Calcium–axonemal microtubuli interactions underlie mechanism(s) of primary cilia morphological changes

Journal of Biological Physics - Tập 44 - Trang 53-80 - 2017
Vlado A. Buljan1,2, Manuel B. Graeber1,2, R. M. Damian Holsinger3,4, Daniel Brown1, Brett D. Hambly5, Edward J. Delikatny6, Vladimira R. Vuletic7, Xavier N. Krebs1, Ilijan B. Tomas8, John J. Bohorquez-Florez1, Guo Jun Liu9, Richard B. Banati1,3,9
1Brain Tumor Research Laboratories, Brain and Mind Center, Sydney Medical School and Faculty of Health Sciences, University of Sydney, Sydney, Australia
2Discipline of Anatomy and Embryology, School of Medical Sciences, Sydney Medical School, Charles Perkins Centre and Bosch Institute, University of Sydney, Sydney, Australia
3 Laboratory of Molecular Neuroscience and Dementia, Brain and Mind Center, Sydney Medical School, University of Sydney, Sydney, Australia
4Discipline of Biomedical Science, School of Medical Sciences, Sydney Medical School, University of Sydney, Lidcombe, Australia
5Discipline of Pathology, School of Medical Sciences, Sydney Medical School, Bosch Institute, University of Sydney, Sydney, Australia
6Department of Radiology, University of Pennsylvania, Philadelphia, USA
7Clinical Department of Neurology, UHC Rijeka, Medical Faculty Rijeka, Rijeka, Croatia
8Department of Oncology and Radiotherapy, Medical Faculty, University ‘Josip Juraj Strossmayer’, Osijek, Croatia
9Australian Nuclear Sciences and Technology Organisation (ANSTO), The Bragg Institute and the Australian Synchrotron, Sydney, Australia

Tóm tắt

We have used cell culture of astrocytes aligned within microchannels to investigate calcium effects on primary cilia morphology. In the absence of calcium and in the presence of flow of media (10 μL.s−1) the majority (90%) of primary cilia showed reversible bending with an average curvature of 2.1 ± 0.9 × 10−4 nm−1. When 1.0 mM calcium was present, 90% of cilia underwent bending. Forty percent of these cilia demonstrated strong irreversible bending, resulting in a final average curvature of 3.9 ± 1 × 10−4 nm−1, while 50% of cilia underwent bending similar to that observed during calcium-free flow. The average length of cilia was shifted toward shorter values (3.67 ± 0.34 μm) when exposed to excess calcium (1.0 mM), compared to media devoid of calcium (3.96 ± 0.26 μm). The number of primary cilia that became curved after calcium application was reduced when the cell culture was pre-incubated with 15 μM of the microtubule stabilizer, taxol, for 60 min prior to calcium application. Calcium caused single microtubules to curve at a concentration ≈1.0 mM in vitro, but at higher concentration (≈1.5 mM) multiple microtubule curving occurred. Additionally, calcium causes microtubule-associated protein-2 conformational changes and its dislocation from the microtubule wall at the location of microtubule curvature. A very small amount of calcium, that is 1.45 × 1011 times lower than the maximal capacity of TRPPs calcium channels, may cause gross morphological changes (curving) of primary cilia, while global cytosol calcium levels are expected to remain unchanged. These findings reflect the non-linear manner in which primary cilia may respond to calcium signaling, which in turn may influence the course of development of ciliopathies and cancer.

