Supporting online materials
Live visualizations of single isolated tubulin protein self-assembly via tunneling current: effect of electromagnetic pumping during spontaneous growth of microtubule
Satyajit Sahu1, Subrata Ghosh1, Daisuke Fujita1, Anirban Bandyopadhyay1,2*
1National Institute for Materials Science (NIMS), Nano Characterization Unit, Advanced Key Technologies Division, 1- 2-1 Sengen, Tsukuba, Japan; 2Massachusetts Institute of Technology (MIT), Harvard-MIT Center for Health Science and Technology, Institute of Medical Science and Engineering, 77 Massachusetts Ave, Boston, USA Figure S1
Figure S1: A. Schematic of heat bath and pink highlighted region is the neutral electric field domain, this is also shown in Figure 2a and Figure 2b (first). LET electrodes external connection (second). LET electrode connection inside (third). LET electrodes are defocused and the cell like environment is zoomed (fourth). B. Another schematic of electrode connections shown in Figure 2a. Figure 2b and in the above panel A. Here we have demonstrated how we observed the output in the two measuring oscilloscopes and function generator. Optimization of the geometry of nano-gaps is important since it attracts a large amount of ions, thus, as soon as an electric field is triggered, ions in the protein solution are automatically collected and they form large clusters in the gaps, as a result,
1 the surface becomes clean. This is one of the most essential criteria for the successful accomplishment of this study. Therefore, during cell geometry optimization, this factor played a vital role. For a particular solution (ionic concentration, taxol percentage etc) we had to manually optimize the geometry so that the deposited microtubules fall on the Si substrate always in a specified "electric-field neutral" region (neutral region is highlighted with a circle), which becomes clean due to natural migration of ions.
Rejection Arguments: Rejection of DEP, rapid crystallization, ion-induced growth, self-assembly in the Protein condensation: Exponential speed-up via synchrony Other chemical/physical processes do take place during protein assembly formation. Collapse neither demands such physical constraints, inhibits chemical bond rupture/formation, nor does it interplay with the weakly interacting forces. Collapse only speeds up all the chemical/physical processes through a massively parallel information exchange. Speeding up a chemical reaction, using microwave is a known synthetic tool in chemistry, however, in collapse, the speeding up refers to a different physical phenomenon. Speeding up is due to simultaneous phase-coherent communication among all participating oscillators, which ensures nearly zero energy loss during exchange; note that any loss in energy during exchange would modify the phase and/or frequency. The advantage of interaction with zero energy loss is that all participating oscillators would exchange exactly the amount of energy required to reach synchrony or single phase, single frequency condition. This simple yet powerful technique drastically reduces the number of steps required to lock the phase and the amplitude in a system of large number of coupled oscillators. Therefore, phase coherent communication ensures a single step to synchrony, depending on the complex set of reactions to be performed for growing the collapsed structure, the speed up factor would vary. In general, unlike the present case, atomic collapse is a very fast process, so a giant star to black hole conversion takes roughly a milli-second, BE condensate forms less than a nano-second to the femto-second time domain. However, for X it is a collapse of giant sized proteins or bio-molecules, even if phase- coherent communication speeds up the collapsing factors to a single step, the condensate can never form within a few nano-seconds or pico-seconds. Simulation shows that it would require around 1 microsecond to 1 millisecond, the delay is due to the searching & bonding of local symmetric structures of a protein at the definite docking sites on a large bio-molecule. We carried out extensive theoretical simulations observing how coupling evolves between two TDs at a gap of one-femtosecond interval. Without intelligent guess found experimentally, it was just impossible to find the right docking sites. The ac induced synchrony increases the probability of finding the right docking sites, -the most essential factors for the bonding. Moreover, neither DEP, rapid crystallization nor any of the process described below can stop TDs assembling into MT beyond ~25μm, only the phase coherent communication can because beyond the coherence length the mechanism described above will not be applicable. 1. Rejection of ion-induced growth: A constant polarity of electrodes for 9ms is essential for fast Mg2+-induced growth of MT3, which is impossible for a MHz signal. The characteristic time
Ch ~ LD D 9ms , where electrode spacing L=600 μm, Debye screening length λD ~ 8nm and diffusion constant for small ions (e.g. Mg2+) D ~ 500 μm2/s. 2. Rejection of DEP: TDs should be electrically constrained for coherent condensation; so we adjust the 4 3 field gradient at ~100Vrms/m, ~10-10 times lower than standard DEP operations . It keeps the oscillating field homogeneous, -just enough to neutralize the Brownian motion of tubulins (UDEP~kBT, T=300K); energetically, resonant dipolar oscillations take over DEP. Dielectrophoresis3 (DEP) or electric field gradient aligns MTs and dc/ac field speeds up growth by ~3%/minute. For our heat bath, energy for electro-
2 2 orientation is zero and DEP trapping energy UDEP isU r l Re f ()E , r is the radius, l is DEP 6 m 0 cm length (rod shape), εm is the real permittivity of the medium and particle, Re[fcm(ω)] is real part of Clausius- Mossotti factor. Here r×l for tubulin dimer is 4×8nm2, water molecule is 0.14×0.3nm2, C-termini is 2 0.11×1.3nm . Therefore, we get the ratio of DEP forces for three MT constituents is U DEP(H2O): UDEP(tubulin): UDEP(C-termini)::1:761:34, which restricts them to assemble into three concentric layers, each with a distinct crystal symmetry. Therefore, existence of MT rules out DEP domination.
