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We establish a new model for ionic waves along microtubules based on polyelectrolyte features of cylindrical biopolymers. The nonlinear transmission line described by a nonlinear differential equation is obtained with stable kink solution... more
We establish a new model for ionic waves along microtubules based on polyelectrolyte features of cylindrical biopolymers. The nonlinear transmission line described by a nonlinear differential equation is obtained with stable kink solution pertinent to the shape of the front of accompanying potential. The localized ionic wave could be used to explain the behavior of microtubules as biomolecular transistors capable
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We investigate the messenger role of calcium ions implicated in the regulation of wave-like bending dynamics of flagella. The emphasis is on microtubules of flagellar axoneme serving as nonlinear transmission lines for bell-shaped spikes... more
We investigate the messenger role of calcium ions implicated in the regulation of wave-like bending dynamics of flagella. The emphasis is on microtubules of flagellar axoneme serving as nonlinear transmission lines for bell-shaped spikes of calcium ions. The calcium sensitive proteins, such as calmodulin, exhibit activation dependence on the spike train frequency and amplitude. Here, we analyze a Ca2+ decoding module IDA-I1 whose activity is controlled by Ca2+ activated kinase. We find that trains of Ca2+ spikes are advantageous compared to a constant rise in Ca2+ concentration as being more efficient and much less prone to noisy fluctuations.
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It has already been shown that it is possible to compare semiconducter properties of silicon with biological carbon. In this paper we give some electronic properties of tubulin and microtubule. Our approach based on a new classification... more
It has already been shown that it is possible to compare semiconducter properties of silicon with biological carbon. In this paper we give some electronic properties of tubulin and microtubule. Our approach based on a new classification of the sxino acid side chzins 2nd their distribution in tubulin. We assumed that in the process of microtubule self-assembly the attaching of
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In this paper we examine the nonlinear dynamics of a DNA chain whose exciton modes are affected by regulatory proteins that may become bound to the DNA chain by hydrogen bonds. The dynamics of the DNA chain is described by the... more
In this paper we examine the nonlinear dynamics of a DNA chain whose exciton modes are affected by regulatory proteins that may become bound to the DNA chain by hydrogen bonds. The dynamics of the DNA chain is described by the Peyrard-Bishop model. Since this model gives rise to large-amplitude broad oscillations of base pairs, we consider the impact of attached regulatory proteins on the so-called breathers or bubbles. Assuming that an ideal gas of bubbles may exist in the DNA chain at physiological temperatures we adopt a statistical approach to calculate the average size of base-pair stretching under the prevailing conditions.
Research Interests: Engineering, Physics, Biophysics, Nonlinear dynamics, Statistical Physics, and 15 moreMedicine, Enzyme Kinetics, DNA, Mathematical Sciences, Physical sciences, Temperature, Oscillations, Physical, Hydrogen Bonding, Nonlinear system, Protein Binding, Adenine, Physical Properties, Nucleic Acid Conformation, and Nucleic Acid
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ABSTRACT The manner in which microtubules, the essential cellular biopolymers, handle and process electrical signals is still uncompleted puzzle. In this paper, we have elaborated some new electrodynamic properties of these protein-based... more
ABSTRACT The manner in which microtubules, the essential cellular biopolymers, handle and process electrical signals is still uncompleted puzzle. In this paper, we have elaborated some new electrodynamic properties of these protein-based nanotubes, specifically, their ability to conduct ionic currents. In that context, it has been established an improved electrical model of microtubule as biomolecular nonlinear transmission line. We described the basic nanoscale electric elements of model and estimated the corresponding parameters, stressing the particular importance of tubulin C-termini. The properties of the localized electric nanocurrent of positive ions and accompanying voltage along a microtubule are analytically and numerically analyzed here.
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ABSTRACT Extensive research is underway to understand and exploit the interface between biomacromolecules and integrated systems. An ideal biological candidate for use in nanoscale electronic devices is the microtubule, an essential... more
ABSTRACT Extensive research is underway to understand and exploit the interface between biomacromolecules and integrated systems. An ideal biological candidate for use in nanoscale electronic devices is the microtubule, an essential component of the eukaryotic cytoskeleton, which has been shown to be electrically conductive. In this paper, we theoretically analysed the possible use of microtubules as protein structure for building biomolecular nanoscale nonlinear transmission lines in the context of the polyelectrolyte character of these cytoskeletal filaments. We verify these hypotheses both analytically and computationally through a quantitative electrical model based on the atomic resolution structures of the key functional proteins. Each tubulin dimmer protein is an electric element with a capacitive, inductive, and resistive property due to the molecular structure of microtubules.
