Compliance profile of the human cornea as measured by atomic force microscopy

The ability to accurately determine the elastic modulus of each layer of the human cornea is a crucial step in the design of better corneal prosthetics. In addition, knowledge of the elastic modulus will allow design of substrates with relevant mechanical properties for in vitro investigations of cellular behavior. Previously, we have reported elastic modulus values for the anterior basement membrane and Descemet's membrane of the human cornea, the surfaces in contact with the epithelial and endothelial cells, respectively. We have completed the compliance profile of the stromal elements of the human cornea by obtaining elastic modulus values for Bowman's layer and the anterior stroma. Atomic force microscopy (AFM) was used to determine the elastic modulus, which is a measure of the tissue stiffness and is inversely proportional to the compliance. The elastic response of the tissue allows analysis with the Hertz equation, a model that provides a relationship between the indentation force and depth and is a function of the tip radius and the modulus of the substrate. The elastic modulus values for each layer of the cornea are: 7.5±4.2 kPa (anterior basement membrane), 109.8±13.2 kPa (Bowman's layer), 33.1±6.1 kPa (anterior stroma), and 50±17.8 kPa (Descemet's membrane). These results indicate that the biophysical properties, including elastic modulus, of each layer of the human cornea are unique and may play a role in the maintenance of homeostasis as well as in the response to therapeutic agents and disease states. The data will also inform the design and fabrication of improved corneal prosthetics.     

Effects of membrane pre-stress and intrinsic viscoelasticity on nanoindentation of cells using AFM

Nanoindentation using atomic force microscopy (AFM) has found a wide range of applications in characterizing the mechanical properties of cells. However, both conventional Hertz theory and Sneddon's solution face difficulties in interpreting cell indentation data due to lack of considerations of the bilayered structure of cells, the pre-stress of cell membranes and the intrinsic viscoelasticity of cell interior phases. In the present study, the indentation of a cell using AFM is modelled as that of a pre-tensed elastic shell supported by a viscoelastic half-space. Analytical solutions are derived for the shallow indentation of the elastic counterpart of the bilayered structure and then extended to moderate-depth indentation. The cell membrane and its pre-tension are important in interpreting the indentation data if a small indenter is used. Based on the elastic solutions, viscoelastic solutions are derived for creep tests, relaxation tests and linear loading tests, and verified by finite element analysis. Parametric studies were performed to investigate the effects of the membrane pre-stress and the intrinsic viscoelasticity of the cell on the relation between the indentation load vs. indentation depth. In addition, an inverse analysis was performed to extract the viscoelastic parameters of the cell interior phase and the uniqueness of the extraction was assessed.     

Numerical study of the hydrodynamic drag force in atomic force microscopy measurements undertaken in fluids

When atomic force microscopy (AFM) is employed for in vivo study of immersed biological samples, the fluid medium presents additional complexities, not least of which is the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. This force should be considered when interpreting experimental results and any calculated material properties. In this paper, a numerical model is presented to study the influence of the drag force on experimental data obtained from AFM measurements using computational fluid dynamics (CFD) simulation. The model provides quantification of the drag force in AFM measurements of soft specimens in fluids.The numerical predictions were compared with experimental data obtained using AFM with a V-shaped cantilever fitted with a pyramidal tip. Tip velocities ranging from 1.05 to 105 μm/s were employed in water, polyethylene glycol and glycerol with the platform approaching from a distance of 6000 nm. The model was also compared with an existing analytical model. Good agreement was observed between numerical results, experiments and analytical predictions. Accurate predictions were obtained without the need for extrapolation of experimental data. In addition, the model can be employed over the range of tip geometries and velocities typically utilized in AFM measurements.     