2 3. Rejection of microwave induced self-assembly: Szent-Györgyi discussed two different mechanisms for energy transfer, an individual resonant transfer and a collective transfer, wherein the energy is delocalized, an aggregate of molecules receives a quantum of energy, meaning that it behaves more like a wave than a particle4. Our direct detection of coherent signals from heat bath during MT growth supports the Szent-Györgyi formulation. The proposal "aggregate behave like a wave" rejects the possibility of conventional self-assembly alone during MT condensation. 4. Rejection of microwave induced rapid crystallization: If strongly coupled phase coherent signal processing is not there, microwave induced rapid crystallization speeds up the reaction process of the order of 10, not by 200000 times as observed here. Majority of microwave-induced chemical reactions generate enormous heat. Maintaining a low temperature is hardly a pre-requisite; therein a massive IR radiation ensures non-coherence of the signals controlling the reaction kinetics. Such a non-coherent system cannot program coherence length of the architecture. Unless massively parallel phase coherence is ensured, chemical reaction of TDs cannot run 200,000 times faster (~25μm/100ms) than the known/established rate of reactions (10-60μm/min, 40-65 TD/min). 5. Why conventional self-assembly model is not accurate: First, in self-assembly, rate of collision determines its speed, therefore it is very slow, while ac triggered collapse is 200000 times faster, no existing self-assembly models can explain this speed. Condensation chemical reaction has another beautiful property, several parts of the structure reacts and form simultaneously. Second, self-assembly terminology is used when assembly is formed by itself, not triggered externally as we do. Self-assembly is weak- interaction based assembly and the physics of self-assembly is significantly different from the physics of synchrony induced collapse. Third, taking cylindrical shape without using GTP unravels that synchrony delivers the shape and then chemical bonding takes place, which is the origin of our rapid speed.
6. Four-level signaling: Numerical analysis of detuning parameters for multi-channel synchronization (Figure S2). The mechanism of protein-protein interaction: Phase coherent signal detection described here is a transient process;, the radiation coming out of self-assembling tubulin dimers (TD)s sustains only for the duration of condensation time. In a living cell, even for microtubule (MT)s, there are several distinct collapse processes, all these transient radiations add up to an apparent continuous emission. However, in our controlled study, we have only one heat bath, radiation comes out only for once, moreover, it is a ultra-low signal, synchronizing the characterization units with the collapse event occurring at the molecular scale is not possible. Therefore, we used an alternative trick, using nano-sensors we wired the region sending and reading out signals continuously. Multiple sensors from independent electronic circuitries send signals continuously during self-assembly, then all quanta propagating across proteins would acquire the same frequency and the same phase. Moreover, since we have wired the region with probe signals, continuously measured signals from heat bath are perturbed phase coherently, only if there is null incoherence in the heat bath. In other words, a phase coherent perturbation cannot survive if non-coherent signaling exists in water. Following this principle, nano-probes capture ultra-low emissions from an atomic scale reaction process.
