The electrical properties of isolated microtubules

<jats:title>Abstract</jats:title><jats:p>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<jats:sup>–17</jats:sup> 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.</jats:p>

section_content: with brain MT bundles 8, in contrast to the high seal resistances usually obtained with MT sheets 7, 8. Isolated MTs formed in the absence of Paclitaxel were initially voltage-clamped at zero mV, showing no electrical activity in any successful experiments (n = 14). However, under these conditions, the variance of the current at 0 mV was statistically different from that of the pipette in solution (solution vs. MT-attached: 1. 17 ± 0. 15 pA 2, n = 6, vs. 2. 27 ± 0. 49 pA 2, n = 6, p = 0. 04) that was concomitant with the presence of oscillatory peak frequencies (Fig. 1C ). MTs displayed spontaneous, self-sustained electrical oscillations in 69% of cases (20/29) in direct response to the magnitude and polarity of the electrical stimulus (Figs. 1D and 2A ). The most prominent frequency peaks Currents elicited by different holding potentials obtained with the pipette in solution before (Red) and after (Black) attachment to an isolated MT. Bottom. Frequency spectra at 0 mV for the pipette in solution (Black) and after MT apposition (Red). Please, note that notch filtering was applied to eliminate contaminating line frequencies at 50 and 100 Hz. (D) Electrical recordings from an isolated MT at different holding potentials (± 100 mV) as indicated. Expanded tracings on the Right show electrical oscillations of regions numbered "1" through "5". Applied voltages represented the driving potentials at the patch clamp amplifier. 

with the simplest oscillations observed were at 43-47 Hz and 90 Hz at negative holding potentials. At positive holding potential, only 43-47 Hz was observed, at least at the beginning of the experiments. These oscillations showed monoperiodic limit cycles, as shown in the three-dimensional phase portrait (Fig. 2B ). At zero mV, only the 50 Hz line interference frequency was present. Current-to-voltage relationship and frequencies of non-Paclitaxel stabilized isolated microtubules. The mean oscillatory currents were linear concerning the corrected holding potential (Fig. 4A, B ), showing at least two different "high" and "low" conductances of 103. 0 ± 3. 5 nS (n = 3) and 11. 3 ± 1. 2 nS (n = 4), respectively. Freedman et al. 12 calculated single MT current-voltage relationships from a cation conductance circuit model with a conductance in the order of 10 nS. Three-dimensional phase-space portraits showing monoperiodic limit cycles were observed for both conductance levels (Fig. 4C ). 

Fundamental frequencies were seen at approximately 7, 13, 28, 39, 47, 90, 140, and 147 Hz (Fig. 5 ). However, not all the frequencies were prominent in experiments with low and high conductance. The 13 and 147 Hz were observed only in the high conductance experiments, while the 140 Hz was noticeable in the low conductance experiments. 

A richer oscillatory behavior was observed when the same holding potential was applied for several minutes (Fig. 6 ). In these instances, the oscillation patterns observed were variable in the time with low frequencies periods alternating with high frequencies periods, making evident a more coherent activity at different fundamental frequencies (Fig. 6 ) for positive and negative potentials, respectively.

section_content: To further explore the rich oscillatory behavior of isolated MTs, similar experiments were conducted under identical conditions in MT sheets from the same preparation (Fig. 7 ). The unattached pipette showed a predominantly white noise spectrum with contaminant power line frequency peaks at 50 and 100 Hz (Fig. 7A, D ), while the isolated MT-attached spectra displayed colored peaks of relevant frequencies in the oscillatory behavior. We observed clear differences with the MT sheets (n = 4), showing fundamental oscillatory frequencies around 38 and 90 Hz (Fig. 7B, D ). In all cases, the frequency peaks were richer in the isolated MTs compared to their corresponding MT sheet (Fig. 7A-C, Right). Thus, MTs in the larger surface area of the MT sheet (with a tighter seal) displayed more coherent behavior regarding the observed fundamental frequencies. Thus, an interesting electrical difference between isolated MTs and MT structures became evident, namely, a richer oscillatory behavior of isolated MTs that drastically changed by assembling into flat surfaces showing fewer but stronger oscillatory peaks (Fig. 7 ). 

