Large deformation of isotropic biological tissue

The requirements for the development of a general potential function describing the behavior of homogeneous, isotropic biological tissue are discussed and such a function is proposed. It is shown that this function yields both tensile and torsional results compatible with existing data.     

Generalizations of the Roginsky-Zeldovich (or Elovich) equation for charge transport across biological surfaces

The Roginsky-Zeldovich (or Elovich) equation, which is −dx/dt=m exp (nx) (x=substrate concentration,t=time,m andn=constants), describes the kinetics of various biological electron and ion transport processes, and has been derived from the concept of charge transport across an activation energy barrier at an interface between dissimilar phases, driven by a difference in redox or ion potentials, with the simplifying assumptions that charge carrier concentration is constant, backward current across the interface is zero, and diffusion of substrate is fast. If charge carrier concentration is proportional to substrate concentration, then the kinetic equation is −dx/dt=mx exp (nx). If backward current is not zero, then −dx/dt=m ₁ exp (n ₁x) −m ₂ exp (n ₂ x), wherem ₁,m ₂,n ₁ andn ₂ are constants. Kinetic equations for interfacial charge transport in the presence of a significant substrate diffusion potential are also derived.     

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated ¹⁴N- and ¹⁵N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DP_II is reduced by a factor of between six and thirty compared to the value of D found for the spin labels in bulk water, its value for T = 295 K is given by (1.3±0.6)·10^–10m²s^–1 D (2.4±0.3) 10^–11 m²s^–1. Offprint requests to: H.-J. Steinhoff     

Myxobacteria (Myxobacteriales) on leaf surfaces

140 leaf samples were examined, 73 of which (= 52.1%) contained myxobacteria. Three species of the genus Myxococcus, M. virescens, M. fulvus and M. coralloides, could be found more or less frequently in the phyllosphere of woody plants and annuals. Archangium gephyra was observed only once. There was no significant difference in the occurrence of myxobacteria between evergreen leaves and leaves from deciduous trees and shrubs. Fruit-trees yielded the best results.     

FtsZ bacterial cytoskeletal polymers on curved surfaces: the importance of lateral interactions

A recent theoretical article provided a mechanical explanation for the formation of cytoskeletal rings and helices in bacteria assuming that these shapes arise, at least in part, from the interaction of the inherent mechanical properties of the protein polymers and the constraints imposed by the curved cell membrane (Andrews, S., and A. P. Arkin. 2007. Biophys. J. 93:1872-1884). Due to the lack of experimental data regarding the bending rigidity and preferential bond angles of bacterial polymers, the authors explored their model over wide ranges of preferred curvature values. In this letter, we present the shape diagram of the FtsZ bacterial polymer on a curved surface but now including recent experimental data on the in vitro formed FtsZ polymers. The lateral interactions between filaments observed experimentally change qualitatively the shape diagram and indicate that the formation of rings over spirals is more energetically favored than estimated in the above-mentioned article.     

Two-step cell patterning on planar and complex curved surfaces by precision spraying of polymers

Controlling adhesion of living animal cells plays a key role in biosensor fabrication, drug-testing technologies, basic biological research, and tissue engineering applications. Current techniques for cell patterning have two primary limitations: (1) they require photolithography, and (2) they are limited to patterning of planar surfaces. Here we demonstrate a simple, precision spraying method for both positive and negative patterning of planar and curved surfaces to achieve cell patterns rapidly and reproducibly. In this method, which we call precision spraying (PS), a polymer solution is aerosolized, focused with sheath airflow through an orifice, and deposited on the substrate using a deposition head to create approximately 25 microm sized features. In positive patterning, adhesive molecules, such as laminin or polyethylenimine (PEI) were patterned on polydimethylsiloxane (PDMS) substrates in a single spraying operation. A variety of animal cell types were found to adhere to the adhesive regions, and avoid the non-adhesive (bare PDMS) regions. In negative patterning, hydrophobic materials, such as polytetrafluoroethylene (PTFE) and PDMS, were patterned on glass substrates. Cells then formed patterns on the exposed glass regions and avoided the hydrophobic regions. Cellular patterns were maintained for up to 2 weeks in the presence of serum, which normally fouls non-adhesive regions. Additionally, we found that precision spraying enabled micropatterning of complex-curved surfaces. Our results show that precision spraying followed by cell plating enables rapid and flexible cellular micropatterning in two simple steps.     

Effects of non-local diffusion on structural MRI preprocessing and default network mapping: statistical comparisons with isotropic/anisotropic diffusion

Neuroimaging community usually employs spatial smoothing to denoise magnetic resonance imaging (MRI) data, e.g., Gaussian smoothing kernels. Such an isotropic diffusion (ISD) based smoothing is widely adopted for denoising purpose due to its easy implementation and efficient computation. Beyond these advantages, Gaussian smoothing kernels tend to blur the edges, curvature and texture of images. Researchers have proposed anisotropic diffusion (ASD) and non-local diffusion (NLD) kernels. We recently demonstrated the effect of these new filtering paradigms on preprocessing real degraded MRI images from three individual subjects. Here, to further systematically investigate the effects at a group level, we collected both structural and functional MRI data from 23 participants. We first evaluated the three smoothing strategies' impact on brain extraction, segmentation and registration. Finally, we investigated how they affect subsequent mapping of default network based on resting-state functional MRI (R-fMRI) data. Our findings suggest that NLD-based spatial smoothing maybe more effective and reliable at improving the quality of both MRI data preprocessing and default network mapping. We thus recommend NLD may become a promising method of smoothing structural MRI images of R-fMRI pipeline.     

