Model of ionic currents through microtubule nanopores and the lumen

The bacterial tubulin homolog FtsZ generates electrical oscillations

FtsZ, a major cytoskeletal protein in all bacteria and archaea, forms a ring that directs cytokinesis. Bacterial FtsZ is considered the ancestral homolog of the eukaryotic microtubule (MT)-forming tubulins, sharing GTPase activity and the ability to assemble into protofilaments, rings, and sheets, but not MTs. Previous studies from our laboratory demonstrated that structures of isolated brain MTs spontaneously generate electrical oscillations and bursts of electrical activity similar to action potentials. No information about whether the prokaryotic tubulins may share similar properties is available. Here, we obtained by ammonium sulfate precipitation an enriched protein fraction of the endogenous FtsZ from wild-type Escherichia coli ATCC 25922 without any transfection or overexpression of the protein. As revealed by electron microscopy, FtsZ was detected by dot blot analysis and immunofluorescence that assembled into filaments and sheets in a polymerization buffer. We used the patch-clamp technique to explore the electrical properties of sheets of FtsZ and bacterial cells. Electrical recordings at various holding potentials ranging from ±200 mV showed a complex oscillatory behavior, with several peak frequencies between 12 and 110 Hz in the power spectra and a linear mean current response. To confirm the oscillatory electrical behavior of FtsZ we also conducted experiments with commercial recombinant FtsZ, with similar results. We also detected, by local field potentials, similar electrical oscillations in K+-depolarized pellets of E. coli cultures. FtsZ oscillations had a wider range of frequency peaks than MT sheets from eukaryotic origin. The findings indicate that the bacterial cytoskeleton generates electrical oscillators that may play a relevant role in cell division and unknown signaling mechanisms in bacterial populations.

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).

The electrical properties of isolated microtubules

This study examines the electrical properties of isolated brain microtubules (MTs), which are long hollow cylinders assembled from αβ-tubulin dimers that form cytoskeletal structures engaged in several functions. MTs are implicated in sensory functions in cilia and flagella and cellular activities that range from cell motility, vesicular traffic, and neuronal processes to cell division in the centrosomes and centrioles. We determined the electrical properties of the MTs with the loose patch clamp technique in either the presence or absence of the MT stabilizer Paclitaxel. We observed electrical oscillations at different holding potentials that responded accordingly in amplitude and polarity. At zero mV in symmetrical ionic conditions, a single MT radiated an electrical power of 10-17 W. The spectral analysis of the time records disclosed a single fundamental peak at 39 Hz in the Paclitaxel-stabilized MTs. However, a richer oscillatory response and two mean conductances were observed in the non-Paclitaxel MTs. The findings evidence that the brain MTs are electrical oscillators that behave as "ionic-based" transistors to generate, propagate, and amplify electrical signals.

Microtubules as a potential platform for energy transfer in biological systems: a target for implementing individualized, dynamic variability patterns to improve organ function

Variability characterizes the complexity of biological systems and is essential for their function. Microtubules (MTs) play a role in structural integrity, cell motility, material transport, and force generation during mitosis, and dynamic instability exemplifies the variability in the proper function of MTs. MTs are a platform for energy transfer in cells. The dynamic instability of MTs manifests itself by the coexistence of growth and shortening, or polymerization and depolymerization. It results from a balance between attractive and repulsive forces between tubulin dimers. The paper reviews the current data on MTs and their potential roles as energy-transfer cellular structures and presents how variability can improve the function of biological systems in an individualized manner. The paper presents the option for targeting MTs to trigger dynamic improvement in cell plasticity, regulate energy transfer, and possibly control quantum effects in biological systems. The described system quantifies MT-dependent variability patterns combined with additional personalized signatures to improve organ function in a subject-tailored manner. The platform can regulate the use of MT-targeting drugs to improve the response to chronic therapies. Ongoing trials test the effects of this platform on various disorders.

