Abstract
Microtubules (MT) are composed of 13 protofilaments, each of which is a series of two-state tubulin dimers. In the MT wall, these dimers can be pictured as “lattice” sites similar to crystal lattices. Based on the pseudo-spin model, two different location states of the mobile electron in each dimer are proposed. Accordingly, the MT wall is described as an anisotropic two-dimensional (2D) pseudo-spin system considering a periodic triangular “lattice”. Because three different “spin-spin” interactions in each cell exist periodically in the whole MT wall, the system may be shown to be an array of three types of two-pseudo-spin-state dimers. For the above-mentioned condition, the processing of quantum information is presented by using the scheme developed by Lloyd.
Key words: MT, tubulin dimer, 2-D pseudo-spin, “lattice” site, two-state, information processing
References
- 1.Toffoli, T.: Bicontinuous extensions of invertible combinatorial functions. Math. Syst. Theory 14, 13–23 (1981) [DOI]
- 2.Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. Lond. A 400, 97–117 (1985)
- 3.Feynman, R.P.: Quantum mechanical computers. Opt. News 11, 11–20 (1985)
- 4.Monroe, C., Meekhof, D.M., King, B.E., Itano, W.M., Wineland, D.J.: Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995) [DOI] [PubMed]
- 5.Shahriar, M.S., Bowers, J.A., Demsky, B.: Cavity dark states for quantum computing. Opt. Commun. 195, 411–417 (2001) [DOI]
- 6.Beznosyuk, S.A.: Modern quantum theory and computer simulation in nanotechnologies: quantum topology approaches to kinematic and dynamic structures of self-assembling processes. Mater. Sci. Eng. C 19, 369–372 (2002) [DOI]
- 7.Medvedev, D.M., Dmitry, M., Goldfield, E.M.: An open MP/ MPI approach to the parallelization of iterative four-atom quantum mechanics. Comput. Phys. Commun. 166, 94–108 (2005) [DOI]
- 8.Lloyd, S.: A potentially realizable quantum computer. Science 261, 1569–1571 (1993) [DOI] [PubMed]
- 9.Davies, P.C.W.: Does quantum mechanics play a non-trivial role in life? Biosystems 78, 69–79 (2004) [DOI] [PubMed]
- 10.Patel, A.: Quantum algorithms and the genetic code. Pramana 56, 367–381 (2001)
- 11.Bashford, J.D., Tsohantjis, I., Jarvis, P.D.: A supersymmetric model for the evolution of the genetic code. Biochemistry 95, 987–992 (1998) [DOI] [PMC free article] [PubMed]
- 12.Silverman, G.J., Cary, S., Aguilar, S., Dwyer, D.: A B-cell superantigen induced persistent “hole” in the B-1 repertoire. J. Exp. Med. 192, 87–98 (2000) [DOI] [PMC free article] [PubMed]
- 13.Hameroff, S.R., Penrose, R.: Conscious events as orchestrated space-time selections. J. Conscious. Stud. 3, 36–53 (1996)
- 14.Woolf, N.J., Hameroff, S.R.: A quantum approach to visual consciousness. Trends Cogn. Sci. 5, 472–478 (2001) [DOI] [PubMed]
- 15.Nogales, E.S., Wolf, G., Downing, K.H.: Structure of the tubulin dimer by electron crystallography. Nature 391, 199–203 (1998) [DOI] [PubMed]
- 16.Nogales, E.S., Downing, K.H., Amos, L.A., Lowe, J.: Tubulin and FtsZ form a distinct family of GTPases. Nat. Struct. Biol. 5, 451–458 (1998) [DOI] [PubMed]
- 17.Nogales, E.S., Whittaker, M., Milligan, R.A., Downing, K.H.: High-resolution model of the microtubule. Cell 96, 79–88 (1999) [DOI] [PubMed]
