Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules

Localized discrete and asymmetric dark-bright soliton-like modes as nonlinear dynamics in microtubules

In the present work, we focus on the longitudinal model of microtubules (MTs) proposed by Satarić et al. (1993) [12], and that considers MT cells to have ferroelectric properties (behaviors) due to dipolar oscillations of dimers within MTs, i.e., a displacive ferrodistortive system of heterodimers in MTs and usually referred to as u-model of MTs. It has been shown that during the hydrolysis of guanosine 5'- triphosphate into guanosine 5'-diphosphate, the energy released is transferred along the MTs through kink-like solitons. Substantially, we propose to theoretically investigate the dynamic of MTs by intrinsically taking into account the effect of oriented molecules of polarized cytoplasmic water and enzymes surrounding the MT. In this regards, we introduce a cubic nonlinear term in the electric potential characterizing the polyelectrolyte features of MTs and show that in addition to the kink and anti-kink dynamics, asymmetrical bright and dark solitons, and discrete modes can also propagate along the MTs. These results are supported by numerical analysis. The investigation shows us that the nonlinear dynamics of MTs is strongly impacted by the intrinsic electric field, the polyelectrolyte and the viscous effects. Moreover, new solitonic dynamics and discrete solitary modes might aid in the discovery of novel microtubulin system phenomena.

Thermosensory Spiking Activity of Proteinoid Microspheres Cross-Linked by Actin Filaments

Actin, found in all eukaryotic cells as globular (G) or filamentous (F) actin, undergoes polymerization, with G-actin units changing shape to become F-actin. Thermal proteins, or proteinoids, are created by heating amino acids (160-200 °C), forming polymeric chains. These proteinoids can swell in an aqueous solution at around 50 °C, producing hollow microspheres filled with a solution, exhibiting voltage spikes. Our research explores the signaling properties of proteinoids, actin filaments, and hybrid networks combining actin and proteinoids. Proteinoids replicate brain excitation dynamics despite lacking specific membranes or ion channels. We investigate enhancing conductivity and spiking by using pure actin, yielding improved coordination in networks compared with individual filaments or proteinoids. Temperature changes (20 short-peptide supramolecular C to 80 °C) regulate conduction states, demonstrating external control over emergent excitability in protobrain systems. Adding actin to proteinoids reduces spike timing variability, providing a more uniform feature distribution. These findings support theoretical models proposing cytoskeletal matrices for functional specification in synthetic protocell brains, promoting stable interaction complexity. The study concludes that life-like signal encoding can emerge spontaneously within biological polymer scaffolds, incorporating abiotic chemistry.

Electrodynamic interaction between tumor treating fields and microtubule electrophysiological activities

Tumor treating fields (TTFields) are a type of sinusoidal alternating current electric field that has proven effective in inhibiting the reproduction of dividing tumor cells. Despite their recognized impact, the precise biophysical mechanisms underlying the unique effects of TTFields remain unknown. Many of the previous studies predominantly attribute the inhibitory effects of TTFields to mitotic disruption, with intracellular microtubules identified as crucial targets. However, this conceptual framework lacks substantiation at the mesoscopic level. This study addresses the existing gap by constructing force models for tubulin and other key subcellular structures involved in microtubule electrophysiological activities under TTFields exposure. The primary objective is to explore whether the electric force or torque exerted by TTFields significantly influences the normal structure and activities of microtubules. Initially, we examine the potential effect on the dynamic stability of microtubule structures by calculating the electric field torque on the tubulin dimer orientation. Furthermore, given the importance of electrostatics in microtubule-associated activities, such as chromosome segregation and substance transport of kinesin during mitosis, we investigate the interaction between TTFields and these electrostatic processes. Our data show that the electrodynamic effects of TTFields are most likely too weak to disrupt normal microtubule electrophysiological activities significantly. Consequently, we posit that the observed cytoskeleton destruction in mitosis is more likely attributable to non-mechanical mechanisms.