Brain Microtubule Electrical Oscillations-Empirical Mode Decomposition Analysis

Microtubules (MTs) are essential cytoskeletal polymers of eukaryote cells implicated in various cell functions, including cell division, cargo transfer, and cell signaling. MTs also are highly charged polymers that generate electrical oscillations that may underlie their ability to act as nonlinear transmission lines. However, the oscillatory composition and time-frequency differences of the MT electrical oscillations have not been identified. Here, we applied the Empirical Mode Decomposition (EMD) to bovine brain MT sheet recordings to determine the number and fundamental frequencies of the Intrinsic Modes Functions (IMF) and evaluate their energetic contribution to the electrical signal. As previously reported, raw signals were obtained from cow brain MTs (Cantero et al. Sci Rep 6:27143, 2016), sampled, filtered, and subjected to signal decomposition from representative experiments. Filtered signals (200 Hz) allowed us to identify either six or seven IMFs. The reconstructed tracings faithfully resembled the original signals, with identifiable frequency peaks. To extend the analysis to obtain time-frequency information and the energy implicated in each IMF, we applied the Hilbert-Huang Transform (HHT) and the Continuous Wavelet Transform (CWT) to the same samples. The analyses disclosed the presence of more fundamental frequency peaks than initially reported and evidenced the advantages and disadvantages of each transform. The study indicates that the EMD is a robust approach to quantifying signal decomposition of brain MT oscillations and suggests novel similarities with human brain wave electroencephalogram (EEG) recordings. The evidence points to the potentially fundamental role of MT oscillations in brain electrical activity.

Modeling Microtubule Counterion Distributions and Conductivity Using the Poisson-Boltzmann Equation

Microtubules are highly negatively charged proteins which have been shown to behave as bio-nanowires capable of conducting ionic currents. The electrical characteristics of microtubules are highly complicated and have been the subject of previous work; however, the impact of the ionic concentration of the buffer solution on microtubule electrical properties has often been overlooked. In this work we use the non-linear Poisson Boltzmann equation, modified to account for a variable permittivity and a Stern Layer, to calculate counterion concentration profiles as a function of the ionic concentration of the buffer. We find that for low-concentration buffers ([KCl] from 10 μM to 10 mM) the counterion concentration is largely independent of the buffer's ionic concentration, but for physiological-concentration buffers ([KCl] from 100 to 500 mM) the counterion concentration varies dramatically with changes in the buffer's ionic concentration. We then calculate the conductivity of microtubule-counterion complexes, which are found to be more conductive than the buffer when the buffer's ionic concentrations is less than ≈100 mM and less conductive otherwise. These results demonstrate the importance of accounting for the ionic concentration of the buffer when analyzing microtubule electrical properties both under laboratory and physiological conditions. We conclude by calculating the basic electrical parameters of microtubules over a range of ionic buffer concentrations applicable to nanodevice and medical applications.

All Wired Up: An Exploration of the Electrical Properties of Microtubules and Tubulin

Microtubules are hollow, cylindrical polymers of the protein α, β tubulin, that interact mechanochemically with a variety of macromolecules. Due to their mechanically robust nature, microtubules have gained attention as tracks for precisely directed transport of nanomaterials within lab-on-a-chip devices. Primarily due to the unusually negative tail-like C-termini of tubulin, recent work demonstrates that these biopolymers are also involved in a broad spectrum of intracellular electrical signaling. Microtubules and their electrostatic properties are discussed in this Review, followed by an evaluation of how these biopolymers respond mechanically to electrical stimuli, through microtubule migration, electrorotation and C-termini conformation changes. Literature focusing on how microtubules act as nanowires capable of intracellular ionic transport, charge storage, and ionic signal amplification is reviewed, illustrating how these biopolymers attenuate ionic movement in response to electrical stimuli. The Review ends with a discussion on the important questions, challenges, and future opportunities for intracellular microtubule-based electrical signaling.

When Stiffness Matters: Mechanosensing in Heart Development and Disease

During embryonic morphogenesis, the heart undergoes a complex series of cellular phenotypic maturations (e.g., transition of myocytes from proliferative to quiescent or maturation of the contractile apparatus), and this involves stiffening of the extracellular matrix (ECM) acting in concert with morphogenetic signals. The maladaptive remodeling of the myocardium, one of the processes involved in determination of heart failure, also involves mechanical cues, with a progressive stiffening of the tissue that produces cellular mechanical damage, inflammation, and ultimately myocardial fibrosis. The assessment of the biomechanical dependence of the molecular machinery (in myocardial and non-myocardial cells) is therefore essential to contextualize the maturation of the cardiac tissue at early stages and understand its pathologic evolution in aging. Because systems to perform multiscale modeling of cellular and tissue mechanics have been developed, it appears particularly novel to design integrated mechano-molecular models of heart development and disease to be tested in ex vivo reconstituted cells/tissue-mimicking conditions. In the present contribution, we will discuss the latest implication of mechanosensing in heart development and pathology, describe the most recent models of cell/tissue mechanics, and delineate novel strategies to target the consequences of heart failure with personalized approaches based on tissue engineering and induced pluripotent stem cell (iPSC) technologies.