- 18.Löwe, J., Li, H., Downing, K.H., Nogales, E.: Refined structure of ab-tubulin at 3.5 Å. J. Mol. Biol. 313, 1045–1057 (2001) [DOI] [PubMed]
- 19.Hud, N.V., Downing, K.H.: Cryoelectron microscopy of l phage DNA condensates in vitreous ice: the fine structure of DNA toroids. Proc. Natl. Acad. Sci. U.S.A. 98, 14925–14930 (2001) [DOI] [PMC free article] [PubMed]
- 20.Zhong, S., Dadarlat, V.M., Glaeser, R.M., Head-Gordon, T., Downing, K.H.: Modeling chemical bonding effects for protein electron crystallography: the transferable fragmental electrostatic potential (TFESP) method. Acta Cryst. A 58, 162–170 (2002) [DOI] [PubMed]
- 21.Amos, L.A., Klug, A.: Arrangement of subunits in flagellar microtubules. J. Cell Sci. 14, 523–549 (1974) [DOI] [PubMed]
- 22.Engelborghs, Y., Audenaert, A., Heremans, L., Heremans, K.: Secondary structure analysis of tubulin and microtubules with Raman spectroscopy. Biochim. Biophys. Acta 996, 110–115 (1989) [DOI] [PubMed]
- 23.Tuszynski, J.A., Hameroff, S.H., Sataric, M.V., Trpisova, B., Nip, M.L.A.: Ferroelectric behaviour in microtubule dipole lattices: implications for information processing, signalling and assembly/disassembly. J. Theor. Biol. 174, 371–380 (1995) [DOI]
- 24.Mavromatos, N.E., Nanopoulos, D.V.: On quantum mechanical aspects of microtubules. Int. J. Mod. Phys. B 12, 517–542 (1998) [DOI]
- 25.Mavromatos, N.E., Mershin, A., Nanopoulos, D.V.: QED-cavity model of microtubules implies dissipationless energy transfer and biological quantum teleportation. Int. J. Mod. Phys. B 16, 3623–3642 (2002) [DOI]
- 26.Satarć, M.V., Tuszyński, J.A., Žakula, R.B.: Kinklike excitations as an energy-transfer mechanism in microtubules. Phys. Rev. E 48, 589–597 (1993) [DOI] [PubMed]
- 27.Jibu, M., Hagan, S., Hameroff, S.R., Pribram, K.H., Yasue, K.: Quantum optical coherence in cytoskeletal microtubules: implications for brain function. Biosystems 32, 195–209 (1994) [DOI] [PubMed]
- 28.Chen, Y., Qiu, X.J.: Collective radiation of water in cyto skeletal microtubule. Acta Phys. Sin. 52, 1554–1560 (2003)
- 29.Sataric, M.V., Koruga D., Ivic, Z., Zakula, R.: The detachment of dimers in the tube of microtubulin as a result of a solitonic mechanism. J. Mol. Electron. 6, 63–69 (1990)
- 30.Collins, M.A., Blumen, A., Currie, J.F., Ross, J.: Dynamics of domain walls in ferrodistortive materials. I. Theory. Phys. Rev. B 19, 3630–3644 (1979) [DOI]
- 31.Chen, Y., Qiu, X.J., Dong, X.L.: A theory for cell microtubule wall in external field and pseudo–spin wave excitation. Physica, A (2006) (in press)
- 32.Haken, H.: Quantum Field Theory of Solids – An Introduction. North-Holland, New York (1976)
- 33.Hall, J.L., Ye, J., Diddams, S.A., Ma, L.-S., Cundiff, S. T., Jones D.J.: Ultrasensitive spectroscopy, the ultrastable lasers, the ultrafast lasers, and the seriously nonlinear fiber: a new alliance for physics and metrology. IEEE J. Quantum Electron. 37, 1482–1492 (2001) [DOI]
- 34.Pokorny, J., Jelnek, F., Trkal, V.: Electric field around microtubules. Bioelectroch. Bioener. 45, 239–245 (1998) [DOI]
- 35.Fröhlich, H.: Long-range coherence and energy storage in biological systems. Int. J. Quantum Chem. 2, 641–649 (1968)