Nonlinear dynamics of microtubules - A new model

In the present paper we describe a model of nonlinear dynamics of microtubules (MT) assuming a single longitudinal degree of freedom per tubulin dimer. This is a longitudinal displacement of a dimer at a certain position with respect to the neighbouring one. A nonlinear partial differential equation, describing dimer`s dynamics within MT, is solved both analytically and numerically. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. Internal electrical field strength is calculated using two procedures and a perfect agreement between the results is demonstrated. This enabled estimation of total energy, kink velocity and kink width. To simplify the calculation of the total energy we proved a useful theorem.Comment: 14 pages, 4 figure

Electromechanical vibration of microtubules and its application in biosensors

An electric field (EF) has the potential to excite the vibration of polarized microtubules (MTs) and thus enable their use as a biosensor for the biophysical properties of MTs or cells. To facilitate the development, this paper aims to capture the EF-induced vibration modes and the associated frequency for MTs. The analyses were carried out based on a molecular structural mechanics model accounting for the structural details of MTs. Transverse vibration, radial breathing vibration and axial vibration were achieved for MTs subject to a transverse or an axial EF. The frequency shift and stiffness alteration of MTs were also examined due to the possible changes of the tubulin interactions in physiological or pathological processes. The strong correlation achieved between the tubulin interaction and MT vibration excited by EF provides a new avenue to a non-contacting technique for the structural or property changes in MTs, where frequency shift is used as a biomarker. This technique can be used for individual MTs and is possible for those in cells when the cytosol damping on MT vibrations is largely reduced by the unique features of MT–cytosol interface

Modelling on the nanomechanics of cytoskeletal filaments

Cytoskeleton is a structure that enables cells to maintain their shape and internal organization. The proper functions of cytoskeleton depend crucially on the mechanical responses and properties of its component filaments (e.g., microtubules and actin filaments). Thus, an in-depth understanding of cytoskeletal filaments mechanics is essential in revealing how cells fulfil their biological functions via cytoskeleton, stimulating the innovative idea in designing biomimetic structure or materials and facilitating to develop novel techniques in disease diagnosis and treatment. This thesis thus focuses on studying the inherent and environmental factors that determine the nanomechanics of cytoskeletal components, i.e., the monomeric feature of cytoskeletal filaments at microscale, the relation between the helical structure and the mechanical properties, and the interaction between the protein filaments and the surrounding environment, such as cytosol, filamentous proteins, electrical fields, etc. The thesis starts with a comprehensive review of the existing cytoskeletal filaments models. It is followed by the molecular structural mechanics models developed for microtubules and actin filaments. Subsequently, the models with monomeric feature were employed to identify the origin of the inter-protofilament sliding and its role in bending and vibration of microtubules. After that, helix structure effects on the mechanics of cytoskeletal filaments were explored. A three-dimensional transverse vibration was reported for microtubules with chiral structures, where the bending axis of the cross-section rotates in an anticlockwise direction and the adjacent half-waves oscillate in different planes. The tension-induced bending was also studied for actin filaments as a result of the helicity. Then, the subcellular environment effect on the filament mechanics was explored. Attempts were also made to reveal the physics of the experimentally observed localized buckling of microtubules and the crucial role of the cross-linker in regulating microtubule stiffness. Also the role of actin-binding proteins in determining the stiffness of actin bundle was examined during the formation of filopodia protrusion. Finally, the studies were carried out for the microtubule vibration excited by the alternating external electric field. Strong correlation was achieved between the tubulin interaction and the frequency shift. Meanwhile, the unique feature of nanoscale microtubule-cytosol interface was studied in detail. Large reduction of the viscous damping of cytosol was achieved in the presence of the nanoscale solid-liquid interface. At the end of the thesis, the contributions of the dissertation research were summarised and remarks were given on future research directions

Electrical Oscillations in Two-Dimensional Microtubular Structures

Microtubules (MTs) are unique components of the cytoskeleton formed by hollow cylindrical structures of αβ tubulin dimeric units. The structural wall of the MT is interspersed by nanopores formed by the lateral arrangement of its subunits. MTs are also highly charged polar polyelectrolytes, capable of amplifying electrical signals. The actual nature of these electrodynamic capabilities remains largely unknown. Herein we applied the patch clamp technique to two-dimensional MT sheets, to characterize their electrical properties. Voltage-clamped MT sheets generated cation-selective oscillatory electrical currents whose magnitude depended on both the holding potential, and ionic strength and composition. The oscillations progressed through various modes including single and double periodic regimes and more complex behaviours, being prominent a fundamental frequency at 29 Hz. In physiological K+ (140 mM), oscillations represented in average a 640% change in conductance that was also affected by the prevalent anion. Current injection induced voltage oscillations, thus showing excitability akin with action potentials. The electrical oscillations were entirely blocked by taxol, with pseudo Michaelis-Menten kinetics and a KD of ~1.29 μM. The findings suggest a functional role of the nanopores in the MT wall on the genesis of electrical oscillations that offer new insights into the nonlinear behaviour of the cytoskeleton.Fil: Cantero, Maria del Rocio. Universidad de Buenos Aires. Facultad de Odontología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pérez, Paula Luciana. Universidad de Buenos Aires. Facultad de Odontología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Smoler, Mariano. Universidad de Buenos Aires. Facultad de Odontología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Villa Etchegoyen, Cecilia. Universidad de Buenos Aires. Facultad de Odontología; ArgentinaFil: Cantiello, Horacio Fabio. Universidad de Buenos Aires. Facultad de Odontología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin