Tubulin dipole moment, dielectric constant and quantum behavior: computer simulations, experimental results and suggestions

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 review of tumor treating fields (TTFields): advancements in clinical applications and mechanistic insights

BACKGROUND

Tumor Treating Fields (TTFields) is a non-invasive modality for cancer treatment that utilizes a specific sinusoidal electric field ranging from 100 kHz to 300 kHz, with an intensity of 1 V/cm to 3 V/cm. Its purpose is to inhibit cancer cell proliferation and induce cell death. Despite promising outcomes from clinical trials, TTFields have received FDA approval for the treatment of glioblastoma multiforme (GBM) and malignant pleural mesothelioma (MPM). Nevertheless, global acceptance of TTFields remains limited. To enhance its clinical application in other types of cancer and gain a better understanding of its mechanisms of action, this review aims to summarize the current research status by examining existing literature on TTFields' clinical trials and mechanism studies.

CONCLUSIONS

Through this comprehensive review, we seek to stimulate novel ideas and provide physicians, patients, and researchers with a better comprehension of the development of TTFields and its potential applications in cancer treatment.

Intermittent F-actin Perturbations by Magnetic Fields Inhibit Breast Cancer Metastasis

F-actin (filamentous actin) has been shown to be sensitive to mechanical stimuli and play critical roles in cell attachment, migration, and cancer metastasis, but there are very limited ways to perturb F-actin dynamics with low cell toxicity. Magnetic field is a noninvasive and reversible physical tool that can easily penetrate cells and human bodies. Here, we show that 0.1/0.4-T 4.2-Hz moderate-intensity low-frequency rotating magnetic field-induced electric field could directly decrease F-actin formation in vitro and in vivo, which results in decreased breast cancer cell migration, invasion, and attachment. Moreover, low-frequency rotating magnetic fields generated significantly different effects on F-actin in breast cancer vs. noncancerous cells, including F-actin number and their recovery after magnetic field retrieval. Using an intermittent treatment modality, low-frequency rotating magnetic fields could significantly reduce mouse breast cancer metastasis, prolong mouse survival by 31.5 to 46.0% (P < 0.0001), and improve their overall physical condition. Therefore, our work demonstrates that low-frequency rotating magnetic fields not only can be used as a research tool to perturb F-actin but also can inhibit breast cancer metastasis through F-actin modulation while having minimum effects on normal cells, which reveals their potential to be developed as temporal-controlled, noninvasive, and high-penetration physical treatments for metastatic cancer.

Model-based investigation of elasticity and spectral exponent from atomic force microscopy and electrophysiology in normal versus Schizophrenia human cerebral organoids

The physiological origin of the aperiodic signal present in the electrophysiological recordings, called l/f neural noise, is unknown; nevertheless, it has been associated with health and disease. The power spectrum slope, -α in 1/f^α, has been postulated to be related to the dynamic balance between excitation (E) and inhibition (I). Our study found that human cerebral organoids grown from induced pluripotent stem cells (iPSCs) from Schizophrenia patients (SCZ) showed structural changes associated with altered elasticity compared to that of the normal cerebral organoids. Furthermore, mitochondrial drugs modulated the elasticity in SCZ that was found related to the changes in the spectral exponent. Therefore, we developed an electro-mechanical model that related the microtubular-actin tensegrity structure to the elasticity and the 1/f^α noise. Model-based analysis showed that a decrease in the number and length of the constitutive elements in the tensegrity structure decreased its elasticity and made the spectral exponent more negative while thermal white noise will make α = 0.. Based on the microtubularactin model and the cross-talk in structural (elasticity) and functional (electrophysiology) response, aberrant mitochondrial dynamics in SCZ are postulated to be related to the deficits in mitochondrial-cytoskeletal interactions for long-range transport of mitochondria to support synaptic activity for E/I balance. Clinical Relevance-Our experimental data and modeling present a structure-function relationship between mechanical elasticity and electrophysiology of human cerebral organoids that differentiated SCZ patients from normal controls.

Spontaneous circulation of active microtubules confined by optical traps

We propose an experiment to demonstrate spontaneous ordering and symmetry breaking of kinesin-driven microtubules confined to an optical trap. Calculations involving the feasibility of such an experiment are first performed which analyze the power needed to confine microtubules and address heating concerns. We then present the results of first-principles simulations of active microtubules confined in such a trap and analyze the types of motion observed by the microtubules as well as the velocity of the surrounding fluid, both near the trap and in the far-field. We find three distinct phases characterized by breaking of distinct symmetries and also analyze the power spectrum of the angular momenta of polymers to further quantify the differences between these phases. Under the correct conditions, microtubules were found to spontaneously align with one another and circle the trap in one direction.

