Three-State Model for One-Dimensional Brownian Motion of Charged Nanoparticles Along Microtubules

Abstract

A variety of motor proteins, such as dynein, KIF1A and MCAK, are known to exhibit one-dimensional (1D) Brownian motion along microtubules. The electrostatic interaction between the proteins and microtubules appears to be crucial for 1D Brownian motion, although the underlying mechanism has not been fully clarified. We examined the interactions of positively-charged nanoparticles composed of polyacrylamide gels with microtubules. These hydrophilic nanoparticles bound to the microtubules and displayed 1D Brownian motion in a charge-dependent manner, which indicates that nonspecific electrostatic interaction is sufficient for 1D Brownian motion. While the diffusion coefficient decreased exponentially with an increasing particle charge (with the exponent being 0.10 kBTper charge), the duration of the interaction increased exponentially (with an exponent of 0.22 kBT per charge). These results can be consistently explained if one assumes that a particle repeats a cycle of ‘binding’ and ‘diffusion’ along a microtubule until it finally ‘dissociates’ from the microtubule. This entire process can be described by a three-state model analogous to the Michaelis-Menten scheme, in which two parameters - the equilibrium constant between ‘binding’ and ‘diffusion’, and the rate of ‘dissociation’ from the microtubule - are derived as a function of the particle charge density.Further, to understand the molecular basis for this ‘binding’ and ‘diffusion’ mechanism, we engineered microtubules with variable charges at the tubulin C-terminal tail (CTT) and measured 1D Brownian motion of the particles along these mutant microtubules. The measurements revealed an unexpected result: the negative charges in the CTT did not significantly affect the diffusion coefficient of the particles, but the equilibrium between ‘binding’ and ‘diffusion’ shifted more towards ‘diffusion’ with increasing charges of the CTT. These results indicate that the negatively-charged CTT provides a field that facilitates the ‘diffusion’ of charged particles.