A Comprehensive Study on the Electrostatic Properties of Tubulin-Tubulin Complexes in Microtubules

Microtubules are key players in several stages of the cell cycle and are also involved in the transportation of cellular organelles. Microtubules are polymerized by α/β tubulin dimers with a highly dynamic feature, especially at the plus ends of the microtubules. Therefore, understanding the interactions among tubulins is crucial for characterizing microtubule dynamics. Studying microtubule dynamics can help researchers make advances in the treatment of neurodegenerative diseases and cancer. In this study, we utilize a series of computational approaches to study the electrostatic interactions at the binding interfaces of tubulin monomers. Our study revealed that among all the four types of tubulin-tubulin binding modes, the electrostatic attractive interactions in the α/β tubulin binding are the strongest while the interactions of α/α tubulin binding in the longitudinal direction are the weakest. Our calculations explained that due to the electrostatic interactions, the tubulins always preferred to form α/β tubulin dimers. The interactions between two protofilaments are the weakest. Thus, the protofilaments are easily separated from each other. Furthermore, the important residues involved in the salt bridges at the binding interfaces of the tubulins are identified, which illustrates the details of the interactions in the microtubule. This study elucidates some mechanistic details of microtubule dynamics and also identifies important residues at the binding interfaces as potential drug targets for the inhibition of cancer cells.

Large and stable: actin aster networks formed via entropic forces

Biopolymer networks play a major role as part of the cytoskeleton. They provide stable structures and act as a medium for signal transport. These features encourage the application of such networks as organic computation devices. While research on this topic is not advanced yet, previous results are very promising. The protein actin in particular appears advantageous. It can be arranged to various stable structures and transmit several signals. In this study aster shaped networks were self-assembled via entropic forces by the crowding agent methyl cellulose. These networks are characterised by a regular and uniquely thick bundle structure, but have so far only been accounted in droplets of 100 μm diameter. We report now regular asters in an area of a few mm² that could be observed even after months. Such stability outside of an organism is striking and underlines the great potential actin aster networks display.

Hierarchical Assembly Pathways of Spermine-Induced Tubulin Conical-Spiral Architectures

Tubulin, an essential cytoskeletal protein, assembles into various morphologies by interacting with an array of cellular factors. One of these factors is the endogenous polyamine spermine, which may promote and stabilize tubulin assemblies. Nevertheless, the assembled structures and their formation pathways are poorly known. Here we show that spermine induced the in vitro assembly of tubulin into several hierarchical architectures based on a tubulin conical-spiral subunit. Using solution X-ray scattering and cryo-TEM, we found that with progressive increase of spermine concentration tubulin dimers assembled into conical-frustum-spirals of increasing length, containing up to three helical turns. The subunits with three helical turns were then assembled into tubules through base-to-top packing and formed antiparallel bundles of tubulin conical-spiral tubules in a distorted hexagonal symmetry. Further increase of the spermine concentration led to inverted tubulin tubules assembled in hexagonal bundles. Time-resolved experiments revealed that tubulin assemblies formed at higher spermine concentrations assembled from intermediates, similar to those formed at low spermine concentrations. These results are distinct from the classical transition between twisted ribbons, helical, and tubular assemblies, and provide insight into the versatile morphologies that tubulin can form. Furthermore, they may contribute to our understanding of the interactions that control the composition and construction of protein-based biomaterials.

Challenges in coupling atmospheric electricity with biological systems

The atmosphere is host to a complex electric environment, ranging from a global electric circuit generating fluctuating atmospheric electric fields to local lightning strikes and ions. While research on interactions of organisms with their electrical environment is deeply rooted in the aquatic environment, it has hitherto been confined to interactions with local electrical phenomena and organismal perception of electric fields. However, there is emerging evidence of coupling between large- and small-scale atmospheric electrical phenomena and various biological processes in terrestrial environments that even appear to be tied to continental waters. Here, we synthesize our current understanding of this connectivity, discussing how atmospheric electricity can affect various levels of biological organization across multiple ecosystems. We identify opportunities for research, highlighting its complexity and interdisciplinary nature and draw attention to both conceptual and technical challenges lying ahead of our future understanding of the relationship between atmospheric electricity and the organization and functioning of biological systems.

