Simulations of the spreading of a vesicle on a substrate surface mediated by receptor-ligand binding

A continuum model was introduced for the adhesion of vesicles to substrate surfaces. In the model, the vesicle membrane was assumed to be a closed shell with hyperelasticity. The vesicle cavity is filled with a liquid of fixed volume. The receptors on the membrane are mobile and initially uniformly distributed while the ligands on the substrate surface are fixed and also uniformly distributed. The formation of localized regions of tight binding between receptors and ligands, results in vesicle adhesion to the substrate surface. An adhesive model was introduced to describe the adhesive interaction between the receptors and the ligands. The growth of the adhesion area occurs via recruiting receptors from the non-adhered region through diffusion. Finite-element methods were used to solve the governing equations for the deformation of the vesicle and the receptor diffusion on the membrane surface. Effects of the membrane stiffness, the cohesive parameters and the receptor density on the adhesion kinetics of the vesicle were studied. In addition, the instability of the advancing front of the adhesion was also analyzed.     

Snap transitions in adhesion

Equilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Nonuniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is found to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading.     

Why do receptor–ligand bonds in cell adhesion cluster into discrete focal-adhesion sites?

Cell adhesion often exhibits the clustering of the receptor–ligand bonds into discrete focal-adhesion sites near the contact edge, thus resembling a rosette shape or a contracting membrane anchored by a small number of peripheral forces. The ligands on the extracellular matrix are immobile, and the receptors in the cell plasma membrane consist of two types: high-affinity integrins (that bond to the substrate ligands and are immobile) and low-affinity integrins (that are mobile and not bonded to the ligands). Thus the adhesion energy density is proportional to the high-affinity integrin density. This paper provides a mechanistic explanation for the clustering/assembling of the receptor–ligand bonds from two main points: (1) the cellular contractile force leads to the density evolution of these two types of integrins, and results into a large high-affinity integrin density near the contact edge and (2) the front of a propagating crack into a decreasing toughness field will be unstable and wavy. From this fracture mechanics perspective, the chemomechanical equilibrium is reached when a small number of patches with large receptor–ligand bond density are anticipated to form at the cell periphery, as opposed to a uniform distribution of bonds on the entire interface. Cohesive fracture simulations show that the de-adhesion force can be significantly enhanced by this nonuniform bond density field, but the de-adhesion force anisotropy due to the substrate elastic anisotropy is significantly reduced.     

受体与配体结合的动力学研究进展

受体（Ｒｅｃｅｐｔｏｒ）与配体（Ｌｉｇａｎｄ）分子之间的结合是特异性的、可逆性的,其反应动力学特征通常用正向或逆向反应速度常数κｆ或κｒ,及亲和力κａ表示．κｆ与κｋｒ,可分别反映受体与配体结合与解离的速率, κａ＝ κｆ／κｒ,表示两者的结合能力．当受体或配体分子至少一种处于游离状态时,受体与配体之间的结合是三维的．目前,已有许多方法研究三维受体配体反应动力学．当受体配体均位于细胞表面时,受体与配体之间的结合则局限于两细胞之间的二维空间．很长时间以来,由于缺乏研究二维动力学的方法,故直到９０年代流动腔和微吸管技术的相继引入,关于受体配体结合动力学的研究才由三维转入到二维水平．二维动力学研究的指导思想是通过粘附概率与接触时间的相关性求得动力学参数．     

薄壁细胞受微吸管与探针共同作用接触模型及数值模拟

建立了以典型的薄壁球型植物细胞为原型的细胞、微吸管及探针接触模型.模型的细胞壁采用封闭球形薄膜,其本构关系为体积不可压超弹性,膜球内充满有压流体以模拟细胞质.应用轴对称几何非线性方法得出了基本微分方程组,并应用龙格-库塔法进行了求解;同时,应用流固耦合有限元法进行了数值模拟以资比较.两种方法得出了较为一致的变形和应力分...     

