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.

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.

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.