A Novel Method for Localizing Reporter Fluorescent Beads Near the Cell Culture Surface for Traction Force Microscopy

PA gels have long been used as a platform to study cell traction forces due to ease of fabrication and the ability to tune their elastic properties. When the substrate is coated with an extracellular matrix protein, cells adhere to the gel and apply forces, causing the gel to deform. The deformation depends on the cell traction and the elastic properties of the gel. If the deformation field of the surface is known, surface traction can be calculated using elasticity theory. Gel deformation is commonly measured by embedding fluorescent marker beads uniformly into the gel. The probes displace as the gel deforms. The probes near the surface of the gel are tracked. The displacements reported by these probes are considered as surface displacements. Their depths from the surface are ignored. This assumption introduces error in traction force evaluations. For precise measurement of cell forces, it is critical for the location of the beads to be known. We have developed a technique that utilizes simple chemistry to confine fluorescent marker beads, 0.1 and 1 µm in diameter, in PA gels, within 1.6 μm of the surface. We coat a coverslip with poly-D-lysine (PDL) and fluorescent beads. PA gel solution is then sandwiched between the coverslip and an adherent surface. The fluorescent beads transfer to the gel solution during curing. After polymerization, the PA gel contains fluorescent beads on a plane close to the gel surface.     

Investigation of Preparation and Mechanisms of a Dispersed Particle Gel Formed from a Polymer Gel at Room Temperature

A dispersed particle gel (DPG) was successfully prepared from a polymer gel at room temperature. The polymer gel system, morphology, viscosity changes, size distribution, and zeta potential of DPG particles were investigated. The results showed that zirconium gel systems with different strengths can be cross-linked within 2.5 h at low temperature. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), and atomic force microscopy (AFM) results showed that the particles were polygonal particles with nano-size distribution. According to the viscosity changes, the whole preparation process can be divided into two major stages: the bulk gel cross-linking reaction period and the DPG particle preparation period. A polymer gel with a 3-dimensional network was formed in the bulk gel cross-linking reaction period whereas shearing force and frictional force were the main driving forces for the preparation of DPG particles, and thus affected the morphology of DPG particles. High shearing force and frictional force reduced the particle size distribution, and then decreased the zeta potential (absolute value). The whole preparation process could be completed within 3 h at room temperature. It could be an efficient and energy-saving technology for preparation of DPG particles.     

Validation of the Boussinesq equation for use in traction field determination

Cell traction force plays an important role in many biological processes. Several traction force microscopy methods have been developed to determine cell traction forces based on the Boussinesq solution. This approach, however, is rooted in a half-space assumption. The purpose of this study was to determine the error induced in the half-space assumption using a finite element method (FEM). It demonstrates that displacement error between the FEM and the Boussinesq equation can be used to measure the accuracy of the Boussinesq equation, although singularity exists in the loading point. For one concentrated force, significant difference between the FEM and the Boussinesq equation occurs in the whole field; this difference decreases with an increase in the plate thickness. However, in the case of the balanced forces, the offset of the balanced forces decreases the errors in the middle area. Overall, this study demonstrates that increasing the thickness of the polyacrylamide gel is important for reducing the error of the Boussinesq equation when determining the displacement field of the gel under loads.     

Modeling sickle hemoglobin fibers as one chain of coarse-grained particles

Sickle cell disease (SCD) is caused by a single point mutation in the beta-chain hemoglobin gene, resulting in the presence of abnormal hemoglobin S (HbS) in the patients' red blood cells (RBCs). In the deoxygenated state, the defective hemoglobin tetramers polymerize forming stiff fibers which distort the cell and contribute to changes in its biomechanical properties. Because the HbS fibers are essential in the formation of the sickle RBC, their material properties draw significant research interests. Here, a solvent-free coarse-grain molecular dynamics (CGMD) model is introduced to simulate single HbS fibers as a chain of particles. First, we show that the proposed model is able to efficiently simulate the mechanical behavior of single HbS fibers. Then, the zippering process between two HbS fibers is studied and the effect of depletion forces is investigated. Simulation results illustrate that depletion forces play a role comparable to direct fiber-fiber interaction via Van der Waals forces. This proposed model can greatly facilitate studies on HbS polymerization, fiber bundle and gel formation as well as interaction between HbS fiber bundles and the RBC membrane.     