Calculation of the power and energy dissipated by an isolated microtubule. The power radiated by the oscillating MT can be obtained as an equivalent wire that allows the flow of an alternating current. Although the wave equation of a sheet of brain MTs requires up to seven fundamental frequencies with their respective weight and phase 18, in this case, for simplicity we assumed an oscillating structure with a single fundamental frequency f, such that ω = 2πf. The mean value of such alternating current is zero. However, the mean square values (both generated current I, and voltage V) are not. Thus, the non-zero effective values are calculated, where the effective voltage is V eff = (1/2)V 2 max = 0. 707V max, and likewise the effective current is

where Z is the impedance of the equivalent circuit connecting the MT with the pipette. Under resonance (pure dissipative conditions), Z = R, and the phase angle between parameters φ = 0 and cos φ = 1. However, normally Z > R, such that the factor cos φ = R/Z, relates them. 

Although the instantaneous power (P) of the MT is zero, its mean value is P mean = V eff I eff cosϕ, where cos φ, as indicated above, is the power factor, which has to be considered from the intrinsic values of the dissipating (R), and energy storing components of the equivalent circuit representing the connection between the pipette and the MT (Fig. 8 ). 

By definition, the instantaneous power of the current element is P = RI 2, where the mean value is P mean = RI 2 mean, which is equivalent to P mean = V eff I eff cosϕ. To calculate the angle of power radiated by the oscillating MT that is sensed by the pipette, we apply the vectorial analysis of the Poynting theorem ( P = E × H ) establishing the connection between the electric and magnetic field intensities generated by the oscillator. If we place a current element of length dL from the MT, where L is the length of the MT, with the value IdLcos ωt, (where ω = 2πf), the field intensities sensed by a point P (Fig. 8 ) at a distance r where the pipette tip is located, three field contributions (in spherical coordinates r, θ, ϕ), are sensed, which are perpendicular to each other. The power Poynting vector is then obtained by the cross product ( P = E × H ) (to be developed elsewhere). At point P, there are two contributions to the electric field, in the r direction (E r ), and the θ direction (E θ ), whereas the orthogonal magnetic field is in the ϕ direction (H ϕ ). 

Thus, P θ = -E r × H θ = 0 and P r = E θ × H φ = 0. The total dissipated power P T is then obtained from the surface integration of the mean power, such that P T = R r I 2 eff, where R r is the radiation resistance. The importance of these equations is their ability to provide a means to calculate the energy emanated from a single MT that could then be used to compare with the intensity of fields sensed from single axons and cells, and other values obtained by methods such as the EEG of the human scalp. 

To apply the theory to our results, we first calculated the area under the curve of the power spectrum around 41. 5 Hz (fundamental frequency peak observed in all the experiments without Paclitaxel, Fig. 8 ), obtaining a variance of 2. 65 × 10 -6 nA 2. In what follows, the dissipating resistance of the pipette-MT connection used was 10 MΩ, with the caveat that most of it would represent the resistance of the pipette and not the MT resistance. From the consideration above, we know that P mean = V eff I eff cosϕ, and we will assume that cos φ = 1. From our experiments, we calculate an I max of ~ 60 pA, where I eff = 0. 707I max, such that Replacing, we obtain: which is the electrical driving force present in the MT in the absence of an external holding potential, that drives the oscillatory current. By applying the Nernst equation an estimation could be made of the ionic concentrations that generate such intrinsic MT potential (between MT lumen and bathing solution). We obtain: from which we could infer the minimal charges implicated in the voltage difference. Thus, recalculating with the minimal ΔC necessary to generate a voltage in the pipette tip considering Vol MT, we obtain a luminal concentration of cation (K + ) of 2. 65 × 10 -25 mol, that represents a total charge Q = FC of 2. 56 × 10 -20 C, where F has the usual meaning of 96. 500 C/mol.
section_name: Comparison between MT sheets and non-Paclitaxel stabilized isolated MTs.