Tài liệu tham khảo

Satir, P., Christensen, S.T.: Overview of structure and function of mammalian cilia. Annu. Rev. Physiol. 69, 377–400 (2007). https://doi.org/10.1146/annurev.physiol.69.040705.141236 Delling, M., DeCaen, P.G., Doerner, J.F., Febvay, S., Clapham, D.E.: Primary cilia are specialized calcium signalling organelles. Nature 504(7479), 311–314 (2013). https://doi.org/10.1038/nature12833 DeCaen, P.G., Delling, M., Vien, T.N., Clapham, D.E.: Direct recording and molecular identification of the calcium channel of primary cilia. Nature 504(7479), 315–318 (2013). https://doi.org/10.1038/nature12832 Nauli, S.M., Zhou, J.: Polycystins and mechanosensation in renal and nodal cilia. BioEssays 26(8), 844–856 (2004). https://doi.org/10.1002/bies.20069 Toftgard, R.: Two sides to cilia in cancer. Nat. Med. 15(9), 994–996 (2009). https://doi.org/10.1038/nm0909-994 Nauli, S.M., Jin, X., AbouAlaiwi, W.A., El-Jouni, W., Su, X., Zhou, J.: Non-motile primary cilia as fluid shear stress mechanosensors. Methods Enzymol. 525, 1–20 (2013). https://doi.org/10.1016/B978-0-12-397944-5.00001-8 Davenport, J.R., Yoder, B.K.: An incredible decade for the primary cilium: a look at a once-forgotten organelle. Am. J. Physiol. Renal Physiol. 289(6), F1159–F1169 (2005). https://doi.org/10.1152/ajprenal.00118.2005 Moorman, S.J., Ardon, Z., Shorr, A.Z.: The primary cilium as a gravitational force transducer and a regulator of transcriptional noise. Dev. Dynam. 237, 1955–1959 (2008). https://doi.org/10.1002/dvdy.21493 Seeley, E.S., Nachury, M.V.: The perennial organelle: assembly and disassembly of the primary cilium. J. Cell Sci. 123, 511–518 (2010). https://doi.org/10.1242/jcs.061093 Praetorius, H.A., Spring, K.R.: Removal of the MDCK cell primary cilium abolishes flow sensing. J. Membrane Biol. 191, 69–76 (2002) Salisbury, J.L.: Primary cilia: putting sensors together. Curr. Biol. 14, R765–R767 (2004). https://doi.org/10.1016/j.cub.2004.09.016 Wheatley, D.N.: Primary cilia in normal and pathological tissues. Pathobiology 63(4), 222–238 (1995) Abdul-Majeed, S., Moloney, B.C., Nauli, S.M.: Mechanisms regulating cilia growth and cilia function in endothelial cells. Cell. Mol. Life Sci. 69(1), 165–173 (2012). https://doi.org/10.1007/s00018-011-0744-0 Abdul-Majeed, S., Nauli, S.M.: Dopamine receptor type 5 in the primary cilia has dual chemo- and mechano-sensory roles. Hypertension 58(2), 325–331 (2011). https://doi.org/10.1161/hypertensionaha.111.172080 Abou Alaiwi, W.A., Lo, S.T., Nauli, S.M.: Primary cilia: highly sophisticated biological sensors. Sensors (Basel) 9(9), 7003–7020 (2009). https://doi.org/10.3390/s90907003 Nauli, S.M., Alenghat, F.J., Luo, Y., Williams, E., Vassilev, P., Li, X., Elia, A.E., Lu, W., Brown, E.M., Quinn, S.J., Ingber, D.E., Zhou, J.: Polycystins 1 and 2 mediate mechanosensation in the primary cilium of kidney cells. Nat. Genet. 33(2), 129–137 (2003). https://doi.org/10.1038/ng1076 Pazour, G.J., Witman, G.B.: The vertebrate primary cilium is a sensory organelle. Curr. Opin. Cell Biol. 15(1), 105–110 (2003) Scholey, J.M., Anderson, K.V.: Intraflagellar transport and cilium-based signaling. Cell 125(3), 439–442 (2006). https://doi.org/10.1016/j.cell.2006.04.013 Shah, J.V.: Cells in tight spaces: the role of cell shape in cell function. J. Cell Biol. 191(2), 233–236 (2010). https://doi.org/10.1083/jcb.201009048 Pitaval, A., Tseng, Q., Bornens, M., Thery, M.: Cell shape and contractility regulate ciliogenesis in cell cycle-arrested cells. J. Cell Biol. 191(2), 303–312 (2010). https://doi.org/10.1083/jcb.201004003 Goto, H., Inoko, A., Inagaki, M.: