The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Three-dimensional tracking of motile bacteria near a solid planar surface.

Knowing how motile bacteria move near and along a solid surface is crucial to understanding such diverse phenomena as the migration of infectious bacteria along a catheter, biofilm growth, and the movement of bacteria through the pore spaces of saturated soil, a critical step in the in situ bioremediation of contaminated aquifers. In this study, a tracking microscope is used to record the three-dimensional motion of Escherichia coli near a planar glass surface. Data from the tracking microscope are analyzed to quantify the effects of bacteria-surface interactions on the swimming behavior of bacteria. The speed of cells approaching the surface is found to decrease in agreement with the mathematical model of Ramia et al. [Ramia, M., Tullock, D. L. & Phan-Tien, N. (1993) Biophys J. 65,755-778], which represents the bacteria as spheres with a single polar flagellum rotating at a constant rate. The tendency of cells to swim adjacent to the surface is shown in computer-generated reproductions of cell traces. The attractive interaction potential between the cells and the solid surface is offered as one of several possible explanations for this tendency.

Effect of cellular filamentation on adventurous and social gliding motility of Myxococcus xanthus

Filamentous bacterial cells often provide biological information that is not readily evident in normal-size cells. In this study, the effect of cellular filamentation on gliding motility of Myxococcus xanthus, a Gram-negative social bacterium, was investigated. Elongation of the cell body had different effects on adventurous and social motility of M. xanthus. The rate of A-motility was insensitive to cell-body elongation whereas the rate of S-motility was reduced dramatically as the cell body got longer, indicating that these two motility systems work in different ways. The study also showed that filamentous wild-type cells glide smoothly with relatively straight, long cell bodies. However, filamentous cells of certain social motility mutants showed zigzag, tangled cell bodies on a solid surface, apparently a result of a lack of coordination between different fragments within the filaments. Further genetic and biochemical analyses indicated that the uncoordinated movements of these mutant filaments were correlated with the absence of cell surface fibril materials, indicating a possible new function for fibrils.

Unbinding process of adsorbed proteins under external stress studied by atomic force microscopy spectroscopy

We report the study of the dynamics of the unbinding process under a force load f of adsorbed proteins (fibrinogen) on a solid surface (hydrophilic silica) by means of atomic force microscopy spectroscopy. By varying the loading rate rf, defined by f = rf t, t being the time, we find that, as for specific interactions, the mean rupture force increases with rf. This unbinding process is analyzed in the framework of the widely used Bell model. The typical dissociation rate at zero force entering in the model lies between 0.02 and 0.6 s−1. Each measured rupture is characterized by a force f0, which appears to be quantized in integer multiples of 180–200 pN.

A peptide that inhibits hydroxyapatite growth is in an extended conformation on the crystal surface

Proteins play an important role in the biological mechanisms controlling hard tissue development, but the details of molecular recognition at inorganic crystal interfaces remain poorly characterized. We have applied a recently developed homonuclear dipolar recoupling solid-state NMR technique, dipolar recoupling with a windowless sequence (DRAWS), to directly probe the conformation of an acidic peptide adsorbed to hydroxyapatite (HAP) crystals. The phosphorylated hexapeptide, DpSpSEEK (N6, where pS denotes phosphorylated serine), was derived from the N terminus of the salivary protein statherin. Constant-composition kinetic characterization demonstrated that, like the native statherin, this peptide inhibits the growth of HAP seed crystals when preadsorbed to the crystal surface. The DRAWS technique was used to measure the internuclear distance between two 13C labels at the carbonyl positions of the adjacent phosphoserine residues. Dipolar dephasing measured at short mixing times yielded a mean separation distance of 3.2 ± 0.1 Å. Data obtained by using longer mixing times suggest a broad distribution of conformations about this average distance. Using a more complex model with discrete α-helical and extended conformations did not yield a better fit to the data and was not consistent with chemical shift analysis. These results suggest that the peptide is predominantly in an extended conformation rather than an α-helical state on the HAP surface. Solid-state NMR approaches can thus be used to determine directly the conformation of biologically relevant peptides on HAP surfaces. A better understanding of peptide and protein conformation on biomineral surfaces may provide design principles useful for the modification of orthopedic and dental implants with coatings and biological growth factors that are designed to enhance biocompatibility with surrounding tissue.

Structural changes in hemoglobin during adsorption to solid surfaces: Effects of pH, ionic strength, and ligand binding

We have studied the adsorption of two structurally similar forms of hemoglobin (met-Hb and HbCO) to a hydrophobic self-assembled methyl-terminated thiol monolayer on a gold surface, by using a Quartz Crystal Microbalance (QCM) technique. This technique allows time-resolved simultaneous measurements of changes in frequency (f) (c.f. mass) and energy dissipation (D) (c.f. rigidity/viscoelastic properties) of the QCM during the adsorption process, which makes it possible to investigate the viscoelastic properties of the different protein layers during the adsorption process. Below the isoelectric points of both met-Hb and HbCO, the ΔD vs. Δf graphs displayed two phases with significantly different slopes, which indicates two states of the adsorbed proteins with different visco-elastic properties. The slope of the first phase was smaller than that of the second phase, which indicates that the first phase was associated with binding of a more rigidly attached, presumably denatured protein layer, whereas the second phase was associated with formation of a second layer of more loosely bound proteins. This second layer desorbed, e.g., upon reduction of Fe3+ of adsorbed met-Hb and subsequent binding of carbon monoxide (CO) forming HbCO. Thus, the results suggest that the adsorbed proteins in the second layer were in a native-like state. This information could only be obtained from simultaneous, time-resolved measurements of changes in both D and f, demonstrating that the QCM technique provides unique information about the mechanisms of protein adsorption to solid surfaces.

Red blood cell adhesion on a solid/liquid interface

Red blood cells (RBCs), previously fixed with glutaraldehyde, adhere to glass slides coated with fibrinogen. The RBC deposition process on the horizontal glass surface is investigated by analyzing the relative surface covered by the RBCs, as well as the variance of this surface coverage, as a function of the concentration of particles. This study is performed by optical microscopy and image analysis. A model, derived from the classical random sequential adsorption model, has been developed to account for the experimental results. This model highlights the strong influence of the hydrodynamic interactions during the deposition process.