Modelling of in vitro chondrocyte detachment

The experimental work of Huang et al. [Huang, W., Bahman, A., Torres, J.H., LeBaron R.G., Athanasiou, K.A., 2003. Temporal effects of cell adhesion on mechanical characteristics of the single chondrocyte. J. Orthop. Res. 21, 88-95] provides a novel experimental characterisation of the force required to detach single chondrocytes from a flat substrate with a horizontally moving probe. Measurements reveal that the force required to detach cells spread for six hours is eleven times greater than that required to detach cells spread for one hour. However, it is not clear if this phenomenon is entirely due to geometric changes of chondrocytes during spreading and the consequent increase in adhesion area between cell and substrate. The current computational study, using experimentally measured cell geometries and a cohesive zone model to simulate the cell-substrate interface, reveals that this is not the case. It is demonstrated that both an increase in cell stiffness and an increase in the cell-substrate interface strength during cell spreading are necessary to explain the experimental measurements. It is also revealed that the mechanism of cell detachment involves exclusively tangential debonding, with no lifting of the cell taking place at the cell-substrate interface. Finally, the effect of discrete focal adhesion regions on cell detachment is considered.     

ADVANCES IN EXPERIMENTAL APPROACHES FOR INVESTIGATING CELL AGGREGATE MECHANICS

Cells tend to form hierarchy structures in native tissues.Formation of cell aggregates in vitro such as cancer spheroids and embryonic bodies provides a unique means to study the mechanical properties and biological behaviors/functions of their counterparts in vivo.In this paper,we review state-of-the-art experimental approaches to assess the mechanical properties and mechanically-induced responses of cell aggregates in vitro.These approaches are classified into five categories according to loading modality,including micropipette aspiration,centrifugation,compression loading,substrate distention,and fluid shear loading.We discussed the advantages and disadvantages of each approach,and the potential biomedical applications.Understanding of the mechanical behavior of cell aggregates provides insights to physical interactions between cells and integrity of biological functions,which may enable mechanical intervention for diseases such as atheromatosis and cancer.     

Specific adhesion of vesicles to compliant bio-adhesive substrates

Cell behavior is mediated by variety of physiochemical properties of the extracellular matrix (ECM). Mechanical stiffness of ECM, in particular, is found to be a major regulator for the multiple aspects of cellular function. Experiments show that cells generally exhibit an apparent adhesion preference for stiffer substrates. The effect of substrate elasticity is also found to be strongly coupled with adhesivity of the substrate. To understand the underlying physics of rigidity sensing mechanism in cells, in this study we use a vesicle-substrate system to model cell adhesion as a first order approximation. Within this framework, an equilibrium thermodynamic analysis is undertaken to elucidate the interplay between substrate compliance and equilibrium configuration of an adherent vesicle. The equilibrium adhesion is assumed to ensure minimization of the free energy contributed by substrate deformation and interfacial adhesive and repulsive interactions between the membrane and substrate. The predictions of this purely mechanistic model are found to be qualitatively analogous to some of the characteristic features of cell adhesion to compliant bio-adhesive substrates. This observation suggests that the physical aspects of the membrane–substrate interfacial interactions could passively contribute in regulation of the rigidity sensing by cells.     

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP

Considering the adhesive effect and geometric nonlinearity, the adhesive contactbetween an elastic substrate and a clamped miniature circular plate with two different centralrigid bumps under the action of uniform transverse pressure and in-plane tensile force in theradial direction was analyzed. And an analytical solution is presented by using the perturbationmethod. The relation of surface adhesive energies with critical load to detach the contacted surfacesis obtained. In the numerical results, the effects of adhesive energy, in-plane tensile force, rigidbump size and contact radius on the critical load are discussed, and the relation of critical contactradius with the gap between the central rigid bump and the substrate for different adhesive energiesis investigated.     

Analytical and experimental study of a circular membrane in Hertzian contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in contact with a rigid substrate. A closed-form membrane analysis with Hertz-type contact is developed to describe the relationship between pressure, contact radius and contact force. Both the variation in the slope of the deflection profile of the portion of the membrane outside the contact zone and the contact radius itself are measured by an apparatus based on moiré deflectometry. Contact experiments with a 3 μm PET film and a glass substrate show that this analysis predicts both the slope field and contact radius well.     

