3.1. Triplet of Triplet Fractal Electromagnetic Resonance Band of Single Brain Extracted Microtubule
We provide more profound support to an earlier experimental observation by Pizzi et al. [29
] that microtubule nanowire acts as both antenna and receiver during long-range communication. Microtubule was synthesized by the standard protocol described elsewhere [28
]. We grow four 200 nm wide parallel gold electrodes on top of a single microtubule via e-beam lithography method (Figure 1
b), both two probe and four probe measurements are carried out. In the initial days, we used to grow electrodes on the nanowire (11% device survived), similar to carbon nanotube measurements, however, later we changed and dropped microtubule or biomaterials on the pre-grown electrodes. The method helps in the survival of a greater number of devices, though the formation of a proper contact became challenging (88% devices made good contact).
demonstrates a series of electromagnetic resonance measurements. Normally, after forming a biomaterial–electrode contact transmission and reflection coefficients are measured under AC signal. The peaks at specific resonance frequencies are considered to be the resonance frequencies. For years, Sahu et al. [18
] and Ghosh et al. [7
] adopted a different methodology, they observed at which frequencies the DC conductivity shows a sharp increase, it means, a dual check on resonance. To detect a resonance peak of a single microtubule nanowire, here, either we measure drop in DC resistance under AC pumping using the circuit in Figure 1
b, (see Figure 2
a) or, we measure transmission coefficients along the length of the biomaterial in dB under AC signal varying the frequency from 1 Hz to 20 GHz (Figure 2
b,c) using a vector analyzer. Though subtracting background data are a common practice, we never do that, only for the reason that a blind subtraction brings noise artifacts as peaks and neglects important ones. In all resonance peak detection, we neglect open and short circuit responses to avoid noise. The peaks that appear in the open and short conditions are simply deleted; we consider that peak region as non-accessible. Finally, we observe three distinct regions. First, 10–100 kHz domain (Figure 2
a) was depending on the AC bias amplitude, we observe the superposition of three distinct peaks of resistance loss, which becomes more distinct with more injection current, finally, we get quality factor, Q ~ 3–5. Second, 8–240 MHz, (Figure 2
b) peaks are sharp (Q ~ 100–300), energy is distributed nonlinearly among particularly allowed 8 resonance peaks in this domain; microtubule’s length strictly determines which resonance frequencies are to be blocked. In more than 88% of devices, we found that the peaks with low intensities blink, i.e., appear and disappear, some peaks are negative, and some peaks are positive while continuously changing intensities. MHz peaks of microtubule are the treasure of enormous dynamic activities. Finally, in the 7–13 GHz domain, (Figure 2
c) we have two Gaussian-like resonant transmissions if single microtubule was pumped at 7 GHz, near 19 GHz we get a transmission band, which was remarkable since frequency was amplified. It means we get very different kinds of signal as output than what we send as input. At 13 GHz pumping we observe another Gaussian-like stochastic resonance, however, in this case, it was peaked around 13 GHz only.
The kHz and GHz bands do not change the phase of AC input signal (Figure 2
d) while a quantized phase modulation by
occurs during MHz transmission across the microtubule (Figure 2
e,f), which suggests that MHz band was strongly engaged in electromagnetic radiation. Quantization of phase naturally by microtubule to a non-coherent AC signal was a remarkable discovery for multiple reasons. First, it suggests that for phase-coherent signal transmission we do not need to send phase-coherent electronic, magnetic or electromagnetic signal through the microtubule, microtubule spontaneously converts non-coherent signals into a coherent one. However, depending on the input frequency, the output signal gets a predetermined phase.