Cell cycle progression by the repression of primary cilia formation in proliferating cells. Cell. Mol. Life Sci. 70(20), 3893–3905 (2013). https://doi.org/10.1007/s00018-013-1302-8 Tucker, R.W., Pardee, A.B., Fujiwara, K.: Centriole ciliation is related to quiescence and DNA synthesis in 3T3 cells. Cell 17(3), 527–535 (1979) Plotnikova, O.V., Golemis, E.A., Pugacheva, E.N.: Cell cycle-dependent ciliogenesis and cancer. Cancer Res. 68(7), 2058–2061 (2008). https://doi.org/10.1158/0008-5472.CAN-07-5838 Fry, A.M., Leaper, M.J., Bayliss, R.: The primary cilium: guardian of organ development and homeostasis. Organ 10(1), 62–68 (2014). https://doi.org/10.4161/org.28910 Gerdes, J.M., Davis, E.E., Katsanis, N.: The vertebrate primary cilium in development, homeostasis, and disease. Cell 137(1), 32–45 (2009). https://doi.org/10.1016/j.cell.2009.03.023 Oishi, I., Kawakami, Y., Raya, A., Callol-Massot, C., Izpisua Belmonte, J.C.: Regulation of primary cilia formation and left-right patterning in zebrafish by a noncanonical Wnt signaling mediator, duboraya. Nat. Genet. 38(11), 1316–1322 (2006). https://doi.org/10.1038/ng1892 Moser, J.J., Fritzler, M.J., Rattner, J.B.: Ultrastructural characterization of primary cilia in pathologically characterized human glioblastoma multiforme (GBM) tumors. BMC Clin. Pathol. 14, 40 (2014). https://doi.org/10.1186/1472-6890-14-40 Hassounah, N.B., Nagle, R., Saboda, K., Roe, D.J., Dalkin, B.L., McDermott, K.M.: Primary cilia are lost in preinvasive and invasive prostate cancer. PLoS ONE 8(7), e68521 (2013). https://doi.org/10.1371/journal.pone.0068521 Yuan, K., Frolova, N., Xie, Y., Wang, D., Cook, L., Kwon, Y.J., Steg, A.D., Serra, R., Frost, A.R.: Primary cilia are decreased in breast cancer: analysis of a collection of human breast cancer cell lines and tissues. J. Histochem. Cytochem. 58(10), 857–870 (2010). https://doi.org/10.1369/jhc.2010.955856 Christensen, S.T., Pedersen, L.B., Schneider, L., Satir, P.: Sensory cilia and integration of signal transduction in human health and disease. Traffic 8(2), 97–109 (2007). https://doi.org/10.1111/j.1600-0854.2006.00516.x Badano, J.L., Mitsuma, N., Beales, P.L., Katsanis, N.: The ciliopathies: an emerging class of human genetic disorders. Annu. Rev. Genomics Hum. Genet. 7, 125–148 (2006). https://doi.org/10.1146/annurev.genom.7.080505.115610 Prasad, R.M., Jin, X., Nauli, S.M.: Sensing a sensor: identifying the mechanosensory function of primary cilia. Biosensors (Basel) 4(1), 47–62 (2014). https://doi.org/10.3390/bios4010047 Jin, X., Mohieldin, A.M., Muntean, B.S., Green, J.A., Shah, J.V., Mykytyn, K., Nauli, S.M.: Cilioplasm is a cellular compartment for calcium signaling in response to mechanical and chemical stimuli. Cell. Mol. Life Sci. 71(11), 2165–2178 (2014). https://doi.org/10.1007/s00018-013-1483-1 Ishihara, Y., Sugawara, Y., Kamioka, H., Kawanabe, N., Hayano, S., Balam, T.A., Naruse, K., Yamashiro, T.: Ex vivo real-time observation of Ca2+ signaling in living bone in response to shear stress applied on the bone surface. Bone 53(1), 204–215 (2013). https://doi.org/10.1016/j.bone.2012.12.002 Praetorius, H.A., Spring, K.R.: Bending the MDCK cell primary cilium increases intracellular calcium. J. Membr. Biol. 184, 71–79 (2001) Grantham, J.J.: Clinical practice. Autosomal dominant polycystic kidney disease. N. Engl. J. Med. 359(14), 1477–1485 (2008). https://doi.org/10.1056/NEJMcp0804458 Torres, V.E., Harris, P.C., Pirson, Y.: Autosomal dominant polycystic kidney disease. Lancet 369, 1287–1300 (2007). https://doi.org/10.1016/S0140-6736(07)60601-1 Bichet, D., Peters, D., Patel, A.J., Delmas, P., Honore, E.: Cardiovascular polycystins: insights from autosomal dominant polycystic kidney disease and transgenic animal models. Trends Cardiovasc. Med. 16(8), 292–298 (2006). https://doi.org/10.1016/j.tcm.2006.07.002 Patel, A., Honoré, E.: Polycystins and renovascular mechanosensory transduction. Nat. Rev. Nephrol. 