Force Generation by Endocytic Actin Patches in Budding Yeast

Membrane deformation during endocytosis in yeast is driven by local, templated assembly of a sequence of proteins including polymerized actin and curvature-generating coat proteins such as clathrin. Actin polymerization is required for successful endocytosis, but it is not known by what mechanisms actin polymerization generates the required pulling forces. To address this issue, we develop a simulation method in which the actin network at the protein patch is modeled as an active gel. The deformation of the gel is treated using a finite-element approach. We explore the effects and interplay of three different types of force driving invagination: 1), forces perpendicular to the membrane, generated by differences between actin polymerization rates at the edge of the patch and those at the center; 2), the inherent curvature of the coat-protein layer; and 3), forces parallel to the membrane that buckle the coat protein layer, generated by an actomyosin contractile ring. We find that with optimistic estimates for the stall stress of actin gel growth and the shear modulus of the actin gel, actin polymerization can generate almost enough force to overcome the turgor pressure. In combination with the other mechanisms, actin polymerization can the force over the critical value.     

Squeezing flows of vaginal gel formulations relevant to microbicide drug delivery

Efficacy of topical microbicidal drug delivery formulations against HIV depends in part on their ability to coat, distribute, and be retained on epithelium. Once applied to the vagina, a formulation is distributed by physical forces including: gravity, surface tension, shearing, and normal forces from surrounding tissues, i.e., squeezing forces. The present study focused on vaginal microbicide distribution due to squeezing forces. Mathematical simulations of squeezing flows were compared with squeezing experiments, using model vaginal gel formulations. Our objectives were: (1) to determine if mathematical simulations can accurately describe squeezing flows of vaginal gel formulations; (2) to find the best model and optimized parameter sets to describe these gels; and (3) to examine vaginal coating due to squeezing using the best models and summary parameters for each gel. Squeezing flow experiments revealed large differences in spreadability between formulations, suggesting different coating distributions in vivo. We determined the best squeezing flow models and summary parameters for six test gels of two compositions, cellulose and polyacrylic acid (PAA). We found that for some gels it was preferable to deduce model input parameters directly from squeezing flow experiments. For the cellulose gels, slip conditions in squeezing flow experiments needed to be evaluated. For PAA gels, we found that in the absence of squeezing experiments, rotational viscometry measurements (to determine Herschel-Bulkley parameters) led to reasonably accurate predictions of squeezing flows. Results indicated that yield stresses may be a strong determinant of squeezing flow mechanics. This study serves as a template for further investigations of other gels and determination of which sources of rheological data best characterize potential microbicidal formulations. These mathematical simulations can serve as useful tools for exploring drug delivery parameters, and optimizing formulations, prior to costly clinical trials.     

Preparative protein purification on underivatized silica

This article describes the use of underivatized silica gel as a preparative stationary phase for process purification of proteins. Although silica has been frequently used as a stationary phase backbone matrix, direct adsorption of proteins on underivatized silica has not been widely exploited for industrial applications. In this study an effort was made to fundamentally understand the interaction mechanisms between a protein and silica surface by using several proteins with a wide range of isoelectric points (pIs) and surface hydrophobicity. Interactions in silica were found to be largely dominated by a combination of ionic and hydrophobic forces. Accordingly, a predictive model was derived for describing linear retention of proteins on silica. Finally, a case study is described investigating the role of silica in an industrial purification process. It was found that the integration of the two modes of interaction confers silica with a unique selectivity that can be very effectively utilized in downstream bioprocessing.     

Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Balanced mechanical forces and microtubule contribution to fibroblast contraction

Fibroblast locomotion is thought to generate tractional forces which lead to contraction and reorganisation of collagen in tissue development and repair. A culture force monitor device (CFM) was used to measure changes in force in fibroblast populated collagen lattices, which resulted from cytoskeletal reorganisation by cytochalasin B, colchicine, vinblastine, and taxol. Microfilament disruption abolished contraction forces, microtubule disruption elicited a new peak of contraction, while taxol stabilisation of microtubules produced a gradual fall in measured force across the collagen gel. Based on these measurements, it is suggested that the cell can be viewed as an engineering structure in which residual intracellular forces, from contractile microfilaments, exert compressive loading on microtubular elements. This microtubular structure appears to act as a “balanced space frame” (analogous to an aeroplane chassis), maintaining cell shape and consequently storing a residual internal tension (RIT). In dermal fibroblasts this hidden RIT was up to 33% of the measurable force exerted on the collagen gel. Phenotypic differences between space frame organisation and RIT levels could explain site and pathological variations in fibroblast contraction. © 1996 Wiley-Liss, Inc.     

Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command

This paper provides an overview of forward dynamic neuromusculoskeletal modeling. The aim of such models is to estimate or predict muscle forces, joint moments, and/or joint kinematics from neural signals. This is a four-step process. In the first step, muscle activation dynamics govern the transformation from the neural signal to a measure of muscle activation-a time varying parameter between 0 and 1. In the second step, muscle contraction dynamics characterize how muscle activations are transformed into muscle forces. The third step requires a model of the musculoskeletal geometry to transform muscle forces to joint moments. Finally, the equations of motion allow joint moments to be transformed into joint movements. Each step involves complex nonlinear relationships. The focus of this paper is on the details involved in the first two steps, since these are the most challenging to the biomechanician. The global process is then explained through applications to the study of predicting isometric elbow moments and dynamic knee kinetics.     

Effect of the phase state of lipids on their interaction with cobra cytotoxin

Interaction between cytotoxin of the Central Asia cobra venom and dimiristoylphosphatidylcholine bilayer depending on its phase state was studied by ESR with spin label. A conclusion can be drawn that the efficiency of cytotoxin effect on the membranes depends on their phase state. Cytotoxin molecules are incorporated into myophile region of the bilayer, only if the latter is in the liquid crystal state. The interaction between cytotoxins and lipids of the bilayer in a gel state is in the main conditioned by electrostatic forces.     

Lateral forces acting between particles in liquid films or lipid membranes

To investigate the mechanism of formation of 2D arrays of protein macromolecules in liquid films we carried out model experiments with μm-sized latex particles. The direct observations revealed that the process of ordering is triggered by attractive lateral capillary forces due to the overlap of the menisci formed around the particles. Two types of lateral capillary forces, flotation and immersion, can be distinguished, and a theory of these interactions is developed. Similar forces are operative between inclusions (proteins) incorporated in lipid membranes. We develop an appropriate model of a lipid bilayer, which is described as an elastic layer (the hydrocarbon chain region) sandwiched between two Gibbs dividing surfaces (the two headgroup regions). The range of the interaction between two cylindrical inclusions turns out to be of the order of several inclusion radii. The results, which are in qualitative agreement with the experimental observations, can be applied to the interpretation of membrane processes and mechanisms such as protein aggregation in lipid membranes.     

The gel matrix of gastric mucus is maintained by a complex interplay of transient and nontransient associations

The gel nature of mucus is fundamental to its physiological functions; however, the structure of the mucus gel matrix is unclear. Here, small and large deformation rheology has been used to investigate the physical nature of the gel matrix and the forces that maintain this matrix in pig gastric mucus. The gelation process in mucus has been shown to be comparable with that of other polymer gel systems. Nongelling portions of mucin have been identified within the gel network, and the importance of transient, relaxable interactions to the maintenance of the mucus gel matrix has been demonstrated. The structure of the mucus gel matrix is considered in relation to the functional properties of mucus gels.     

Melting behaviour of schizophyllan extracellular polysaccharide gels in the temperature range between 5 and 20°C

Gels of the glucan schizophyllan, consisting of a 1,3-β- -linked backbone of glucose residues with 1,6-β- -glucosyl side groups, were found to show melting behaviour in the temperature range between 5 and 20°C, depending on the glucose concentration in the solvent (0–50 wt% glucose). While the qualitative features of the modulus-versus-concentration and modulus-versus-temperature rheological data for the gels can be modelled using modified cascade theory (which implicitly assumes that no sub-level of organisation exists in the gel structure), a consistent quantitative fit cannot be achieved. The inconsistencies found are consistent with the idea that the gel is composed of bundles (consisting of many triple helices of schizophyllan) with strong intra-bundle attraction and weak inter-bundle forces. Transmission Electron Microscopy (TEM) micrographs of diluted samples indicate that schizophyllan polymers engage in lateral aggregation of triple helical strands at temperatures below the melting temperature, suggesting that indeed bundles of polymers will be present in the gel state.     

Proteomics: quantitative and physical mapping of cellular proteins

Genome sequencing provides a wealth of information on predicted gene products (mostly proteins), but the majority of these have no known function. Two-dimensional gel electrophoresis and mass spectrometry have, coupled with searches in protein and EST databases, transformed the protein-identification process. The proteome is the expressed protein complement of a genome and proteomics is functional genomics at the protein level. Proteomics can be divided into expression proteomics, the study of global changes in protein expression, and cell-map proteomics, the systematic study of protein-protein interactions through the isolation of protein complexes.     