Revealing and Attenuating the Electrostatic Properties of Tubulin and Its Polymers

Tubulin is an electrostatically negative protein that forms cylindrical polymers termed microtubules, which are crucial for a variety of intracellular roles. Exploiting the electrostatic behavior of tubulin and microtubules within functional microfluidic and optoelectronic devices is limited due to the lack of understanding of tubulin behavior as a function of solvent composition. This work displays the tunability of tubulin surface charge using dimethyl sulfoxide (DMSO) for the first time. Increasing the DMSO volume fractions leads to the lowering of tubulin's negative surface charge, eventually causing it to become positive in solutions >80% DMSO. As determined by electrophoretic mobility measurements, this change in surface charge is directionally reversible, i.e., permitting control between -1.5 and + 0.2 cm²  (V s)^-1 . When usually negative microtubules are exposed to these conditions, the positively charged tubulin forms tubulin sheets and aggregates, as revealed by an electrophoretic transport assay. Fluorescence-based experiments also indicate that tubulin sheets and aggregates colocalize with negatively charged g-C₃ N₄ sheets while microtubules do not, further verifying the presence of a positive surface charge. This study illustrates that tubulin and its polymers, in addition to being mechanically robust, are also electrically tunable.

Fractal, Scale Free Electromagnetic Resonance of a Single Brain Extracted Microtubule Nanowire, a Single Tubulin Protein and a Single Neuron

Biomaterials are primarily insulators. For nearly a century, electromagnetic resonance and antenna–receiver properties have been measured and extensively theoretically modeled. The dielectric constituents of biomaterials—if arranged in distinct symmetries, then each vibrational symmetry—would lead to a distinct resonance frequency. While the literature is rich with data on the dielectric resonance of proteins, scale-free relationships of vibrational modes are scarce. Here, we report a self-similar triplet of triplet resonance frequency pattern for the four-4 nm-wide tubulin protein, for the 25-nm-wide microtubule nanowire and 1-μm-wide axon initial segment of a neuron. Thus, preserving the symmetry of vibrations was a fundamental integration feature of the three materials. There was no self-similarity in the physical appearance: the size varied by 106 orders, yet, when they vibrated, the ratios of the frequencies changed in such a way that each of the three resonance frequency bands held three more bands inside (triplet of triplet). This suggests that instead of symmetry, self-similarity lies in the principles of symmetry-breaking. This is why three elements, a protein, it’s complex and neuron resonated in 106 orders of different time domains, yet their vibrational frequencies grouped similarly. Our work supports already-existing hypotheses for the scale-free information integration in the brain from molecular scale to the cognition.

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.

Reversible and Irreversible Modulation of Tubulin Self-Assembly by Intense Nanosecond Pulsed Electric Fields

Tubulin self-assembly into microtubules is a fascinating natural phenomenon. Its importance is not just crucial for functional and structural biological processes, but it also serves as an inspiration for synthetic nanomaterial innovations. The modulation of the tubulin self-assembly process without introducing additional chemical inhibitors/promoters or stabilizers has remained an elusive process. This work reports a versatile and vigorous strategy for controlling tubulin self-assembly by nanosecond electropulses (nsEPs). The polymerization assessed by turbidimetry is dependent on nsEPs dosage. The kinetics of microtubules formation is tightly linked to the nsEPs effects on structural properties of tubulin, and tubulin-solvent interface, assessed by autofluorescence, and the zeta potential. Moreover, the overall size of tubulin assessed by dynamic light scattering is affected as well. Additionally, atomic force microscopy imaging reveals the formation of different assemblies reflecting applied nsEPs. It is suggested that changes in C-terminal modification states alter tubulin polymerization-competent conformations. Although the assembled tubulin preserve their integral structure, they might exhibit a broad range of new properties important for their functions. Thus, these transient conformation changes of tubulin and their collective properties can result in new applications.