Microtubules as Sub-Cellular Memristors

Memristors represent the fourth electrical circuit element complementing resistors, capacitors and inductors. Hallmarks of memristive behavior include pinched and frequency-dependent I–V hysteresis loops and most importantly a functional dependence of the magnetic flux passing through an ideal memristor on its electrical charge. Microtubules (MTs), cylindrical protein polymers composed of tubulin dimers are key components of the cytoskeleton. They have been shown to increase solution’s ionic conductance and re-orient in the presence of electric fields. It has been hypothesized that MTs also possess intrinsic capacitive and inductive properties, leading to transistor-like behavior. Here, we show a theoretical basis and experimental support for the assertion that MTs under specific circumstances behave consistently with the definition of a memristor. Their biophysical properties lead to pinched hysteretic current–voltage dependence as well a classic dependence of magnetic flux on electric charge. Based on the information about the structure of MTs we provide an estimate of their memristance. We discuss its significance for biology, especially neuroscience, and potential for nanotechnology applications.

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.

Two-Dimensional Brain Microtubule Structures Behave as Memristive Devices

Microtubules (MTs) are cytoskeletal structures that play a central role in a variety of cell functions including cell division and cargo transfer. MTs are also nonlinear electrical transmission lines that produce and conduct electrical oscillations elicited by changes in either electric field and/or ionic gradients. The oscillatory behavior of MTs requires a voltage-sensitive gating mechanism to enable the electrodiffusional ionic movement through the MT wall. Here we explored the electrical response of non-oscillating rat brain MT sheets to square voltage steps. To ascertain the nature of the possible gating mechanism, the electrical response of non-oscillating rat brain MT sheets (2D arrays of MTs) to square pulses was analyzed under voltage-clamping conditions. A complex voltage-dependent nonlinear charge movement was observed, which represented the summation of two events. The first contribution was a small, saturating, voltage-dependent capacitance with a maximum charge displacement in the range of 4 fC/μm². A second, major contribution was a non-saturating voltage-dependent charge transfer, consistent with the properties of a multistep memristive device. The memristive capabilities of MTs could drive oscillatory behavior, and enable voltage-driven neuromorphic circuits and architectures within neurons.

Integration of intracellular signaling: Biological analogues of wires, processors and memories organized by a centrosome 3D reference system

BACKGROUND

Myriads of signaling pathways in a single cell function to achieve the highest spatio-temporal integration. Data are accumulating on the role of electromechanical soliton-like waves in signal transduction processes. Theoretical studies strongly suggest feasibility of both classical and quantum computing involving microtubules.

AIM

A theoretical study of the role of the complex composed of the plasma membrane and the microtubule-based cytoskeleton as a system that transmits, stores and processes information.

METHODS

Theoretical analysis presented here refers to (i) the Penrose-Hameroff theory of consciousness (Orchestrated Objective Reduction; Orch OR), (ii) the description of the centrosome as a reference system for construction of the 3D map of the cell proposed by Regolini, (iii) the Heimburg-Jackson model of the nerve pulse propagation along axons' lipid bilayer as soliton-like electro-mechanical waves.

RESULTS AND CONCLUSION

The ideas presented in this paper provide a qualitative model for the decision-making processes in a living cell undergoing a differentiation process.

OUTLOOK

This paper paves the way for the real-time live-cell observation of information processing by microtubule-based cytoskeleton and cell fate decision making.

Ionic wave propagation and collision in an excitable circuit model of microtubules

In this paper, we report the propensity to excitability of the internal structure of cellular microtubules, modelled as a relatively large one-dimensional spatial array of electrical units with nonlinear resistive features. We propose a model mimicking the dynamics of a large set of such intracellular dynamical entities as an excitable medium. We show that the behavior of such lattices can be described by a complex Ginzburg-Landau equation, which admits several wave solutions, including the plane waves paradigm. A stability analysis of the plane waves solutions of our dynamical system is conducted both analytically and numerically. It is observed that perturbed plane waves will always evolve toward promoting the generation of localized periodic waves trains. These modes include both stationary and travelling spatial excitations. They encompass, on one hand, localized structures such as solitary waves embracing bright solitons, dark solitons, and bisolitonic impulses with head-on collisions phenomena, and on the other hand, the appearance of both spatially homogeneous and spatially inhomogeneous stationary patterns. This ability exhibited by our array of proteinic elements to display several states of excitability exposes their stunning biological and physical complexity and is of high relevance in the description of the developmental and informative processes occurring on the subcellular scale.

