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Microtubule Protofilament Number Is Modulated in a Stepwise Fashion by the Charge Density of an Enveloping Layer

Uri Raviv ^* , Toan Nguyen , Rouzbeh Ghafouri , Daniel J. Needleman ^* , Youli Li ^* , Herbert P. Miller , Leslie Wilson , Robijn F. Bruinsma  and Cyrus R. Safinya ^* 

^* Materials Department, Physics Department, and Molecular, Cellular, and Developmental Biology Department, Biomolecular Science and Engineering Program, University of California, Santa Barbara, California; and Department of Physics and Astronomy, University of California, Los Angeles, California

Correspondence: Address reprint requests to Uri Raviv at his present address, Physical Chemistry Department, The Institute of Chemistry, The Hebrew University of Jerusalem, Givat Ram, 91904, Israel. Tel.: 972-2-6585325; Fax: 972-2-5660425; E-mail: raviv{at}chem.ch.huji.ac.il; or to Cyrus R. Safinya, Materials Research Laboratory, UCSB, Santa Barbara, CA 93106. Tel.: 805-893-8635; Fax: 805-893-7221; E-mail: safinya{at}mrl.ucsb.edu.

Microtubules are able to adjust their protofilament (PF) number and, as a consequence, their dynamics and function, to the assembly conditions and presence of cofactors. However, the principle behind such variations is poorly understood. Using synchrotron x-ray scattering and transmission electron microscopy, we studied how charged membranes, which under certain conditions can envelop preassembled MTs, regulate the PF number of those MTs. We show that the mean PF number, N, is modulated primarily by the charge density of the membranes. N decreases in a stepwise fashion with increasing membrane charge density. N does not depend on the membrane-protein stoichiometry or the solution ionic strength. We studied the effect of taxol and found that N increases logarithmically with taxol/tubulin stoichiometry. We present a theoretical model, which by balancing the electrostatic and elastic interactions in the system accounts for the trends in our findings and reveals an effective MT bending stiffness of order 10–100 k_BT/nm, associated with the observed changes in PF number.