Using CST (computer simulation technology), we created several model structures of tubulin, microtubule and single neuron and solved Maxwell’s equations using the time domain solver. Two ports were connected to the two ends of the microtubule, tubulin and neuron and we could estimate electromagnetic energy absorption and radiation behaviors. Helical structures have unique properties. The positive and negative resonance at different frequencies ensure that—for a particular resonance frequency—if a microtubule’s one end acts as a receiver, the other end would act as an antenna, the selectivity of signal frequency was independent of its length. However, radiation resistance was
(tubulin dimer, MHz),
(lattice period, kHz),
(water channel, GHz), and
, hence 0.001 Ω < R
< 1 Ω (MHz) or 0.04 Ω < R
< 720 Ω (kHz) as a function of length and for GHz, its 720 Ω (constant). Antenna efficiency was ≤0.01, which demands to bundle of microtubules like carbon nanotubes [30
] for long-range wireless communication systems. DC conductivity decreases under electromagnetic measurements were first reported by Sanabria et al. [31
]. However, Sanabria et al. [31
] measured data only within the domain of 1MHz.Sahu et al. [18
] confirmed that and going further from 1 MHz up to 20 GHz, showed that at certain frequencies there are sharp increments in the DC conductance. Microtubules are normally incredibly good insulators, i.e., resistance was greater than 400 GΩ. However, the resistance decreases to a few MΩ; at certain frequencies, input signal reflects, as if there was a negative resistance (Ghosh et al. [7
]). Looking beyond AC triggered plasmonic, for a polaronic case, the microtubule’s length is the wavelength of IR radiation i.e., λ
~25 μm P~(λn)2
, n = integer). Oscillatory conductance jump with temperature was identified as IR emission. The cavities for the kHz, MHz and GHz antenna–receiver actions are C-termini/MAP, secondary structures of tubulin and water channel respectively, it was not a classical dipolar antenna [32
] origin of resonance is the presence of multiple conduction pathways along the microtubule [8
]. Multiple resonance peaks at a wide range of frequencies are required to match impedances for the high-resolution communication in a complex network of antennas. In microtubule, kHz and GHz band-based communications offer robust impedance match due to wide bandwidth (Q ~ 2), which nullifies the antenna’s directivity. The closely spaced yet discrete MHz band ensures secured phase-locked communication (narrowband Q ~ 300). In MHz domain, microtubule can create a phased array of the current source, by changing its length (period controls λp
) and received frequency. Its ~300 MΩ contact resistance suggests that antenna–receiver protocol offers the most feasible and reliable communication mode.
3.2. Triplet of Triplet Fractal Ionic Resonance Band of a Single Neuron
As above, we mapped the frequency response of a single microtubule. One basic problem of developing a similar frequency map of a neuron is to find a trick to fine-tune the sub-threshold neural firing. We carried out an extensive search to find a set of frequencies using coaxial probe and patch-clamp simultaneously as shown in Figure 1
d,e targeting the axon initial segment (AIS) so that while operating at 5–20 mV below the threshold of −55 mV, i.e., at around −65 mV to −60 mV, we control the transmission along the nerve membrane. We artificially send a wireless AC signal at resonance frequencies of microtubule (220 MHz) using an antenna locating it very near to the AIS and monitor using our coaxial atom probe what neuron does after absorbing the signal. Two coaxial probes show that a signal back propagates from AIS to the soma, just opposite to the commonly believed direction of a nerve impulse. It was a decaying signal. This back-propagated signal builds up the potential of the soma. At certain frequencies (30 MHz + 220 MHz + 7 GHz), depending on the topology of a neuron, the soma assists AIS, which eventually sends back a neural spike through axon, else, if the buildup potential was more than −60 mV at Soma, a full-scale firing of nerve impulse is triggered by AIS. Vertical gates make sure that neuron does not build-up to the axon potential, protein and its complexes do not resonate robustly.
We cultured a pair of rat hippocampal neurons on a pre-grown electrode array (see Experimental sections, Figure 3
a). The growth was monitored so that the neural branches did not touch any electrode, using atom probes and DC fields one can regulate branching. Prior to any resonance measurement [14
], we placed a pair of patch-clamp probes, rupturing the soma membrane in one/two neighboring neurons to measure the potential difference between them. We also measured the potential of a nerve impulse concerning the solution. On the chip, the AC electromagnetic signals of wide ranges of frequencies were applied via a pair of electrodes (PQ and RS Figure 3
a) along the axon horizontally, as if dendritic branches are the sources of a signal and axonal branches are the drains. Perpendicular to it using MN electrode (Figure 3
a) gating signal was applied to regulate the nerve impulse. PQ and RS electrodes change frequencies synchronously. Keeping the perpendicularly applied AC signal of MN fixed at a particular frequency we changed the frequency of the AC signal applied along the axon length via PQ and RS. We then changed the transverse AC signal frequency via MN and repeated the frequency scan via PQ and RS. This is how a 2D input frequency pattern is generated not just in a neuron, but in all the materials studied here. The basic electronic setup used to measure and filter the resonance frequency is described in detail recently. In addition to that a gating frequency was applied here, so, we get an interference pattern as an output of a nanowire.
