Estimates of lateral and longitudinal bond energies within the microtubule lattice

Abstract

We developed a stochastic model of microtubule (MT) assembly dynamics that estimates tubulin-tubulin bond energies, mechanical energy stored in the lattice dimers, and the size of the tubulin-GTP cap at MT tips. First, a simple assembly͞disassembly state model was used to screen possible combinations of lateral bond energy (⌬G Lat) and longitudinal bond energy (⌬GLong) plus the free energy of immobilizing a dimer in the MT lattice (⌬G S) for rates of MT growth and shortening measured experimentally. This analysis predicts ⌬G Lat in the range of ؊3.2 to ؊5.7 kBT and ⌬GLong plus ⌬GS in the range of ؊6.8 to ؊9.4 kBT. Based on these estimates, the energy of conformational stress for a single tubulin-GDP dimer in the lattice is 2.1-2.5 k BT. Second, we studied how tubulin-GTP cap size fluctuates with different hydrolysis rules and show that a mechanism of directly coupling subunit addition to hydrolysis fails to support MT growth, whereas a finite hydrolysis rate allows growth. By adding rules to mimic the mechanical constraints present at the MT tip, the model generates tubulin-GTP caps similar in size to experimental estimates. Finally, by combining assembly͞ disassembly and cap dynamics, we generate MT dynamic instability with rates and transition frequencies similar to those measured experimentally. Our model serves as a platform to examine GTPcap dynamics and allows predictions of how MT-associated proteins and other effectors alter the energetics of MT assembly.M icrotubule (MT) dynamic instability plays a critical role in chromosome movement and separation during mitosis. MTs grow, shorten, and transition between these states at rates governed by the presence of various MT effectors, such as divalent cations, MT-associated proteins (MAPs), and drugs such as Taxol (1).MTs are composed of heterodimer subunits of ␣-and ␤-tubulin. A guanine nucleotide (GTP or GDP) is positioned on the ␤ monomer opposite the interface between the two monomers, where it is hydrolyzable (if it is GTP) and exchangeable. The ␤ monomer end of the dimer faces the (ϩ) end of the MT, which is the end of more active dynamics and kinetochore attachment during cell division. The ␣ monomer faces the (Ϫ) end of the MT, which originates at the centrosome. MTs are thought to transition from a state of growth to a state of rapid shortening, termed a ''catastrophe'', when the tubulin-GTP ''cap'' is stochastically lost from the tip of the MT. The tubulin-GTP cap must exist because it has been demonstrated that tubulin-GTP subunits are added to the ends during assembly. A tubulin-GTP cap, however, has not been detected in experiments with porcine brain tubulin, and therefore must be small. Experiments suggest that the cap must be less than Ϸ200 dimers (2-4). Presumably, the transition from rapid shortening to growth, termed ''rescue,'' occurs when the tubulin-GTP cap is reestablished.Interactions at the surfaces of adjacent dimers occur through discrete lateral and longitudinal noncovalent bonds. Thermodynamic studies of MT assembly are unable to qua...

A driving and coupling “Pac-Man” mechanism for chromosome poleward translocation in anaphase A

“…For in vivo situation, the effective kinetochore diffusion coefficient includes the large chromosome effect and thus it is very small Ϸ400-800 nm 2 ͞s. Because the microtubule bending strain is usually low (Ϸ3 k B T) [this value is supported by experimental measurement (23) and theoretical calculations (21,22)], it alone could not drive the kinetochore to overcome local binding potential Ϸ12.5 k B T (5,14,19). Thus, according to Fig.…”

“…Upon microtubule depolymerization, the bending strain is released and provides a driving force for the kinetochore translocation (2,12,20). However, given the strong attachment of the kinetochore to microtubule of Ϸ12.5 k B T (5,14,19), as our calculations in this paper suggest, a bending strain of Ϸ3 k B T (2,3,(20)(21)(22)(23) is not sufficient. It has also been proposed that a ratchet-like biased one-dimensional diffusion model could account for the kinetochore translocation (17).…”

“…The bound GDP-tubulin subunit has a preferred angle with respect to its neighbor (0) ϭ 0.4 rad (24). The bending strain Ϸ3 k B T is thus stored in the subunits held in straight configuration (2,3,(20)(21)(22)(23), which is favored by lateral bonds Ϸ3 k B T between the neighboring subunits in the adjacent protofilaments (19,21,22). In this paper, the kinetochore is represented as the Dam1 ring-like structure from budding yeast (5-7), which has a radius of 16 nm and consists of 16 identical components (5)(6)(7), each carrying at least six positive charges q kt Ն 6 under physiological conditions (5,6).…”

Theoretical Analysis of Microtubule Dynamics at All Times

“…1. 15,21 The hydrolysis mechanism for the cytoskeleton filament is still under discussion, [21][22][23][24][25][26][27][28][29][30] and we assume here that all T-subunits on microtubules can be hydrolyzed with the same rate r as indicated in Fig.1. The hydrolyzed D-subunits can detach from the "plus" end of the microtubules with a rate W D (see Fig.…”

Modeling Three-Dimensional Spatial Regulation of Bacterial Cell Division (Dissertation)

“…Intracellular spatial features that can influence polymer assembly and function include the 3D position of subunits and polymer nucleation sites (Lutkenhaus, 2007), volume exclusion by polymer filaments (Haviv et al, 2006), molecular crowding (Popp et al, 2007;Wieczorek and Zielenkiewicz, 2008), intercompartmental interaction and subcellular localization of reacting molecules (Lutkenhaus, 2007), and diffusion-influenced reactions of molecules that are either small numbered or heterogeneously distributed (Shih et al, 2002;Lutkenhaus, 2007). Diffusion and small numbers of reacting molecules may also induce stochasticity (Rao et al, 2002;Bhalla, 2004;Wilkinson, 2009) in polymer assembly (VanBuren et al, 2002).…”