β-Sheet-induced chirogenesis in polymerization of oligopeptides

The origin of long homochiral biopolymers in living systems has recently been the focus of intense research. In one particular research line, scientists studied, experimentally and theoretically, chiral amplification obtained during peptide formation by polymerization of amino acid building blocks. It was suggested that processes leading to temporal or spatial separation, and thus, to the growth of homochiral polymers at the expense of their heterochiral counterparts, can explain the chirality observed in larger molecules. We introduce a simple model and stochastic simulation for the polymerization of amino acids and β-sheet formation, showing the crucial effects of the β sheets on the distributions of peptide lengths. When chiral affinities are included, racemic β sheets of alternating homochiral strands lead to the formation of chiral peptides, the isotacticity of which increases with length, consistent with previous experimental results in aqueous solutions. The tendency to form isotactic peptides is shown for both initially racemic and initially nonracemic systems, as well as for closed and open systems. We suggest that these or similar mechanisms may explain the origin of chiroselectivity in prebiotic environments.     

The instability of the flow in a suddenly blocked pipe

This paper considers the decay of Poiseuille flow within a suddenlyblocked pipe. For small to moderate times the flow is shownto consist of an inviscid core flow coupled with a boundarylayer at the pipe wall. A small-time asymptotic solution isdeveloped and it is shown that this solution is valid for timesup to the point at which the boundary layer fills the wholepipe. A small-time composite solution is used to initiate anumerical marching procedure which overcomes the small-timesingularity that arises in the flow and so allows us to describethe ultimate decay of the flow within a blocked pipe. The stabilityof this flow is then considered using both a quasi-steady approximationand a transient-growth analysis based upon marching solutionsof the linearized Navier–Stokes equations. Our transientstability analysis predicts a critical Reynolds number, fortransition to turbulence, in the range 970 < Re < 1370.     

A stability analysis for a semilinear parabolic partial differential equation

We consider a parabolic partial differential equation u_t = u_xx + f(u), where ? ∞ < x < + ∞ and 0 < t < + ∞. Under suitable hypotheses pertaining to f, we exhibit a class of initial data φ(x), ? ∞ < x < + ∞, for which the corresponding solutions u(x, t) approach zero as t → + ∞. This convergence is uniform with respect to x on any compact subinterval of the real axis.     

Behavior of solutions leaving the neighborhood of a saddle point for a nonlinear evolution equation

We consider a nonlinear evolution equation on a Banach space X for which the origin is an equilibrium point having a saddle point structure. We give a condition guaranteeing that, for a certain neighborhood B₀ of the origin and for any initial point belonging to B₀ but not to the stable manifold, the corresponding solution not only leaves B₀ but, after a certain time $\text{t1}$, never returns.     

Surface analysis of erodible multilayered polyelectrolyte films: nanometer-scale structure and erosion profiles

Atomic force microscopy (AFM) and scanning electron microscopy (SEM) coupled with ellipsometry have been used to characterize the microscale and nanoscale structures of erodible multilayered films fabricated from degradable polyamine 1 and either sodium poly(styrene sulfonate) (SPS) or plasmid DNA. Striking differences were found in the topography, structures, and erosion profiles of these two materials upon incubation in PBS buffer at 37 degrees C. For films fabricated from SPS, AFM data are consistent with an erosion process that occurs uniformly without the generation of holes or pits over large, micrometer-scale areas. By contrast, films fabricated from plasmid DNA undergo structural rearrangements to present surface-bound particles ranging in size from 50 to 400 nm. Additional characterization of these particulate structures by SEM suggested that they are interpenetrated with or fused to underlying polyelectrolyte layers on the silicon surface, providing a potential mechanism to manipulate the adhesive forces with which these particles are bound to the surface. The erosion profile observed for polymer 1/SPS films suggests that it may be possible to design assemblies that release two film components with well-defined release kinetics. In the context of gene delivery, the presentation of condensed DNA as nanoparticles at these surfaces may be advantageous with respect to stimulating the internalization and processing of DNA by cells. A quantitative understanding of the factors influencing the fabrication, structure, and erosion profiles of these materials will be useful for the design of multilayered assemblies for specific applications in which controlled film erosion or the release of therapeutic materials is desired.     

Temporal onset-order discrimination through the tactual sense: effects of frequency and site of stimulation

This research extends the study of temporal resolution of the tactual sensory system through measurements of temporal-onset order discrimination for continuous tonal signals addressing (a) the effects of frequency separation of the two stimuli whose onset orders are to be discriminated and (b) the effects of redundant coding of frequency and site of stimulation on performance. Sinusoidal signals were presented either at two separate digits (thumb and index finger of the left hand) or at a single site of stimulation (left index finger) using a multifinger tactual stimulation system. Measurements were obtained using a one-interval two-alternative forced choice procedure in which each interval consisted of the random-order presentation of two different stimuli with roving values of amplitude and duration. Thresholds were estimated from psychometric functions of d' as a function of stimulus-onset asynchrony (SOA). On average, temporal onset-order thresholds were larger for one-finger conditions (mean SOA of 74.8 ms) than for two-finger conditions (mean SOA of 48.5 ms) and decreased as frequency separation increased, particularly for single-site presentation. Redundant coding of frequency and site of stimulation resulted in higher resolution by a factor of 1.5 compared to frequency alone and by a factor of 1.2 compared to site alone.     

Electrochemical wettability switches gate aqueous liquids in microfluidic systems

We demonstrate a simple low-voltage technique for gating the flow of aqueous liquids in microfluidic systems employing the electrochemically-controlled surface energy of the conjugated polymer poly(3-hexylthiophene).     

Computer-assisted bijectification of Franel's recurrence

We show how to automatically translate algebraic proofs into bijective proofs. As an example, we bijectify Franel's recurrence relation on the sum of the cubes of the binomial coefficients.     

Determination of Fucose Concentration in a Lectin-Based Displacement Microfluidic Assay

We compare three different methods to quantify the monosaccharide fucose in solutions using the displacement of a large glycoprotein, lactoferrin. Two microfluidic analysis methods, namely fluorescence detection of (labeled) lactoferrin as it is displaced by unlabeled fucose and the displacement of (unlabeled) lactoferrin in SPR, provide fast responses and continuous data during the experiment, theoretically providing significant information regarding the interaction kinetics between the saccharide groups and binding sites. For comparison, we also performed a static displacement ELISA. The stationary binding site in all cases was immobilized S2-AAL, a monovalent polypeptide based on Aleuria aurantia lectin. Although all three assays showed a similar dynamic range, the microfluidic assays with fluorescent or SPR detection show an advantage in short analysis times. Furthermore, the microfluidic displacement assays provide a possibility to develop a one-step analytical platform.