Synthesis and spectroscopic characterisation of BODIPY based fluorescent off-on indicators with low affinity for calcium

Two fluorescent off-on Ca2+ indicators based on APTRA (o-aminophenol-N,N,O-triacetic acid) as low-affinity ligand for Ca2+ and BODIPY(4,4-difluoro-4-bora-3a,4a-diaza-s-indacene) as a fluorophore were synthesized. The new BODIPY-APTRA compounds absorb in the visible spectrum, with absorption maxima from 505 nm to 570 nm, and have fluorescence spectra that span the visible spectrum, with emission maxima ranging from 525 nm to 625 nm dependent on the substituents at the alpha-positions to the nitrogen atoms. The indicators show a large increase of the fluorescence quantum yield upon increasing Ca2+ concentration. The ground-state dissociation constants Kd estimated at 20 degrees C in 100 mM KCl aqueous buffered solution, pH 7.20, for the two complexes with Ca2+ were found to be around 100 microM.     

Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction–diffusion equations

We consider front propagation in a family of scalar reaction–diffusion equations in the asymptotic limit where the polynomial degree of the potential function tends to infinity. We investigate the Gevrey properties of the corresponding critical propagation speed, proving that the formal series expansion for that speed is Gevrey-1 with respect to the inverse of the degree. Moreover, we discuss the question of optimal truncation. Finally, we present a reliable numerical algorithm for evaluating the coefficients in the expansion with arbitrary precision and to any desired order, and we illustrate that algorithm by calculating explicitly the first ten coefficients. Our analysis builds on results obtained previously in [F. Dumortier, N. Popovi?, T.J. Kaper, The asymptotic critical wave speed in a family of scalar reaction–diffusion equations, J. Math. Anal. Appl. 326 (2) (2007) 1007–1023], and makes use of the blow-up technique in combination with geometric singular perturbation theory and complex analysis, while the numerical evaluation of the coefficients in the expansion for the critical speed is based on rigorous interval arithmetic.     

A geometric analysis of front propagation in a family of degenerate reaction-diffusion equations with cutoff

We investigate the effects of a Heaviside cutoff on the dynamics of traveling fronts in a family of scalar reaction-diffusion equations with degenerate polynomial potential that includes the classical Zeldovich equation. We prove the existence and uniqueness of front solutions in the presence of the cutoff, and we derive the leading-order asymptotics of the corresponding propagation speed in terms of the cutoff parameter. For the Zeldovich equation, an explicit solution to the equation without cutoff is known, which allows us to calculate higher-order terms in the resulting expansion for the front speed; in particular, we prove the occurrence of logarithmic (switchback) terms in that case. Our analysis relies on geometric methods from dynamical systems theory and, in particular, on the desingularization technique known as ‘blow-up.’     

Anion-templated supramolecular C3 assembly for efficient inclusion of charge-dispersed anions into hydrogen-bonded networks

The binding properties and conformational adaptability of a known nitrate/sulfate receptor N,N'-3-azapentane-1,5-bis[3-(1-aminoethylidene)-6-methyl-3H-pyran-2,4-dione] (L) toward various charge-dispersed monoanions (HSO(3)(-), ClO(4)(-), IO(4)(-), PF(6)(-), and SbF(6)(-)) are considered. These anions template the folding of three HL(+) species through a self-assembly process into a new hollow supramolecular trication. During the self-assembly, all strong hydrogen-bond donors of the podand become coordinatively saturated by interactions with the oxo functionalities from other HL(+) molecules. In that way, only the weak hydrogen-bond-donating groups in the exterior part of the receptor are accessible for anion binding. The investigated anions are accommodated in the hydrophobic pockets of the isomorphous hydrogen-bonded frameworks, which serve as a basis for selective crystallization from the highly competitive anion/solvent systems. This behavior is discussed in terms of size and geometry of the anions as well as the receptor's coordination capabilities to provide the most favorable surroundings for guest inclusion both in solution and in the solid state.     

Photophysics of the fluorescent pH indicator BCECF

The photophysical behavior of BCECF [2',7'-bis-(2-carboxyethyl)-5-(and-6)-carboxyfluorescein]--currently the most widely used fluorescent pH indicator for near-neutral intracellular pH measurements--has been explored by using absorption and steady-state and time-resolved fluorescence measurements. The influence of ionic strength as well as total buffer concentration on the absorbance and steady-state fluorescence has been investigated. The apparent acidity constant of the pH indicator determined by absorbance and fluorescence titration is dependent on the added buffer and salt concentrations. A semiempirical model is proposed to rationalize the variations in the apparent pKa values. The excited-state proton exchange of BCECF at physiological pH becomes reversible upon addition of phosphate buffer, inducing a pH-dependent change of the fluorescence decay times. Fluorescence decay traces collected as a function of total buffer concentration and pH were analyzed by global compartmental analysis yielding the following values of the rate constants describing excited-state dynamics of BCECF: k01 = 3.4 x 10(8) s(-1), k02 = 2.6 x 10(8) s(-1), k21 approximately 1 x 10(6) M(-1) s(-1), k12(B) = 1.4 x 10(8) M(-1) s(-1), and k21(B) = 4.3 x 10(7) M(-1) s(-1).     

A geometric approach to bistable front propagation in scalar reaction–diffusion equations with cut-off

‘Cut-offs’ were introduced to model front propagation in reaction–diffusion systems in which the reaction is effectively deactivated at points where the concentration lies below some threshold. In this article, we investigate the effects of a cut-off on fronts propagating into metastable states in a class of bistable scalar equations. We apply the method of geometric desingularization from dynamical systems theory to calculate explicitly the change in front propagation speed that is induced by the cut-off. We prove that the asymptotics of this correction scales with fractional powers of the cut-off parameter, and we identify the source of these exponents, thus explaining the structure of the resulting expansion. In particular, we show geometrically that the speed of bistable fronts increases in the presence of a cut-off, in agreement with results obtained previously via a variational principle. We first discuss the classical Nagumo equation as a prototypical example of bistable front propagation. Then, we present corresponding results for the (equivalent) cut-off Schlögl equation. Finally, we extend our analysis to a general family of reaction–diffusion equations that support bistable fronts, and we show that knowledge of an explicit front solution to the associated problem without cut-off is necessary for the correction induced by the cut-off to be computable in closed form.     

Adaptive microphone array for unknown desired speaker's transfer function

The main drawback of minimum variance distortionless response (MVDR) beamformer is the cancellation of the desired speech signal and its degradation in multi-path wave propagation environment. To make the adaptive algorithm robust against room reverberation and to prevent desired signal cancellation an estimation of unknown desired speaker's transfer function was proposed. The estimation is based on the signal and the interference covariance matrices. The estimated transfer function is then applied to the MVDR beamformer. The proposed algorithm was tested on a simulated room with reverberation. The results showed better quality of the restored speech compared to some typical adaptive algorithms.     

Decoherence and classical behavior with a chaotic macroscopic environment

Quantum state diffusion approach to open system dynamics is used to study decoherence and dynamics of the pointer observable of an angular momentum system in interaction with a macroscopic nonlinear and dissipative environment. It is shown that dispersion of the pointer observable in the mixed state of the open system is clearly larger if the environment is classically chaotic then in the case of the environment with regular dynamics.