Mechanokinetics of receptor–ligand interactions in cell adhesion

Receptor-ligand interactions in blood flow are crucial to initiate such biological processes as inflammatory cascade,platelet thrombosis,as well as tumor metastasis.To mediate cell adhesion,the interacting receptors and ligands must be anchored onto two apposing surfaces of two cells or a cell and a substratum,i.e.,two-dimensional(2D)binding,which is different from the binding of a soluble ligand in fluid phase to a receptor,i.e.,three-dimensional(3D) binding.While numerous works have been focused on3 D kinetics of receptor-ligand interactions in the immune system,2D kinetics and its regulations have been less understood,since no theoretical framework or experimental assays were established until 1993.Not only does the molecular structure dominate 2D binding kinetics,but the shear force in blood flow also regulates cell adhesion mediated by interacting receptors and ligands.Here,we provide an overview of current progress in 2D binding and regulations,mainly from our group.Relevant issues of theoretical frameworks,experimental measurements,kinetic rates and binding affinities,and force regulations are discussed.     

单微吸管测量细胞切向粘附力方法的研究

本文对单微吸管测量细胞切向粘附力的方法进行简要的力学分析,结果表明该方法不失为一种简单易行的切向粘附力测量方法,有助于研究个体细胞与不同基底材料之间的粘附性能,以及不同药物、粘附分子对细胞切向粘附力的影响,扩大了微管吸吮技术的应用范围,并对单微吸管细胞切向粘附力测量方法的测量左范围进行了讨论。通过对人成骨细胞切向粘附力的测量,结果表明该方法可满足细胞生物力学实验的要求。     

心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法. 在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性. 本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应. 基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比. 结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.      

Characteristics of Seepage and Diffusion in Gas Drainage and Its Application for Enhancing the gas utilization rate

Although gas drainage technology has greatly developed, gas concentration and utilization rates are still very low, resulting in substantial quantities of low concentration gas emissions in coal mine. To study the roles of suction pressure on gas drainage, a mathematical model is developed in this study for coupled gas migration and coal deformation based on a dual-porosity medium. The simulation results reveal the initial gas production is mainly contributed by the seepage in the fracture, and then the dominating factor rapidly transitions to diffusion which provides relatively stable gas production in most drainage time. In addition, the increase in gas production is tiny while the gas concentration clearly decreases because of air leakage as the suction pressure increases. Therefore, a concentration-based suction pressure regulating method is proposed to extend the time period of effective gas drainage and increase the gas utilization rate through adjusting the suction pressure of the bedding borehole. Field tests were performed to constrain the gas drainage process under different suction pressures, and the results gained verify the effectiveness and applicability of this method. This study proves that the concentration-based suction pressure regulating method may be a promising technology to realize safe, economical and efficient underground gas drainage in coal mines in the future.

     

力敏感受体介导细胞功能调控的力学生物学研究

细胞膜是细胞与外部环境进行物质与能量交换的界面,是调节细胞正常生命活动的重要结构基础.细胞膜上力敏感受体可通过力学作用方式参与并影响细胞的力信号转导等功能.整合素和钙黏素是细胞膜上典型的力敏感受体,可介导细胞与细胞周围基质或邻近细胞发生力学作用,并将力学刺激信号转导为生化信号,进而激活细胞内一系列应答反应,最终影响细胞生长、分化、增殖、凋亡和迁移等功能.力敏感受体介导细胞功能调控研究已成为探索细胞主动响应外界复杂力学微环境的力学生物学机制的关键,为进一步深入认识生理和病理状态下细胞功能变化规律,为揭示疾病的发生、发展机制提供重要的力学生物学理论与实验依据.本文总结了力敏感受体介导细胞功能调控的国内外研究进展;介绍了黏附界面处典型力敏感受体的结构和功能;总结了这些力敏感受体参与的细胞力信号感知与响应的数理模型;概述了细胞通过力敏感受体进行力学信号转导的过程;介绍了黏附介导细胞功能调控的力学生物学过程和机制;简述了体外构建模拟细胞力学微环境中细胞-细胞外基质和细胞-细胞力学相互作用的技术;指出了力敏感受体介导细胞功能调控的力学生物学研究发展趋势和未来方向.     