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We study DNA dynamics relying on the plane-base rotator model for DNA. It is shown that this dynamics can be represented by kink and antikink solitons. We demonstrate that two velocities are relevant and these are the velocities of both a... more
We study DNA dynamics relying on the plane-base rotator model for DNA. It is shown that this dynamics can be represented by kink and antikink solitons. We demonstrate that two velocities are relevant and these are the velocities of both a double and a single stranded DNA. A key question is which one is bigger as this is related to a value of the ratio of two parameters describing the hydrogen and the covalent interactions in DNA. If the velocity of double stranded DNA is larger than one of the single stranded chain then the two ferromagnetic strands are coupled antiferromagnetically. Otherwise, the two DNA strands are coupled ferromagnetically. We discuss possible experiments based on micromanipulation techniques that should be carried out to determine these velocities and the solitonic width.
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ABSTRACT We argue that a breather wave, describing DNA dynamics, behaves like a real soliton. We rely on a Peyrard–Bishop–Dauxois (PBD) model. In addition, we propose a couple of experiments to confirm or reject this statement. These... more
ABSTRACT We argue that a breather wave, describing DNA dynamics, behaves like a real soliton. We rely on a Peyrard–Bishop–Dauxois (PBD) model. In addition, we propose a couple of experiments to confirm or reject this statement. These experiments should study solitonic interactions using micromanipulation technique. Also, we suggest how to measure a solitonic width and its amplitude.
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Research Interests: Physics, Gravitation, Pattern Formation, Biological Physics, Chemical Physics, and 12 moreMedicine, Chemical Kinetics, Space flight, Diffusion, Microtubule Dynamics, Symmetry Breaking, Length scale, Liquid Crystal, Gravitational Field, Liquid Crystalline, Thermal fluctuation, and Electrostatic interaction
ABSTRACT 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... more
ABSTRACT 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.
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ABSTRACT 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... more
ABSTRACT 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.
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ABSTRACT We compare optical and acoustical frequencies in the Peyrard–Bishop–Dauxois model, i.e. an extended Peyrard–Bishop model, of DNA molecules. We discuss how ratio of those frequencies depends on a value of the harmonic constant of... more
ABSTRACT We compare optical and acoustical frequencies in the Peyrard–Bishop–Dauxois model, i.e. an extended Peyrard–Bishop model, of DNA molecules. We discuss how ratio of those frequencies depends on a value of the harmonic constant of the helicoidal spring K. Also, we suggest that the most favourable mode could be a resonance mode.
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Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into... more
Cellular long-range transport involves motor proteins (MPs) (especially, kinesin and myosin) which contain a so-called relay helix. Its motion is of crucial importance to the conversion of chemical energy released in ATP hydrolysis into the coordinated mechanical movement of the entire motor protein. In this paper, we propose two combined nonlinear mechanisms for this particular functional activity and suggest the application of neutron scattering assays to experimentally determine the incoherent dynamic structure factor S(q,ω). We argue that this type of experiment is not only feasible but it could offer significant insights into the mechanism of MP function at a molecular level.
Research Interests: Mathematics, Applied Mathematics, Nonlinear dynamics, Neutron Diffraction, Medicine, and 15 moreChaos, Computer Simulation, Feasibility Studies, Myosin, Molecular motor proteins, Motion, Kinesin, Numerical Analysis and Computational Mathematics, RELAY, Protein Conformation, Neutron Scattering, Neutron, Structure activity Relationship, Molecular Motor, and ATP hydrolysis
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Research Interests: Mathematics, Applied Mathematics, Computer Science, Symbolic Computation, Cell Signaling, and 12 moreComputation, Maple Computer Algebra System, Cognitive Process, Microtubules, PARTIAL DIFFERENTIAL EQUATION, Nonlinear system, Numerical Analysis and Computational Mathematics, Transmission Line, Solitary Wave, Soliton, nonlinear equation, and Nonlinear partial differential equation
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Research Interests: Engineering, Biophysics, Nonlinear dynamics, Crystallization, Chemical Physics, and 15 moreMedicine, Cytoskeleton, Mathematical Sciences, Animals, Energy Balance, Iron, Microtubules, Physical, Ferroelectricity, Liquid Crystal, Nonlinear system, Dimer, Hydrolysis, Physical Properties, and Dimerization
In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation... more
In this paper, we performed analytical, numerical and experimental studies on the generation of soliton waves in discrete nonlinear transmission lines (NLTL) with varactors, as well as the analysis of the losses impact on the propagation of these waves. Using the reductive perturbation method, we derived a nonlinear Schrödinger (NLS) equation with a loss term and determined an analytical expression that completely describes the bright soliton profile. Our theoretical analysis predicts the carrier wave frequency threshold above which a formation of bright solitons can be observed. We also performed numerical simulations to confirm our analytical results and we analyzed the space–time evolution of the soliton waves. A good agreement between analytical and numerical findings was obtained. An experimental prototype of the lossy NLTL, built at the discrete level, was used to validate our proposed model. The experimental shape of the envelope solitons is well fitted by the theoretical wav...
