Monte Carlo simulation and experimental validation of plant microtubules cathode in biodegradable battery

For the first time, electrochemical methods are utilized to study the response of tubulin monomers (extracted from plant source such as Green Peas: Arachis Hypogea) towards charge perturbations in the form of conductivity, conformational changes via self-assembly and adsorption on Au surface. The obtained dimerization and surface adsorption energetics of the tubulins from Cyclic Voltammetry agree well with the literature value of 6.9 and 14.9 kCal/mol for lateral and longitudinal bond formation energy respectively. In addition to the effects of charge perturbations on change in structure, ionic and electronic conductivity of tubulin with increasing load are investigated and found to be 1.25 Sm^-1 and 2.89 mSm^-1 respectively. The electronic conductivity is 1.93 times higher than the literature value of 1.5 mSm^-1, demonstrating the fact that the microtubules (dimer of tubulins, MTs) from plant source can be used as a semiconductor electrode material in energy conversion and storage applications. Thus, motivated by the Monte Carlo simulation and electrochemical results the MTs extracted from plant source are used as cathode material for energy storage device such as Bio-battery and the Galvanostatic Charge/Discharge studies are carried out in coin cell configuration. The configuration of the bio-battery cell is as follows: Al/CB//PP-1M KCl//MTs/SS; where SS and Al are used as current collectors for cathode and anode respectively, Polypropylene (PP) membrane soaked in 1M KCl as electrolyte and Carbon Black (CB) is the anode material. Another configuration of the cell would be replacement of CB by biopolymer such as ethyl cellulose anode (Al/EC/PP-1M KCl/MTs/SS).

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.

Modified Exp-Function Method to Find Exact Solutions of Ionic Currents along Microtubules

A number of solitary wave solutions for microtubules (MTs) are observed in this article by using the modified exp-function approach. We tackle the problem by treating the results as nonlinear RLC transmission lines, and then finding exact solutions to Nonlinear Evolution Equation (NLEE) containing parameters of particular importance in biophysics and nanobiosciences. For this equation, we find trigonometric, hyperbolic, rational, and exponential function solutions, as well as soliton-like pulse solutions. A comparison with other approach indicates the legitimacy of the approach we devised as well as the fact that our method offers extra solutions. Finally, we plot 2D, 3D and contour visualizations of the exact results that we observed using our approach using appropriate parameter values with the help of software Mathematica 10.

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.

Investigation of the Electrical Properties of Microtubule Ensembles under Cell-Like Conditions

Microtubules are hollow cylindrical polymers composed of the highly negatively-charged (~23e), high dipole moment (1750 D) protein α, β- tubulin. While the roles of microtubules in chromosomal segregation, macromolecular transport, and cell migration are relatively well-understood, studies on the electrical properties of microtubules have only recently gained strong interest. Here, we show that while microtubules at physiological concentrations increase solution capacitance, free tubulin has no appreciable effect. Further, we observed a decrease in electrical resistance of solution, with charge transport peaking between 20-60 Hz in the presence of microtubules, consistent with recent findings that microtubules exhibit electric oscillations at such low frequencies. We were able to quantify the capacitance and resistance of the microtubules (MT) network at physiological tubulin concentrations to be 1.27 × 10^-5 F and 9.74 × 10⁴ Ω. Our results show that in addition to macromolecular transport, microtubules also act as charge storage devices through counterionic condensation across a broad frequency spectrum. We conclude with a hypothesis of an electrically tunable cytoskeleton where the dielectric properties of tubulin are polymerisation-state dependent.

Actin droplet machine

The actin droplet machine is a computer model of a three-dimensional network of actin bundles developed in a droplet of a physiological solution, which implements mappings of sets of binary strings. The actin bundle network is conductive to travelling excitations, i.e. impulses. The machine is interfaced with an arbitrary selected set of k electrodes through which stimuli, binary strings of length k represented by impulses generated on the electrodes, are applied and responses are recorded. The responses are recorded in a form of impulses and then converted to binary strings. The machine's state is a binary string of length k: if there is an impulse recorded on the ith electrode, there is a '1' in the ith position of the string, and '0' otherwise. We present a design of the machine and analyse its state transition graphs. We envisage that actin droplet machines could form an elementary processor of future massive parallel computers made from biopolymers.

