Measuring and modeling forces generated by microtubules.

Tubulins are essential proteins, which are conserved across all eukaryotic species. They polymerize to form microtubules, cytoskeletal components of paramount importance for cellular mechanics. The microtubules combine an extraordinarily high flexural rigidity and a non-equilibrium behavior, manifested in their intermittent assembly and disassembly. These chemically fueled dynamics allow microtubules to generate significant pushing and pulling forces at their ends to reposition intracellular organelles, remodel membranes, bear compressive forces, and transport chromosomes during cell division. In this article, we review classical and recent studies, which have allowed the quantification of microtubule-generated forces. The measurements, to which we owe most of the quantitative information about microtubule forces, were carried out in biochemically reconstituted systems in vitro. We also discuss how mathematical and computational modeling has contributed to the interpretations of these results and shaped our understanding of the mechanisms of force production by tubulin polymerization and depolymerization.

Theory of tip structure-dependent microtubule catastrophes and damage-induced microtubule rescues.

Microtubules are essential cytoskeletal polymers that exhibit stochastic switches between tubulin assembly and disassembly. Here, we examine possible mechanisms for these switches, called catastrophes and rescues. We formulate a four-state Monte Carlo model, explicitly considering two biochemical and two conformational states of tubulin, based on a recently conceived view of microtubule assembly with flared ends. The model predicts that high activation energy barriers for lateral tubulin interactions can cause lagging of curled protofilaments, leading to a ragged appearance of the growing tip. Changes in the extent of tip raggedness explain some important but poorly understood features of microtubule catastrophe: weak dependence on tubulin concentration and an increase in its probability over time, known as aging. The model predicts a vanishingly rare frequency of spontaneous rescue unless patches of guanosine triphosphate tubulin are artificially embedded into microtubule lattice. To test our model, we used in vitro reconstitution, designed to minimize artifacts induced by microtubule interaction with nearby surfaces. Microtubules were assembled from seeds overhanging from microfabricated pedestals and thus well separated from the coverslip. This geometry reduced the rescue frequency and the incorporation of tubulins into the microtubule shaft compared with the conventional assay, producing data consistent with the model. Moreover, the rescue positions of microtubules nucleated from coverslip-immobilized seeds displayed a nonexponential distribution, confirming that coverslips can affect microtubule dynamics. Overall, our study establishes a unified theory accounting for microtubule assembly with flared ends, a tip structure-dependent catastrophe frequency, and a microtubule rescue frequency dependent on lattice damage and repair.

Elastic deformations mediate interaction of the raft boundary with membrane inclusions leading to their effective lateral sorting.

Liquid-ordered lipid domains represent a lateral inhomogeneity in cellular membranes. These domains have elastic and physicochemical properties different from those of the surrounding membrane. In particular, their thickness exceeds that of the disordered membrane. Thus, elastic deformations arise at the domain boundary in order to compensate for the thickness mismatch. In equilibrium, the deformations lead to an incomplete register of monolayer ordered domains: the elastic energy is minimal if domains in opposing monolayers lie on the top of each other, and their boundaries are laterally shifted by about 3 nm. This configuration introduces a region, composed of one ordered and one disordered monolayers, with an intermediate bilayer thickness. Besides, a jump in a local monolayer curvature takes place in this intermediate region, concentrating here most of the elastic stress. This region can participate in a lateral sorting of membrane inclusions by offering them an optimal bilayer thickness and local curvature conditions. In the present study, we consider the sorting of deformable lipid inclusions, undeformable peripheral and deeply incorporated peptide inclusions, and undeformable transmembrane inclusions of different molecular geometry. With rare exceptions, all types of inclusions have an affinity to the ordered domain boundary as compared to the bulk phases. The optimal lateral distribution of inclusions allows relaxing the elastic stress at the boundary of domains.

Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry.

Sphingomyelin- and cholesterol- enriched membrane domains, commonly referred to as "rafts" play a crucial role in a large number of intra- and intercellular processes. Recent experiments suggest that not only the volumetric inhomogeneity of lipid distribution in rafts, but also the arrangement of the 1D boundary between the raft and the surrounding membrane is important for the membrane-associated processes. The reason is that the boundary preferentially recruits different peptides, such as HIV (human immunodeficiency virus) fusion peptide. In the present work, we report a theoretical investigation of mechanisms of influence of the raft boundary arrangement upon virus-induced membrane fusion. We theoretically predict that the raft boundary can act as an attractor for viral fusion peptides, which preferentially distribute into the vicinity of the boundary, playing the role of 'line active components' of the membrane ('linactants'). We have calculated the height of the fusion energy barrier and demonstrated that, in the case of fusion between HIV membrane and the target cell, presence of the raft boundary in the vicinity of the fusion site facilitates fusion. The results we obtained can be further generalized to be applicable to other enveloped viruses.