Analysis of the induction of the myelin basic protein binding to the plasma membrane phospholipid monolayer

Myelin basic protein(MBP) is an essential structure involved in the generation of central nervous system(CNS)myelin.Myelin shape has been described as liquid crystal structure of biological membrane.The interactions of MBP with monolayers of different lipid compositions are responsible for the multi-lamellar structure and stability of myelin.In this paper,we have designed MBP-incorporated model lipid monolayers and studied the phase behavior of MBP adsorbed on the plasma membrane at the air/water interface by thermodynamic method and atomic force microscopy(AFM).By analyzing the pressure–area(π–A) and pressure–time(π–T) isotherms,univariate linear regression equation was obtained.In addition,the elastic modulus,surface pressure increase,maximal insertion pressure,and synergy factor of monolayers were detected.These parameters can be used to modulate the monolayers binding of protein,and the results show that MBP has the strongest affinity for 1,2-dipalmitoyl-sn-glycero-3-phosphoserine(DPPS) monolayer,followed by DPPC/DPPS mixed and1,2-dipalmitoyl-sn-glycero-3-phospho-choline(DPPC) monolayers via electrostatic and hydrophobic interactions.AFM images of DPPS and DPPC/DPPS mixed monolayers in the presence of MBP(5 n M) show a phase separation texture at the surface pressure of 20 m N/m and the incorporation of MBP put into the DPPC monolayers has exerted a significant effect on the domain structure.MBP is not an integral membrane protein but,due to its positive charge,interacts with the lipid head groups and stabilizes the membranes.The interaction between MBP and phospholipid membrane to determine the nervous system of the disease has a good biophysical significance and medical value.     

Mechanical characteristics of Fe-based coating obtained by nanoindentation

In this study, clad layers of iron-based alloy with a nature of self-fluxing were melted on low carbon steel by plasma cladding process. Nanoindentation with atomic force microscopy (AFM) has been used to investigate the mechanical properties of the coating. Hardness and elastic modulus at ultra-low loads were first determined using the method proposed by Giannakopoulos and Suresh (G&S method). The true contact area and mechanical properties were then determined using atomic force microscopy (AFM) combined with the Oliver and Pharr method (new proposed method) as the correction group. The mechanical properties calculated by the two methods showed the same distribution while had deviation in specific values. The effect of surface roughness to the calculated mechanical properties was investigated. Both hardness and elastic modulus were found to exhibit certain surface roughness dependence. When root mean square (RMS) roughness ranged from 2.2 nm to 4.4 nm, hardness calculated by both the methods increased obviously and reached maximums around 4.1 nm. Elastic modulus calculated by G&S method at different RMS showed the same distribution with that of hardness, while reduced elastic modulus obtained by AFM was insensitive to the range of RMS.     

Ab initio calculations and experimental determination of the structure of Cr2AlC

We have calculated the equilibrium volume and the density of states (DOS) of Cr₂AlC for antiferromagnetic (AFM), ferromagnetic (FM) and paramagnetic (PM) configurations by ab initio total energy calculations. Based on a comparison of the cohesive energies as well as the DOS for all three magnetic configurations we have identified the FM configuration to be metastable. Furthermore, we report the structural characterization of polycrystalline Cr₂AlC thin films grown by magnetron sputtering. Our calculated interplanar distances and equilibrium volume for the PM and AFM configurations are in good agreement with our experiment. The charge density distribution suggests that the chemical bonding between Cr and C in Cr₂AlC is very similar to the one in cubic CrC.     

Theories of surface elasticity for nanoscale objects

The emergence of nanotechnology has driven recent interest in systems having surface atoms as a significant fraction of all atoms present, in particular nano-sheets (ultra-thin slabs), nano-wires, and nano-particles. In these systems, the bulk (i.e. non-surface region or interior) is typically strained in response to the stress of the surface. This elastic strain of the bulk in turn changes the surface lattice constants. Since the bulk and the surface are coupled, the problem must be solved self-consistently. Solving this problem requires a quantitative model of the surface elastic properties which are different from the bulk. In this paper we consider various models that have been proposed for surface elasticity. Our goal is to elucidate the relationship between two contrasting approaches: (1) the Shuttleworth equation which defines a surface stress based on the strain derivative of the surface energy and (2) the Gurtin-Murdoch (GM) theory which considers the surface layer as a membrane with residual strain and with elastic constants different from the bulk. The GM theory is analogous to the 2-D Frenkel-Kontorova (FK) model and can be used to obtain quantitative parameters for the FK model. We present an embedded atom method calculation of the surface elastic constants of Cu(1 1 1) using the GM theory with the surface represented by a membrane one atomic layer thick. This quantitative approach describes the elastic properties of surfaces in a physically appealing way. Just as the bulk elastic constants provide direct information regarding the stress/strain relationship in a bulk material, the surface elastic constants provide similar information for a surface monolayer. This theory will allow elasticity analysis and atomistic calculations of properties of nano-scale objects.     