6, 530–538 (2010). https://doi.org/10.1038/nrneph.2010.97 Montalbetti, N., Li, Q., Wu, Y., Chen, X.Z., Cantiello, H.F.: Polycystin-2 cation channel function in the human syncytiotrophoblast is regulated by microtubular structures. J. Physiol. 579(Pt 3), 717–728 (2007). https://doi.org/10.1113/jphysiol.2006.125583 Scemes, E., Suadicani, S.O., Spray, D.C.: Intercellular communication in spinal cord astrocytes: fine tuning between gap junctions and P2 nucleotide receptors in calcium wave propagation. J. Neurosci. 20(4), 1435–1445 (2000) Cole, R., De Vellis, J.: Astrocyte and oligodendrocyte cultures. In: Fedoroff, S.S., Richardson, A. (eds.) Protocols for Neural Cell Cultures Pp. 117–130. Humana Press, New Jersey (1997) Wiesinger, H., Schuricht, B., Hamprecht, B.: Replacement of glucose by sorbitol in growth medium causes selection of astroglial cells from heterogeneous primary cultures derived from newborn mouse brain. Brain Res. 550(1), 69–76 (1991) Bennett, M.R., Buljan, V., Farnell, L., Gibson, W.G.: Purinergic junctional transmission and propagation of calcium waves in spinal cord astrocyte networks. Biophys. J. 91(9), 3560–3571 (2006). https://doi.org/10.1529/biophysj.106.082073 Bennett, M.R., Buljan, V., Farnell, L., Gibson, W.G.: Purinergic junctional transmission and propagation of calcium waves in cultured spinal cord microglial networks. Purinergic Signal. 4(1), 47–59 (2008). https://doi.org/10.1007/s11302-007-9076-9 Takano, H., Sul, J.Y., Mazzanti, M.L., Doyle, R.T., Haydon, P.G., Porter, M.D.: Micropatterned substrates: approach to probing intercellular communication pathways. Anal. Chem. 74(18), 4640–4646 (2002) Recknor, J.B., Recknor, J.C., Sakaguchi, D.S., Mallapragada, S.K.: Oriented astroglial cell growth on micropatterned polystyrene substrates. Biomaterials 25, 2753–2767 (2004). https://doi.org/10.1016/j.biomaterials.2003.11.045 Whitesides, G.M., Ostuni, E., Takayama, S., Jiang, X., Ingber, D.E.: Soft lithography in biology and biochemistry. Annu. Rev. Biomed. Eng. 3, 335–373 (2001). https://doi.org/10.1146/annurev.bioeng.3.1.335 Ott, C., Lippincott-Schwartz, J.: Visualization of live primary cilia dynamics using fluorescence microscopy. Curr. Protoc. Cell Biol. Unit 4(26), 1–22 (2012). https://doi.org/10.1002/0471143030.cb0426s57 Shelanski, M.L., Gaskin, F., Cantor, C.R.: Microtubule assembly in the absence of added nucleotides. Proc. Natl. Acad. Sci. U. S. A. 70(3), 765–768 (1973) Kim, H., Binder, L.I., Rosenbaum, J.L.: The periodic association of MAP-2 with brain microtubules in vitro. J. Cell Biol. 80(2), 266–276 (1979) Buljan, V., Ivanova, E.P., Cullen, K.M.: How calcium controls microtubule anisotropic phase formation in the presence of microtubule-associated proteins in vitro. Biochem. Biophys. Res. Commun. 