Noncausal time response in frustrated total internal reflection?

Tunneling of photons in frustrated total internal reflection has been studied in the time domain with single-cycle femtosecond pulses. It is seen that both the phase and energy of the pulse travel faster than the speed of light in vacuum. Theoretical analysis of the experiments shows that the time-response function for electromagnetic waves propagating in the air gap is noncausal. However, it is found that superluminal signal propagation is not possible in this case because of the inevitable diffractive spreading of the signal beam.     

Resonant phase patterns in a reaction-diffusion system

Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model.     

Chirp response of an active-controlled thickness-drive tunable transducer

The chirp response of a thickness-drive tunable transducer for wide range time-bandwidth and sweep rates chirp signals is demonstrated experimentally and computationally. The computational evaluation uses recursive digital-filter model based on the z-transform method. The model is limited to simple lossless structure with no front and backing layers. The model and experimental results show that there is no limit on the maximum sweep rate of the chirp signal but practically the limit is determined by the limitation of the circuit that generates the control voltage that simulates a variable electric load.     

Direct measurement of a pK(a) near neutrality for the catalytic cytosine in the genomic HDV ribozyme using Raman crystallography

The hepatitis delta virus (HDV) ribozyme uses a cytosine to facilitate general acid-base catalysis. Biochemical studies suggest that C75 has a pKa perturbed to near neutrality. To measure this pKa directly, Raman spectra were recorded on single ribozyme crystals using a Raman microscope. A spectral feature arising from a single neutral cytosine was identified at 1528 cm(-1). At low pH, this mode was replaced with a new spectral feature. Monitoring these features as a function of pH revealed pKa values for the cytosine that couple anticooperatively with Mg2+ binding, with values of 6.15 and 6.40 in the presence of 20 and 2 mM Mg2+, respectively. These pKa values agree well with those obtained from ribozyme activity experiments in solution. To correlate the observed pKa with a specific nucleotide, crystals of C75U, which is catalytically inactive, were examined. The Raman difference spectra show that this mutation does not affect the conformation of the ribozyme. However, crystals of C75U did not produce a signal from a protonatable cytosine, providing strong evidence that protonation of C75 is being monitored in the wild-type ribozyme. These studies provide the first direct physical measurement of a pKa near neutrality for a catalytic residue in a ribozyme and show that ribozymes, like their protein enzyme counterparts, can optimize the pKa of their side chains for proton transfer.     

The case of the missing ring: radical cleavage of a carbon-carbon bond and implications for GFP chromophore biosynthesis

The green fluorescent protein (GFP) creates its fluorophore by promoting spontaneous peptide backbone cyclization and amino acid oxidation chemistry on its own Ser65, Tyr66, Gly67 tripeptide sequence. Here we use high-resolution crystallography and mutational analyses to characterize GFP variants that undergo backbone cyclization followed by either anticipated chromophore synthesis via Y66F Calpha-Cbeta double-bond formation or unprecedented loss of a Y66F benzyl moiety via Calpha-Cbeta bond cleavage. We discovered a Y66F cleavage variant that subsequently incorporates an oxygen atom, likely from molecular oxygen, at the Y66 Calpha position. The post-translational products identified from these Y66F GFP structures support a common intermediate that partitions between Calpha-Cbeta oxidation and homolytic cleavage pathways. Our data indicate that Glu222 is the branchpoint control for this partitioning step and also influences subsequent oxygen incorporation reactions. From these results, we propose mechanisms for Y66F Calpha-Cbeta cleavage, oxygen incorporation, and chromophore biosynthesis with shared features that include radical chemistry. By revealing how GFP and RFP protein environments steer chemistry to favor fluorophore biosynthesis and disfavor alternative reactivity, we identify strategies for protein design. The proposed, common, one-electron oxidized, radical intermediate for post-translation modifications in the GFP family has general implications for how proteins drive and control spontaneous post-translational chemical modifications in the absence of metal ions.     

