Electrokinetic transport of heterogeneous particles in suspension

The Smoluchowski equation for electrophoresis predicts that the electrophoretic velocity of a particle is proportional to its zeta potential but not its size, shape, or orientation. Furthermore, the equation predicts that the rotation rate is identically zero. The Smoluchowski equation fails for heterogeneous particles (i.e., those with nonuniform zeta potentials). Recent theories and experiments show that particles with a dipole moment of zeta potential rotate into alignment with an externally applied electric field. For doublets (particles composed of two spheres) the rotation rate depends on (1) whether the spheres are rigidly rocked or freely rotating, and (2) the gap distance between the spheres. The relative configuration of two coagulated spheres is determined by the colloidal forces of the system. The goal of our research is to use measurements of electrophoretic rotation to determine the gap between two spheres of a colloidal doublet and also to determine whether or not the doublet is rigid

A Mathematical Model of Liver Cell Aggregation In Vitro

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work

Automated Force Volume Image Processing for Biological Samples

Atomic force microscopy (AFM) has now become a powerful technique for investigating on a molecular level, surface forces, nanomechanical properties of deformable particles, biomolecular interactions, kinetics, and dynamic processes. This paper specifically focuses on the analysis of AFM force curves collected on biological systems, in particular, bacteria. The goal is to provide fully automated tools to achieve theoretical interpretation of force curves on the basis of adequate, available physical models. In this respect, we propose two algorithms, one for the processing of approach force curves and another for the quantitative analysis of retraction force curves. In the former, electrostatic interactions prior to contact between AFM probe and bacterium are accounted for and mechanical interactions operating after contact are described in terms of Hertz-Hooke formalism. Retraction force curves are analyzed on the basis of the Freely Jointed Chain model. For both algorithms, the quantitative reconstruction of force curves is based on the robust detection of critical points (jumps, changes of slope or changes of curvature) which mark the transitions between the various relevant interactions taking place between the AFM tip and the studied sample during approach and retraction. Once the key regions of separation distance and indentation are detected, the physical parameters describing the relevant interactions operating in these regions are extracted making use of regression procedure for fitting experiments to theory. The flexibility, accuracy and strength of the algorithms are illustrated with the processing of two force-volume images, which collect a large set of approach and retraction curves measured on a single biological surface. For each force-volume image, several maps are generated, representing the spatial distribution of the searched physical parameters as estimated for each pixel of the force-volume image

Combined numerical and experimental biomechanical characterization of soft collagen hydrogel substrate.

This work presents a combined experimental-numerical framework for the biomechanical characterization of highly hydrated collagen hydrogels, namely with 0.20, 0.30 and 0.40 % (by weight) of collagen concentration. Collagen is the most abundant protein in the extracellular matrix of animals and humans. Its intrinsic biocompatibility makes collagen a promising substrate for embedding cells within a highly hydrated environment mimicking natural soft tissues. Cell behaviour is greatly influenced by the mechanical properties of the surrounding matrix, but the biomechanical characterization of collagen hydrogels has been challenging up to now, since they present non-linear poro-viscoelastic properties. Combining the stiffness outcomes from rheological experiments with relevant literature data on collagen permeability, poroelastic finite element (FE) models were developed. Comparison between experimental confined compression tests available in the literature and analogous FE stress relaxation curves showed a close agreement throughout the tests. This framework allowed establishing that the dynamic shear modulus of the collagen hydrogels is between 0.0097 ± 0.018 kPa for the 0.20 % concentration and 0.0601 ± 0.044 kPa for the 0.40 % concentration. The Poisson's ratio values for such conditions lie within the range of 0.495-0.485 for 0.20 % and 0.480-0.470 for 0.40 %, respectively, showing that rheology is sensitive enough to detect these small changes in collagen concentration and thus allowing to link rheology results with the confined compression tests. In conclusion, this integrated approach allows for accurate constitutive modelling of collagen hydrogels. This framework sets the grounds for the characterization of related hydrogels and to the use of this collagen parameterization in more complex multiscale models

Cell traction forces on soft biomaterials. I. Microrheology of type I collagen gels.

A laser-trap microrheometry technique was used to determine the local shear moduli of Type I collagen gels. Embedded 2.1 microm polystyrene latex particles were displaced 10-100 nm using a near-infrared laser trap with a trap constant of 0.0001 N/m. The trap was oscillated transversely +/- 200 nm using a refractive glass plate mounted on a galvanometric scanner. The displacement of the microspheres was in phase with the movement of the laser trap at frequencies less than 1 rad/s, indicating that at least locally, the gels behaved as elastic media. The local shear modulus was measured at various positions throughout the gel, and, for gels at 2.3 mg/mL and 37 degrees C, values ranged from G = 3 to 80 Pa. The average shear modulus G = 55 Pa, which compares well with measurements from parallel plate rheometry