On the role of calcium diffusion and its rapid buffering in intraflagellar signaling.

We have considered the realistic mechanism of rapid Ca (calcium ion) buffering within the wave of calcium ions progressing along the flagellar axoneme. This buffering is an essential part of the Ca signaling pathway aimed at controlling the bending dynamics of flagella. It is primarily achieved by the mobile region of calmodulin molecules and by stationary calaxin, as well as by the part of calmodulin bound to calcium/calmodulin-dependent kinase II and kinase C.

Calcium messages in flagella are faster than messenger particles.

Calcium is one of the most versatile messengers for intracellular signaling. In the case of cilia and flagella calcium has the central role in transfer of communications between extracellular stimuli and intracellular formation of frequency modulated signal and their deciphering by target proteins. In this paper, the diffusion of fluorescently or otherwise tagged and un-tagged Ca particles is analyzed by solving the system of pertaining reaction-diffusion equations.

Decoding the Bell-Shaped Calcium Spikes in Phosphorylation Cycles of Flagella.

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.

Calcium signal transmission by axonemal microtubules as an optimized information pathway in cilia and flagella.

Calcium plays a key role in signal transduction in eukaryotic cells. Besides controlling local functions of cells calcium ions are responsible for the generation of global signals such as waves and spikes. Pulsatile increases of calcium concentrations are generally considered to have a much higher fidelity of information transfer than simple tonic changes, since they are much less prone to noisy fluctuations.

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 Ca signals in the axoneme.

Calcium ions tune the beats of cilia and flagella.

The cytoskeleton of cilia and flagella is so called axoneme a stable cylindrical architecture of nine microtubule doublets. Axoneme performs periodic bending motion by utilizing specific dynein motor family powered by ATP hydrolysis. It is still unclear how this highly organized "ciliary beat" is being initiated and strongly coordinated by the combined action of hundreds dynein motors.

How signals of calcium ions initiate the beats of cilia and flagella.

Cilia 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.

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.

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

Calcium ions (Ca) tune and control numerous diverse aspects of cochlear and vestibular physiological processes. This paper is focused on the Ca 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 Ca ions inside stereocilia.

A biophysical model of how α-tubulin carboxy-terminal tails tune kinesin-1 processivity along microtubule.

It appears that so-called post-translational modifications of tubulin heterodimers are mostly focussed at positions of amino acid sequences of carboxy-terminal tails. These changes have very profound effects on microtubule functions especially in connection with cellular traffic in terms of motor proteins. In this study, we elaborated the biophysical model aimed to explain the strategy governing these subtle interplays between structural and functional properties of microtubules.

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.

Actin filaments as the fast pathways for calcium ions involved in auditory processes.

We investigated 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.

Role of nonlinear localized Ca(2+) 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, Ca(2+) 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.

Morse potential in DNA molecule - an experiment proposal.

We rely on the helicoidal Peyrard-Bishop model for DNA dynamics. Interaction between nucleotides at a same site belonging to different strands is modelled by a Morse potential energy. This potential depends on two parameters that are different for AT and CG pairs, which is a possible source for inhomogeneity.

Modeling of relay helix functional dynamics and feasibility of experimental verification by neutron scattering.

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).

Nonlinear ionic pulses along microtubules.

Microtubules are cylindrically shaped cytoskeletal biopolymers that are essential for cell motility, cell division and intracellular trafficking. Here, we investigate their polyelectrolyte character that plays a very important role in ionic transport throughout the intra-cellular environment. The model we propose demonstrates an essentially nonlinear behavior of ionic currents which are guided by microtubules.

Transverse interaction in DNA molecule.

Interaction between nucleotides at a same site belonging to different strands is studied. This interaction is modelled by a Morse potential which depends on two parameters. We study a relationship between the parameters characterizing AT and CG pairs.

DNA-RNA transcription as an impact of viscosity.

The impact of viscosity on DNA dynamics is studied both analytically and numerically. It is assumed that the viscosity exists at the segments where DNA molecule is surrounded by RNA polymerase. We demonstrate that the frictional forces destroy the modulation of the incoming solitonic wave.

A nonlinear model of ionic wave propagation along microtubules.

Microtubules (MTs) are important cytoskeletal polymers engaged in a number of specific cellular activities including the traffic of organelles using motor proteins, cellular architecture and motility, cell division and a possible participation in information processing within neuronal functioning. How MTs operate and process electrical information is still largely unknown. In this paper we investigate the conditions enabling MTs to act as electrical transmission lines for ion flows along their lengths.

Modelling the role of intrinsic electric fields in microtubules as an additional control mechanism of bi-directional intracellular transport.

Active transport is essential for cellular function, while impaired transport has been linked to diseases such as neuronal degeneration. Much long distance transport in cells uses opposite polarity molecular motors of the kinesin and dynein families to move cargos along microtubules. It is clear that many types of cargo are moved by both sets of motors, and frequently in a reverse direction.

Solitonic speed in DNA.

We propose a single molecule experiment that could be carried out in order to measure a solitonic wave speed in DNA. In addition, we discuss possible values of the speed according to the Peyrard-Bishop-Dauxois model of DNA dynamics.

Complex movements of motor protein relay helices during the power stroke.

We use the Toda soliton formalism to propose a possible complex movement of alpha helices with a very important role in energy transduction during the power stroke of motor proteins. We find that this approach has advantages in comparison with the Davydov soliton model and its variants. We estimated the model's parameters and calculated corresponding properties of the predicted solitary waves including propagation velocities and energies.

Single-molecule unzippering experiments on DNA and Peyrard-Bishop-Dauxois model.

In this paper, we rely on a nonlinear Peyrard-Bishop-Dauxois (PBD) model. This mechanical model explains DNA dynamics assuming only transversal oscillations of nucleotides. The potential energy for the hydrogen bonds, connecting AT or CG base pairs, is modeled by a Morse potential.

Nonlinear dynamics of microtubules: biophysical implications.

A recently developed model of nonlinear dynamics for microtubules is further expanded based on the biophysical arguments involving the secondary structure of the constitutive protein tubulin and on the ferroelectric properties of microtubules. It is demonstrated that kink excitations arise due to GTP hydrolysis that causes a dynamical transition in the structure of tubulin. The presence of an intrinsic electric field associated with the structure of a microtubule leads to unidirectional propagation of the kink excitation along the microtubule axis.

Gravitational symmetry breaking leads to a polar liquid crystal phase of microtubules in vitro.

Recent space-flight experiments performed by Tabony's team provided further evidence that a microgravity environment strongly affects the spatio-temporal organization of microtubule assemblies. Characteristic time and length scales were found that govern the organization of oriented bundles under Earth's gravitational field (GF). No such organization has been observed in a microgravity environment.