Characterization of nonlinear optical absorption and refraction

We discuss the characterization of nonlinear optical processes that give rise to changes in the absorption coefficient and refractive index. We primarily concentrate on methods for determining the dominant nonlinearities present in condensed matter and the responsible physical mechanisms. In extensive studies of a wide variety of material, we have found that there is seldom a single nonlinear process occurring. Often several processes occur simultaneously, sometimes in unison, sometimes competing. It is necessary to experimentally distinguish and separate these processes in order to understand and model the interaction. There are a variety of methods and techniques for determining the nonlinear optical response, each with its own weaknesses and advantages. In general, it is advisable to use as many complementary techniques as possible over a broad spectral range in order to unambiguously determine the active nonlinearities. Here we concentrate on the use of nonlinear transmittance, Z-scan and degenerate four-wave mixing experiments as applied to polycrystalline and single crystal semiconductors and dielectric materials.     

Reaction of gadolinium chelates with endogenously available ions

The extent of reaction of 153Gd-radiolabeled Gd(L) chelates with 25 mM CO23- (25 mF), PO34-, Zn2+ and Cu2+ at pH 7 was determined for L = EDTA, DTPA, DOTA, HP-DO3A, and DO3A. Gd(EDTA)- and Gd(DTPA)2- reacted (greater than 20% in 10 min) with Cu2+ and Zn2+ in the presence of PO34-. These double replacement reactions yielded precipitated GdPO4 and chelated Cu(L). Gd(HP-DO3A), Gd(DO3A) and Gd(DOTA)- were inert to reaction with all four ions at room temperature (less than or equal to 1% reaction detected). The thermodynamic binding constants of the ligands for Gd3+ and Cu2+ were found to be equal (10(20) M-1) for DO3A, while DOTA and HP-DO3A favored Gd3+ over Cu2+ by greater than or equal to 10(2) M-1. The low order of reactivity of Gd(DOTA)- and Gd(HP-DO3A) was anticipated by the binding constants, but the lack of reactivity of Gd(DO3A) is attributed to kinetic inertia. This latter property, desirable in MRI contrast agents, is promoted by the conformational stability of the tetraazacyclododecane macrocycle, which forms the backbone of the ligand. It is concluded that this class of chelates is exceptionally inert in solutions of endogenously available ions, and that thermodynamics alone is an insufficient predictor of the reactivity of the highly inert Gd complexes based on the tetraazamacrocycle.     

Stratified layer formation in particle suspensions

Initially homogeneous suspensions of colloidal particles often develop patterns during sedimentation. Commonly, the concentration profile of the particles evolves into a “staircase”: layers of nearly constant concentration, separated by sharp boundaries between successive layers, with the concentration of each successive layer increasing with depth. Siano [1] has demonstrated experimentally that uphill diffusion, diffusion against the concentration gradient, occurs during this pattern formation. Thus, these patterns appear to be the result of spinodal decomposition. We find that these staircase patterns cannot be explained by the classical spinodal decomposition theory of Cahn and Hilliard, but that they can be explained if the linear gradient-energy term of Tiller, Pound, and Hirth is added to the free energy. Such a term plays a central role in the faceting of crystals. In the present application we believe that the physical origin of this extra term may be the Rayleigh—Taylor instability.     

S-nitrosothiol chemistry at the single-molecule level

SNO patrol: S-Nitrosothiols (RSNO) are important molecules involved in cell signaling, which control physiological processes such as vasodilation and bronchodilation. By using the protein pore α-hemolysin as a nanoreactor, the biological chemistry of RSNO has been investigated at the single-molecule level.     

Continuous stochastic detection of amino Acid enantiomers with a protein nanopore

A stochastic sensing method: Discrimination between enantiomeric amino acids is achieved when the amino acids bind to a Cu(II) complex within a protein nanopore sensor, which provides a chiral environment. The potential of the method is demonstrated by real-time observation of the increase in enantiomeric excess during an enzymatic kinetic resolution.     

Protein detection by nanopores equipped with aptamers

Protein nanopores have been used as stochastic sensors for the detection of analytes that range from small molecules to proteins. In this approach, individual analyte molecules modulate the ionic current flowing through a single nanopore. Here, a new type of stochastic sensor based on an αHL pore modified with an aptamer is described. The aptamer is bound to the pore by hybridization to an oligonucleotide that is attached covalently through a disulfide bond to a single cysteine residue near a mouth of the pore. We show that the binding of thrombin to a 15-mer DNA aptamer, which forms a cation-stabilized quadruplex, alters the ionic current through the pore. The approach allows the quantification of nanomolar concentrations of thrombin, and provides association and dissociation rate constants and equilibrium dissociation constants for thrombin·aptamer interactions. Aptamer-based nanopores have the potential to be integrated into arrays for the parallel detection of multiple analytes.     

Equivalent Black volatilities

We consider European calls and puts on an asset whose forward price F(t) obeys dF(t)=α(t)A(F)dW(t,) under the forward measure. By using singular perturbation techniques, we obtain explicit algebraic formulas for the implied volatility σ _B in terms of today's forward price F ₀ ≡ F(0), the strike K of the option, and the time to expiry t_ex . The price of any call or put can then be calculated simply by substituting this implied volatility into Black's formula. For example, for a power law (constant elasticity of variance) model dF(t)=aF^β dW(t) we obtain σ _B = a/f _aυ ^1? β {1 + (1?β)(2+β)/24 (F ₀ ? K/f _aυ)² + (1 ? β)²/24 a ² t_ex /f _aυ ^2?2β +…} where f _aυ = ½(F ₀ + K). Our formula for the implied volatility is not exact. However, we show that the error is insignificant, rarely approaching 1/1000 of the time value of the option. We also present more accurate (albeit more complicated) formulas which can be used for the implied volatility.     

Stochastic sensing of nanomolar inositol 1,4,5-trisphosphate with an engineered pore

The introduction of a ring of arginine residues near the constriction in the transmembrane beta barrel of the staphylococcal alpha-hemolysin heptamer yielded a pore that could be almost completely blocked by phosphate anions at pH 7.5. Block did not occur with other oxyanions, including nitrate, sulfate, perchlorate, and citrate. Based on this finding, additional pores were engineered with high affinities for important cell signaling molecules, such as the Ca(2+)-mobilizing second messenger inositol 1,4,5-trisphosphate (IP(3)), that contain phosphate groups. One of these engineered pores, P(RR-2), provides a ring of fourteen arginines that project into the lumen of the transmembrane barrel. Remarkably, P(RR-2) bound IP(3) with low nanomolar affinity while failing to bind another second messenger, adenosine 3', 5'-cyclic monophosphate (cAMP). The engineered alpha-hemolysin pores may be useful as components of stochastic sensors for cell signaling molecules.