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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... more
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.
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ABSTRACTCilia and flagella are cell organelles serving basic roles in cellular motility. Ciliary movement is performed by a sweeping-like repeated bending motion, which gives rise to a self-propagating “ciliary beat”. The hallmark... more
ABSTRACTCilia and flagella are cell organelles serving basic roles in cellular motility. Ciliary movement is performed by a sweeping-like repeated bending motion, which gives rise to a self-propagating “ciliary beat”. The hallmark structure in cilia is the axoneme, a stable architecture of microtubule doublets. The motion of axoneme is powered by the axonemal dynein motor family powered by ATP hydrolysis. It is still unclear how the organized beat of cilium and flagella emerges from the combined action of hundreds of dynein molecules. It has been hypothesized that such coordination is mediated by mechanical stress due to transverse, radial or sliding deformations. The beating asymmetry is crucial for airway ciliary function and it requires tubulin glutamination a unique posttranslational modification of C-termini of constituent microtubules that is highly abundant in cilia and flagella. The exact role of tubulin glutamination in ciliary or flagellar function is still unclear. Here w...
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ABSTRACT Without Abstract
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ABSTRACT We investigate the polyelectrolyte properties of actin filaments which are in interaction with myosin motors, basic participants in mechano–electrical transduction in the stereocilia of the inner ear. Here, we elaborated a model... more
ABSTRACT We investigate the polyelectrolyte properties of actin filaments which are in interaction with myosin motors, basic participants in mechano–electrical transduction in the stereocilia of the inner ear. Here, we elaborated a model in which actin filaments play the role of guides or pathways for localized flow of calcium ions. It is well recognized that calcium ions are implicated in tuning of actin–myosin cross–bridge interaction, which controls the mechanical property of hair bundle. Actin filaments enable much more efficient delivery of calcium ions and faster mechanism for their distribution within the stereocilia. With this model we were able to semiquantitatively explain experimental evidences regarding the way of how calcium ions tune the mechanosensitivity of hair cells.
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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... more
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 for divalent ions (Ca2+ and Mg2+) based on the cylindrical structure of microtubule 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.
... Parameter selection in a Peyrard–Bishop–Dauxois model for DNA dynamics. ... Available online 21 May 2009. Abstract. In this Letter we study possible intervals for some parameters existing in the Peyrard–Bishop–Dauxois (PBD) model for... more
... Parameter selection in a Peyrard–Bishop–Dauxois model for DNA dynamics. ... Available online 21 May 2009. Abstract. In this Letter we study possible intervals for some parameters existing in the Peyrard–Bishop–Dauxois (PBD) model for the DNA dynamics. ...
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In recent years, the use of biological molecules has offered exciting alternatives to conventional synthetic methods. Specific methods use various biological templates to direct the deposition and patterning of inorganic materials. Here... more
In recent years, the use of biological molecules has offered exciting alternatives to conventional synthetic methods. Specific methods use various biological templates to direct the deposition and patterning of inorganic materials. Here we have established a new electrical model of microtubules as a biological nanoscale circuit based on polyelectrolyte features of cylindrical biopolymers. Our working hypothesis is that microtubules play an active role in sub-cellular computation and signaling via electronic and protonic conductivity and can thus be made useful in hybrid materials that offer novel electronic characteristics. We verify these hypotheses both computationally and analytically through a quantitative model based on the atomic resolution structures of the key functional proteins.
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... View Within Article. A single TB dimer has about 40e negative charges [13]. If only 10% of this charge is unscreened by counterions, then qeff=4e and the Bjerrum length , with ε=80 for water, at room temperature, can reach about 15... more
... View Within Article. A single TB dimer has about 40e negative charges [13]. If only 10% of this charge is unscreened by counterions, then qeff=4e and the Bjerrum length , with ε=80 for water, at room temperature, can reach about 15 nm. ...
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We study a possible solitary wave solution of the nonlinear Schrodinger equation (NLSE). It is shown that the wave can be both modulated and nonmodulated depending on a ratio of the envelope and the carrier wave velocities. We also study... more
We study a possible solitary wave solution of the nonlinear Schrodinger equation (NLSE). It is shown that the wave can be both modulated and nonmodulated depending on a ratio of the envelope and the carrier wave velocities. We also study the same type of the soliton solution in DNA dynamics. We show that the ratio of these two velocities is a measure of modulation and we conclude that the modulated wave is more stable than the nonmodulated one. Finally, we solved the problem concerning three parameters arising from the applied procedure for the solution of the NLSE.