Tubulin response to intense nanosecond-scale electric field in molecular dynamics simulation

Intense pulsed electric fields are known to act at the cell membrane level and are already being exploited in biomedical and biotechnological applications. However, it is not clear if electric pulses within biomedically-attainable parameters could directly influence intra-cellular components such as cytoskeletal proteins. If so, a molecular mechanism of action could be uncovered for therapeutic applications of such electric fields. To help clarify this question, we first identified that a tubulin heterodimer is a natural biological target for intense electric fields due to its exceptional electric properties and crucial roles played in cell division. Using molecular dynamics simulations, we then demonstrated that an intense - yet experimentally attainable - electric field of nanosecond duration can affect the bβ-tubulin’s C-terminus conformations and also influence local electrostatic properties at the GTPase as well as the binding sites of major tubulin drugs site. Our results suggest that intense nanosecond electric pulses could be used for physical modulation of microtubule dynamics. Since a nanosecond pulsed electric field can penetrate the tissues and cellular membranes due to its broadband spectrum, our results are also potentially significant for the development of new therapeutic protocols.

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.

Electromechanical vibration of microtubules and its application in biosensors

An electric field (EF) has the potential to excite the vibration of polarized microtubules (MTs) and thus enable their use as a biosensor for the biophysical properties of MTs or cells. To facilitate the development, this paper aims to capture the EF-induced vibration modes and the associated frequency for MTs. The analyses were carried out based on a molecular structural mechanics model accounting for the structural details of MTs. Transverse vibration, radial breathing vibration and axial vibration were achieved for MTs subject to a transverse or an axial EF. The frequency shift and stiffness alteration of MTs were also examined due to the possible changes of the tubulin interactions in physiological or pathological processes. The strong correlation achieved between the tubulin interaction and MT vibration excited by EF provides a new avenue to a non-contacting technique for the structural or property changes in MTs, where frequency shift is used as a biomarker. This technique can be used for individual MTs and is possible for those in cells when the cytosol damping on MT vibrations is largely reduced by the unique features of MT-cytosol interface.

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.

Oxidative species-induced excitonic transport in tubulin aromatic networks: Potential implications for neurodegenerative disease

Oxidative stress is a pathological hallmark of neurodegenerative tauopathic disorders such as Alzheimer's disease and Parkinson's disease-related dementia, which are characterized by altered forms of the microtubule-associated protein (MAP) tau. MAP tau is a key protein in stabilizing the microtubule architecture that regulates neuron morphology and synaptic strength. When MAP tau is degraded in tauopathic disorders, neuron dysfunction results. The precise role of reactive oxygen species (ROS) in the tauopathic disease process, however, is poorly understood. Classically, mitochondrial dysfunction has been viewed as the major source of oxidative stress and has been shown to precede tau and amyloid pathology in various dementias, but the exact mechanisms are not clear. It is known that the production of ROS by mitochondria can result in ultraweak photon emission (UPE) within cells. While of low intensity, surrounding proteins within the cytosol can still absorb these energetic photons via aromatic amino acids (e.g., tryptophan and tyrosine). One likely absorber of these photons is the microtubule cytoskeleton, as it forms a vast network spanning neurons, is highly co-localized with mitochondria, and shows a high density of aromatic amino acids. Functional microtubule networks may traffic this ROS-generated endogenous photon energy for cellular signaling, or they may serve as dissipaters/conduits of such energy to protect the cell from potentially harmful effects. Experimentally, after in vitro exposure to exogenous photons, microtubules have been shown to reorient and reorganize in a dose-dependent manner with the greatest effect being observed around 280nm, in the tryptophan and tyrosine absorption range. In this paper, recent modeling efforts based on ambient temperature experiment are presented, showing that tubulin polymers can feasibly absorb and channel these photoexcitations via resonance energy transfer, on the order of dendritic length scales and neuronal fine structure. Since microtubule networks are compromised in tauopathic diseases such as Alzheimer's and Parkinson's dementias, patients with these illnesses would be unable to support effective channeling of these photons for signaling or dissipation. Consequent emission surplus due to increased UPE production or decreased ability to absorb and transfer may lead to increased cellular oxidative damage, thus hastening the neurodegenerative process.

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.

