A combination of different methods was applied to investigate the occurrence of anaerobic processes in aerated activated sludge. Microsensor measurements (O2, NO2 −, NO3 −, and H2S) were performed on single sludge flocs to detect anoxic niches, nitrate reduction, or sulfate reduction on a microscale. Incubations of activated sludge with15NO3 − and35SO4 2− were used to determine denitrification and sulfate reduction rates on a batch scale. In four of six investigated sludges, no anoxic zones developed during aeration, and consequently denitrification rates were very low. However, in two sludges anoxia in flocs coincided with significant denitrification rates. Sulfate reduction could not be detected in any sludge in either the microsensor or the batch investigation, not even under short-term anoxic conditions. In contrast, the presence of sulfate-reducing bacteria was shown by fluorescence in situ hybridization with 16S rRNA-targeted oligonucleotide probes and by PCR-based detection of genes coding for the dissimilatory sulfite reductase. A possible explanation for the absence of anoxia even in most of the larger flocs might be that oxygen transport is not only diffusional but enhanced by advection, i.e., facilitated by flow through pores and channels. This possibility is suggested by the irregularity of some oxygen profiles and by confocal laser scanning microscopy of the three-dimensional floc structures, which showed that flocs from the two sludges in which anoxic zones were found were apparently denser than flocs from the other sludges.

Intracellular signaling induced by peptide growth factors can stimulate secretion of these molecules into the extracellular medium. In autocrine and paracrine networks, this can establish a positive feedback loop between ligand binding and ligand release. When coupled to intercellular communication by autocrine ligands, this positive feedback can generate constant-speed traveling waves. To demonstrate that, we propose a mechanistic model of autocrine relay systems. The model is relevant to the physiology of epithelial layers and to a number of in vitro experimental formats. Using asymptotic and numerical tools, we find that traveling waves in autocrine relays exist and have a number of unusual properties, such as an optimal ligand binding strength necessary for the maximal speed of propagation. We compare our results to recent observations of autocrine and paracrine systems and discuss the steps toward experimental tests of our predictions.

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Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.

Electrokinetic properties and morphology of PDMS microfluidic chips intended for bioassays are studied. The chips are fabricated by a casting method followed by polymerization bonding. Microchannels are coated with 1% solution of bovine serum albumin ͑BSA͒ in Tris buffer. Albumin passively adsorbs on the PDMS surface. Electrokinetic characteristics ͑electro-osmotic velocity, electro-osmotic mobility, and zeta potential͒ of the coated PDMS channels are experimentally determined as functions of the electric field strength and the characteristic electrolyte concentration. Atomic force microscopy ͑AFM͒ analysis of the surface reveals a "peak and ridge" structure of the protein layer and an imperfect substrate coating. On the basis of the AFM observation, several topologies of the BSA-PDMS surface are proposed. A nonslip mathematical model of the electro-osmotic flow is then numerically analyzed. It is found that the electrokinetic characteristics computed for a channel with the homogeneous distribution of a fixed electric charge do not fit the experimental data. Heterogeneous distribution of the fixed electric charge and the surface roughness is thus taken into account. When a flat PDMS surface with electric charge heterogeneities is considered, the numerical results are in very good agreement with our experimental data. An optimization analysis finally allowed the determination of the surface concentration of the electric charge and the degree of the PDMS surface coating. The obtained findings can be important for correct prediction and possibly for robust control of behavior of electrically driven PDMS microfluidic chips. The proposed method of the electro-osmotic flow analysis at surfaces with a heterogeneous distribution of the surface electric charge can also be exploited in the interpretation of experimental studies dealing with protein-solid phase interactions or substrate coatings.

Prompted by the recent growing evidence of oscillatory behavior involving MAPK cascades we present a systematic approach of analyzing models and elucidating the nature of biochemical oscillations based on reaction network theory. In particular, we formulate a minimal biochemically consistent mass action subnetwork of the Huang-Ferrell model of the MAPK signalling that provides an oscillatory response when a parameter controlling the activation of the top-tier kinase is varied. Such dynamics are either intertwined with or separated from the earlier found bistable/hysteretic behavior in this model. Using the theory of stability of stoichiometric networks, we reduce the original MAPK model, convert kinetic to convex parameters and examine those properties of the minimal subnetwork that underlie the oscillatory dynamics. We also use the methods of classification of chemical oscillatory networks to explain the rhythmic behavior in physicochemical terms, i.e., we identify of the role of individual biochemical species in positive and negative feedback loops and describe their coordinated action leading to oscillations. Our approach provides an insight into dynamics without the necessity of knowing rate coefficients and thus is useful prior the statistical evaluation of parameters.

We experimentally observed oscillatory motion of water droplets in microfluidic systems with coplanar microelectrodes under imposed DC electric fields. Two-electrode arrangement with no bipolar electrode and eight-electrode arrangement with six bipolar microelectrodes were investigated. Kerosene was used as the continuous phase. We studied the dependences of the oscillation frequency on the electric field intensity and ionic strength of the water phase. We found that the electric field dependence is strongly nonlinear and discussed possible reasons of this phenomenon, e.g., the droplet deformation at electrode edges that affects the charge transfer between the electrode and droplet or the interplay between the Coulomb force on free charge and the dielectrophoretic force. Our experiments further revealed that the oscillation frequency decreases with growing salt concentration in the two-electrode arrangement, but increases in the eight-electrode arrangement, which was attributed to surface tension related processes and electrochemical processes on the bipolar electrodes. Finally, we analyzed the effects of the electric field on the oscillatory motion by means of a simplified mathematical model. It was shown that the electric force imposed on the droplet charge is the key factor to induce the oscillations and the dielectrophoretic force significantly contributes to the momentum transfer at the electrode edges. For the same electric field strength, the model is able to predict the same oscillation frequency as that observed in the experiments.

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