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.

Limitations on electromagnetic communication by vibrational resonances in biological systems

Previous research in biology and physics speculates that high-frequency electromagnetic fields may be an unexplored method of cellular and subcellular communication. The predominant theory for generating electric fields in the cell is mechanical vibration of charged or polar biomolecules such as cell membranes or microtubules. The challenge to this theory is explaining how high-frequency vibrations would not be overdamped by surrounding biological media. As many of these suspected resonators are too large for atomistic molecular dynamics simulations, accurately modeling biological resonators remains an ongoing challenge. While many resonators have been studied and simulated, the general limitations on communication imposed by energy transfer arguments have not been considered. Starting with energy transfer expressions from coupled-mode theory, we derive expressions for the minimum quality factor (Q factor) required to sustain communication for both near- and far-field interactions. We compare previous simulation studies and our theory. We determine the flexing mode of microtubules as an identified resonance in the literature which meets our criteria. Our results suggest the major obstacle to meeting our criteria for effective electromagnetic communication is the trade-off between the Q factor and the plasma frequency: Resonators must be large enough to have a large Q factor, but small enough to resonate at frequencies greater than the plasma frequency.

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.

Simulation of electric fields generated from microtubule vibrations

Microtubules are tubular proteins that form part of the cytoskeleton in eukaryotic cells. Because of their unique mechanical properties, many studies have theorized microtubules could show high-frequency mechanical vibrations. Others have further suggested these vibrations of the electrically polar microtubules could be a source of electric fields inside the cell that could serve some biological function, such as a role in organizing mitosis or also possibly in cell-to-cell communication. In this work, we use a transient method to simulate the electric fields that would be generated from a single microtubule supposing they could sustain vibrations. We evaluate the biological significance of the electric fields and the potential energy microtubules might exert on one another. Our simulation method allows us to evaluate vibrational modes that have not previously been studied. The simulations suggest the acoustic branch flexing mode would actually be the most electrically active. Our results suggest a single vibrating microtubule could potentially exert significant forces (those that exceed thermal energy) on biological dipoles or charges at distances larger then the Debye length, on the order of 10nm from the surface of the microtubule, but interaction is not likely at greater distances.

Tubulin Polarizability in Aqueous Suspensions

We report accurate optical measurements of tubulin polarizability in aqueous suspensions. We determined the dependence of polarizability on tubulin concentration and on the suspension's pH, providing benchmark numbers for quantifying the optical response of this protein in various artificial and cellular environments. We compare our measurement data with a few estimates found in the previous literature and also with our simplified model estimations.

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.

Bundles of Brain Microtubules Generate Electrical Oscillations

Microtubules (MTs) are long cylindrical structures of the cytoskeleton that control cell division, intracellular transport, and the shape of cells. MTs also form bundles, which are particularly prominent in neurons, where they help define axons and dendrites. MTs are bio-electrochemical transistors that form nonlinear electrical transmission lines. However, the electrical properties of most MT structures remain largely unknown. Here we show that bundles of brain MTs spontaneously generate electrical oscillations and bursts of electrical activity similar to action potentials. Under intracellular-like conditions, voltage-clamped MT bundles displayed electrical oscillations with a prominent fundamental frequency at 39 Hz that progressed through various periodic regimes. The electrical oscillations represented, in average, a 258% change in the ionic conductance of the MT structures. Interestingly, voltage-clamped membrane-permeabilized neurites of cultured mouse hippocampal neurons were also capable of both, generating electrical oscillations, and conducting the electrical signals along the length of the structure. Our findings indicate that electrical oscillations are an intrinsic property of brain MT bundles, which may have important implications in the control of various neuronal functions, including the gating and regulation of cytoskeleton-regulated excitable ion channels and electrical activity that may aid and extend to higher brain functions such as memory and consciousness.