Continuum modeling of cell membranes

In this paper, we develop a finite-deformation model for cell membranes with a view toward characterizing the local mechanical response of membranes in atomic force microscope (AFM) experiments. The membrane is modeled as a 2-D fluid continuum endowed with bending resistance. The general theory is used to obtain equations that describe axisymmetric equilibrium states. The membrane is assumed to enclose a fluid medium, which transmits hydrostatic pressure to the membrane, and a point load is applied at the pole to simulate an AFM probe. Both types of loading are associated with a potential and the problem is then cast in a variational setting. The equilibrium equations and boundary conditions are obtained by applying standard variational procedures, resulting in a pair of coupled fourth-order differential equations to be solved for the shape of the meridian. Further refinements associated with global constraints on the enclosed volume and contact with a rigid substrate are introduced, and a solution strategy is proposed which relies on an iterative scheme for calculating the associated Lagrange multipliers.     

Large deformation adhesive contact mechanics of circular membranes with a flat rigid substrate

We study the large deformation mechanics of contact and adhesion between an inflated hyperelastic membrane and a rigid substrate. The initial configuration of the membrane is flat and circular and is clamped at the edge. Two types of friction conditions between the membrane and the substrate are considered: frictionless and no-slip contact. We derive an exact expression for the energy release rate in terms of local variables at the contact edge, thus linking adhesion to the contact angle. Our model can account for the effects of fluid pressure for experiments performed in solution. We also extend our formulation to include surface tension. Numerical simulations for a neo-Hookean membrane are carried out to study the relation between applied pressure and contact area.     

Adhesion behavior of endothelial progenitor cells to endothelial cells in simple shear flow

The adhesion of endothelial progenitor cells(EPCs) on endothelial cells(ECs) is one of the critical physiological processes for the regenesis of vascular vessels and the prevention of serious cardiovascular diseases.Here,the rolling and adhesion behavior of EPCs on ECs was studied numerically.A two-dimensional numerical model was developed based on the immersed boundary method for simulating the rolling and adhesion of cells in a channel flow.The binding force arising from the catch bond of a receptor and ligand pair was modeled with stochastic Monte Carlo method and Hookean spring model.The effect of tumor necrosis factor alpha(TNF-α) on the expression of the number of adhesion molecules in ECs was analyzed experimentally.A flow chamber system with CCD camera was set up to observe the top view of the rolling of EPCs on the substrate cultivated with ECs.Numerical results prove that the adhesion of EPC on ECs is closely related to membrane stiff-ness of the cell and shear rate of the flow.It also suggests that the adhesion force between EPC and EC by P-selectin glycoprotein ligand-1 only is not strong enough to bond the cell onto vessel walls unless contributions of other catch bond are considered.Experimental results demonstrate that TNF-α enhanced the expressions of VCAM,ICAM,P-selectin and E-selectin in ECs,which supports the numerical results that the rolling velocity of EPC on TNF-α treated EC substrate decreases obviously compared with its velocity on the untreated one.It is found that because the adhesion is affected by both the rolling velocity and the deformability of the cell,an optimal stiffness of EPC may exist at a given shear rate of flow for achieving maximum adhesion rates.     

Experimental study of the effects of spanwise rotation on the flow in a low aspect ratio diffuser for turbomachinery applications

Two dimensional time accurate PIV measurements of the flow between pressure and suction side at different spanwise positions of a rotating channel are presented. The Reynolds and Rotation numbers are representative for the flow in radial impellers of micro gas turbines. Superposition of the 2D results at the different spanwise positions provides a quasi-3D view of the flow and illustrates the impact of Coriolis forces on the 3D flow structure. It is shown that the inlet flow is little affected by rotation. An increasing/decreasing boundary layer thickness is reported on the suction/pressure side wall halfway between the channel inlet and outlet. The turbulence intensity moves away from the suction side wall and remains close to the pressure side wall. The instantaneous measurements at mid-height of the rotating channel reveal the presence of hairpin vortices in the pressure side boundary layer and symmetric vortices near the suction side. Hairpin vortices occur in rotation in the pressure and in the suction side, for the measurement plane close to the channel bottom wall.