Long-wavelength deformations and vibrational modes in empty and liquid-filled microtubules and nanotubes: A theoretical study

Abstract

We propose a continuum model to predict long-wavelength vibrational modes of empty and liquid-filled tubules that are very hard to reproduce using the conventional force-constant matrix approach based on atomistic ab initio calculation. We derive simple quantitative expressions for long-wavelength longitudinal and torsional acoustic modes, flexural acoustic modes, as well as the radial breathing mode of empty or liquid-filled tubular structures that are based on continuum elasticity theory expressions for a thin elastic plate. We furthermore show that longitudinal and flexural acoustic modes of tubules are well described by those of an elastic beam resembling a nanowire. Our numerical results for biological microtubules and carbon nanotubes agree with available experimental data.

Sounds Stimulation on In Vitro HL1 Cells: A Pilot Study and a Theoretical Physical Model

“…It is, on the other hand, reasonable that a relationship between trains of acoustic waves and proteins [ 77 ] may exist, given that protein chains may support wave excitations according to different dynamical regimes [ 79 ], including nonlinear solitary waves [ 80 , 81 , 82 ], and may interact with each other through an exchange of quantum modes, such as dipole quantum waves, mediated by the water bath in which they are embedded [ 80 , 81 , 82 , 83 ]. In this respect, it is remarkable that acoustic stimulations deform [ 66 , 84 ] and are conveyed [ 58 , 85 , 86 , 87 , 88 ] by the cytoskeleton to the nucleus [ 59 ] and on the other hand, the tubulin monomers exhibit different oscillatory and assembly modes [ 89 ] depending on the stimulating frequencies [ 38 ].…”

Using nanotubes to study the phonon spectrum of two-dimensional materials

“…Typical manifestations of the problem are spurious imaginary frequencies close to the G point. [25][26][27] It is therefore important to correct such artifacts, which can have a significant effect on derived quantities like thermal conductivity or lead to a mischaracterization of the mechanical stability of a system. To overcome this issue, two very different approaches have been devised.…”

“…A first possibility is to exploit the fact that continuum theory can provide the longwavelength limit of the acoustic modes, and to use electronicstructure software to estimate the elastic parameters defining those. 26,27 A second approach consists in finding the maximum projection of the interatomic-force-constant (IFC) tensor on a subspace of internal coordinates that cannot express rigid translations or rotations, hence removing the artifactual elements introduced by periodic boundary conditions and recovering the phonon dispersions that fulfill the physical constraints by construction. 25 Here we apply a consistent, ab initio methodology to illustrate the connection between the phonon spectra of the MoS 2 NTs and both the continuum limit and the spectrum of the corresponding ML.…”

Origin of Unusually High Rigidity in Selected Helical Coil Structures

“…1(b), and a rubber hose share one important property: all elastic material is on the surface of a hollow cylinder, forming a tube. In a further degree of simplification, we may ignore the interior structure of this elastic tube and describe its stretching, twisting or bending deformations using continuum elasticity theory 7 . So far, we have considered stretching as the dominant response to tensile stress.…”

“…In the following we explore the elastic behavior of this structure using continuum elasticity theory in order to identify the reason for its rigidity [2][3][4] . Since continuum elasticity theory applies from nanometer-sized fullerenes and nanotubes [5][6][7] to the macro-scale, we expect our approach to be useful to explore the rigidity of helical structures on the microand nanometer scale.…”