section_content: While the mechanical and biochemical aspects of MT formation and stability have been thoroughly studied, their electrical properties and ability to generate electromagnetic fields have not. Here we demonstrated that isolated MTs generate electrical oscillations, which constitute the basis of their electromagnetic power. Previous studies with Paclitaxel-stabilized brain MTs showed the propagation and amplification of electrical signals but not the presence of electrical oscillations 4, 5. In those studies, MTs amplified the electrical pulse injected at the stimulus and the collection sites, with transfer amplification ratios up to 2. 35 under high ionic strength conditions. In retrospect, the absence of oscillations was hypothesized to be caused by the use of Paclitaxel to stabilize and hold the MTs to the pipettes 4, 5. However, electrical oscillations have been observed in MT sheets and bundles that were readily inhibited by the addition of Paclitaxel 7, 8. Thus, herein, we explored Paclitaxel-free, non-stabilized single brain MTs, which instead made it more difficult to find and handle. For comparison, we also studied Paclitaxel-stabilized MTs, without adding the drug to the pipette tip or saline solution during the experiment. We observed that the oscillatory behavior of the isolated MTs was different from that of MT sheets present in the same preparation. In particular, we consistently observed a broader spectrum of fundamental frequencies in the isolated non-stabilized MTs compared to the MT sheets. Paclitaxel-stabilized MTs sustained electrical oscillations with a more restrictive power spectrum than the non-stabilized MTs, showing a single fundamental frequency around 39 Hz, similar to that observed in the more structured MT complexes (i. e., bundles and sheets). This finding raises the hypothesis that assembling MTs into higher structures (e. g., cilia and flagella) may tend to entrain MT oscillations. Different oscillatory modes have been postulated for other MT structures 7, 8. 

We present evidence for the intrinsic electrical properties of MTs without external stimulation. At zero mV applied holding potential, under symmetrical ionic conditions (lack of an electrochemical gradient), the oscillatory current generated by an isolated MT in solution was evidenced over the noise of its respective patch pipette alone. The power spectrum revealed the presence of minimal oscillations, which in the absence of holding voltage could only be sustained by the existence of a driving force, likely generated by an electrochemical gradient originated by the geometrical parameters of the MT and the permeable ionic species between the MT lumen and the bath solution. To calculate the power radiated by the oscillating MT and sensed by the pipette, we applied the Poynting theorem, establishing the connection between the oscillator's electric and magnetic field intensities. The power Poynting vector is then obtained by the cross product (P = E x H). An analysis of the power spectrum at zero mV of an MT in the absence of Paclitaxel, revealed that the area under the curve in the region 43-47 Hz was 2. 65 × 10 -6 nA 2 from which we calculated a V eff at the pipette tip of 63 µV which could be maintained by a K + concentration difference as little as 3. 38 µM. Thus, a minimal concentration difference can generate and sustain electrical oscillations in MTs, consistent with a radiating power in the order of 2. 65 × 10 -17 W per MT. Thus, MTs contribute to the electrodynamic properties of the cell in which they are immersed. In comparison, the power dissipated by the neuronal cytoskeleton of the permeabilized brain in the honeybee, as recently measured by local field potentials 17, was approximately 300 times larger. The electrodynamic properties of the MTs may contribute to the electric fields measured in EEGs and other technical approaches to assess the vector fields generated by the brain's electrical activity. MT electrical oscillations in the neuronal environment may provide a novel means for electrical interactions between different cellular organelles or cytoskeletal structures, such as the actin cytoskeleton 16. They may explain the existence and propagation of traveling waves recently ascribed to endogenous electric fields [18] [19] [20] [21] [22]. Interestingly, Freedman et al. 12 predicted a current-voltage relationship of an MT, calculated using a resonant circuit model for a cationic conductance in the order of 10 nS, in agreement with our results. Moreover, the conductance was predicted as dependent of the length on the MT. Length and structure of the MTs, including nanopore density could be the reason(s) for the existence of low and high conductance levels. 

The MT electrical oscillations are mechanistically consistent with the behavior of an organic electrochemical transistor 23, 24 that supports amplification and self-sustained current (and voltage) oscillations. In this hypothetical mechanism, a gate region of the electrochemical transistor 4, 25, associated with uneven charge distribution on the MT's surface 26, would drive the opening of the ion-permeable nanopores that elicit the electrodiffusional circuit. Thus, electrostatically-induced vibrations of adjacent αβ tubulin heterodimers may act as electrical oscillators allowing electrodiffusional ionic transport through the nanopores. The gating mechanism would share similarities with piezoelectric materials to elicit electromechanical transduction such that their mechanical and electrical properties differ upon voltage-induced changes in conformational state 10. The memristive behavior unmasked by a voltage-dependent capacitance in non-oscillating MT sheets suggested that the electrical response has a complex voltage-dependent nonlinear response. However plausible, this hypothesis and its implications will require further investigation. Nonetheless, in pursuing a better understanding of the molecular nature of the electrical oscillations, we have focused on our prior findings that the oncology drug Paclitaxel (Taxol), an MT stabilizer that traverses the nanopores of the MT wall [26] [27] [28] [29], inhibits the oscillatory phenomenon 4, but not the ability to amplify electrical signals. 

