Vibration and length-dependent flexural rigidity of protein microtubules using higher order shear deformation theory

Multiscale FEM simulations of cross-linked actin network embedded in cytosol with the focus on the filament orientation

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill-Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel-Ogden β-model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo-Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

Structure-property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

FREE VIBRATION OF MICROTUBULES AS ELASTIC SHELL MODEL BASED ON MODIFIED COUPLE STRESS THEORY

In this study, first, the thin cylindrical shell theory was derived from the modified couple stress theory and, afterwards, the vibration of protein microtubules (MTs) was investigated using the developed model. In order to model protein MTs more precisely, the cylindrical micro-shell model was used. Also, to take account of small size effects, equations of motion were obtained on the basis of the modified couple stress theory. For this purpose, first, using Hamilton's principle, vibration equations of cylindrical shell with boundary conditions were derived from the modified couple stress theory. Finally, the effects of size parameters, MT dimensions, and the medium surrounding on the axial and circumferential vibration frequency of the MT were examined. It should be noted that the results obtained from the cylindrical micro-shell model, unlike those from the beam model, have lower dependency on MT length, but they have extreme dependency on MT thickness and radius. In the end, it is worth noting that the model developed in this study can predict experimental results with greater precision compared to classic models. In other words, this model narrows the gap existing between experimental results and previous models and theories.

Localized vibration of a microtubule surrounded by randomly distributed cross linkers

Based on finite element simulation, the present work studies free vibration of a microtubule surrounded by 3D randomly distributed cross linkers in living cells. A basic result of the present work is that transverse vibration modes associated with the lowest frequencies are highly localized, in sharp contrast to the through-length modes predicted by the commonly used classic elastic foundation model. Our simulations show that the deflected length of localized modes increases with increasing frequency and approaches the entire length of microtubule when frequency approaches the minimum classic frequency given by the elastic foundation model. In particular, unlike the length-sensitive classic frequencies predicted by the elastic foundation model, the lowest frequencies of localized modes predicted by the present model are insensitive to the length of microtubules and are at least 50% lower than the minimum classic frequency for infinitely long microtubules and could be one order of magnitude lower than the minimum classic frequency for shorter microtubules (only a few microns in length). These results suggest that the existing elastic foundation model may have overestimated the lowest frequencies of microtubules in vivo. Finally, based on our simulation results, some empirical relations are proposed for the critical (lowest) frequency of localized modes and the associated wave length. Compared to the classic elastic foundation model, the localized vibration modes and the associated wave lengths predicted by the present model are in better agreement with some known experimental observations.

Vibration of bioliquid-filled microtubules embedded in cytoplasm including surface effects using modified couple stress theory

This paper aims to investigate vibrational behavior of bioliquid-filled microtubules (MTs) embedded in cytoplasm considering surface effects. The interactions between the MT, considered as an orthotropic beam within the framework of Euler-Bernoulli beam (EBB) and Timoshenko beam (TB) models, and its surrounding elastic media are simulated by Pasternak foundation model. The modified couple stress theory (MCST) is applied so as to consider the small scale effects while motion equations are derived using energy method and Hamilto's principle for both EBB and TB models. Finally, an analytical method is employed to obtain the frequency of a bioliquid-filled MT, and therefore frequency-response curves are plotted to investigate the influences of small scale parameter, mass density of bioliquid, surface layer and surrounding elastic medium graphically. The results indicate that bioliquid and surface layers play a key role on the frequency of MTs and that the frequency of MTs is decreased with increasing of the mass density of the bioliquid. Vibration analysis of MTs is being considered as a vital problem since MTs look like the nervous system of the biological cells and transmit vibrational signals. It should be noted that the results of this work are hoped to be of use in advanced medical applications especially in the forthcoming use of MTs in transporters for bio-nanosensors.

Variational principles for buckling of microtubules modeled as nonlocal orthotropic shells

A variational principle for microtubules subject to a buckling load is derived by semi-inverse method. The microtubule is modeled as an orthotropic shell with the constitutive equations based on nonlocal elastic theory and the effect of filament network taken into account as an elastic surrounding. Microtubules can carry large compressive forces by virtue of the mechanical coupling between the microtubules and the surrounding elastic filament network. The equations governing the buckling of the microtubule are given by a system of three partial differential equations. The problem studied in the present work involves the derivation of the variational formulation for microtubule buckling. The Rayleigh quotient for the buckling load as well as the natural and geometric boundary conditions of the problem is obtained from this variational formulation. It is observed that the boundary conditions are coupled as a result of nonlocal formulation. It is noted that the analytic solution of the buckling problem for microtubules is usually a difficult task. The variational formulation of the problem provides the basis for a number of approximate and numerical methods of solutions and furthermore variational principles can provide physical insight into the problem.

In situ imaging in C. elegans reveals developmental regulation of microtubule dynamics

Microtubules (MTs) are cytoskeletal polymers that undergo dynamic instability, the stochastic transition between growth and shrinkage phases. MT dynamics are required for diverse cellular processes and, while intrinsic to tubulin, are highly regulated. However, little is known about how MT dynamics facilitate or are regulated by tissue biogenesis and differentiation. We imaged MT dynamics in a smooth muscle-like lineage in intact developing Caenorhabditis elegans. All aspects of MT dynamics change significantly as stem-like precursors exit mitosis and, secondarily, as they differentiate. We found that suppression, but not enhancement, of dynamics perturbs differentiated muscle function in vivo. Distinct ensembles of MT-associated proteins are specifically required for tissue biogenesis versus tissue function. A CLASP family MT stabilizer and the depolymerizing kinesin MCAK are differentially required for MT dynamics in the precursor or differentiated cells, respectively. All of these multidimensional phenotypic comparisons were facilitated by a data display method called the diamond graph.

