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Calcium ions (Ca 2+ ) tune and control numerous diverse aspects of cochlear and vestibular physiological processes. This paper is focused on the Ca 2+ 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 2+ ions inside stereocilia. We showed how this can be utilized for tuning of force-generating myosin motors. In an established model, we unified the Ca 2+ 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 Ca 2+ ions in the regulation of processes in the auditory cells of the inner ear., (Copyright © 2018 Elsevier B.V. All rights reserved.)

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., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

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.

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., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

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.

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. The general question of how the direction of transport is regulated is still open. The mechanism of the cell's differential control of diverse cargos within the same cytoplasmic background is still unclear as is the answer to the question how endosomes and mitochondria move to different locations within the same cell. To answer these questions we postulate the existence of a local signaling mechanism used by the cell to specifically control different cargos. In particular, we propose an additional physical mechanism that works through the use of constant and alternating intrinsic (endogenous) electric fields as a means of controlling the speed and direction of microtubule-based transport. A specific model is proposed and analyzed in this paper. The model involves the rotational degrees of freedom of the C-termini of tubulin, their interactions and the coupling between elastic and dielectric degrees of freedom. Viscosity of the solution is also included and the resultant equation of motion is found as a nonlinear elliptic equation with dissipation. A particular analytical solution of this equation is obtained in the form of a kink whose properties are analyzed. It is concluded that this solution can be modulated by the presence of electric fields and hence may correspond to the observed behavior of motor protein transport along microtubules.

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. This mechanism offers an explanation of the dynamic instability phenomenon in terms of the electric field effects. Moreover, a possible elucidation of the unidirectional transport of cargo via motor proteins such as kinesin and dynein is proposed within the model developed in this paper.

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. This paper discusses physical mechanisms resulting in pattern formation under gravity and its disappearance in microgravity. The subtle interplay between chemical kinetics, diffusion, gravitational drift, thermal fluctuations, electrostatic interactions and liquid crystalline characteristics provides a plausible scenario.

Tabony and co-workers [C. Papaseit, N. Pochon, and J. Tabony, Proc. Natl. Acad. Sci. U.S.A. 97, 8364 (2000)] showed that the self-organization of microtubules from purified tubulin solutions is sensitive to gravitational conditions. In this paper, we propose two models of spatial and orientational self-organization of microtubules in a gravitational field. First, the spatial model is based on the dominant chemical kinetics. The pattern formation of microtubule concentration is obtained (1) in terms of a moving kink in the limit when the disassembly rate is negligible, and (2) for the case of no free tubulin and only assembled microtubules present. Second, the orientational pattern of striped microtubule domains is consistent with predictions from a phenomenological Landau-Ginzburg free energy expansion in terms of an orientational order parameter.