381(2), 224–228 (2009). https://doi.org/10.1016/j.bbrc.2009.02.028 Langford, G.M.: Length and appearance of projections on neuronal microtubules in vitro after negative staining: evidence against a crosslinking function for MAPs. J. Ultrastruct. Res. 85(1), 1–10 (1983) Karr, T.L., Kristofferson, D., Purich, D.L.: Calcium ion induces endwise depolymerization of bovine brain microtubules. J. Biol. Chem. 255(24), 11853–11856 (1980) Schiff, P.B., Fant, J., Horwitz, S.B.: Promotion of microtubule assembly in vitro by taxol. Nature 277(5698), 665–667 (1979) Arnal, I., Wade, R.H.: How does taxol stabilize microtubules? Curr. Biol. 5(8), 900–908 (1995) Vater, W., Bohm, K.J., Unger, E.: Tubulin assembly in the presence of calcium ions and taxol: microtubule bundling and formation of macrotubule-ring complexes. Cell Motil. Cytoskeleton 36(1), 76–83 (1997). https://doi.org/10.1002/(SICI)1097-0169(1997)36:1<76::AID-CM7>3.0.CO;2-F Amos, L.A., Lowe, J.: How taxol stabilises microtubule structure. Chem. Biol. 6(3), R65–R69 (1999) Kern, W.F., Bland, J.R.: “Theorem of Pappus.” Solid Mensuration with Proofs, vol. 2. Wiley, New York (1948) Fong, K.C., Babitch, J.A., Anthony, F.A.: Calcium binding to tubulin. Biochim. Biophys. Acta 952, 13–19 (1988) Solomon, F.: Binding sites for calcium on tubulin. Biochemistry 16(3), 358–363 (1977) Serrano, L., Valencia, A., Caballero, R., Avila, J.: Localization of the high affinity calcium-binding site on tubulin molecule. J. Biol. Chem. 261(15), 7076–7081 (1986) Sui, H., Downing, K.H.: Molecular architecture of axonemal microtubule doublets revealed by cryo-electron tomography. Nature 442(7101), 475–478 (2006). https://doi.org/10.1038/nature04816 Hernandez, M.A., Serrano, L., Avila, J.: Microtubule-associated protein, MAP2, is a calcium-binding protein. Biochim. Biophys. Acta 965(2–3), 195–201 (1988) Vassilev, P.M., Guo, L., Chen, X.-Z., Segal, Y., Peng, J.-B., Basora, N., Babakhanlou, H., Cruger, G., Kanazirska, M., Ye, C.-P., Brown, E.M., Hediger, M.A., Zhou, J.: Polycystin-2 is a novel cation channel implicated in defective intracellular Ca2+ homeostasis in polycystic kidney disease. Biochem. Biophys. Res. Commun. 282, 341–350 (2001) Cantero, M.R., Cantiello, H.F.: Calcium transport and local pool regulate polycystin-2 (TRPP2) function in human syncytiotrophoblast. Biophys. J. 15, 365–375 (2013). https://doi.org/10.1016/j.bpj.2013.05.058 Lobert, S., Hennington, B.S., Correia, J.J.: Multiple sites for subtilisin cleavage of tubulin: effects of divalent cations. Cell Motil. Cytoskeleton 25(3), 282–297 (1993). https://doi.org/10.1002/cm.970250308 Ferralli, J., Doll, T., Matus, A.: Sequence analysis of MAP2 function in living cells. J. Cell Sci. 107(Pt 11), 3115–3125 (1994) Tuszynski, J.A., Brown, J.A., Crawford, E., Carpenter, E.J., Nip, M.L.A., Dixon, J.M., Sataric, M.V.: Molecular dynamics simulations of tubulin structure and calculations of electrostatic properties of microtubules. Math. Comput. Model. 41, 1055–1070 (2005). https://doi.org/10.1016/j.mcm.2005.05.002 Lefèvre, J., Chernov, K.G., Joshi, V., Delga, S., Toma, F., Pastrè, D., Curmi, P.A., Savarin, P.: The C-terminus of tubulin, a versatile partner for cationic molecules. J. Biol. Chem. 286(4), 3065–3078 (2011). https://doi.org/10.1074/jbc.M110.144089 Priel, A., Ramos, A.J., Tuszynski, J.A., Cantiello, H.F.: Effect of calcium on electrical energy transfer by microtubules. J. Biol. Phys. 34, 475–485 (2008). https://doi.org/10.1007/s10867-008-9106-z Siwy, Z.S., Powell, M.R., Petrov, A., Kalman, E., Trautmann, C., Eisenberg, R.S.: Calcium-induced voltage gating in single conical nanopores. Nano Lett. 6(8), 1729–1734 (2006). https://doi.org/10.1021/nl061114x Sataric, M.V., Sekulic, D., Živanov, M.: Solitonic ionic currents along microtubules. J. Comput. Theor. Nanosci. 