Computing on actin bundles network

Actin filaments are conductive to ionic currents, mechanical and voltage solitons. These travelling localisations can be utilised to generate computing circuits from actin networks. The propagation of localisations on a single actin filament is experimentally unfeasible to control. Therefore, we consider excitation waves propagating on bundles of actin filaments. In computational experiments with a two-dimensional slice of an actin bundle network we show that by using an arbitrary arrangement of electrodes, it is possible to implement two-inputs-one-output circuits.

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.

On discovering functions in actin filament automata

We simulate an actin filament as an automaton network. Every atom takes two or three states and updates its state, in discrete time, depending on a ratio of its neighbours in some selected state. All atoms/automata simultaneously update their states by the same rule. Two state transition rules are considered. In semi-totalistic Game of Life like actin filament automaton atoms take binary states '0' and '1' and update their states depending on a ratio of neighbours in the state '1'. In excitable actin filament automaton atoms take three states: resting, excited and refractory. A resting atom excites if a ratio of its excited neighbours belong to some specified interval; transitions from excited state to refractory state and from refractory state to resting state are unconditional. In computational experiments, we implement mappings of an 8-bit input string to an 8-bit output string via dynamics of perturbation/excitation on actin filament automata. We assign eight domains in an actin filament as I/O ports. To write True to a port, we perturb/excite a certain percentage of the nodes in the domain corresponding to the port. We read outputs at the ports after some time interval. A port is considered to be in a state True if a number of excited nodes in the port's domain exceed a certain threshold. A range of eight-argument Boolean functions is uncovered in a series of computational trials when all possible configurations of eight-elements binary strings were mapped onto excitation outputs of the I/O domains.

Calcium-axonemal microtubuli interactions underlie mechanism(s) of primary cilia morphological changes

We have used cell culture of astrocytes aligned within microchannels to investigate calcium effects on primary cilia morphology. In the absence of calcium and in the presence of flow of media (10 μL.s^-1) the majority (90%) of primary cilia showed reversible bending with an average curvature of 2.1 ± 0.9 × 10^-4 nm^-1. When 1.0 mM calcium was present, 90% of cilia underwent bending. Forty percent of these cilia demonstrated strong irreversible bending, resulting in a final average curvature of 3.9 ± 1 × 10^-4 nm^-1, while 50% of cilia underwent bending similar to that observed during calcium-free flow. The average length of cilia was shifted toward shorter values (3.67 ± 0.34 μm) when exposed to excess calcium (1.0 mM), compared to media devoid of calcium (3.96 ± 0.26 μm). The number of primary cilia that became curved after calcium application was reduced when the cell culture was pre-incubated with 15 μM of the microtubule stabilizer, taxol, for 60 min prior to calcium application. Calcium caused single microtubules to curve at a concentration ≈1.0 mM in vitro, but at higher concentration (≈1.5 mM) multiple microtubule curving occurred. Additionally, calcium causes microtubule-associated protein-2 conformational changes and its dislocation from the microtubule wall at the location of microtubule curvature. A very small amount of calcium, that is 1.45 × 10¹¹ times lower than the maximal capacity of TRPPs calcium channels, may cause gross morphological changes (curving) of primary cilia, while global cytosol calcium levels are expected to remain unchanged. These findings reflect the non-linear manner in which primary cilia may respond to calcium signaling, which in turn may influence the course of development of ciliopathies and cancer.

Waves transmission and amplification in an electrical model of microtubules

Inspired by standard electrophysiological models of microtubules, a discrete nonlinear equation for ionic wave propagation that incorporates a negative nonlinear resistance is presented. The conditions for wave propagation in forbidden band gap are analyzed without and with dissipation. The nonlinear response manifold method is used to determine the supratransmission threshold of the case of study without dissipation. This threshold is found to be similar to the value obtained by analytical methods. With the dissipation, the monitoring of the accumulated energy is used to estimate the infratransmission threshold. It appears that the value of the supratransmission threshold can be lower than the value of the infratransmission threshold. The system is found to amplify significantly the amplitude of the input signal, thus confirming known experimental results. Nevertheless, a proper choice of the parameter of the nonlinear resistance is required for further validation of our results. A possible biological implication of the obtained results is presented.

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.