Simulations of steady quaternary gas diffusion between alveolar and blood compartments

Fick's law is usually employed to analyze diffusion phenomena in the lung. However, this law is only strictly applicable to two component mixtures. When there are more than two gases in the mixture, Stefan's equations are more appropriate. Under physiological conditions during respiration, at least three gases are involved (O₂, CO₂, N₂). Furthermore, helium is often added in studies on the effect of density on pulmonary mixing. Features of quaternary gas diffusion (O₂, CO₂, N₂, He), and computer simulations of physiologically relevant conditions are presented. The results of the simulations were found to be in agreement with results from studies on normal and disease lungs.     

Modelling biological cell attachment and growth on adherent surfaces

A mathematical model, in the form of an integro-partial differential equation, is presented to describe the dynamics of cells being deposited, attaching and growing in the form of a monolayer across an adherent surface. The model takes into account that the cells suspended in the media used for the seeding have a distribution of sizes, and that the attachment of cells restricts further deposition by fragmenting the parts of the domain unoccupied by cells. Once attached the cells are assumed to be able to grow and proliferate over the domain by a process of infilling of the interstitial gaps; it is shown that without cell proliferation there is a slow build up of the monolayer but if the surface is conducive to cell spreading and proliferation then complete coverage of the domain by the monolayer can be achieved more rapidly. Analytical solutions of the model equations are obtained for special cases, and numerical solutions are presented for parameter values derived from experiments of rat mesenchymal stromal cells seeded onto thin layers of collagen-coated polyethylene terephthalate electrospun fibers. The model represents a new approach to describing the deposition, attachment and growth of cells over adherent surfaces, and should prove useful for studying the dynamics of the seeding of biomaterials.     

The diffusion of ions across biological membranes

Summary The derivation of a diffusion equation is given for the transport of ions across biological membranes. It is suggested that the diffusion proceeds by the jumps of ions from one site to another and the number of such sites in the membrane is restricted.     

Lateral diffusion in biological membranes. A normal-mode analysis of diffusion on a spherical surface.

A new approach is described for the analysis of lateral diffusion in biological membranes. It is shown that a suitably defined first moment of the concentration distribution on a spherical surface decays as a single exponential with a relaxation rate proportional to the diffusion coefficient and inversely proportional to the square of the radius of the sphere. The approach is illustrated with an example of fluorescence redistribution after photobleaching of membrane proteins in a spectrin-deficient spherocytic mouse erythrocyte membrane.     

The role of flexible tethers in multiple ligand-receptor bond formation between curved surfaces

Ligands mounted to surfaces via extensible tethers are present in nature and represent a growing class of molecules used to engineer adhesion in drug targeting, biosensing, self-assembling nanostructures, and in other biophysical research. Using a continuum approach with geometric and thermodynamic arguments, we derive a number of analytical expressions that relate key properties of single-tethered ligand-receptor interactions to multiple bond formation between curved surfaces. The theoretical predictions are in good agreement with measurements made with the surface forces apparatus. We establish that, when ligated, many tethers commonly used in biophysical research exhibit a discrete binding range that can be accurately measured with force spectroscopy. The distribution of bound ligated tethers is independent of the surfaces' interaction radius, R. The bridging force scales linearly with R, the tether's effective spring constant and grafting density, and with the ligand-receptor bond energy when the surfaces are in direct contact. These results are contrasted to bridging forces that evolve between plane-parallel geometries. Last, we show how our simple analytical reductions can be used to predict adhesive forces for STEALTH liposomes and other targeted and self-assembled nanoparticles.     

Anomalous diffusion of water in biological tissues.

This article deals with the characterization of biological tissues and their pathological alterations. For this purpose, diffusion is measured by NMR in the fringe field of a large superconductor with a field gradient of 50 T/m, which is rather homogenous and stable. It is due to the unprecedented properties of the gradient that we are able not only to determine the usual diffusion coefficient, but also to observe the pronounced Non-Debye feature of the relaxation function due to cellular structure. The dynamics of the probability density follow a stretched exponential or Kohlrausch-Williams-Watts function. In the long time limit the Fourier transform of the probability density follows a long-tail Lévy function, whose asymptotic is related to the fractal dimension of the underlying cellular structure. Some of the properties of Lévy walk statistics are discussed and its potential importance in understanding certain biophysical phenomena like diffusion processes in biological tissues are pointed out. We present and discuss for the first time NMR data giving evidence for Lévy processes that capture the essential features of the observed power law (scaling) dynamics of water diffusion in fresh tissue specimens: carcinomas, fibrous mastopathies, adipose and liver tissues.     

Adsorption of CO on Cu (110) and (100) surfaces using COSMO-based DFT

Density functional theory (DFT) combined with the conductor-like solvent model (COSMO) can provide valuable atomistic level insights into CO adsorption on Cu surface interactions in liquid paraffin. The objective of this research was to investigate the solvent effect of liquid paraffin. It was found that both structural parameters and relative energies are very sensitive to the COSMO solvent model. Solvent effects can improve the stability of CO adsorption on Cu (110) and (100) surfaces and the extent of CO activation.