Alternating electric fields (TTFields) in combination with paclitaxel are therapeutically effective against ovarian cancer cells in vitro and in vivo

Long-term survival rates for advanced ovarian cancer patients have not changed appreciably over the past four decades; therefore, development of new, effective treatment modalities remains a high priority. Tumor Treating Fields (TTFields), a clinically active anticancer modality utilize low-intensity, intermediate frequency, alternating electric fields. The goal of this study was to evaluate the efficacy of combining TTFields with paclitaxel against ovarian cancer cells in vitro and in vivo. In vitro application of TTFields on human ovarian cancer cell lines led to a significant reduction in cell counts as compared to untreated cells. The effect was found to be frequency and intensity dependent. Further reduction in the number of viable cells was achieved when TTFields treatment was combined with paclitaxel. The in vivo effect of the combined treatment was tested in mice orthotopically implanted with MOSE-L_TICv cells. In this model, combined treatment led to a significant reduction in tumor luminescence and in tumor weight as compared to untreated mice. The feasibility of effective local delivery of TTFields to the human abdomen was examined using finite element mesh simulations performed using the Sim4life software. These simulations demonstrated that electric fields intensities inside and in the vicinity of the ovaries of a realistic human computational phantom are about 1 and 2 V/cm pk-pk, respectively, which is within the range of intensities required for TTFields effect. These results suggest that prospective clinical investigation of the combination of TTFields and paclitaxel is warranted.

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.

Structure and cohesive energy of dipolar helices

This paper deals with the investigation of cohesive energy in dipolar helices made up of hard spheres. Such tubular helical structures are ubiquitous objects in biological systems. We observe a complex dependence of cohesive energy on surface packing fraction and dipole moment distribution. As far as single helices are concerned, the lowest cohesive energy is achieved at the highest surface packing fraction. Besides, a striking non-monotonic behavior is reported for the cohesive energy as a function of the surface packing fraction. For multiple helices, we discover a new phase, exhibiting markedly higher cohesive energy. This phase is referred to as ZZ tube consisting of stacked crown rings (reminiscent of a pile of zig-zag rings), resulting in a local triangular arrangement with densely packed filaments parallel to the tube axis.

Modification of S. cerevisiae Growth Dynamics Using Low Frequency Electromagnetic Fields in the 1-2 kHz Range

This paper details our further experiments pertaining to the influence of low frequency electromagnetic fields (LF EMF) on the growth dynamics of two wild-type Saccharomyces cerevisiae strands. We opted to explore frequencies beyond the usual 50–60 Hz range, motivated by the ion parametric resonance theory and several studies which discovered and recorded endogenous biosignals in various Saccharomyces cerevisiae strands in the 0.4–2.0 kHz frequency range, most probably stemming from microtubules. Both yeast strands used in our experiments have been subjected to continuous 66-hour session of LF EMF exposure (frequencies 1.2, 1.4, 1.6, 1.8, and 2.0 kHz; average magnetic flux density 2.43 mT) under identical ambient conditions. Experiment results indicate a frequency-dependent proliferative response of both yeast strands.

The feasibility of coherent energy transfer in microtubules

It was once purported that biological systems were far too 'warm and wet' to support quantum phenomena mainly owing to thermal effects disrupting quantum coherence. However, recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherent transport, especially in the 'dry' hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherent energy transfer between uniquely arranged chromophores in light harvesting photosynthetic complexes. The 'tubulin' subunit proteins, which comprise microtubules, also possess a distinct architecture of chromophores, namely aromatic amino acids, including tryptophan. The geometry and dipolar properties of these aromatics are similar to those found in photosynthetic units indicating that tubulin may support coherent energy transfer. Tubulin aggregated into microtubule geometric lattices may support such energy transfer, which could be important for biological signalling and communication essential to living processes. Here, we perform a computational investigation of energy transfer between chromophoric amino acids in tubulin via dipole excitations coupled to the surrounding thermal environment. We present the spatial structure and energetic properties of the tryptophan residues in the microtubule constituent protein tubulin. Plausibility arguments for the conditions favouring a quantum mechanism of signal propagation along a microtubule are provided. Overall, we find that coherent energy transfer in tubulin and microtubules is biologically feasible.

Fast label-free cytoskeletal network imaging in living mammalian cells

We present a full-field technique that allows label-free cytoskeletal network imaging inside living cells. This noninvasive technique allows monitoring of the cytoskeleton dynamics as well as interactions between the latter and organelles on any timescale. It is based on high-resolution quantitative phase imaging (modified Quadriwave lateral shearing interferometry) and can be directly implemented using any optical microscope without modification. We demonstrate the capability of our setup on fixed and living Chinese hamster ovary cells, showing the cytoskeleton dynamics in lamellipodia during protrusion and mitochondria displacement along the cytoskeletal network. In addition, using the quantitative function of the technique, along with simulation tools, we determined the refractive index of a single tubulin microtubule to be ntubu=2.36±0.6 at λ=527 nm.

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.