A Jost–Pais-Type Reduction of Fredholm Determinants and Some Applications

We study the analog of semi-separable integral kernels in \({\mathcal {H}}\) of the type $$ K(x, x') = \left\{\begin{array}{ll} F_1(x) G_1(x'), \quad& a < x' < x < b,\\ F_2 (x)G_2(x'), \quad& a < x < x' < b,\end{array}\right.$$ where \({-\infty \leqslant a < b \leqslant \infty}\) , and for a.e. \({x \in (a, b)}\) , \({F_j (x) \in \mathcal{B}_2(\mathcal{H}_j, \mathcal{H})}\) and \({G_j(x) \in \mathcal {B}_2(\mathcal {H},\mathcal {H}_j)}\) such that F _j (·) and G _j (·) are uniformly measurable, and $$\begin{array}{ll} || F_j ( \cdot) ||_{\mathcal {B}_2(\mathcal {H}_j,\mathcal {H})} \in L^2((a, b)), ||G_j (\cdot)||_{\mathcal {B}_2(\mathcal {H},\mathcal {H}_j)} \in L^2((a, b)), \quad j=1,2, \end{array}$$ with \({\mathcal {H}}\) and \({\mathcal {H}_j}\) , j = 1, 2, complex, separable Hilbert spaces. Assuming that K(·, ·) generates a trace class operator K in \({L^2((a, b);\mathcal {H})}\) , we derive the analog of the Jost–Pais reduction theory that succeeds in proving that the Fredholm determinant \({{\rm det}_{L^2((a,b);\mathcal{H})}}\) (I ? α K), \({\alpha \in \mathbb{C}}\) , naturally reduces to appropriate Fredholm determinants in the Hilbert spaces \({\mathcal{H}}\) (and \({\mathcal{H}_1 \oplus \mathcal{H}_2}\) ). Explicit applications of this reduction theory to Schrödinger operators with suitable bounded operator-valued potentials are made. In addition, we provide an alternative approach to a fundamental trace formula first established by Pushnitski which leads to a Fredholm index computation of a certain model operator.     

Assessing chiral self-recognition using chiral stationary phases

Chiral stationary phases were synthesized and their ability to separate racemic precursors from which they were derived was assessed. Taken in conjunction with homochiral recognition previously observed in the solid state, the results of this study reveal that a geometrically controlling π-π interaction has a profound influence on molecular recognition.     

Preliminary investigation of Spartina alterniflora for phytoextraction of selected heavy metals in soils from Southwest Louisiana

Spartina alterniflora plants were collected at the Rockefeller Wildlife Refuge near Lake Charles, Louisiana for phytoremediation (phytoextraction) studies. In order to determine whether the plant would thrive in different soils and undergo phytoremediation, three soils were used and analyzed: experimental controlled soil (minimum heavy metal contamination), spiked soil (spiked with 100 ppm of selected heavy metals of Cr, Cu, Pb, Fe and Zn) collected from a local store and contaminated soil collected from the known contaminated (with metals) Bayou d'Inde in Lake Charles, Louisiana. The plant grew evenly in each of the three soils. Based on the inductively coupled plasma-optical emission spectrometric determination of the plant in each soil, it was shown that S. alterniflora exhibited potential for phytoremediation of metals in soils via phytoextraction into the roots.     

Implications of partial tryptic digestion in organic-aqueous solvent systems for bottom-up proteome analysis

For bottom-up MS, the digestion step is critical and is typically performed with trypsin. Solvent-assisted digestion in 80% acetonitrile has previously been shown to improve protein sequence coverage at shorter digestion times. This has been attributed to enhanced enzyme digestion efficiency in this solvent. However, our results demonstrate that tryptic digestion in 80% acetonitrile is less efficient than that of conventional (aqueous) digestion. This is a consequence of decreased enzyme activity beyond ∼40% acetonitrile, increased enzyme autolysis and lower protein solubility in 80% acetonitrile. We observe multiple missed cleavages and reduced concentration of fully cleaved digestion products. Nonetheless we confirm, through room temperature solvent-assisted digestion, a consistent improvement in protein sequence coverage when analyzed by mass spectrometry. These results are explained through the increased number of unique digestion products available for detection. Thus, while solvent-assisted digestion has clear merits for proteome analysis, one should be aware of the inefficiency of protein digestion though this protocol, particularly with absolute protein quantitation experiments.