Copper-Catalyzed Syntheses of Pyrene-Pyrazole Pharmacophores and Structure Activity Studies for Tubulin Polymerization

Tubulin polymerization is critical in mitosis process, which regulates uncontrolled cell divisions. Here, we report a new class of pyrene-pyrazole pharmacophore (PPP) for targeting microtubules. Syntheses of seven pyrenyl-substituted pyrazoles with side-chain modification at N-1 and C-3 positions of the pyrazole ring were accomplished from alkenyl hydrazones via C-N dehydrogenative cross-coupling using copper catalyst under aerobic condition. Tubulin polymerization with PPPs was investigated using docking and biological tools to reveal that these ligands are capable of influencing microtubule polymerization and their interaction with α-, β-tubulin active binding sites, which are substituent specific. Furthermore, cytotoxicity response of these PPPs was tested on cancer cells of different origin, such as MCF-7, MDA-MB231, and C32, and also noncancerous normal cells, such as MCF-10A. All newly synthesized PPPs showed excellent anticancer activities. The anticancer activities and half-maximal inhibitory concentration (IC₅₀) values of all PPPs across different cancer cell lines (MCF-7, MDA-MB231, and C32) have been demonstrated. 1,3-Diphenyl-5-(pyren-1-yl)-1H-pyrazole was found to be best among all other PPPs in killing significant population of all of the cancerous cell with IC₅₀ values 1 ± 0.5, 0.5 ± 0.2, and 5.0 ± 2.0 μM in MCF-7, MDA-MB231, and C32 cells, respectively.

Ion Permeability of a Microtubule in Neuron Environment

Microtubules, constituted by end-to-end negatively charged α- and β-tubulin dimers, are long, hollow, pseudohelical cylinders with internal and external diameters of about 16 and 26 nm, respectively, and widely exist in cell cytoplasm, neuron axons, and dendrites. Although their structural functions in physiological processes, such as cell mitosis, cell motility, and motor protein transport, have been widely accepted, their role in neuron activity remains attractively elusive. Here we show a new function of microtubules: they can generate instant response to a calcium pulse because of their specific permeability for ions. Our comprehensive simulations from all-atom molecular dynamics to potential of mean force and continuum modeling reveal that K⁺ and Na⁺ ions can permeate through the nanopores in the microtubule wall easily, while Ca²⁺ ions are blocked by the wall with a much higher free energy barrier. These cations are adsorbed to the surfaces of the wall with affinity decreasing in the sequence Ca²⁺, Na⁺, and K⁺. As a result, when the concentration of Ca²⁺ ions increases outside the microtubule during neuronal excitation, K⁺ and Na⁺ ions will be driven into the microtubule, triggering subsequent axial ion redistribution within the microtubule. The results shed light on the possibility of the ion-permeable microtubules being involved in neural signal processing.

Elastic, dipole-dipole interaction and viscosity impact on vibrational properties of anisotropic hexagonal microtubule lattice

The paper investigates microtubules lattice properties taking into consideration elastic, dipole-dipole interaction of tubulins and viscosity. A microtubule is modeled as a system of bound tubulins, forming a skewed hexagonal two-dimensional lattice. Wave frequencies and group velocities have been calculated. Calculations have been performed for various directions of wave front propagation: helix, along the protofilament, and anti-helix. Three different wave polarization directions have been considered. It has been shown that the direction of the wave polarization influences the frequency and wave group velocity values in the lattice considerably. The impact of dipole-dipole interaction greatly depends on the direction of the wave polarization; thus, it is only moderate for the longitudinally (LA) polarized waves while it is sufficient for the transversely (TA), and out-of-plane (ZA) polarized waves. Moreover dipole-dipole interaction may result in the waves which are able to cause the rupture of microtubules. With viscosity considered, lattice oscillations become harmonically damped only over a certain wavelength range when longitudinal polarization occurs. Out of this range as well as for the other polarization directions, lattice deviations from equilibrium are dampened exponentially. Taking viscosity into consideration also results in a noticeable decrease in frequency and increase in the group wave velocity when the waves are longitudinally polarized. Reverse wave domains which may be associated with a possible phenomenon of negative refraction have been determined for hexagonal microtubule lattice.

