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.

We examine the behavior of a charged particle in a two dimensional quantum dot in the presence of a magnetic field. Emphasis is placed on the high magnetic field regime. Compared to free space geometry, confinement in a dot geometry provides a more realistic system where edge effects arise naturally. It also serves to remove the otherwise infinite degeneracy due to the magnetic field; nonetheless, as described in this paper, additional ingredients are required to produce sensible results. We treat both circular and square geometries, and in the latter, we explicitly demonstrate the gauge invariance of the energy levels and wave function amplitudes. The characteristics of bulk states closely resemble those of free space states. For edge states, with sufficiently high quantum numbers, we achieve significant differences in the square and circular geometries. Both circular and square geometries are shown to exhibit level crossing phenomena, similar to parabolic dots, where the confining potential is a parabolic trap. Confinement effects on the probability current are also analyzed; it is the edge states that contribute non-zero current to the system. The results are achieved using straightforward matrix mechanics, in a manner that is accessible to novices in the field. On a more pedagogical note, we also provide a thorough review of the theory of single electron Landau levels in free space and illustrate how the introduction of surfaces naturally leads to a more physically transparent description of a charged particle in a magnetic field.

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TTField (Tumor-treating field) therapy utilizes low intensity intermediate frequency AC electric fields to reduce the spread of cancer. While it has attained FDA approval for the treatment of recurrent glioblastoma multiforme, the exact molecular targets of TTField therapy are not well understood. Microtubules are pipe-like polymers of the highly charged (–31 e) and strongly dipolar (dipole moment 1666 D) protein, α, β- tubulin. Studies on the electrical properties of microtubules have recently gained interest, with them being modelled as molecular targets of TTFields. Here, we experimentally show that while tubulin polymerized into microtubules leads to an increase in solution capacitance, unpolymerized tubulin has no appreciable effect. To the best of our knowledge, we present the first experimental quantification of the capacitance of a 20 μm-long microtubule. Using these results, we calculate the resonant frequency of a microtubule meshwork in a cell-like environment to be in the TTField regime. Our results utilize high ionic strength solutions and cell-like concentrations of tubulin to show the potential of microtubules as the targets of TTField action and as intracellular charge-storage devices. We conclude with a hypothesis of an electrically-tunable cell, where the dielectric properties of the cytoskeleton alter local and global charge storage and transport.

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