7, 1–10 (2010). https://doi.org/10.1166/jctn.2010.1609 Li, H., DeRosier, D.J., Nicholson, W.V., Nogales, E., Downing, K.H.: Microtubule structure at 8Å resolution. Structure 10, 1317–1328 (2002) Tagliazucchi, M., Szleifer, I.: Transport mechanisms in nanopores and nanochannels: can we mimic nature? Mater. Today 18(3), 131–142 (2015). https://doi.org/10.1016/j.mattod.2014.10.020 Ma, L., Cockroft, S.L.: Biological nanopores for single-molecule biophysics. Chembiochem 11(1), 25–34 (2010). https://doi.org/10.1002/cbic.200900526 Melki, R., Carlier, M.F., Pantaloni, D., Timasheff, S.N.: Cold depolymerization of microtubules to double rings: geometric stabilization of assemblies. Biochemistry 28(23), 9143–9152 (1989) Berkowitz, S.A., Wolff, J.: Intrinsic calcium sensitivity of tubulin polymerization. The contributions of temperature, tubulin concentration, and associated proteins. J. Biol. Chem. 256(21), 11216–11223 (1981) Brouhard, G.J., Rice, L.M.: The contribution of αβ-tubulin curvature to microtubule dynamics. J. Cell Biol. 207(3), 323–334 (2014). https://doi.org/10.1083/jcb.201407095 Mitchison, T., Kirschner, M.: Dynamic instability of microtubule growth. Nature 312(5991), 237–242 (1984) Kirschner, M., Mitchison, T.: Beyond self-assembly: from microtubules to morphogenesis. Cell 45(3), 329–342 (1986) Tuszynski, J.A., Hameroff, S., Sataric, M.V., Trpisova, B., Nip, M.L.A.: Ferroelectric behavior in microtubule dipole lattices - implications for information-processing, signaling and assembly disassembly. J. Theor. Biol. 174, 371–380 (1995) Tuszynski, J.A., Brown, J.A., Hawrylak, P.: Dielectric polarization, electrical conduction, information processing and quantum computation in microtubules. Are they plausible? Phil. Trans. R. Soc. Lond. A 356, 1897–1926 (1998) Tuszynski, J.A., Portet, S., Dixon, J.M., Luxford, C., Cantiello, H.F.: Ionic wave propagation along actin filaments. Biophys. J. 86, 1890–1903 (2004). https://doi.org/10.1016/S0006-3495(04)74255-1 Sekulić, D.L., Satarić, B.M., Tuszynski, J.A., Satarić, M.V.: Nonlinear ionic pulses along microtubules. Eur. Phys. J. E. Soft Matter 34, 49 (2011). https://doi.org/10.1140/epje/i2011-11049-0 Vanag, V.K., Epstein, I.R.: Pattern formation mechanisms in reaction-diffusion systems. Int. J. Dev. Biol. 53, 673–681 (2009). https://doi.org/10.1387/ijdb.072484vv Minoura, I., Muto, E.: Dielectric measurement of individual microtubules using the electroorientation method. Biophys. J. 90(10), 3739–3748 (2006). https://doi.org/10.1529/biophysj.105.071324 Priel, A., Tuszynski, J.A., Cantiello, H.F.: The dendritic cytoskeleton as a computational device: an hypothesis. In: Tuszynski, J.A. (ed.) The Emerging Physics of Consciousness. pp. 293–325. Springer, (2006) Brown, J.A., Tuszynski, J.A.: The possible relationship between cell shape and electric fields. J. Theor. Biol. 200(2), 245–247 (1999). https://doi.org/10.1006/jtbi.1999.0984 Satarić, M.V., Ilić, D.I., Ralević, N., Tuszynski, J.A.: A nonlinear model of ionic wave propagation along microtubules. Eur. Biophys. J. 38, 637–647 (2009). https://doi.org/10.1007/s00249-009-0421-5 Sataric, M.V., Sataric, B.M.: Ionic pulses along cytoskeletal protophilaments. J. Physics: Conf. Ser. 329, 012009 (2011). https://doi.org/10.1088/1742-6596/329/1/012009 Dye, R.B., Fink, S.P., Williams, R.C.J.: Taxol-induced flexibility of microtubules and its reversal by MAP-2 and tau. J. Biol. Chem. 268(10), 6847–6850 (1993) Felgner, H., Frank, R., Biernat, J., Mandelkow, E.M., Mandelkow, E., Ludin, B., Matus, A., Schliwa, M.: Domains of neuronal microtubule-associated proteins and flexural rigidity of microtubules. J. Cell Biol. 138(5), 1067–1075 (1997) Kim, H., Jensen, C.G., Rebhun, L.I.: The binding of MAP-2 and tau on brain microtubules in vitro: implications for microtubule structure. Ann. N. Y. Acad. Sci. 466, 218–239 (1986)