Since oscillating TDs exchange phase coherent signals similar to a solid-state structure, we consider TD- assembly in solution as unit super-molecule and that enables us to implement non-inversion lasing theory to de-convolute the frequency (ω)-microtubule length (L) response in Figure 2e. De-convolution extracts the
3 complex resonant band structure of “super-molecule” state of TDs in water, which transforms into distinct resonant levels in its Protein-collapse state, MT. We consider a four-level lasing theory, since it naturally generates phase-coherent signal; |0>, |1>, |2>, |3>, the meta-stable state ωp lies in between |1> and |2>. The stimulated emission cross-section normalized to continuum cross-section is 2 q2 2 (q q )2 (2E)2 e 2 3 2 3 3 where . Normalized cross-section 2 2 ( )2 2 2 c 2 2 3 2 3 2 (2 3 ) (2E) 2 e / c measures effective positive feedback; thus, proportional to L(ω). Here, e / c kL() (L ), -3 k~10 ; E 21 , where 21 and 31 are the detuning frequencies for |2>, |3> are a life-time
2 ,3 broadened states located around ωp (21 depicts transition |2>→|1>) (Figure S2 a). 5 6 1/ 2 1/ 2 Rabi frequency 13 ~10 Hz, 12 ~10 Hz, Fano parameters, q2 12 /(2WC ) , q3 13 /(3WC ) ,
2 21 (2 / 2) , 3 31 (3 / 2) , where, WC is transition rate to continuum ~10, q2 ~5, 2 ~1,
70< 3 <1000, 21 is the electromagnetic pumping in water, 42kHz< 31 <15MHz. WC and q2 makes significant changes to when their values reach ~10±12 and ~10±8 orders respectively. However, we operated at much lower values. Figure S2 b shows how two transitions |2>→|1> and |3>→|1> mutually contribute generating the phase coherent signal. Most interestingly, the detuning of 31 reaches singularity at ωp, where the critical X-condensate structure is generated. By rigorous numerical analysis, we s determine the limiting values of 31 , which exactly fit the p s of the de-convoluted eight resonant energy levels as resolved in Fig. S2 c. The resemblance proves that non-inversion lasing action is truly responsible for generating the phase-coherence signal in the water, when X-condensate forms. Using the Lorentzian distribution function, when we simulate the L-ω plot, we get eight de-convoluted energy levels ( s p ) as (we keep |0>0.042MHz aside), |1>0.29MHz, ωp~3.77MHz |2>1.18MHz, |3>4MHz, |4>7.5MHz, | 5>13.3MHz, |6>20MHz, |7>35MHz) with A~5.6×10-6, 1.17×10-5, 2×10-5, 2×10-5, 1.8×10-5, 1.37×10-5, 9.84×10-5, 7.74×10-5; B→FWHM 42kHz, 83kHz, 260kHz, 900kHz, 1.6MHz, 3.5MHz, 6MHz, 12.5MHz s ( p ) respectively, where the Lorentzian function is given by N A1 1 2 . Figure S2d shows B broadening of these levels in a TD-assembly; this is the frequency dispersion among different vibrational modes (red).
Figure S3: Experimental set up description
4 Figure 1. Radio frequency-induced assembly of microtubules. a, Ultrafast assembly of tubulin dimers into microtubules in a heat bath is initiated by triggering an a.c. signal through a function generator (FG). After τ~100 ms the 200 nm PS and MR gates close. Assembly and precipitation are completed when the input (IN) and output (OUT) waves (U at the oscilloscope, OS) superpose into wave V. The L-L, E-E, and T-T electrode-pairs detect a coherent signal in the electrically neutral circular region Z. b, Circuits L, E and T are disconnected from the circuits that measure U and V. The two-electrode leads of the L (E2), E (E3) and T (E4), circuit connections with E1 are E1–E2, E1–E3, and E1–E4 (top). Phase and synchronization detection circuits (PDC, SDC) are connected to the L, E, and T circuits such that a non-zero output is obtained only when perfect synchrony is achieved. Thus, simultaneously instantaneous bursts are counted at the SDC
(bottom). c, Three coherent signals (E1–E2, red; E1–E3, blue; E1–E4, green) are measured between 1 pW and 10 fW (voltage 10 mV–1 mV, current 0.1 nA–10 pA), during assembly (n denotes tubulin dimer), five electrodes are chosen as example system. d, Nonlinear frequency pulling in the low-to-high (AB) and high-to-low (CD) frequency domains. The spontaneous pulling to 3.7 MHz bears the evidence of 'positive feedback'. The inset shows the threshold voltages needed to trigger microtubule assembly at 500 kHz, 5 MHz and 15 MHz. e, Average length of microtubules in the presence of GTP in radio-frequency induced assembly (red) and in in vitro diffusion- limited growth (blue). The coherence length Lф~25 μm. Growth rates are shown in the inset. f, Lф depends on synchrony (Colchicine, CH, and GTP induce negative and positive synchrony, respectively) and not on pump voltage or concentration of tubulin dimer (TD).
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