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

We have considered the realistic mechanism of rapid Ca2+ (calcium ion) buffering within the wave of calcium ions progressing along the flagellar axoneme. This buffering is an essential part of the Ca2+ 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. We derived and elaborated a model of Ca2+ diffusion within a signaling wave in the presence of these molecules which rapidly buffer Ca2+. This approach has led to a single nonlinear transport equation for the Ca2+ wave that contains the effects brought about by both as necessary buffers for signaling. The presence of mobile buffer calmodulin gives rise to a transport equation that is not strictly diffusive but also exhibits a sink-like effect. We solved straightforwardly the final transport equation in an analytical framework and obtained the implied function of calcium concentration. The effective diffusion coefficient depends on local Ca2+ concentration. It is plausible that these buffers' presence can impact Ca2+ wave speed and shape, which are essential for decoding Ca2+ signaling in flagella. We present the solution of the transport equation for a few specified cases with physiologically reasonable sets of parameters involved.

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.g., RNA polymerase molecules. We explain why this is biologically convenient and show that our results match the experimental ones. In addition, we suggest how to experimentally determine crucial constant describing covalent bonds within DNA.

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. These features are primarily due to the dynamics of tubulin C-terminal tails which are extended out of the surface of the microtubule cylinder. We also demonstrate that the origin of nonlinearity stems from the nonlinear capacitance of each tubulin dimer. This brings about conditions required for the creation and propagation of solitonic ionic waves along the microtubule axis. We conclude that a microtubule plays the role of a biological nonlinear transmission line for ionic currents. These currents might be of particular significance in cell division and possibly also in cognitive processes taking place in nerve cells.

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. We introduce a model in which each tubulin dimer is viewed as an electric element with a capacitive, inductive and resistive characteristics arising due to polyelectrolyte nature of MTs. Based on Kirchhoff's laws taken in the continuum limit, a nonlinear partial differential equation is derived and analyzed. We demonstrate that it can be used to describe the electrostatic potential coupled to the propagating localized ionic waves.

Relationship between the nonlinear ferroelectric and liquid crystal models for microtubules

Microtubules (MTs), which are the main components of the cytoskeleton, are important in a variety of cellular activities, but some physical properties underlying the most important features of their behavior are still lacking satisfactory explanation. One of the essential enigmas regarding the energy balance in MTs is the hydrolysis of the exchangeable guanosine 5'-triphosphate bound to the beta monomer of the molecule. The energy released in the hydrolysis process amounts to 6.25 x 10(-20) J and has been the subject of many attempts to answer the questions of its utilization. Earlier, we put forward a hypothesis that this energy can cause a local conformational distortion of the dimer. This distortion should have nonlinear character and could lead to the formation of a traveling kink soliton. In this paper we use the formalism of the liquid crystal theory to consider the nonlinear dynamics of MTs. We demonstrate that this new model is formally equivalent to our earlier ferroelectric model which was widely exploited in an attempt to elucidate some important dynamical activities in MTs. We also study the stability of kink solitons against small perturbations and their unusual mutual interactions as well as the interactions with structural inhomogeneities of MTs. Our new approach based on liquid crystal properties of microtubules has been recently corroborated by new insights gained from the electrostatic properties of tubulin and microtubules.

Impact of regulatory proteins on the nonlinear dynamics of DNA

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.

Nonlinear dynamics of a DNA chain affected by endogenous AC fields

In this paper we investigate the nonlinear dynamics of a DNA chain in the presence of endogenous AC fields (EACF) generated by the living cell itself. The dynamics of the DNA chain is described in the framework of the nonlinear breather mode. The transition of breather localized modes into open states, affected by AC fields is calculated by using Kubo's formalism for the linear response of the system.

The enigma of microtubules and their self-organizing behavior in the cytoskeleton

The cytoskeleton of eukaryotic cells contains networks of protein polymers called microtubules which structurally and functionally organize their interiors. Both in vivo and in vitro microtubules exhibit a fascinating and yet poorly understood array of important functions involving complex self-organization phenomena which are very sensitive to physiological and laboratory conditions, respectively. In this paper we discuss the main physical characteristics of microtubules focusing our attention on four particular aspects: (a) the dynamics of their assembly and disassembly processes (b) the types and the range of existence of ordered dipolar phases and (c) modes of energy transfer and (d) information processing capabilities.

The change of microtubule length caused by endogenous AC fields in cell

In this paper we investigate the change of microtubule cylinder's length in the presence of endogenous AC fields generated by the cell itself. The dynamics of microtubule is described on the basis of classical u4 model. The average stretching is calculated by using Kubo's formalism for linear response of system.