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.

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.

An Overview of Sub-Cellular Mechanisms Involved in the Action of TTFields

Long-standing research on electric and electromagnetic field interactions with biological cells and their subcellular structures has mainly focused on the low- and high-frequency regimes. Biological effects at intermediate frequencies between 100 and 300 kHz have been recently discovered and applied to cancer cells as a therapeutic modality called Tumor Treating Fields (TTFields). TTFields are clinically applied to disrupt cell division, primarily for the treatment of glioblastoma multiforme (GBM). In this review, we provide an assessment of possible physical interactions between 100 kHz range alternating electric fields and biological cells in general and their nano-scale subcellular structures in particular. This is intended to mechanistically elucidate the observed strong disruptive effects in cancer cells. Computational models of isolated cells subject to TTFields predict that for intermediate frequencies the intracellular electric field strength significantly increases and that peak dielectrophoretic forces develop in dividing cells. These findings are in agreement with in vitro observations of TTFields' disruptive effects on cellular function. We conclude that the most likely candidates to provide a quantitative explanation of these effects are ionic condensation waves around microtubules as well as dielectrophoretic effects on the dipole moments of microtubules. A less likely possibility is the involvement of actin filaments or ion channels.

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.

Cytoplasmic dynein binding, run length, and velocity are guided by long-range electrostatic interactions

Dyneins are important molecular motors involved in many essential biological processes, including cargo transport along microtubules, mitosis, and in cilia. Dynein motility involves the coupling of microtubule binding and unbinding to a change in the configuration of the linker domain induced by ATP hydrolysis, which occur some 25 nm apart. This leaves the accuracy of dynein stepping relatively inaccurate and susceptible to thermal noise. Using multi-scale modeling with a computational focusing technique, we demonstrate that the microtubule forms an electrostatic funnel that guides the dynein's microtubule binding domain (MTBD) as it finally docks to the precise, keyed binding location on the microtubule. Furthermore, we demonstrate that electrostatic component of the MTBD's binding free energy is linearly correlated with the velocity and run length of dynein, and we use this linearity to predict the effect of mutating each glutamic and aspartic acid located in MTBD domain to alanine. Lastly, we show that the binding of dynein to the microtubule is associated with conformational changes involving several helices, and we localize flexible hinge points within the stalk helices. Taken all together, we demonstrate that long range electrostatic interactions bring a level of precision to an otherwise noisy dynein stepping process.

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.

Nonlinear dynamics of dipoles in microtubules: Pseudospin model

We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.

The effect of multivalent cations and Tau on paclitaxel-stabilized microtubule assembly, disassembly, and structure

In this review we describe recent studies directed at understanding the formation of novel nanoscale assemblies in biological materials systems. In particular, we focus on the effects of multivalent cations, and separately, of microtubule-associated protein (MAP) Tau, on microtubule (MT) ordering (bundling), MT disassembly, and MT structure. Counter-ion directed bundling of paclitaxel-stabilized MTs is a model electrostatic system, which parallels efforts to understand MT bundling by intrinsically disordered proteins (typically biological polyampholytes) expressed in neurons. We describe studies, which reveal an unexpected transition from tightly spaced MT bundles to loose bundles consisting of strings of MTs as the valence of the cationic counter-ion decreases from Z=3 to Z=2. This transition is not predicted by any current theories of polyelectrolytes. Notably, studies of a larger series of divalent counter-ions reveal strong ion specific effects. Divalent counter-ions may either bundle or depolymerize paclitaxel-stabilized MTs. The ion concentration required for depolymerization decreases with increasing atomic number. In a more biologically related system we review synchrotron small angle x-ray scattering (SAXS) studies on the effect of the Tau on the structure of paclitaxel-stabilized MTs. The electrostatic binding of MAP Tau isoforms leads to an increase in the average radius of microtubules with increasing Tau coverage (i.e. a re-distribution of protofilament numbers in MTs). Finally, inspired by MTs as model nanotubes, we briefly describe other more robust lipid-based cylindrical nanostructures, which may have technological applications, for example, in drug encapsulation and delivery.