Response to Alternating Electric Fields of Tubulin Dimers and Microtubule Ensembles in Electrolytic Solutions

Microtubules (MTs), which are cylindrical protein filaments that play crucial roles in eukaryotic cell functions, have been implicated in electrical signalling as biological nanowires. We report on the small-signal AC (“alternating current”) conductance of electrolytic solutions containing MTs and tubulin dimers, using a microelectrode system. We find that MTs (212 nM tubulin) in a 20-fold diluted BRB80 electrolyte increase solution conductance by 23% at 100 kHz, and this effect is directly proportional to the concentration of MTs in solution. The frequency response of MT-containing electrolytes exhibits a concentration-independent peak in the conductance spectrum at 111 kHz (503 kHz FWHM that decreases linearly with MT concentration), which appears to be an intrinsic property of MT ensembles in aqueous environments. Conversely, tubulin dimers (42 nM) decrease solution conductance by 5% at 100 kHz under similar conditions. We attribute these effects primarily to changes in the mobility of ionic species due to counter-ion condensation effects, and changes in the solvent structure and solvation dynamics. These results provide insight into MTs’ ability to modulate the conductance of aqueous electrolytes, which in turn, has significant implications for biological information processing, especially in neurons, and for intracellular electrical communication in general.

Effects of static magnetic fields on the structure, polymerization, and bioelectric of tubulin assemblies

Due to widespread exposure of human being to various sources of static magnetic fields (SMF), their effect on the spatial and temporal status of structure, arrangement, and polymerization of tubulin was studied at the molecular level. The intrinsic fluorescence intensity of tubulin was increased by SMF, indicating the repositioning of tryptophan and tyrosine residues. Circular Dichroism spectroscopy revealed variations in the ratios of alpha helix, beta, and random coil structures of tubulin as a result of exposure to SMF at 100, 200, and 300 mT. Transmission Electron microscopy of microtubules showed breaches and curvatures whose risk of occurrence increased as a function of field strength. Dynamic light scattering revealed an increase in the surface potential of tubulin aggregates exposed to SMF. The rate and extent of polymerization increased by 9.8 and 33.8%, at 100 and 300 mT, respectively, but decreased by 36.16% at 200 mT. The conductivity of polymerized tubulin increased in the presence of 100 and 300 mT SMF but remained the same as the control at 200 mT. The analysis of flexible amino acids along the sequence of tubulin revealed higher SMF susceptibility in the helical electron conduction pathway set through histidines rather than the vertical electron conduction pathway formed by tryptophan residues. The results reveal structural and functional effects of SMF on tubulin assemblies and microtubules that can be considered as a potential means to address the safety issues and for manipulation of bioelectrical characteristics of cytosol, intracellular trafficking and thus, the living status of cells, remotely.

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.

Electrical Oscillations in Two-Dimensional Microtubular Structures

Microtubules (MTs) are unique components of the cytoskeleton formed by hollow cylindrical structures of αβ tubulin dimeric units. The structural wall of the MT is interspersed by nanopores formed by the lateral arrangement of its subunits. MTs are also highly charged polar polyelectrolytes, capable of amplifying electrical signals. The actual nature of these electrodynamic capabilities remains largely unknown. Herein we applied the patch clamp technique to two-dimensional MT sheets, to characterize their electrical properties. Voltage-clamped MT sheets generated cation-selective oscillatory electrical currents whose magnitude depended on both the holding potential, and ionic strength and composition. The oscillations progressed through various modes including single and double periodic regimes and more complex behaviours, being prominent a fundamental frequency at 29 Hz. In physiological K(+) (140 mM), oscillations represented in average a 640% change in conductance that was also affected by the prevalent anion. Current injection induced voltage oscillations, thus showing excitability akin with action potentials. The electrical oscillations were entirely blocked by taxol, with pseudo Michaelis-Menten kinetics and a KD of ~1.29 μM. The findings suggest a functional role of the nanopores in the MT wall on the genesis of electrical oscillations that offer new insights into the nonlinear behaviour of the cytoskeleton.

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.

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.

Keeping time: could quantum beating in microtubules be the basis for the neural synchrony related to consciousness?