Traction Force Measurements of Human Aortic Smooth Muscle Cells Reveal a Motor-Clutch Behavior

The contractile behavior of smooth muscle cells (SMCs) in the aorta is an important determinant of growth, remodeling, and homeostasis. However, quantitative values of SMC basal tone have never been characterized precisely on individual SMCs. Therefore, to address this lack, we developed an in vitro technique based on Traction Force Microscopy (TFM). Aortic SMCs from a human lineage at low passages (4-7) were cultured 2 days in conditions promoting the development of their contractile apparatus and seeded on hydrogels of varying elastic modulus (1, 4, 12 and 25 kPa) with embedded fluorescent microspheres. After complete adhesion, SMCs were artificially detached from the gel by trypsin treatment. The microbeads movement was tracked and the deformation fields were processed with a mechanical model, assuming linear elasticity, isotropic material, plane strain, to extract the traction forces formerly applied by individual SMCs on the gel. Two major interesting and original observations about SMC traction forces were deduced from the obtained results: 1. they are variable but driven by cell dynamics and show an exponential distribution, with 40% to 80% of traction forces in the range 0-10 μN. 2. They depend on the substrate stiffness: the fraction of adhesion forces below 10 μN tend to decrease when the substrate stiffness increases, whereas the fraction of higher adhesion forces increases. As these two aspects of cell adhesion (variability and stiffness dependence) and the distribution of their traction forces can be predicted by the probabilistic motor-clutch model, we conclude that this model could be applied to SMCs. Further studies will consider stimulated contractility and primary culture of cells extracted from aneurysmal human aortic tissue.     

Maternal bodies, breast-feeding, and consumer desire in urban China

Urban Chinese women in the 1990s formulated their infant-feeding decisions in the context of a society undergoing radical transformation as the nation moved from a centrally planned socialist economy to a global, market-oriented one. Narratives of new mothers in Beijing in the 1990s provide insights into the multiple forces that shaped their infant-feeding practices. These personal histories also illustrate the limitations of multilateral breast-feeding programs that emphasize breast-feeding as a natural interaction between mother and infant. The cases I present here demonstrate instead that the material, bodily manifestations of breast-feeding require nursing mothers to continually renegotiate relations with husbands, coworkers, and family. Chinese women's accounts also add insight to theoretical deliberations on gender and the body, for they demonstrate that cultural expectations and the demands of the lactating body must be considered to understand fully the process of women's decisions in a social and not strictly reproductive context. On a larger scale, the data also illustrate how global intervention, in the form of the WHO-UNICEF-sponsored Baby-Friendly Hospital Initiative, promotes breast-feeding as a woman's primary duty at the same time that market forces counter this message as women redefine their individual expectations and social relationships.     

Self-association studies on the EphB2 receptor SAM domain using analytical ultracentrifugation

The self-association behavior of the Eph-kinases SAM domain has been studied in phosphate buffer, pH 7.4, containing 0.14 M NaCl using concentration-dependent sedimentation equilibrium experiments. Only weak interactions typical for a monomer-dimer equilibrium up to at least 12 mg/mL were observed. Such concentrated solutions require a consideration of the non-ideality expressed by virial coefficients. A special centrifuge equation was used for the global analysis to estimate equilibrium constants based on the thermodynamic activities of the reactants. When neglecting this, the parameters deviate by about 20%. Association constants for dimerization of the EphB2-SAM domain vary between 163 M(-1) at 10 degrees C and 395 M(-1) at 32 degrees C, indicating hydrophobic forces are involved in the dimerization process. In solutions of about 12 mg/mL, less than 50% dimers are in solution and higher oligomers can be excluded.     

Intriguing effects of selection intensity on the evolution of prosocial behaviors

In many models of evolving populations, genetic drift has an outsized role relative to natural selection, or vice versa. While there are many scenarios in which one of these two assumptions is reasonable, intermediate balances between these forces are also biologically relevant. In this study, we consider some natural axioms for modeling intermediate selection intensities, and we explore how to quantify the long-term evolutionary dynamics of such a process. To illustrate the sensitivity of evolutionary dynamics to drift and selection, we show that there can be a “sweet spot” for the balance of these two forces, with sufficient noise for rare mutants to become established and sufficient selection to spread. This balance allows prosocial traits to evolve in evolutionary models that were previously thought to be unconducive to the emergence and spread of altruistic behaviors. Furthermore, the effects of selection intensity on long-run evolutionary outcomes in these settings, such as when there is global competition for reproduction, can be highly non-monotonic. Although intermediate selection intensities (neither weak nor strong) are notoriously difficult to study analytically, they are often biologically relevant; and the results we report suggest that they can elicit novel and rich dynamics in the evolution of prosocial behaviors.