A higher-order mathematical modeling for dynamic behavior of protein microtubule shell structures including shear deformation and small-scale effects

Microtubules in mammalian cells are cylindrical protein polymers which structurally and dynamically organize functional activities in living cells. They are important for maintaining cell structures, providing platforms for intracellular transport, and forming the spindle during mitosis, as well as other cellular processes. Various in vitro studies have shown that microtubules react to applied mechanical loading and physical environment. To investigate the mechanisms underlying such phenomena, a mathematical model based on the orthotropic higher-order shear deformation shell formulation and Hamilton's principle is presented in this paper for dynamic behavior of microtubules. The numerical results obtained by the proposed shell model are verified by the experimental data from the literature, showing great consistency. The nonlocal elasticity theory is also utilized to describe the nano-scale effects of the microtubule structure. The wave propagation and vibration characteristics of the microtubule are examined in the presence and absence of the cytosol employing proposed formulations. The effects of different system parameters such as length, small scale parameter, and cytosol viscosity on vibrational behavior of a microtubule are elucidated. The definitions of critical length and critical viscosity are introduced and the results obtained using the higher order shell model are compared with those obtained employing a first-order shear deformation theory. This comparison shows that the small scale effects become important for higher values of the wave vector and the proposed model gives more accurate results for both small and large values of wave vectors. Moreover, it is shown that for higher circumferential wave number, the torsional wave velocity obtained by the higher-order shell model tend to be higher than the one predicted by the first-order shell model.

Measuring microtubule persistence length using a microtubule gliding assay

The mechanical properties of microtubules have been an area of active research for the past two decades, in part because understanding the mechanics of individual microtubules contributes to modeling whole-cell rigidity and structure and hence to better understanding the processes underlying motility and transport. Moreover, the role of microtubule structure and microtubule-associated proteins (MAPs) in microtubule stiffness remains unclear. In this chapter, we present a kinesin-driven microtubule gliding assay analysis of persistence length that is amenable to simultaneous variation of microtubule parameters such as length, structure, or MAP coverage and determination of persistence length. By combining sparse fluorescent labeling of individual microtubules with single particle tracking of individual fluorophores, microtubule gliding trajectories are tracked with nanometer-level precision. The fluctuations in these trajectories, due to thermal fluctuations in the microtubules themselves, are analyzed to extract the microtubule persistence length. In the following, we describe this gliding assay and analysis and discuss two example microtubule variables, length and diameter, in anticipation that the method may be of wide use for in vitro study of microtubule mechanical properties.

Coupled oscillations of a protein microtubule immersed in cytoplasm: an orthotropic elastic shell modeling

Revealing vibration characteristics of sub-cellular structural components such as membranes and microtubules has a principal role in obtaining a deeper understanding of their biological functions. Nevertheless, limitations and challenges in biological experiments at this scale necessitates the use of mathematical and computational models as an alternative solution. As one of the three major cytoskeletal filaments, microtubules are highly anisotropic structures built from tubulin heterodimers. They are hollow cylindrical shells with a ∼ 25 nm outer diameter and are tens of microns long. In this study, a mechanical model including the effects of the viscous cytosol and surrounding filaments is developed for predicting the coupled oscillations of a single microtubule immersed in cytoplasm. The first-order shear deformation shell theory for orthotropic materials is used to model the microtubule, whereas the motion of the cytosol is analyzed by considering the Stokes flow. The viscous cytosol and the microtubule are coupled through the continuity condition across the microtubule-cytosol interface. The stress and velocity fields in the cytosol induced by vibrating microtubule are analytically determined. Finally, the influences of the dynamic viscosity of the cytosol, filament network elasticity, microtubule shear modulus, and circumferential wave-number on longitudinal, radial, and torsional modes of microtubule vibration are elucidated.

Surveillance culture monitoring of double-balloon enteroscopy reprocessing with high-level disinfection

BACKGROUND

Inadequate reprocessing of double-balloon enteroscopy (DBE) or of endoscopic accessories may result in iatrogenic infections and present a risk to public health.

AIM

To use microbiological surveillance culture monitoring (SCM) to assess the adequacy of high-level disinfection (HLD) with standard reprocessing procedures of DBE.

MATERIALS AND METHODS

We performed a prospective study on cultures collected from DBEs that had been treated by HLD by an automated endoscope washing machine (AEWM) decontamination cycle. This study included 42 cases with 57 cultures, which were collected consecutively between October 2009 and December 2010. In 31 cases, 31 cultures were collected from oral route DBE (mean patient age, 68·9 years), and in 23 cases, 26 cultures were collected from anal route DBE (mean patient age, 67·9 years). The results obtained were compared with those of our previous study of SCM on gastroscopy (GS) and colonoscopy (CS). The samples were collected by flushing 50 mL sterile distilled water into the suction channel and collecting the flow-through in a sterile container. The samples were then incubated at 37 °C and examined for bacterial growth.

RESULTS

Before HLD, the positive culture rate was 83·9% (26/31) for the oral route DBE and 100% (26/26) for the anal route DBE (P = 0·0406). After HLD, the positive culture rate was 12·9% (4/31) for the oral route DBE and 19·2% (5/26) for the anal route DBE (P > 0·05). A linear trend relationship was found between positive SCM and the length and category of diagnostic instruments--GS, CS, oral route DBE and anal route DBE.

CONCLUSIONS

Surveillance culture monitoring is a useful method to assess the effectiveness of HLD reprocessing of DBE. Machine washing may not achieve complete disinfection. Using AEWM regularly is mandatory to minimize cross-contamination and to ensure quality assurance. Additional procedures are necessary to employ for the longer and anal route DBE.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.