A first-principles study of the structural and elastic properties of orthorhombic and tetragonal Ca3Mn2O7

The structural and elastic properties of multiferroic Ca3Mn2O7 with ferroelectric orthorhombic （O-phase） and paraelectric tetragonal structures （T-phase） have been studied by first-principles calculations within the generalized gradient approximation （GGA） and the GGA plus Hubbard U approaches （GGA ＋ U）. The calculated theoretical structures are in good agreement with the experimental values. The T-phase is found to be antiferromagnetic （AFM） and the AFM O-phase is more stable than the T-phase, which also agree with the experiments. On these bases, the single-crystal elastic constants （Cijs） and elastic properties of polycrystalline aggregates are investigated for the two phases. Our elasticity calculations indicate Ca3Mn2O7 is mechanically stable against volume expansions. The AFM O-phase is found to be a ductile material, while the AFM T-phase shows brittle nature and tends to be elastically isotropic. We also investigate the influence of strong correlation effects on the elastic properties, qualitatively consistent results are obtained in a reasonable range of values of U. Finally, the ionicity is discussed by Bader analysis. Our work provides useful guidance for the experimental elasticity measurements of Ca3Mn2O7, and makes the strain energy calculation in multiferroic Ca3Mn2O7 thin films possible.     

Thermodynamics and elastic properties of Ta from first-principles calculations

<正>Within the framework of the quasiharmonic approximation,the thermodynamics and elastic properties of Ta, including phonon density of states(DOS),equation of state,linear thermal expansion coefficient,entropy,enthalpy, heat capacity,elastic constants,bulk modulus,shear modulus,Young’s modulus,microhardness,and sound velocity, are studied using the first-principles projector-augmented wave method.The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and the Debye model.The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS.By comparing the experimental results with the calculation results from the first-principles and the Debye model,it is found that the thermodynamic properties of Ta are depicted well by the first-principles.The elastic properties of Ta from the first-principles are consistent with the available experimental data.     

MgSiO3钙钛矿高温高压特性的第一性原理研究

本文采用第一性原理方法,计算了MgSiO3钙钛矿在零温和0 ~ 150 GPa静水压范围内的晶体结构和弹性模量,并利用准简谐近似Debye模型,拟合三阶Birch-Murnaghan物态方程得到了其高温高压下的热力学性质。通过与现有的理论和实验的结果数据比较,确认在0 ~ 2000 K的温度区间内,第一性原理计算结合Debye模型能够较可靠地模拟在下地幔压力范围内MgSiO3钙钛矿的热力学性质。     

MgSiO_3钙钛矿高温高压特性的第一性原理研究

本文采用第一性原理方法,计算了MgSiO_3钙钛矿在零温和0～150 GPa静水压范围内的晶体结构和弹性模量,并利用准简谐近似Debye模型,拟合三阶Birch-Murnaghan物态方程得到了其高温高压下的热力学性质.通过与现有的理论和实验的结果数据比较,确认在0～2000 K的温度区间内,第一性原理计算结合Debye模型能够较可靠地模拟在下地幔压力范围内MgSiO_3钙钛矿的热力学性质.     

Domain structures of phospholipid monolayer Langmuir-Blodgett films determined by atomic force microscopy

Atomic Force Microscopy (AFM) has been used to show the formation of solid-phase domains from fluid-phase domains on compression of DiPalmitoyl-PhosphatidylCholine (DPPC) monolayer Langmuir-Blodgett (LB) films. The chiral structures on the solid substrates were observed for the first time. By applying the friction force technique, we were able to distinguish the different regions of LB films according to their elastic properties. The influence of rates of compression on the domain shape as well as the microstructure within the domain were also studied.     