This paper discusses the possibility of quantum coherent oscillations playing a role in neuronal signaling. Consciousness correlates strongly with coherent neural oscillations, however the mechanisms by which neurons synchronize are not fully elucidated. Recent experimental evidence of quantum beats in light-harvesting complexes of plants (LHCII) and bacteria provided a stimulus for seeking similar effects in important structures found in animal cells, especially in neurons. We argue that microtubules (MTs), which play critical roles in all eukaryotic cells, possess structural and functional characteristics that are consistent with quantum coherent excitations in the aromatic groups of their tryptophan residues. Furthermore we outline the consequences of these findings on neuronal processes including the emergence of consciousness.

Computing by physical interaction in neurons

The electrodynamics of action potentials represents the fundamental level where information is integrated and processed in neurons. The Hodgkin-Huxley model cannot explain the non-stereotyped spatial charge density dynamics that occur during action potential propagation. Revealed in experiments as spike directivity, the non-uniform charge density dynamics within neurons carry meaningful information and suggest that fragments of information regarding our memories are endogenously stored in structural patterns at a molecular level and are revealed only during spiking activity. The main conceptual idea is that under the influence of electric fields, efficient computation by interaction occurs between charge densities embedded within molecular structures and the transient developed flow of electrical charges. This process of computation underlying electrical interactions and molecular mechanisms at the subcellular level is dissimilar from spiking neuron models that are completely devoid of physical interactions. Computation by interaction describes a more powerful continuous model of computation than the one that consists of discrete steps as represented in Turing machines.

Cytoskeletal signaling: is memory encoded in microtubule lattices by CaMKII phosphorylation?

Memory is attributed to strengthened synaptic connections among particular brain neurons, yet synaptic membrane components are transient, whereas memories can endure. This suggests synaptic information is encoded and 'hard-wired' elsewhere, e.g. at molecular levels within the post-synaptic neuron. In long-term potentiation (LTP), a cellular and molecular model for memory, post-synaptic calcium ion (Ca²⁺) flux activates the hexagonal Ca²⁺-calmodulin dependent kinase II (CaMKII), a dodacameric holoenzyme containing 2 hexagonal sets of 6 kinase domains. Each kinase domain can either phosphorylate substrate proteins, or not (i.e. encoding one bit). Thus each set of extended CaMKII kinases can potentially encode synaptic Ca²⁺ information via phosphorylation as ordered arrays of binary 'bits'. Candidate sites for CaMKII phosphorylation-encoded molecular memory include microtubules (MTs), cylindrical organelles whose surfaces represent a regular lattice with a pattern of hexagonal polymers of the protein tubulin. Using molecular mechanics modeling and electrostatic profiling, we find that spatial dimensions and geometry of the extended CaMKII kinase domains precisely match those of MT hexagonal lattices. This suggests sets of six CaMKII kinase domains phosphorylate hexagonal MT lattice neighborhoods collectively, e.g. conveying synaptic information as ordered arrays of six "bits", and thus "bytes", with 64 to 5,281 possible bit states per CaMKII-MT byte. Signaling and encoding in MTs and other cytoskeletal structures offer rapid, robust solid-state information processing which may reflect a general code for MT-based memory and information processing within neurons and other eukaryotic cells.

Molecular dynamics modeling of tubulin C-terminal tail interactions with the microtubule surface

Tubulin, an α/β heterodimer, has had most of its 3D structure analyzed; however, the carboxy (C)-termini remain elusive. Importantly, the C-termini play critical roles in regulating microtubule structure and function. They are sites of most of the post-translational modifications of tubulin and interaction sites with molecular motors and microtubule-associated proteins. Simulated annealing was used in our molecular dynamics modeling to predict the interactions of the C-terminal tails with the tubulin dimer. We examined differences in their flexibility, interactions with the body of tubulin, and the existence of structural motifs. We found that the α-tubulin tail interacts with the H11 helix of β-tubulin, and the β-tubulin tail interacts with the H11 helix of α-tubulin. Tail domains and H10/B9 loops interact with each other and compete for interactions with positively-charged residues of the H11 helix on the neighboring monomer. In a simulation in which α-tubulin's H10/B9 loop switches on sub-nanosecond intervals between interactions with the C-terminal tail of α-tubulin and the H11 helix of β-tubulin, the intermediate domain of α-tubulin showed more fluctuations compared to those in the other simulations, indicating that tail domains may cause shifts in the position of this domain. This suggests that C-termini may affect the conformation of the tubulin dimer which may explain their essential function in microtubule formation and effects on ligand binding to microtubules. Our modeling also provides evidence for a disordered-helical/helical double-state system of the T3/H3 region of the microtubule, which could be linked to depolymerization following GTP hydrolysis.

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.