Physics of microtubule:
It is the polyelectrolyte nature of microtubules that allows various microtubule binding proteins to move along the microtubules.
(1) Dielectric measurement of microtubules using the electroorientation method
Electrostatic interactions are thought to play an essential role in mediating the intermolecular interaction of microtubules with motor proteins. However, little is known about the electrostatic/dynamic properties of microtubules that underly this interaction. In order to measure the dielectric properties of microtubules, we developed an experimental system in which the electroorientation of microtubules could be observed under a dark-field microscope. Upon the application of an alternating electric field (0.5–1.9 x 105 V/m, 10 kHz – 3 MHz), the microtubules were oriented parallel to the field line in a few seconds because of the dipole moment induced along their long axes (Fig. A, Video). The process of this orientation was analyzed based on a dielectric ellipsoid model, and the conductivity and dielectric constant of each microtubule were calculated (Fig. B).
Orientation of microtubule upon application of an electric field. The arrow indicates the direction of the electric field.
Analysis revealed that microtubules were highly conductive (1.5 ± 0.1 x 102 mS/m), which was about 15 times more than that of the surrounding medium. Such a high conductivity is consistent with the counterion polarization model, where counterions bound to a highly negatively charged microtubule can move along the long axis, and that this mobility might be the origin of the high conductivity (Fig. C & D). Our experiment system provides a useful tool to quantitatively evaluate the polyelectrolyte nature of microtubules. It could pave the way for future studies aiming to understand the physicochemical mechanism underlying the motor-microtubule interaction during the weak binding state.
Dielectric Measurement of Individual Microtubules Using the Electroorientation Methodractions.
Itsushi Minoura and Etsuko Muto
Biophys J., 90:3739-48 (2006).
(2) One-dimensional Brownian motion of charged nanoparticles along microtubules: A model system for weak binding interactions
Like the counterions condensed on the microtubules, proteins with a sufficient number of positive charges may interact electrostatically with microtubules while retaining their freedom of motion along the microtubule long axis. If the one-dimensional Brownian motion is purely electrostatic in origin, it should be possible for any charged molecule or particle to bind to and move along a microtubule. We tested this hypothesis using nanoparticles composed of a polyacrylamide gel.
The results showed that, while the noncharged nanoparticles did not interact with the microtubules, positively-charged nanoparticles bound to microtubules and displayed undirected, one-dimensional Brownian motion in a charge-dependent manner.
The diffusion coefficient decreased exponentially with an increasing particle charge, whereas the duration of the interaction increased exponentially. These results can be explained semiquantitatively if we assume that a particle repeats a cycle of ‘binding’ to and ‘moving’ along a microtubule until finally ‘dissociating’ itself from the microtubule (Fig. A). The entire process can be described using a three-state model analogous to the Michaelis-Menten scheme, thus the values for the energies ΔGB-A and ΔGesc, can be calculated.
This model provides a useful framework for analyses of one-dimensional Brownian motion. In particular, for motor proteins, the present approach will expedite the elucidation of the mechanism underlying the weak binding interaction.