Radiofrequency and microwave interactions between biomolecular systems

The knowledge of mechanisms underlying interactions between biological systems, be they biomacromolecules or living cells, is crucial for understanding physiology, as well as for possible prevention, diagnostics and therapy of pathological states. Apart from known chemical and direct contact electrical signaling pathways, electromagnetic phenomena were proposed by some authors to mediate non-chemical interactions on both intracellular and intercellular levels. Here, we discuss perspectives in the research of nanoscale electromagnetic interactions between biosystems on radiofrequency and microwave wavelengths. Based on our analysis, the main perspectives are in (i) the micro and nanoscale characterization of both passive and active radiofrequency properties of biomacromolecules and cells, (ii) experimental determination of viscous damping of biomacromolecule structural vibrations and (iii) detailed analysis of energetic circumstances of electromagnetic interactions between oscillating polar biomacromolecules. Current cutting-edge nanotechnology and computational techniques start to enable such studies so we can expect new interesting insights into electromagnetic aspects of molecular biophysics of cell signaling.

Direct force measurements reveal that protein Tau confers short-range attractions and isoform-dependent steric stabilization to microtubules

Microtubules (MTs) are hollow cytoskeletal filaments assembled from αβ-tubulin heterodimers. Tau, an unstructured protein found in neuronal axons, binds to MTs and regulates their dynamics. Aberrant Tau behavior is associated with neurodegenerative dementias, including Alzheimer's. Here, we report on a direct force measurement between paclitaxel-stabilized MTs coated with distinct Tau isoforms by synchrotron small-angle X-ray scattering (SAXS) of MT-Tau mixtures under osmotic pressure (P). In going from bare MTs to MTs with Tau coverage near the physiological submonolayer regime (Tau/tubulin-dimer molar ratio; ΦTau = 1/10), isoforms with longer N-terminal tails (NTTs) sterically stabilized MTs, preventing bundling up to PB ∼ 10,000-20,000 Pa, an order of magnitude larger than bare MTs. Tau with short NTTs showed little additional effect in suppressing the bundling pressure (PB ∼ 1,000-2,000 Pa) over the same range. Remarkably, the abrupt increase in PB observed for longer isoforms suggests a mushroom to brush transition occurring at 1/13 < ΦTau < 1/10, which corresponds to MT-bound Tau with NTTs that are considerably more extended than SAXS data for Tau in solution indicate. Modeling of Tau-mediated MT-MT interactions supports the hypothesis that longer NTTs transition to a polyelectrolyte brush at higher coverages. Higher pressures resulted in isoform-independent irreversible bundling because the polyampholytic nature of Tau leads to short-range attractions. These findings suggest an isoform-dependent biological role for regulation by Tau, with longer isoforms conferring MT steric stabilization against aggregation either with other biomacromolecules or into tight bundles, preventing loss of function in the crowded axon environment.

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.

