Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Purification and characterization of acetone carboxylase from Xanthobacter strain Py2

Acetone metabolism in the aerobic bacterium Xanthobacter strain Py2 proceeds by a carboxylation reaction forming acetoacetate as the first detectable product. In this study, acetone carboxylase, the enzyme catalyzing this reaction, has been purified to homogeneity and characterized. Acetone carboxylase was comprised of three polypeptides with molecular weights of 85,300, 78,300, and 19,600 arranged in an α2β2γ2 quaternary structure. The carboxylation of acetone was coupled to the hydrolysis of ATP and formation of 1 mol AMP and 2 mol inorganic phosphate per mol acetoacetate formed. ADP was also formed during the course of acetone consumption, but only accumulated at low, substoichiometric levels (≈10% yield) relative to acetoacetate. Inorganic pyrophosphate could not be detected as an intermediate or product of acetone carboxylation. In the absence of CO2, acetone carboxylase catalyzed the acetone-dependent hydrolysis of ATP to form both ADP and AMP, with ADP accumulating to higher levels than AMP during the course of the assays. Acetone carboxylase did not have inorganic pyrophosphatase activity. Acetone carboxylase exhibited a Vmax for acetone carboxylation of 0.225 μmol acetoacetate formed min−1⋅mg−1 at 30°C and pH 7.6 and apparent Km values of 7.80 μM (acetone), 122 μM (ATP), and 4.17 mM (CO2 plus bicarbonate). These studies reveal molecular properties of the first bacterial acetone-metabolizing enzyme to be isolated and suggest a novel mechanism of acetone carboxylation coupled to ATP hydrolysis and AMP and inorganic phosphate formation.

Pattern changes of pituitary peptides in rat after salt-loading as detected by means of direct, semiquantitative mass spectrometric profiling

We have established a differential peptide display method, based on a mass spectrometric technique, to detect peptides that show semiquantitative changes in the neurointermediate lobe (NIL) of individual rats subjected to salt-loading. We employed matrix-assisted laser desorption/ionization mass spectrometry, using a single-reference peptide in combination with careful scanning of the whole crystal rim of the matrix-analyte preparation, to detect in a semiquantitative manner the molecular ions present in the unfractionated NIL homogenate. Comparison of the mass spectra generated from NIL homogenates of salt-loaded and control rats revealed a selective and significant decrease in the intensities of several molecular ion species of the NIL homogenates from salt-loaded rats. These ion species, which have masses that correspond to the masses of oxytocin, vasopressin, neurophysins, and an unidentified putative peptide, were subsequently chemically characterized. We confirmed that the decreased molecular ion species are peptides derived exclusively from propressophysin and prooxyphysin (i.e., oxytocin, vasopressin, and various neurophysins). The putative peptide is carboxyl-terminal glycopeptide. The carbohydrate moiety of the latter peptide was determined by electrospray tandem MS as bisected biantennary Hex3HexNAc5Fuc. This posttranslational modification accounts for the mass difference between the predicted mass of the peptide based on cDNA studies and the measured mass of the mature peptide.

Sequence verification of human creatine kinase (43 kDa) isozymes by high-resolution tandem mass spectrometry.

Amino acid sequencing by recombinant DNA technology, although dramatically useful, is subject to base reading errors, is indirect, and is insensitive to posttranslational processing. Mass spectrometry techniques can provide molecular weight data from even relatively large proteins for such cDNA sequences and can serve as a check of an enzyme's purity and sequence integrity. Multiply-charged ions from electrospray ionization can be dissociated to yield structural information by tandem mass spectrometry, providing a second method for gaining additional confidence in primary sequence confirmation. Here, accurate (+/- 1 Da) molecular weight and molecular ion dissociation information for human muscle and brain creatine kinases has been obtained by electrospray ionization coupled with Fourier-transform mass spectrometry to help distinguish which of several published amino acid sequences for both enzymes are correct. The results herein are consistent with one published sequence for each isozyme, and the heterogeneity indicated by isoelectric focusing due to 1-Da deamidation changes. This approach appears generally useful for detailed sequence verification of recombinant proteins.

Sensitivity to abscisic acid of guard-cell K+ channels is suppressed by abi1-1, a mutant Arabidopsis gene encoding a putative protein phosphatase.

Abscisic acid (ABA) modulates the activities of three major classes of ion channels--inward- and outward-rectifying K+ channels (IK,in and IK,out, respectively) and anion channels--at the guard-cell plasma membrane to achieve a net efflux of osmotica and stomatal closure. Disruption of ABA sensitivity in wilty abi1-1 mutants of Arabidopsis and evidence that this gene encodes a protein phosphatase suggest that protein (de)-phosphorylation contributes to guard-cell transport control by ABA. To pinpoint the role of ABI1, the abi1-1 dominant mutant allele was stably transformed into Nicotiana benthamiana and its influence on IK,in, IK,out, and the anion channels was monitored in guard cells under voltage clamp. Compared with guard cells from wild-type and vector-transformed control plants, expression of the abi1-1 gene was associated with 2- to 6-fold reductions in IK,out and an insensitivity of both IK,in and IK,out to 20 microM ABA. In contrast, no differences between control and abi1-1 transgenic plants were observed in the anion current or its response to ABA. Parallel measurements of intracellular pH (pHi) using the fluorescent dye 2',7'-bis(2-carboxyethyl)-5-(and -6)-carboxyfluorescein (BCECF) in every case showed a 0.15- to 0.2-pH-unit alkalinization in ABA, demonstrating that the transgene was without effect on the pHi signal that mediates in ABA-evoked K+ channel control. In guard cells from the abi1-1 transformants, normal sensitivity of both K+ channels to and stomatal closure in ABA was recovered in the presence of 100 microM H7 and 0.5 microM staurosporine, both broad-range protein kinase antagonists. These results demonstrate an aberrant K+ channel behavior--including channel insensitivity to ABA-dependent alkalinization of pHi--as a major consequence of abi1-1 action and implicate AB11 as part of a phosphatase/kinase pathway that modulates the sensitivity of guard-cell K+ channels to ABA-evoked signal cascades.