Measurement of nanomechanical properties of biomolecules using atomic force microscopy

The capabilities of atomic force microscopy (AFM) have been rapidly expanding beyond topographical imaging to now allow for the analysis of a wide range of properties of diverse materials. The technique of nanoindentation, traditionally performed via dedicated indenters can now be reliably achieved using AFM instrumentation, enabling mechanical property determination at the nanoscale using the high spatial and force resolutions of the AFM. In the study of biological systems, from biomolecules to complexes, this technique provides insight into how mesoscale properties and functions may arise from a myriad of single biomolecules. In vivo and in situ analyses of native structures under physiological conditions as well as the rapid analysis of molecular species under a variety of experimental treatments are made possible with this technique. As a result, AFM nanoindentation has emerged as a critical tool for the study of biological systems in their natural state, further contributing to both biomaterial design and pharmacological research. In this review, we detail the theory and progression of AFM-based nanoindentation, and present several applications of this technique as it has been used to probe biomolecules and biological nanostructures from single proteins to complex assemblies. We further detail the many challenges associated with mechanical models and required assumptions for model validity. AFM nanoindentation capabilities have provided an excellent improvement over conventional nanomechanical tools and by integration of topographical data from imaging, enabled the rapid extraction and presentation of mechanical data for biological samples.     

原子力显微镜在轻敲模式下的动力学模型

基于Hamaker假设、Lennard-Jones势能定律及经典弹性理论建立了一种新型的球体与平面黏着接触的弹性模型，该模型显示黏着力在原子力显微镜(AFM)针尖趋近和撤离样品表面，即加载和卸载的两个过程中存在黏着滞后现象，表明了AFM在轻敲工作模式中存在能量耗散.同时，根据所建的黏着接触弹性模型，建立了AFM在轻敲工作模式下的动力学模型，研究了AFM在轻敲工作模式下的振动幅度、相位差及耗散功率随针尖与样品表面间距的变化规律，仿真结果与现有的实验结果相一致.     

Probing the impact of loading rate on the mechanical properties of viral nanoparticles

The effects of changes in the loading rate during the forced dissociation of single bonds have been studied for a wide variety of interactions. Less is known on the loading rate dependent behaviour of more complex systems that consist of multiple bonds. Here we focus on viral nanoparticles, in particular the protein shell (capsid) that protects the viral genome. As model systems we use the well-studied capsids of the plant virus Cowpea Chlorotic Mottle Virus (CCMV) and of the bacteriophages φ29 and HK97. By applying an atomic force microscopy (AFM) nanoindentation approach we study the loading rate dependency of their mechanical properties. Our AFM results show very diverse behaviour for the different systems. In particular, we find that not only the breaking force, but also the spring constant of some capsids depend on the loading rate. We describe and compare the measured data with simulation results from the literature. The unexpected complex loading rate dependencies that we report present a challenge for the current theoretical considerations aimed at understanding the molecular level interactions of highly ordered protein assemblies.     

Detection of lipopolysaccharide induced inflammatory responses in RAW264.7 macrophages using atomic force microscope

In recent years, LPS activated RAW264.7 cells are widely used as an in vitro inflammatory model for the screen of effective anti-inflammation drugs and the investigation of exact anti-inflammation mechanism of these drugs. But up to now, there are few data about the effect of LPS on the morphology, especially on the membrane ultrastructure and bio-mechanical properties of RAW264.7 macrophages. In this work, the topographical and biophysical changes of RAW264.7 macrophages upon LPS stimulation are detected by high resolution atomic force microscopy (AFM). The AFM results suggested that LPS activated RAW264.7 macrophages changed to be much bigger than control cells with some holes emerged on cell surface. The size of membrane protein clusters and the roughness of membrane significantly increased after LPS exposure. In addition, the AFM force measurement results demonstrated that LPS stimulation increased the adhesion force of RAW264.7 macrophages, and also increased the stiffness of RAW264.7 macrophages, which were attributed to the re-distribution of intracellular F-actin structures induced by LPS. These findings suggested that LPS stimulation could also induce the pathophysiological changes of RAW264.7 macrophages, which would benefit our understanding of the inflammatory processes in macrophages upon pathogen stimulation at nano-scale.     

