Tensile properties of microtubules: A study by nonlinear molecular structural mechanics modelling

A nonlinear molecular structural mechanics (MSM) model is proposed in this paper for studying the tensile properties of microtubules (MTs). In the nonlinear MSM models, the interactions between tubulin monomers in MTs are treated as nonlinear axial and torsional springs, whose stiffness coefficients are extracted from all-atom molecular dynamics simulations. The Young's modulus and fracture properties of MTs under tension extracted from the present nonlinear MSM models are found to agree well with the existing simulation and experiment results, which shows the efficiency and accuracy of the proposed nonlinear MSM models. In addition, the nonlinear MSM models are also extended to investigate the tensile properties including Young's modulus and fracture strain of MTs possessing lattice defects. The results obtained from nonlinear MSM models are utilized to develop a predictive equation for quickly predicting the tensile properties of MTs with different lattice defect levels.     

One-parameter nonrelativistic supersymmetry for microtubules

The one-parameter nonrelativistic supersymmetry of Mielnik [J. Math. Phys. 25 (1984) 3387] is applied to the simple supersymmetric model of Caticha [Phys. Rev. A 51 (1995) 4264] in the form used by Rosu [Phys. Rev. E 55 (1997) 2038] for microtubules. By this means, we introduce Montroll double-well potentials with singularities that move along the positive or negative traveling direction depending on the sign of the free parameter of Mielnik's method. Possible interpretations of the singularity are either microtubule associated proteins (motors) or structural discontinuities in the arrangement of the tubulin molecules.     

Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method

By means of computerized symbolic computation and a modified extended tanh-function method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission line models of microtubules for nano-ionic currents. The nonlinear equations elaborated here are quite original and first proposed in the context of important nanosciences problems related with cell signaling. It could be even of basic importance for explanation of cognitive processes in neurons. As results, we can successfully recover the previously known solitary wave solutions that had been found by other sophisticated methods. The method is straightforward and concise, and it can also be applied to other nonlinear equations in physics.     

Monitoring dynamic systems with multiparameter fluorescence imaging

A new general strategy based on the use of multiparameter fluorescence detection (MFD) to register and quantitatively analyse fluorescence images is introduced. Multiparameter fluorescence imaging (MFDi) uses pulsed excitation, time-correlated single-photon counting and a special pixel clock to simultaneously monitor the changes in the eight-dimensional fluorescence information (fundamental anisotropy, fluorescence lifetime, fluorescence intensity, time, excitation spectrum, fluorescence spectrum, fluorescence quantum yield, distance between fluorophores) in real time. The three spatial coordinates are also stored. The most statistically efficient techniques known from single-molecule spectroscopy are used to estimate fluorescence parameters of interest for all pixels, not just for the regions of interest. Their statistical significance is judged from a stack of two-dimensional histograms. In this way, specific pixels can be selected for subsequent pixel-based subensemble analysis in order to improve the statistical accuracy of the parameters estimated. MFDi avoids the need for sequential measurements, because the registered data allow one to perform many analysis techniques, such as fluorescence-intensity distribution analysis (FIDA) and fluorescence correlation spectroscopy (FCS), in an off-line mode. The limitations of FCS for counting molecules and monitoring dynamics are discussed. To demonstrate the ability of our technique, we analysed two systems: (i) interactions of the fluorescent dye Rhodamine 110 inside and outside of a glutathione sepharose bead, and (ii) microtubule dynamics in live yeast cells of Schizosaccharomyces pombe using a fusion protein of Green Fluorescent Protein (GFP) with Minichromosome Altered Loss Protein 3 (Mal3), which is involved in the dynamic cycle of polymerising and depolymerising microtubules.     

Podophyllotoxin esters with alicyclic residues: an insight into the origin of microtubule-curling effect in cancer cells

Immunofluorescent microscopy of cancer cells A549 treated with novel alicyclic (mostly bridged) podophyllotoxin C⁴-esters at different concentrations gave evidence that the ‘curling’ of microtubules occurred at one of the first steps of their depolymerisation. Molecular dynamics study revealed the differences in curved conformations of tubulin dimer in a complex with adamantane-comprising ester and in a complex with podophyllotoxin.     

Nonlocal shear deformable shell model for torsional buckling and postbuckling of microtubules in thermal environments

Buckling and postbuckling analysis is presented for microtubules subjected to torsion in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on a higher order shear deformation theory. The thermal effects are included and the material properties are assumed to be temperature-dependent. The small scale parameter e₀a is estimated by matching the buckling twist angle of microtubules obtained from the nonlocal shear deformable shell model with the existing result. The results show that the small scale effect plays an important role in the postbuckling of microtubules.     

Nonlocal shear deformable shell model for bending buckling of microtubules embedded in an elastic medium

A nonlocal shear deformable shell model is developed for buckling of microtubules embedded in an elastic matrix of cytoplasm under bending in thermal environments. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large.     

Surface conductance in seamless microtubules

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present a theoretical analysis of the surface conductance of a single seamless MT by representing each tubulin dimer as a resistor. Periodic boundary conditions were utilised both lengthwise (so the MT is pictured as a very large toroidal structure) and around its circumference. Firstly we have investigated the conductance matrix and found the eigenvalues and eigenvectors exactly. Then Wu’s formula has been used to calculate the conductance in terms of them numerically. To check our results we have performed a series of computer simulations of random walks on the lattice of monomers utilising the widely known relationship between such a stochastic process and the theory of electrical networks. We obtain very good agreement between the two approaches.