Electric field around microtubules

Abstract

Living cells are organized by the cytoskeleton with a fundamental role of microtubules. The mechanisms of organization are largely unknown. We analyze the vibrations in the microtubules which are polar and are accompanied by polarization waves. Oscillating electric field generated around microtubules can be as high as 10⁵ Vm⁻¹ and may have an important role in information system and mass transport in living cells. Energy from hydrolysis of guanosine triphosphate (GTP) stored in microtubules can excite the vibrations above thermodynamic equilibrium level.

Introduction

Living cells are structurally and dynamically organized by protein polymer network which is called cytoskeleton. The cytoskeleton is a highly dynamic structure which reorganizes continually as the cell changes its shape, divides, and responds to its environment. The essential data and description of the cytoskeleton, its components, and function are given in the book by Alberts et al. [1]. The cytoskeleton is composed of intermediate filaments, of actin filaments (which are also called microfilaments), and of microtubules. The filaments and the microtubules are connected to a large variety of accessory proteins and form a three dimensional network in the cell. The cytoskeleton is connected to transmembrane proteins. The cytoskeleton enables transport of molecules, structures, and organelles (by means of motor proteins), receives signals from cellular environment through the membrane proteins, and has an important role in the mitotic spindle.

The microtubules are the main organizers of the cytoskeleton. They are formed by cylindrical structures (hollow tubes with the outer and the inner diameters of about 25 nm and 17 nm, respectively) composed of 13 (or 14) protofilaments which are one dimensional chains of heterodimer tubulin molecules. The structure of the microtubules was disclosed by Amos and Klug [2]—Fig. 1a. A tubulin molecule is formed by two globular proteins—α- and β-tubulins; each of them has the relative molecular mass of about 55,000 (`molecular weight' in daltons) but the masses are not equal. Conformation of the heterodimer molecule can be changed from the α state (non tilted) to the β state (tilted by 29° from the microtubule axis)—Fig. 1b. The heterodimer molecule is an electric dipole 3, 4, 5(18 Ca²⁺ ions are bound in the β-monomer). Therefore, the microtubules are polar structures with the plus end (fast growing) and the minus end (slow growing) embedded in the centrosome—a centre of the cytoskeleton. Polarity of the microtubules are closely connected with their function 6, 7. The function of the microtubules can be regulated by phosphorylation and dephosphorylation of microtubule-associated tau protein [8].

The dynamics of the microtubules is one of the most prominent features. The microtubules are capable of rapid polymerization and depolymerization [9]which enables exchange of the subunits between soluble and polymer pools. The microtubules grow toward the cell periphery and then shrink back toward the centrosome. They may shrink partially and grow again or they may disappear to be replaced by new microtubules. This process is called the dynamic instability. The treadmilling (i.e. addition of the tubulin subunits at the plus end and removal of the tubulin subunits at the minus end at an identical rate) appears if both the ends of a microtubule are exposed [1]. Newly polymerized subunits (heterodimer molecules) contain energy rich nucleotide guanosine triphosphate (GTP). After polymerization the guanosine triphospate molecules bound to the β-tubulins are hydrolyzed to the guanosine diphosphate (GDP). The significance of the GTP in microtubule dynamics is analysed in Refs. 10, 11, 12. The growth of a microtubule can continue if an energy rich cap at its plus end is maintained, i.e. if the GTP's in the cap subunits are not hydrolyzed to the GDP's. The microtubule dynamics may depend on kinetochores too [13].

The microtubules depolymerize and repolymerize continually in animal cells. The majority of the microtubules can incorporate new subunits within 20–30 min although complete exchange of the subunits in a cell can be achieved within 1 h [14]. The half-life of an individual microtubule is of about 10 min [1]. Depolymerization removes the subunits with the GDP and repolymerization adds the energy rich subunits with the GTP to a microtubule. The hydrolysis energy is not used for polymerization. The majority of the hydrolysis energy is stored in the microtubule [15]. The mechanism of depolymerization and repolymerization provides continual supply of energy into the microtubule structures in a cell and signifies that the total energy storage is renewed within one hour.

The mechanisms of the cytoskeleton activity are still not well understood. The cytoskeleton exerts forces and generates movements without any major chemical changes [1]. A physical mechanism is probably responsible for the cytoskeleton function. Vibrations in the microtubules can be one of possible mechanisms as follows from the analysis given in Ref. [16]. As the tubulin heterodimers are polar the vibrations generate an oscillating electric field. The vibrations can be excited by the energy released from the hydrolysis of the GTP. The excited vibrations may be far from thermodynamic equilibrium and need not be of random nature. We will analyze the properties of the electric field generated by the microtubules and its possible effects on ordering and on the mass transport in living cells.