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

The significance of bioelectricity on all levels of organization of an organism. Part 1: From the subcellular level to cells

Bioelectricity plays an essential role in the structural and functional organization of biological organisms. In this first article of our three-part series, we summarize the importance of bioelectricity for the basic structural level of biological organization, i.e. from the subcellular level (charges, ion channels, molecules and cell organelles) to cells.

Electrical Propagation of Condensed and Diffuse Ions Along Actin Filaments

In this article, we elucidate the roles of divalent ion condensation and highly polarized immobile water molecules on the propagation of ionic calcium waves along actin filaments. We introduced a novel electrical triple layer model and used a non-linear Debye-Huckel theory with a non-linear, dissipative, electrical transmission line model to characterize the physicochemical properties of each monomer in the filament. This characterization is carried out in terms of an electric circuit model containing monomeric flow resistances and ionic capacitances in both the condensed and diffuse layers. We considered resting and excited states of a neuron using representative mono and divalent electrolyte mixtures. Additionally, we used 0.05V and 0.15V voltage inputs to study ionic waves along actin filaments in voltage clamp experiments. Our results reveal that the physicochemical properties characterizing the condensed and diffuse layers lead to different electrical conductive mediums depending on the ionic species and the neuron state. This region specific propagation mechanism provides a more realistic avenue of delivery by way of cytoskeleton filaments for larger charged cationic species. A new direct path for transporting divalent ions might be crucial for many electrical processes found in localized neuron elements such as at mitochondria and dendritic spines.

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. In that respect, it was clearly revealed that Ca²⁺ has very crucial involvement in many signaling pathways in cilia and flagella. We earlier established a model in which axonemal microtubules exhibit the features of nonlinear polyelectrolitic electric transmissions lines for efficient transport of cations, primarily Ca²⁺. These microtubules guide accumulated "ionic clods" which serve as the pulsatile signals aimed to regulate pertaining motor proteins, dyneins and kinesis. We here consider such Ca²⁺ signals in axoneme in the context of Shannon's and Fisher's information theories. It appears that the fast drift of these "ionic clouds" represents the optimized calcium signaling for control of "flagellary beats" as well as intraflagellary transport of proteins essential for the construction, elongation and maintenance of eukaryotic cilia and flagella themselves.

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 Ca²⁺ signals in the axoneme. This signaling is superimposed with a geometric clutch mechanism for the regulation of flagella bending dynamics and our modeling produces results in agreement with experimental data.

Actin networks voltage circuits

Filaments of the cellular protein actin can form bundles, which can conduct ionic currents as well as mechanical and voltage solitons. These inherent properties can be utilized to generate computing circuits solely based on self-assembled actin bundle structures. Starting with experimentally observed networks of actin bundles, we model their network structure in terms of edges and nodes. We compute and discuss the main electrical parameters, considering the bundles as electrical wires with either low or high filament densities. A set of equations describing the network is solved with several initial conditions. Input voltages, which can be considered as information bits, are applied in a set of points and output voltages are computed in another set of positions. We consider both an idealized situation, where pointlike electrodes can be inserted in any points of the bundles and a more realistic case, where electrodes lay on a surface and have typical dimensions available in the industry. We find that in both cases such a system can implement the main logical gates and a finite state machine.

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.