Possible role of electrodynamic interactions in long-distance biomolecular recognition

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is revisited within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to calculate the frequencies of the normal modes, which are then used to estimate the interaction potential. The possibility that such interactions play a non-negligible role in ensuring the effective functioning of the biomolecular functions is investigated. On the basis of experimental results reported in the literature and simple numerical estimates, it is found that long-range interactions involving electromagnetic fields of frequencies 0.1-1THz could be temporarily activated despite radiation losses and solvent dissipation. Moreover, the theoretical background used to derive the mentioned interactions sheds light on Fröhlich's theory of selective long-range forces between biomolecules. At variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

Measuring cohesion between macromolecular filaments one pair at a time: depletion-induced microtubule bundling

In the presence of nonadsorbing polymers, colloidal particles experience ubiquitous attractive interactions induced by depletion forces. Here, we measure the depletion interaction between a pair of microtubule filaments using a method that combines single filament imaging with optical trapping. By quantifying the dependence of filament cohesion on both polymer concentration and solution ionic strength, we demonstrate that the minimal model of depletion, based on the Asakura-Oosawa theory, fails to quantitatively describe the experimental data. By measuring the cohesion strength in two- and three- filament bundles, we verify pairwise additivity of depletion interactions for the specific experimental conditions. The described experimental technique can be used to measure pairwise interactions between various biological or synthetic filaments and complements information extracted from bulk osmotic stress experiments.

Electro-acoustic behavior of the mitotic spindle: a semi-classical coarse-grained model

The regulation of chromosome separation during mitosis is not fully understood yet. Microtubules forming mitotic spindles are targets of treatment strategies which are aimed at (i) the triggering of the apoptosis or (ii) the interruption of uncontrolled cell division. Despite these facts, only few physical models relating to the dynamics of mitotic spindles exist up to now. In this paper, we present the first electromechanical model which enables calculation of the electromagnetic field coupled to acoustic vibrations of the mitotic spindle. This electromagnetic field originates from the electrical polarity of microtubules which form the mitotic spindle. The model is based on the approximation of resonantly vibrating microtubules by a network of oscillating electric dipoles. Our computational results predict the existence of a rapidly changing electric field which is generated by either driven or endogenous vibrations of the mitotic spindle. For certain values of parameters, the intensity of the electric field and its gradient reach values which may exert a not-inconsiderable force on chromosomes which are aligned in the spindle midzone. Our model may describe possible mechanisms of the effects of ultra-short electrical and mechanical pulses on dividing cells--a strategy used in novel methods for cancer treatment.

Intracellular electric field and pH optimize protein localization and movement

Mammalian cell function requires timely and accurate transmission of information from the cell membrane (CM) to the nucleus (N). These pathways have been intensively investigated and many critical components and interactions have been identified. However, the physical forces that control movement of these proteins have received scant attention. Thus, transduction pathways are typically presented schematically with little regard to spatial constraints that might affect the underlying dynamics necessary for protein-protein interactions and molecular movement from the CM to the N. We propose messenger protein localization and movements are highly regulated and governed by Coulomb interactions between: 1. A recently discovered, radially directed E-field from the NM into the CM and 2. Net protein charge determined by its isoelectric point, phosphorylation state, and the cytosolic pH. These interactions, which are widely applied in elecrophoresis, provide a previously unknown mechanism for localization of messenger proteins within the cytoplasm as well as rapid shuttling between the CM and N. Here we show these dynamics optimize the speed, accuracy and efficiency of transduction pathways even allowing measurement of the location and timing of ligand binding at the CM –previously unknown components of intracellular information flow that are, nevertheless, likely necessary for detecting spatial gradients and temporal fluctuations in ligand concentrations within the environment. The model has been applied to the RAF-MEK-ERK pathway and scaffolding protein KSR1 using computer simulations and in-vitro experiments. The computer simulations predicted distinct distributions of phosphorylated and unphosphorylated components of this transduction pathway which were experimentally confirmed in normal breast epithelial cells (HMEC).

Mechano-electrical vibrations of microtubules--link to subcellular morphology

Spontaneous mechanical oscillations were predicted and experimentally proven on almost every level of cellular structure. Besides morphogenetic potential of oscillatory mechanical force, oscillations may drive vibrations of electrically polar structures or these structures themselves may oscillate on their own natural frequencies. Vibrations of electric charge will generate oscillating electric field, role of which in morphogenesis is discussed in this paper. This idea is demonstrated in silico on the conformation of two growing microtubules.