Flagella as a novel alignment medium for the measurement of residual dipolar couplings in proteins

The two flexible rod-like flagella (∼500 nm in diameter and 5-15 μm long) of Chlamydomonas reinhardtii, a unicellular green alga, can weakly align molecules in an external magnetic field, thereby enabling the measurement of various residual dipolar couplings in solution NMR spectroscopy.

Quantitative imaging of microtubule alteration as an early marker of axonal degeneration after ischemia in neurons

Neuronal death can be preceded by progressive dysfunction of axons. Several pathological conditions such as ischemia can disrupt the neuronal cytoskeleton. Microtubules are basic structural components of the neuronal cytoskeleton that regulate axonal transport and neuronal function. Up-to-date, high-resolution observation of microtubules in living neuronal cells is usually accomplished using fluorescent-based microscopy techniques. However, this needs exogenous fluorescence markers to produce the required contrast. This is an invasive procedure that may interfere with the microtubule dynamics. In this work, we show, for the first time to our knowledge, that by using the endogenous (label-free) contrast provided by second harmonic generation (SHG) microscopy, it is possible to identify early molecular changes occurring in the microtubules of living neurons under ischemic conditions. This is done by measuring the intensity modulation of the SHG signal as a function of the angular rotation of the incident linearly polarized excitation light (technique referred to as PSHG). Our experiments were performed in microtubules from healthy control cultured cortical neurons and were compared to those upon application of several periods of oxygen and glucose deprivation (up to 120 min) causing ischemia. After 120-min oxygen and glucose deprivation, a change in the SHG response to the polarization was measured. Then, by using a three-dimensional PSHG biophysical model, we correlated this finding with the structural changes occurring in the microtubules under oxygen and glucose deprivation. To our knowledge, this is the first study performed in living neuronal cells that is based on direct imaging of axons and that provides the means of identifying the early symptoms of ischemia. Live observation of this process might bring new insights into understanding the dynamics and the mechanisms underlying neuronal degeneration or mechanisms of protection or regeneration.

Dipole-dipole interactions in microtubules

Dimers in microtubules possess a dipole moment with components along three axes. The interaction energy among all dipole components in a microtubule was calculated for an un-deformed and an elliptically deformed microtubule in a "dry" condition. The interaction energy was found to increase with deformation. The total interaction energy among all dipoles is positive, which implies that the un-deformed cylindrical shape of a microtubule represents a condition of minimum energy. This suggests that the cylindrical shape of microtubules is a consequence of dipole-dipole interactions. There may be other causes as well but these are not discussed in this paper. From these results, the contributions of the dipole-dipole interaction energy to the microtubule longitudinal and transverse flexural rigidities were calculated. It is shown that the longitudinal contribution to the elastic modulus is approximately 50-60% of the total measured value while the calculated transverse contribution is smaller than the longitudinal contribution by a factor of approximately 3. The ratio of the measured axial to the measured transverse flexural rigidity is approximately 125, in agreement with recent observations. However, these values are uncertain for reasons discussed in the text.

Neural cytoskeleton capabilities for learning and memory

This paper proposes a physical model involving the key structures within the neural cytoskeleton as major players in molecular-level processing of information required for learning and memory storage. In particular, actin filaments and microtubules are macromolecules having highly charged surfaces that enable them to conduct electric signals. The biophysical properties of these filaments relevant to the conduction of ionic current include a condensation of counterions on the filament surface and a nonlinear complex physical structure conducive to the generation of modulated waves. Cytoskeletal filaments are often directly connected with both ionotropic and metabotropic types of membrane-embedded receptors, thereby linking synaptic inputs to intracellular functions. Possible roles for cable-like, conductive filaments in neurons include intracellular information processing, regulating developmental plasticity, and mediating transport. The cytoskeletal proteins form a complex network capable of emergent information processing, and they stand to intervene between inputs to and outputs from neurons. In this manner, the cytoskeletal matrix is proposed to work with neuronal membrane and its intrinsic components (e.g., ion channels, scaffolding proteins, and adaptor proteins), especially at sites of synaptic contacts and spines. An information processing model based on cytoskeletal networks is proposed that may underlie certain types of learning and memory.

