Jizeng Wang

Lifetime and Strength of Adhesive Molecular Bond Clusters between Elastic Media

With a long-term objective toward a quantitative understanding of cell adhesion, we consider an idealized theoretical model of a cluster of molecular bonds between two dissimilar elastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to obey classical elastic equations whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. Monte Carlo simulations that combine the elastic and stochastic equations are conducted to investigate the lifetime of the bond cluster as a function of the applied load. We show that the interfacial traction is generally nonuniform and for a given adhesion size the average cluster lifetime asymptotically approaches infinity as the applied load is reduced to below a critical value, defined as the strength of the cluster. The effects of elastic moduli, adhesion size, and rebinding rate on the cluster lifetime and strength are studied under strongly nonuniform distributions of interfacial traction. Although overly simplified in a number of aspects, our model seems to give predictions that are consistent with relevant experimental observations on focal adhesion dynamics.

Lifetime and Strength of Periodic Bond Clusters between Elastic Media under Inclined Loading

Focal adhesions are clusters of specific receptor-ligand bonds that link an animal cell to an extracellular matrix. To understand the mechanical responses of focal adhesions, here we develop a stochastic-elasticity model of a periodic array of adhesion clusters between two dissimilar elastic media subjected to an inclined tensile stress, in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction are unified in a single modeling framework. We first establish a fundamental scaling law of interfacial traction distribution and derive a stress concentration index that governs the transition between uniform and cracklike singular distributions of the interfacial traction within molecular bonds. Guided by this scaling law, we then perform Monte Carlo simulations to investigate the effects of cluster size, cell/extracellular matrix modulus, and loading direction on lifetime and strength of the adhesion clusters. The results show that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, and low-angle pulling are factors that contribute to the stability of focal adhesions. The predictions of our model provide feasible explanations for a wide range of experimental observations and suggest possible mechanisms by which cells can modulate adhesion and deadhesion via cytoskeletal contractile machinery and sense mechanical properties of their surroundings.

A generalized bead-rod model for Brownian dynamics simulations of wormlike chains under strong confinement

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions.

Effects of Capillary Condensation in Adhesion between Rough Surfaces

Experiments on the effects of humidity in adhesion between rough surfaces have shown that the adhesion energy remains constant below a critical relative humidity (RHcr) and then abruptly jumps to a higher value at RHcr before approaching its upper limit at 100% relative humidity. A model based on a hierarchical rough surface topography is proposed, which quantitatively explains the experimental observations and predicts two threshold RH values, RHcr and RHdry, which define three adhesion regimes: (1) RH<RHdry, no stable water bridges form between the contacting surfaces; (2) RHdry<RH<RHcr, water bridges form but are confined to the initial solid-solid contact regions; and (3) RH>RHcr, water menisci freely form and spread along the interface between the rough surfaces.

Anomalous flexural behaviors of microtubules.

Apparent controversies exist on whether the persistence length of microtubules depends on its contour length. This issue is particularly challenging from a theoretical point of view due to the tubular structure and strongly anisotropic material property of microtubules. Here we adopt a higher order continuum orthotropic thin shell model to study the flexural behavior of microtubules. Our model overcomes some key limitations of a recent study based on a simplified anisotropic shell model and results in a closed-form solution for the contour-length-dependent persistence length of microtubules, with predictions in excellent agreement with experimental measurements. By studying the ratio between their contour and persistence lengths, we find that microtubules with length at ~1.5 μm show the lowest flexural rigidity, whereas those with length at ~15 μm show the highest flexural rigidity. This finding may provide an important theoretical basis for understanding the mechanical structure of mitotic spindles during cell division. Further analysis on the buckling of microtubules indicates that the critical buckling load becomes insensitive to the tube length for relatively short microtubules, in drastic contrast to the classical Euler buckling. These rich flexural behaviors of microtubules are of profound implication for many biological functions and biomimetic molecular devices.

Understanding large plastic deformation of SiC nanowires at room temperature

Tensile behaviors of SiC [111] nanowires with various possible microstructures have been investigated by molecular-dynamics simulations. The results show that the large plastic deformation in these nanowires is induced by the anti-parallel sliding of 3C grains along an ultrathin intergranular amorphous film parallel to the (11 (1) over bar) plane and inclined at an angle of 19.47 degrees. with respect to the nanowire axis. The resulting large plastic deformation of SiC nanowires at room temperature is attributed to the stretching, breaking and re-forming of Si-C bonds in the intergranular amorphous film, which is also evident from the sawtooth jumps in the stress-strain response. Copyright (C) EPLA, 2011

An effective bead-spring model for polymer simulation

An effective bead-spring model combining the advantages of large time steps of traditional bead-rod models and computational rigor of traditional bead-spring models is proposed to simulate the dynamic behaviors of flexible polymer chains with arbitrary longitudinal stiffness. The proposed model can be used to simulate many types of polymer chains or networks with different chain elasticity via a unified integration scheme with reasonably large time steps.

Specific adhesion of a soft elastic body on a wavy surface

This paper aims at developing a stochastic-elastic model of a soft elastic body adhering on a wavy surface via a patch of molecular bonds. The elastic deformation of the system is modeled by using continuum contact mechanics, while the stochastic behavior of adhesive bonds is modeled by using Bells type of exponential bond association/dissociation rates. It is found that for sufficiently small adhesion patch size or stress concentration index, the adhesion strength is insensitive to the wavelength but decreases with the amplitude of surface undulation, and that for large adhesion patch size or stress concentration index, there exist optimal values of the surface wavelength and amplitude for maximum adhesion strength.

Dynamic fiber inclusions with elliptical and arbitrary cross-sections and related retarded potentials in a quasi-plane piezoelectric medium

Abstract A piezoelectric medium of transversely isotropic symmetry with continuous fiber inclusion parallel to the axis of symmetry is considered. The problem is equivalent to a two-dimensional ‘ quasi-plane ’ piezoelectric medium containing a 2D inclusion. The inclusion is assumed to undergo a spatially uniform δ ( t )-type time domain transformation. The continuous fiber has elliptical, circular and arbitrary cross-sections. The solutions of the inclusion problem is expressed by scalar potentials . In the time domain two of these functions correspond to the retarded potential integrals of the inclusion. Their frequency domain representation which we shall call the ‘ dynamic potentials of the inclusion ’ are also considered. Integral formulae are derived for continuous fiber inclusions with elliptical cross-sections. Known closed-form solutions are reproduced for circular fibers. For fibers with arbitrary cross-sections a numerical method based on Gauss quadrature is applied. High accuracy and efficiency of the numerical method is confirmed. Characteristic superposition and runtime effects for the inclusions are found.

A space–time fully decoupled wavelet Galerkin method for solving two-dimensional Burgers’ equations

Abstract A space–time fully decoupled formulation for solving two-dimensional Burgers’ equations is proposed based on the Coiflet-type wavelet sampling approximation for a function defined on a bounded interval. By applying a wavelet Galerkin approach for spatial discretization, nonlinear partial differential equations are first transformed into a system of ordinary differential equations, in which all matrices are completely independent of time and never need to be updated in the time integration. Finally, the mixed explicit–implicit scheme is employed to solve the resulting semi-discretization system. By numerically studying three widely considered test problems, results demonstrate that the proposed method has a much better accuracy and a faster convergence rate than many existing numerical methods. Most importantly, the study also indicates that the present wavelet method is capable of solving the two-dimensional Burgers’ equation at high Reynolds numbers.