Diffusion of myosin V on microtubules: a fine-tuned interaction for which E-hooks are dispensable

Organelle transport in eukaryotes employs both microtubule and actin tracks to deliver cargo effectively to their destinations, but the question of how the two systems cooperate is still largely unanswered. Recently, in vitro studies revealed that the actin-based processive motor myosin V also binds to, and diffuses along microtubules. This biophysical trick enables cells to exploit both tracks for the same transport process without switching motors. The detailed mechanisms underlying this behavior remain to be solved. By means of single molecule Total Internal Reflection Microscopy (TIRFM), we show here that electrostatic tethering between the positively charged loop 2 and the negatively charged C-terminal E-hooks of microtubules is dispensable. Furthermore, our data indicate that in addition to charge-charge interactions, other interaction forces such as non-ionic attraction might account for myosin V diffusion. These findings provide evidence for a novel way of myosin tethering to microtubules that does not interfere with other E-hook-dependent processes.

High-frequency electric field and radiation characteristics of cellular microtubule network

Microtubules are important structures in the cytoskeleton, which organizes the cell. Since microtubules are electrically polar, certain microtubule normal vibration modes efficiently generate oscillating electric field. This oscillating field may be important for the intracellular organization and intercellular interaction. There are experiments which indicate electrodynamic activity of variety of cells in the frequency region from kHz to GHz, expecting the microtubules to be the source of this activity. In this paper, results from the calculation of intensity of electric field and of radiated electromagnetic power from the whole cellular microtubule network are presented. The subunits of microtubule (tubulin heterodimers) are approximated by elementary electric dipoles. Mechanical oscillation of microtubule is represented by the spatial function which modulates the dipole moment of subunits. The field around oscillating microtubules is calculated as a vector superposition of contributions from all modulated elementary electric dipoles which comprise the cellular microtubule network. The electromagnetic radiation and field characteristics of the whole cellular microtubule network have not been theoretically analyzed before. For the perspective experimental studies, the results indicate that macroscopic detection system (antenna) is not suitable for measurement of cellular electrodynamic activity in the radiofrequency region since the radiation rate from single cells is very low (lower than 10⁻²⁰ W). Low noise nanoscopic detection methods with high spatial resolution which enable measurement in the cell vicinity are desirable in order to measure cellular electrodynamic activity reliably.

Intrinsic bending of microtubule protofilaments

The complex polymerization dynamics of the microtubule (MT) plus end are closely linked to the hydrolysis of the GTP nucleotide bound to the β-tubulin. The destabilization is thought to be associated with the conformational change of the tubulin dimers from the straight conformation in the MT lattice to a curved conformation. It remains under debate whether this transformation is directly related to the nucleotide state, or a consequence of the longitudinal or lateral contacts in the MT lattice. Here, we present large-scale atomistic simulations of short tubulin protofilaments with both nucleotide states, starting from both extreme conformations. Our simulations indicate that both interdimer and intradimer contacts in both GDP and GTP-bound tubulin dimers and protofilaments in solution bend. There are no observable differences between the mesoscopic properties of the contacts in GTP and GDP-bound tubulin or the intradime and interdimer interfaces.

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.

Estimate of the Elastic Property of Microtubule Based on a Multiscale Model

This paper presents a multiscale method to estimate the elastic property of the 13_3 microtubule. A microtubule is viewed as being formed by rolling up its planar encounter into the tubular shape, and the transformation is written into a set of equations with three geometrical parameters. The representative cell is chosen as an unit of two pairs of tubulin momoners. With the appropriate longitudinal and lateral interactive potentials, the strain energy density is calculated by deviding the cell’s energy by its spacial volume. The elastic property of microtubule is determined by minimizing the strain energy density, and the elastic constants are calculated in the thereotical scheme of orthotropic elasticity due to the geometrical meanings of the induced parameters. The advantage of the proposed method and its future application are discussed.