On this 3D pattern, at particular pairs of horizontal and vertical AC frequencies, the neuron generates a potential for nerve impulse and releases ions (<1% of threshold firing current, ~50 nA; i.e., ~100 pA), even at the sub-threshold biases of 20–30 mV. This potential makes the vertical axis; hence, we get a 3D resonance frequency map for the neuron. Figure 3
a shows a 3D plot for the normalized firing potential (vertical axis) as a function of two perpendicular AC frequencies applied across the neuron. The map is unique because, the horizontal plane mapping the frequencies is the electromagnetic resonance and the vertical axis is intrinsic resonance causing the nerve impulse. In the resonance frequency pattern, three bright circles represent the situation when a neuron positively gated by MN electrodes while the low-intensity part shows that MN is arresting the nerve spikes. We could notice that three prime resonance frequency domains host three further resonance frequency domains inside making the triplet of triplet frequency band. Doublet and triplet of resonance frequencies is a common observation atomic orbital resonance of molecules, we find the occurrence of a similar kind of resonance behavior here.
The AC signal applied parallel to the axon triggers AIS only at three distinct frequency ranges, where a short pulse (pulse width 1 µs, total duration 1ms) from the patch-clamp at a sub-threshold bias (~20–30 mV) activates the firing. An additional vertical AC signal resolves each of those three frequency domains into three additional sets; we get nine bands. Inserting two probes into the axon (Figure 1
e) when we measured resonance bands across the AIS, we could see only three resonance bands in the linear plot. An ordered biologic structure exhibits a major longitudinal and a transverse vibration mode [33
] if the AC signal was applied in one direction, only one mode was probed. Resonating with both horizontal and transverse vibrations at different combinations of horizontal and vertical AC signals also reveals additional peaks inside the nine bands. Therefore, the relative angular orientations of the three smaller circles vary by 100–120° in each of the three larger circles, but they unravel an additional dynamic feature hidden in the nine bands. A 3D resonance map of a neuron unravels three distinct time domains or periodic oscillations that regulate the nerve impulse.
As electrical nerve impulse forms at AIS, we measure a collective resonance of the AIS connected axon core. We have already reported the resonance behavior of axons with and without membrane in a single neuron. Consistency of triplet of triplet band with and without membrane prompts us to get inside a single microtubule that constitutes the major part of an axon.
The resonance behavior of a single isolated microtubule is reported [14
] but not its 2D resonance pattern with gating. We dropped freshly reconstituted microtubule solution on the electrode grid (Figure 3
b; see Experimental section) and an AC frequency scan was carried out similar to the neuron study. We measure the intensity of the transmitted signal along microtubule length (vertical axis of Figure 3
b) as a function of two perpendicularly applied AC signals across the microtubule. Similar to the neuron, the microtubule exhibits a triplet-triplet resonance band, but it was electromagnetic, not ionic. Additional transverse field along with the horizontal AC pumping (using two perpendicular electrodes) changes the angular positions of the circles, but their relative areas remain constant. As a result, if we superimpose neuron’s and microtubule’s triplet-triplet bands we find shifts, but the common frequency/time regions never disappear. This suggests that the periodic oscillations of isolated microtubule and AIS are coupled.
An essential component of a single microtubule was a tubulin protein dimer. Tubulin protein solution was dropped in the gap of a four-probe electrode array (Figure 3
c), then we applied a DC bias to orderly arrange the 15–20 molecules (Figure 3
c). For 8–100 tubulins, trapped in the electrode array, the resonance band remained independent of the number of molecules or the electrode geometry. Similar to the microtubule and the neuron cell, we observed here triplet of triplet resonance bands (Figure 3
c right). Normally, it was believed that electromagnetic resonance depends on the carriers, dispersion relation in a classic textbook would show how at different frequency regions, different carriers resonate. However, the classic dispersion relation presented in the textbooks, do not consider self-similar symmetry structures at all scales.
Inside the axon, initial segment microtubules form bundles and they are separated by 50 nm, they are densely packed [35
]. Microtubules are continuous and unidirectional along the axon initial segment (AIS) [36
]. Since thousands of microtubules are aligned in a particular direction, the effective dipole moment of the bundle was high, dendrites have a typical composition of polarities [37
]. Spatial self-organization of microtubules happens by polarity sorting [38
], by which, a perfect polar system was generated [39
]. In the central region of AIS, the microtubules form a nanoporous ordered crystalline structure, however, this ordered cylindrical region was covered with multi-layered ordered architectures up to the neuron membrane. The ankyrin beta spectrin square lattice was located just beneath the membrane. Therefore, the ordered signal transmission pathways link microtubule to neuron membranes. The connection between secondary structures of tubulin protein and the microtubule structure was also very well studied. The symmetry of tubulin’s secondary structure’s arrangement is reflected in its beta sheet’s spiral arrangement and the symmetry of microtubule’s arrangement of proteins in the hollow cylindrical structure is made of a spiral arrangement of tubulin dimers. Similarly, microtubules arranged in a helical shape in the axon initial segment, AIS, while beta–spectrin–actin square cells arrange spirally around the axon just below the membrane (3 nm below). Therefore, spiral symmetry is intact over 106
spatial scale and change in the pitch, width and length or geometry, makes sure symmetries break at all scales in a self-similar manner.