Single centrosome manipulation reveals its electric charge and associated dynamic structure

The centrosome is the major microtubule-organizing center in animal cells and consists of a pair of centrioles surrounded by a pericentriolar material. We demonstrate laser manipulation of individual early Drosophila embryo centrosomes in between two microelectrodes to reveal that it is a net negatively charged organelle with a very low isoelectric region (3.1 +/- 0.1). From this single-organelle electrophoresis, we infer an effective charge smaller than or on the order of 10(3) electrons, which corresponds to a surface-charge density significantly smaller than that of microtubules. We show, however, that the charge of the centrosome has a remarkable influence over its own structure. Specifically, we investigate the hydrodynamic behavior of the centrosome by measuring its size by both Stokes law and thermal-fluctuation spectral analysis of force. We find, on the one hand, that the hydrodynamic size of the centrosome is 60% larger than its electron microscopy diameter, and on the other hand, that this physiological expansion is produced by the electric field that drains to the centrosome, a self-effect that modulates its structural behavior via environmental pH. This methodology further proves useful for studying the action of different environmental conditions, such as the presence of Ca(2+), over the thermally induced dynamic structure of the centrosome.

Microtubule stability studied by three-dimensional molecular theory of solvation

We study microtubular supramolecular architectures of tubulin dimers self-assembling into linear protofilaments, in turn forming a closed tube, which is an important component of the cytoskeleton. We identify the protofilament arrangements with the lowest free energy using molecular dynamics to optimize tubulin conformations. We then use the three-dimensional molecular theory of solvation to obtain the hydration structure of protofilaments built of optimized tubulins and the solvent-mediated effective potential between them. The latter theoretical method, based on first principles of statistical mechanics, is capable of predicting the structure and thermodynamics of solvation of supramolecular architectures. We obtained a set of profiles of the potential of mean force between protofilaments in a periodic two-dimensional sheet in aqueous solution. The profiles were calculated for a number of amino acid sequences, tubulin conformations, and spatial arrangements of protofilaments. The results indicate that the effective interaction between protofilaments in aqueous solution depends little on the isotypes studied; however, it strongly depends on the M loop conformation of beta-tubulin. Based on the analysis of the potential of mean force between adjacent protofilaments, we found the optimal arrangement of protofilaments, which is in good agreement with other studies. We also decomposed the potential of mean force into its energetic and entropic components, and found that both are considerable in the free-energy balance for the stabilized protofilament arrangements.

Impedance spectroscopy of alpha-beta tubulin heterodimer suspensions

Impedance spectroscopy is a technique that reveals information, such as macromolecular charges and related properties about protein suspensions and other materials. Here we report on impedance measurements over the frequency range of 1 Hz to 1 MHz of alpha-beta tubulin heterodimers suspended in a buffer. These and other polyelectrolyte suspensions show enormous dielectric responses at low frequencies, due both to the motion of charges suspended in the medium and to an electrical double layer that forms at each electrode-medium interface. We propose an equivalent circuit model to minimize electrode polarization effects and extract the intrinsic response of the bulk medium. At megaHertz frequencies, the conductivity increases with concentration below the critical concentration of approximately 1 mg/ml for microtubule polymerization, above which the conductivity decreases. This suggests that such measurements can be used to monitor the dynamics of microtubule polymerization. Finally, we obtain the net charge number per tubulin dimer of /Z/ = 306 in the saline buffer, which, if maintained as the dimers polymerized, would yield a linear charge density of 3.8 e/angstroms for the assembled microtubules. These results are potentially important for fundamental electrostatic processes in biomolecules and suggest the possibility of developing future bioelectronic applications.

Microtubules as mechanical force sensors

Microtubules are polymers of tubulin subunits (dimers) arranged on a hexagonal lattice. Each tubulin dimer comprises two monomers, the alpha-tubulin and beta-tubulin, and can be found in two states. In the first state a mobile negative charge is located into the alpha-tubulin monomer and in the second into the beta-tubulin monomer. Each tubulin dimer is modeled as an electrical dipole coupled to its neighbors by electrostatic forces. The location of the mobile charge in each dimer depends on the location of the charges in the dimer's neighborhood. Mechanical forces that act on the microtubule affect the distances between the dimers and alter the electrostatic potential. Changes in this potential affect the mobile negative charge location in each dimer and the charge distribution in the microtubule. The net effect is that mechanical forces affect the charge distribution in microtubules. We propose to exploit this effect and use microtubules as mechanical force sensors. We model each dimer as a two-state quantum system and, following the quantum computation paradigm, we use discrete quantum random walk on the hexagonal microtubule lattice to determine the charge distribution. Different forces applied on the microtubule are modeled as different coin biases leading to different probability distributions of the quantum walker location, which are directly connected to different charge distributions. Simulation results show that there is a strong indication that microtubules can be used as mechanical force sensors and that they can also detect the force directions and magnitudes.