Study of phase transformation and elastic properties of ThX (X = N,P, As and Sb) under high-pressure

An improved interaction potential model (IIPM) has been formulated to theoretically predict the pressure induced phase transition, elastic properties and thermophysical properties of thorium monopnictides (ThX; X = N, P, As and Sb). The phase transition pressures and volume drop obtained from this model show a better agreement with the available experimental than theoretical results. We have achieved elastic moduli, anisotropy factor, Poisson's ratio, Kleinman parameter, shear and stiffness constants on the basis of the calculated elastic constants. To know the anharmonic properties, we have also computed the third-order elastic constants, first-order pressure derivatives of second-order elastic constants and thermophysical quantities. Our results are in reasonable agreement with available measured and others reported data which supports the validity of model.     

TiCN/TiNbCN multilayer coatings with enhanced mechanical properties

Enhancement of mechanical properties by using a TiCN/TiNbCN multilayered system with different bilayer periods (Λ) and bilayer numbers (n) via magnetron sputtering technique was studied in this work. The coatings were characterized in terms of structural, chemical, morphological and mechanical properties by X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and nanoindentation. Results of the X-ray analysis showed reflections associated to FCC (1 1 1) crystal structure for TiCN/TiNbCN films. AFM analysis revealed a reduction of grain size and roughness when the bilayer number is increased and the bilayer period is decreased. Finally, enhancement of mechanical properties was determined via nanoindentation measurements. The best behavior was obtained when the bilayer period (Λ) was 15 nm (n = 200), yielding the highest hardness (42 GPa) and elastic modulus (408 GPa). The values for the hardness and elastic modulus are 1.6 and 1.3 times greater than the coating with n = 1, respectively. The enhancement effects in multilayer coatings could be attributed to different mechanisms for layer formation with nanometric thickness due to the Hall-Petch effect; because this effect, originally used to explain the increase in hardness with decreasing grain size in bulk polycrystalline metals, has also been used to explain hardness enhancements in multilayers taking into account the thickness reduction at individual single layers that make the multilayered system. The Hall-Petch model based on dislocation motion within layers and across layer interfaces, has been successfully applied to multilayers to explain this hardness enhancement.     

Glasslike elastic properties in the ω-β alloys

We have measured the internal friction and speed of sound in several polycrystalline alloys, using compound torsional oscillators at frequencies between 60 kHz and 100 kHz and temperatures between 50 mK and 100 K. By combining these data with existing elastic and thermal data on similar alloys, we find that those alloys which can undergo diffusionsless phase transitions, such as Ti:Nb, Ti:V, or Zr:Nb in certain ranges of composition have glasslike excitations, since they have elastic properties which agree in magnitude and temperature dependence with those of amorphous solids. By contrast. crystalline continuous solution alloys, such as Nb:Ta, or alloys with diffusive phase transitions, such as high-pressure quenched Al₉₄Si₆, have the same elastic properties as are known for crystals.     

Thermo-mechanical properties of the cell surface assessed by atomic force microscopy

Atomic force microscopy (AFM) in lateral force mode was applied to assess the microscale thermo-mechanical (frictional) properties of the air-dried cell surface in the wide temperature range (288-363K/15-90°C). AFM-investigated cell surface layer can be represented as a biocomposite composed of several layers including the glycocalyx, the membrane and the intercellular layer containing membrane (cortical) cytoskeleton. The cells with two different cytoskeleton structures, erythrocytes and thymocytes, were studied. Above a certain temperature (T(g)), the significant change in friction force with temperature was revealed for the both cell types whereas there was no similar change in their topography parameters. The experimentally determined value T(g) for erythrocyte samples was lower than that for thymocyte ones. Treating living cells with the cross-linking agent, glutaraldehyde, led to the weakening of the temperature dependence of air-dried cell surface frictional properties in the studied temperature range. Addition of oxidizing agent, peroxynitrite, to living cell suspensions changed the temperature dependence of air-dried cell surface frictional properties depending on cell type and peroxynitrite concentration. The obtained data indicate that the study of thermo-mechanical properties of air-dried cells with AFM in lateral force mode provides expanded information on the structural characteristics of the living cell surface layer, and sets the stage for the development of AFM-based method (with using a lateral force mode) for the cell pathology diagnostics.