extremely high amplitude (EHA) leading to unzipping of DNA chain in the context of the process of replication. We give arguments that the EHA mode is nothing but the resonance mode (RM). We launched an idea about how molecular mechano-chemical energy transduction can be the origin of the RM. We compared some parameters of the solitonic wave in DNA in resonant and non-resonant regime

High amplitude mode and DNA opening

In this article, we define and analyse an extremely high amplitude (EHA) mode in DNA dynamics. The dynamics of a DNA chain is described by the Peyrard-Bishop-Dauxois model. We show that a local opening of the DNA chain in a process of m-RNA transcription is the EHA behaviour. Also, we point out that the helicoidal structure brings about the possibility for the EHA mode to occur

Role of nonlinear localized Ca2+ pulses along microtubules in tuning the mechano-sensitivity of hair cells

This paper aims to provide an overview of the polyelectrolyte model and the current understanding of the creation and propagation of localized pulses of positive ions flowing along cellular microtubules. In that context, Ca2+ ions may move freely on the surface of microtubule along the protofilament axis, thus leading to signal transport. Special emphasis in this paper is placed on the possible role of this mechanism in the function of microtubule based kinocilium, a component of vestibular hair cells of the inner ear. We discuss how localized pulses of Ca2+ ions play a crucial role in tuning the activity of dynein motors, which are involved in mechano sensitivity of the kinocilium. A prevailing notion holds that the concentration of Ca2+ ions around the microtubules within the kinocilium represents the control parameter for Hopf bifurcation. Therefore, a key feature of this mechanism is that the velocities of these Ca2+ pulses be sufficiently high to exert control at acoustic frequencies. (C) 2015 Elsevier Ltd. All rights reserved

Nonlinear dynamics of C-terminal tails in cellular microtubules

The mechanical and electrical properties, and information processing capabilities of microtubules are the permanent subject of interest for carrying out experiments in vitro and in silico, as well as for theoretical attempts to elucidate the underlying processes. In this paper, we developed a new model of the mechano-electrical waves elicited in the rows of very flexible C-terminal tails which decorate the outer surface of each microtubule. The fact that C-terminal tails play very diverse roles in many cellular functions, such as recruitment of motor proteins and microtubule-associated proteins, motivated us to consider their collective dynamics as the source of localized waves aimed for communication between microtubule and associated proteins. Our approach is based on the ferroelectric liquid crystal model and it leads to the effective asymmetric double-well potential which brings about the conditions for the appearance of kink-waves conducted by intrinsic electric fields embedded in microtubules. These kinks can serve as the signals for control and regulation of intracellular traffic along microtubules performed by processive motions of motor proteins, primarly from kinesin and dynein families. On the other hand, they can be precursors for initiation of dynamical instability of microtubules by recruiting the proper proteins responsible for the depolymerization process. Published by AIP Publishing

Nonlinear calcium ion waves along actin filaments control active hair–bundle motility

Calcium ions (Ca2+) tune and control numerous diverse aspects of cochlear and vestibular physiological processes. This paper is focused on the Ca2+ control of mechanotransduction in sensory hair cells in the context of polyelectrolyte properties of actin filaments within the hair–bundles of inner ear. These actin filaments appear to serve as efficient pathways for the flow of Ca2+ ions inside stereocilia. We showed how this can be utilized for tuning of force–generating myosin motors. In an established model, we unified the Ca2+ nonlinear dynamics involved in the control of myosin adaptation motors with mechanical displacements of hair–bundles. The model shows that the characteristic time scales fit reasonably well with the available experimental data for spontaneous oscillations in the inner ear. This scenario promises to fill a gap in our understanding of the role of Ca2+ ions in the regulation of processes in the auditory cells of the inner ear. © 2018 Elsevier B.V