The axon core, microtubule and tubulin have self-similar bands, with a common frequency region, a similar structural symmetry governs the resonance in all the three systems. Helical distribution of neural branches, rings of proteins in the axonal core, spirals of proteins in the microtubule, α helices in the proteins, are the common structures, and the resonant energy transmission in generic spiral symmetry follows a quantized behavior. Sahu et al. [26
] have patented this feature of microtubule as a new class of fourth circuit element [26
]. Hence, a spiral symmetry possibly ensures coupling of all the periodic oscillations.
For all the three systems, neuron, microtubule and tubulin, each of the nine circles in the triplet–triplet band has 6–8 small circles inside (Figure 3
a–c). Since proteins are basic structures, they are pumped with the same resonating electromagnetic signal and simultaneously imaged (Figure 4
The resonant oscillations images of a tubulin dimer show only two high potential regions, not eight (online Movies in Ref [18
]), so, dimers are not responsible for 6–8 small circles. Then as we scan the isolated tubulin monomer at various resonance frequencies, we visualize live that four major and four minor distinct potential regions inside the monomer exchange energy (Figure 4
]). Total eight for a dimer. Protein dimer makes a doublet, but the monomer makes an octave. The one to one correspondence with the dielectric resonance image suggests that the observed 6–8 peaks in one of the 9 circles of tubulin in Figure 3
are from α- helices localized by the β sheets. Thus, 106
orders of spatial journey from milli to the nanoscale execute milliseconds to sub-nanoseconds periodic oscillations. En route, the GHz periodic oscillation that fires a neuron originates at the single protein structure.
The triplet–triplet resonant band was not exclusive to microtubules and tubulins. We have selected mostly found four components in the axon core and around AIS, and similarly measured their temporal resonance map [41
]. We found that actin microfilament’s resonance bands are complementary to that of the microtubule, they exchange energy covering a wide frequency domain. The resonance bands for all four proteins β-spectrin, ankyrin, actin and tubulin—also their complexes are confined between the two frequency limits (Figure 4
c), they share the time zone of threshold energy bursts. Overlapping time zone in the resonance frequency plot is common energy exchange regions for proteins. Thus, a resonance chain forms that connect wide ranges of proteins forming the layers beneath neuron membrane. The β-spectrin structure has ion-transfer channels and ankyrin a known mechanosensor [43
] have a cascade of α-helix oscillators dominating their resonance band. Hence, they exhibit a topological hysteresis in the 2D resonance plot. Moreover, β-spectrin and ankyrin show signatures of their lone cavities in the resonance band as doublets. A doublet in the 2D resonance pattern means the two periodic oscillations governing its resonance are coupled as part of one periodic oscillation. We understand that there are plenty of other proteins participate in generating the nerve spike. The current map is a fraction of the varieties of proteins available out there. However, the NMR-like doublets and triplets in various compositions suggest that the resonance chain would exhibit much richer topology once more proteins are added to it.
A conventional 1D resonance plot is a single line on the 2D resonance frequency map (Figure 5
), represented as triplet of triplet circles (Figure 5
). The triplet of triplet is not an absolute pattern—one may see pentate, or even doublets—frequency fractal or resonance chain’s topology is not as simple as reported earlier [44
]. The frequency wheel is created by the common time zones shared by the overlapping resonance frequencies of four proteins and their complexes studied here (Figure 5
). We sonified this frequency wheel to feel how vibrating discrete time-periodic oscillations topologically integrate into a single neuron firing. In the sound file, the higher frequencies are the patterns of protein’s oscillations, while the slower frequencies represent protein complexes with larger structures. A complete rotation of the wheel are events that unfold from faster to the slower time scales to eventually trigger a single nerve spike. Until now, the rapid firing of a neuron was sonified as a stream of “ticks”, here we deconstruct one “tick” representing a nerve impulse with 72 frequencies bursting signals in an intricate pattern.