Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws.

This Dissertation is devoted to computational study of the solidification, dynamics and mechanics of model semiflexible polymers with variable chain flexibility as well as a computational investigation of the clogging phenomena observed in granular materials. Chain stiffness is an intrinsic factor that governs single-chain flexibility. It plays a critical role in the physics of polymeric materials. In this work, we employ a coarse-grained polymer model in which chain stiffness can be tuned by a single parameter (bending stiffness kb) that yields chain shape ranging from coil-like to rod-like in the flexible and very stiff limit respectively. In chapter 2, we focus on how chain stiffness affects how polymer melts solidify under thermal cooling. We observe a strong dependence of the solid-state morphology (formed after cooling) upon chain flexibility. In the flexible limit, we find that monomers possess crystalline order while chains retain random-walk like structure. In higher stiffness regime glass formation is obtained while nematic ordering typical of lamellar precursors coexists with close-packing in the rod-like limit. Surprisingly we observe various structures ranging from spiral, to multi-domain nematic phases in the intermediate values of kb. In chapter 3 we go a step further to relate the solidification behaviors of chains discussed in chapter 2 to their melt dynamics. We probe the microstructure and the dynamics of flexible, intermediate-stiffness and rod-like chains. We find that melts of flexible and stiff chains that crystallize under cooling show simple and fast dynamics with Arrhenius temperature dependence. Interestingly, the intermediate-stiffness chains exhibit Vogel-Fulcher dynamical relaxation typical of fragile glass-formers even though their ground states is a nematic-close-packed crystal. There is no compelling argument based on static micro-structure change explaining this dynamical arrest to be found. However, we find that the dynamics of intermediate-stiffness chains is dominated by the stringlike cooperative motion that correlates along their chain backbones. This cooperative rearrangement which is absent in other systems appears to be the main cause of the dynamical arrest observed for intermediate-stiffness chains. In chapter 4, we turn to another class of materials where the negligible contribution of thermal fluctuations gives rise to an interesting phenomenon, i.e. the clogging transition. Clogging is a probabilistic event that occurs through a transition from a homogeneous flowing state to a heterogeneous or phase separated jammed state. The granular system under study is an assemble of bidisperse disks externally driven through a two dimensional periodic substrate. We find that the probability for clogging strongly depend on particle packing, obstacle number and the driving direction. Surprisingly, under relevant conditions we observe a size-specific clogging transition in which the smaller species get trapped while the larger species keep flowing. Chapter 5 returns to discuss the polymer solidification in the context of isostaticity. Results from the simulations of semiflexible polymers described in chapter 2 allow us to derive a generalized isostaticity criterion that can be applied to finite-stiffness chains. The new criterion is based on the characteristic ratio C which characterizes the slow freezing out of configurational freedom of chains as chain stiffness increases. The results of the average coordination number at solidification Z(Ts) suggest a link between jamming in athermal systems and solidification in their thermal counterparts. Finally, in chapter 6 we study the effect of chain stiffness on the mechanical response of glassy polymers. We investigate shear deformation of three systems with a different degree of entanglement. We find that loosely entangled chains display strong shear banding and undergo fracture via chain pullout. In contrast, tightly entangled chains fail at high enough strain along a well-defined plane via chain scission shortly after chains are pulled taut. We explain these chain-stiffness-dependent behaviors qualitatively using the segmental packing efficiency argument and quantitatively using modern plasticity measures

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Microtubules are cytoskeletal protein polymers relevant to a wide range of cell functions. In order to polymerize, the constituent tubulin subunits need to bind the nucleotide GTP, but its subsequent hydrolysis to GDP in the microtubule lattice induces depolymerization. The resulting behaviour of stochastic switching between growth and shrinkage is called dynamic instability. Both dynamic instability and microtubule mechanical properties are integral to many cell functions, yet are poorly understood. The present study uses thermal fluctuation measurements of grafted microtubules with different nucleotide contents to extract stiffnesses, relaxation times, and drag coefficients with an unprecedented precision. Both the stiffness and the relaxation time data indicate that stiffness is a function of length for GDP microtubules stabilized with the chemotherapy drug taxol. By contrast, measurements on microtubules polymerized with the non-hydrolizable GTP-analogue GMPCPP show a significantly higher, but constant, stiffness. The addition of taxol is shown to not significantly affect the properties of these microtubules, but a lowering of the GMPCPP content restores the length-dependent stiffness seen for taxol microtubules. The data are interpreted on the basis of a recent biopolymer model that takes into account the anisotropic architecture of microtubules which consist of loosely coupled protofilaments arranged in a tube. Using taxol microtubules and GMPCPP microtubules as the respective analogues of the GDP and GTP state of microtubules, evidence is presented that shear coupling between neighbouring protofilaments is at least two orders of magnitude stiffer in the GTP state than in the GDP state. Previous studies of nucleotide effects on tubulin have focussed on protofilament bending, and the present study is the first to be able to show a dramatic effect on interprotofilament bonds. The finding’s profound implications for dynamic instability are discussed. In addition, internal friction is found to dominate over hydrodynamic drag for microtubules shorter than ∼ 4 μm and, like stiffness, to be affected by the bound nucleotide, but not by taxol. Furthermore, the thermal shape fluctuations of free microtubules are imaged, and the intrinsic curvatures of microtubules are shown for the first time to follow a spectrum reminiscent of thermal bending. Regarding the extraction of mechanical data, this assay, though previously described in the literature, is shown to suffer from systematic flaws.