Interestingly, the observed oscillation frequencies in isolated MTs were similar to those previously reported by empirical mode decomposition (EMD) of brain MT sheets, which also resembled the physiological brain electrical signals commonly observed in EEG 18. Identified human brain waves associated with normal and pathological brain functions include low-frequency delta waves in the range of 0. 5-4 Hz, followed by increasing frequency theta waves, 4-8 Hz, alpha 8-13 Hz, beta 13-30, and finally gamma waves beyond 30 Hz, from which lower (~ 30 Hz) and higher (~ 90 Hz) gamma patterns are also recognized 30, 31. The electrical activity of MTs would be an essential contribution to brain activity, and they represent the intrinsic unit of a central brain oscillator recently postulated for the honeybee brain 17. 

The electrical activity of isolated MTs may offer a novel paradigm in neuronal signaling. Tubulin protofilaments, which either curl into MTs or attach laterally to form a 2D-sheets 7, 32 by lateral apposition of protofilaments spontaneously extend to larger flat surfaces generate electrical signals, whose oscillatory frequency and amplitude would likely depend on the specific composition of the nanopores in the MT wall. The present study sheds new light on the structural/functional correlates of MT electrical activity.
section_name: Discussion

section_content: Preparation of isolated MTs. For the present study, we used commercial bovine brain tubulin (catalog No T238, Cytoskeleton, Denver, CO, USA). Tubulin was polymerized with a "hybrid" protocol in either the presence or absence of Paclitaxel (Taxol Equivalent, Invitrogen™, P3456), following general guidelines from the Mitchinson Lab's online protocols (http:// mitch ison. med. harva rd. edu/ proto cols/). Briefly, all reactions were conducted in BRB80 solution containing 80 mM PIPES (1,4-piperazinediethanesulfonic acid), 1 mM MgCl 2, 1 mM EGTA, and pH 6. 8 with KOH. MT sheets were obtained as previously reported 7. Correction of voltage for mean current-to-voltage relationships. . To obtain the I-V relationships shown in Fig. 4A, we applied the loose patch correction to the voltage for each experiment considered. Thus, the voltage at the pipette tip (V p ) is given by 33 : where R p, R s, and V cmd are the pipette resistance, seal resistance, and command voltages, respectively (see details in 8 ). 

Other current analyses. Average currents were obtained by integrating one-second tracings expressed as mean ± SEM (n), where (n) represented the number of experiments analyzed for a given condition. To calculate the electrical contribution of the isolated MT in the absence of an electrochemical gradient (i. e., symmetrical ionic conditions and zero mV holding potential), we calculated the variance at 0 mV. We randomly selected ten seconds from recordings of different experiments (n = 6) obtained either with the pipette in solution before or after attachment to an isolated MT. For all experiments, we measured the standard deviation of the average tracing using Clampfit 10. 0, and calculated the variance as the standard deviation squared. The values of each group were averaged and compared using Student's t-test. Statistical difference was considered when p < 0. 05. The Fourier transform subroutine of Clampfit 10. 0 obtained power spectra of the unfiltered tracings. Poincare diagrams were constructed by the time delay (τ) approach, where the lag time τ was chosen arbitrarily at 2f, and f was the data acquisition sampling frequency. 

Schematics. The schemes shown in Fig. 1B were produced with the free software Inkscape 0. 92. 4 (https:// www. inksc ape. org).
section_name: Materials and methods

section_content: Unless otherwise stated, all reagents were obtained from Sigma-Aldrich (St Louis, MI, USA).
section_name: Solutions and chemicals.

section_name: Acknowledgements

section_content: Ministerio de Ciencia, Tecnología e Innovación Productiva de la Nación (Argentina), FONCyT, PICT 2016-3739. Ministerio de Ciencia, Tecnología e Innovación Productiva de la Nación (Argentina), FONCyT, PICT 2018-3337.
section_name: Acknowledgements

section_name: Data availability

section_content: All data are available as reasonable request to the authors. Received: 17 January 2023; Accepted: 12 June 2023
section_name: Data availability

section_name: Author contributions

section_content: The authors declare no competing interests.
section_name: Competing interests