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 Ca2＋ particles is analyzed by solving the system of pertaining reaction-diffusion equations. We used Fourier transform tools to get asymptotic eigenfunctions for tagged (un-tagged) free and buffered Ca2＋ ions. We made some numerical estimations for diffusion coefficients corroborating the fact that messages diffuse faster than Ca2＋ messengers. From the best of our knowledge, this is the first time that Ca2＋ signaling in living cells is biophysically elaborated within the framework of model presented here. We suggest the experimental assay on the basis of radioactive Ca2＋ as tagged probe.

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. 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.

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. Based on the experimental evidences we here elaborate a plausible scenario in which actually calcium ions play the roles of catalytic activators and coordinators of dynein attachments doing it in superposition with already known mechanical control tools of "ciliary beat". Polyelectrolyte properties of microtubules incorporated in axoneme doublets enable the formation and propagation of soliton-like "ionic clouds" of Ca2+ ions along these "coaxial nanocables". The sliding speed of such Ca2+ "clouds" along microtubule doublets is comparable with the speed of propagation of "ciliary beat" itself. We elaborated the interplay between influx of Ca2+ ions in ciliary based body and the sliding of microtubule triplets therein. In second segment we considered how the dynein motors activated by Ca2+ ions contained within solitonic "ionic clouds" in competition with axoneme curvature regulate ciliary and flagellar beating.

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. 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. In this paper we analyze the role of calcium (Ca2+) ions based on the experimental evidence that the flagellar asymmetry can be increased due to the entry of extracellular Ca2+ through, for example, the nimodipine-sensitive pathway located in the flagella. We propose a new scenario based on the polyelectrolyte properties of cellular microtubules (MTs) such that dynamic influx of Ca2+ ions provides the initiation and synchronization of dynein sliding along microtubules. We also point out the possible interplay between tubulin polyglutaminated C-termini and localized pulses of Ca2+ ions along microtubules.

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.

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. We relied onto Langevin equations including fluctuation-dissipation processes. In that context we found out that small interaction between a charged motor neck domain and oppositely charged carboxy-terminal tail of the α-tubulin plays the decisive role in tuning kinesin-1 motor processivity along 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. 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.

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. 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.

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. We discuss how localized pulses of Ca(2+) 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 Ca(2+) 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 Ca(2+) pulses be sufficiently high to exert control at acoustic frequencies.

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. It was shown recently (Zdravkovic and Sataric 2011) that certain values of these parameters bring about a negligible influence of inhomogeneity on the solitonic dynamics. We propose an experiment that should be carried out in order to determine the values of both of these parameters.

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. We show that certain circumstances, i.e. certain values of these parameters, bring about a negligible influence of inhomogeneity on the solitonic dynamics.

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). 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.

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. We show that viscosity, crucial for demodulation, is essential for DNA-RNA transcription.

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.

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. This potential is characterized by the depth D and the inverse width a of the Morse potential well. We discuss one type of single molecule manipulation experiments, which we call unzippering experiments. It is explained that the highest values of two essential parameters of the PBD model, the parameters D and a, can be determined according to the results of those experiments. This statement is supported by theoretical calculations. We show that the inverse width of the Morse potential well a has been overestimated so far. The smallest value for this parameter is determined according to the PBD model, which means that a rather narrow interval can be assumed. Also, we give an idea how to determine the optimal value of the parameter a.

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. The energies are found to be within the expected range.