Modified extended tanh-function method and nonlinear dynamics of microtubules

We here present a model of nonlinear dynamics of microtubules (MT) in the context of modified extended tanh-function (METHF) method. We rely on the ferroelectric model of MTs published earlier by Satari\'c et al [1] where the motion of MT subunits is reduced to a single longitudinal degree of freedom per dimer. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. An analytical solution of the basic equation, describing MT dynamics, was compared with the numerical one and a perfect agreement was demonstrated. It is now clearer how the values of the basic parameters of the model, proportional to viscosity and internal electric field, impact MT dynamics. Finally, we offer a possible scenario of how living cells utilize these kinks as signaling tools for regulation of cellular traffic as well as MT depolymerisation.Comment: 20 pages, 6 figure

Nonlinear DNA dynamics: nonlinearity versus dispersion

In the present paper we study the impact of dispersion and nonlinearity on DNA dynamics. We rely on the helicoidal Peyrard-Bishop model and use the fact that nonlinear DNA dynamics represents an interplay between nonlinearity and dispersion. We state that a dispersion coefficient and a coefficient of nonlinearity, existing in nonlinear Schr\"odinger equation, are mutually dependent and show how function and can be obtained. Also, we show how all this can be used to find a possible interval for the parameter describing helicoidal structure of DNA.Comment: 3 figure

Nonlinear dynamics of microtubules - A new model

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 neighbouring one. A nonlinear partial differential equation, describing dimer`s dynamics within MT, is solved both analytically and numerically. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. Internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled estimation of total energy, kink velocity and kink width. To simplify the calculation of the total energy we proved a useful theorem.Comment: 14 pages, 4 figure

Parallel data transposition in numerical algorithm for solving the Gross-Pitaevski equation

Ova doktorska teza se bavi proučavanjem i razvojem paralelnih algoritama za transponovanje distribuiranih trodimenzionalnih struktura podataka, kao i implementacijom ovih algoritama u okviru C/OpenMP/MPI programske paradigme. Razvijena implementacija je primenjena na rešavanje nelinearne parcijalne diferencijealne jednačine Šredingerovog tipa (Gros-Pitaevski jednačina) korišćenjem Krenk-Nikolson metoda, a u okviru teze je predstavljen ciklus razvoja odgovarajućeg softvera, kao i rezultati testova validnosti i merenja performansi dobijenih na računarskom klasteru.This thesis studies and develops parallel algorithms for transposing distributed three-dimensional data structures, and describes their technical implementation in C/OpenMP/MPI programing paradigm. The developed implementation is applied for solving of nonlinear partial differential equation of the Schroedinger type (Gross-Pitaevskii equation) using Crank-Nicolson method. The thesis presents the corresponding software development cycle, as well as results of validity tests and performance measurements obtained on a computer cluster

Diffusion of Classical Solitons

We study the diffusion and deformation of classical solitons coupled to thermal noise. The diffusion coefficient for kinks in the $\phi^4$ theory is predicted up to the second order in $kT$. The prediction is verified by numerical simulations. Multiskyrmions in the vector O(3) sigma model are studied within the same formalism. Thermal noise results in a diffusion on the multisoliton collective coordinate space (moduli space). There are entropic forces which tend, for example, to bind pairs of solitons into bi-solitonic molecules.Comment: 5 Revtex pages, 2 .ps file

AN IMPROVED NANOSCALE TRANSMISSION LINE MODEL OF MICROTUBULE: THE EFFECT OF NONLINEARITY ON THE PROPAGATION OF ELECTRICAL SIGNALS

In what manner the microtubules, cytoskeletal nanotubes, handle and process electrical signals is still uncompleted puzzle. These bio–macromolecules have highly charged surfaces that enable them to conduct electric signals. In the context of electrodynamic properties of microtubule, the paper proposes an improved electrical model based on its cylindrical structure with nano–pores in its wall. Relying on our earlier ideas, we represent this protein–based nanotube with the surrounding ions as biomolecular nonlinear transmission line with corresponding nanoscale electric elements in it. One of the key aspects is the nonlinearity of associated capacitance due to the effect of shrinking/stretching and oscillation of C–terminal tails. Accordingly, a characteristic voltage equation of electrical model of microtubule and influence of capacitance nonlinearity on the propagation of electrical pulses are numerically analyzed here

One-parameter nonrelativistic supersymmetry for microtubules

The one-parameter nonrelativistic supersymmetry of Mielnik [J. Math. Phys. 25, 3387 (1984)] is applied to the simple supersymmetric model of Caticha [Phys. Rev. A 51, 4264 (1995)] in the form used by Rosu [Phys. Rev. E 55, 2038 (1997)] for microtubules. By this means, we introduce Montroll double-well potentials with singularities that move along the positive or negative traveling direction depending on the sign of the free parameter of Mielnik's method. Possible interpretations of the singularity are either microtubule associated proteins (motors) or structural discontinuities in the arrangement of the tubulin moleculesComment: 6 pages, 5 figures, minor change

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

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

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