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This paper develops a rigorous analysis of the microtubule elastic deformations in terms of the torsional degrees of freedom using the helix-based cylindrical structure of this biopolymer. Methods of differential geometry and the theory of elasticity are employed in our analysis. We find equilibrium conditions and constitutive equations in the linear regime. We estimate the value of torsional rigidity for microtubules based on their structure and some experimentally known elastic properties. The paper concludes with the derivation of a bulk modulus formula for a microtubule in solution. Both the entropy change and the fluctuation of the twist angle are obtained. [ABSTRACT FROM AUTHOR]

Parameters characterizing elastic properties of microtubules, measured in several recent experiments, reflect an anisotropic character. We describe the microscopic dynamical properties of microtubules using a discrete model based on an appropriate lattice of dimers. Adopting a harmonic approximation for the dimer–dimer interactions and estimating the lattice elastic constants, we make predictions regarding vibration dispersion relations and vibration propagation velocities. Vibration frequencies and velocities are expressed as functions of the elastic constants and of the geometrical characteristics of the microtubules. We show that vibrations which propagate along the protofilament do so significantly faster than those along the helix. [ABSTRACT FROM AUTHOR]

We investigate the Hubbard Hamiltonian's properties in the continuum limit by implementing the procedures of the Method of Coherent Structures (MCS). We obtain field equations of motion and analyse the phase dynamics of the resultant classical spin fields. We have performed analytical and numerical calculations to find appropriate physically acceptable solutions to the equations of motion in one-dimensional space. In two-dimensional space, among other types, we have found several different spin phases of vortex type, spiral patterns and parabolic spin arrangements. Our results are consistent with earlier Hartree-Fock finite-grid numerical simulations. [ABSTRACT FROM AUTHOR]

We analyse the statistical properties of the exact solutions obtained recently from the minimisation procedure in the one-dimensional φ-model. Constant, periodic and localised solutions are included in the analysis and their energy spectra found. Subsequently, each class of solutions is examined as to their contributions towards statistical quantities such as the partition function and the specific heat. Information regarding stability and signatures of the individual types of excitations in the system has been obtained. [ABSTRACT FROM AUTHOR]

A number of particular solutions of a class of non-linear Klein-Gordon equations are analysed from the viewpoint of their usefulness as quantum bound states in many-body systems. Similarities and differences between quantum and classical solutions are discussed. [ABSTRACT FROM AUTHOR]