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Notes: Necessary and sufficient conditions for unitary ray representations of connected Lie groups are reexamined. Thus a systematic constructive method is obtained for calculating the admissible exponent factors (two-cocycles). The gauge freedom of the unitary ray representation formalism is also considered. This introduces the distinction between trivial and genuine ray representations. A special gauge is then adopted, within which the two-cocycle is almost unique. The only prerequisite of the exponent factor calculus is the knowledge of the binary combination rules for the essential parameters of the group. The attained method affords a simple, general, and explicit (i.e., coordinate-dependent) two-cocycle calculus. The aim of this paper is merely instrumental.

Notes: The SL(3,R) theory of projective transformations of the plane is applied to the Lagrangians of all one-dimensional Newtonian linear systems. Noether and non-Noether equivalent Lagrangians, as well as the associated Noether and non-Noether constants of motion, are thus obtained in a completely general and systematic way. Complete unification is achieved by this group-theoretic approach to Lagrangians of one-dimensional linear systems.

Notes: The formalism of non-Abelian group quantization is briefly revisited, within the regular representation of noncompact Lie groups. It is shown that some of such r-dimensional groups have a set of r basic quantum-kinematic invariants, which substantially differ from the traditional invariants. The relation of the traditional invariants of the Lie algebra with the new quantum-kinematic invariants is also briefly examined. This paper contains two miscellaneous examples of quantum-kinematic invariant operators.

Notes: Abstract: The rat substance P (SP) receptor (SPR) was expressed in insect Sf9 cells by infection with recombinant baculovirus. The receptor bound SP with high affinity (KD = 360 pM) and had a rank order of affinity of SP 〉 neurokinin A 〉 neurokinin B. Ligand activation of the receptor resulted in an increase in both inositol lipid hydrolysis and intracellular Ca2+ concentration ([Ca2+]i). However, high-level expression of the receptor, in the absence of ligand, was correlated with increased basal turnover of inositol lipids and an elevated rate of Ca2+ influx. These results demonstrate that the Sf9 cells provide a suitable environment for the high-level expression of a functionally active SPR. Two carboxy-terminal epitope-tagged receptors (SPR-KT3 = SPR-TPPPEPET, COOH; SPR-Glu = SPR-EEEEYMPME, COOH) were also expressed. The affinity of the KT3-tagged receptor for ligand was similar to that of the wild-type receptor (KD = 405 pM), and that of the Glu-tagged receptor was slightly lower (KD = 1,082 pM). The high-affinity SP binding site of all three receptors was sensitive to guanosine 5′-O-(3-thiotriphosphate) pretreatment. The maximal signal-transducing ability of the epitope-tagged receptors was comparable to that of the wild-type receptor ([Ca2+]i rise as a percentage of wild-type: SPR-KT3, 80–100%; SPR-Glu, 88–100%). These data show that heterologous expression in the baculovirus system results in high expression of functional wild-type and tagged receptors.

Notes: Abstract: The influence of deprivation of the neurotransmitter dopamine (DA) on the development of [Met5]-enkephalin (ME) and substance P (SP) neuropeptide systems of the stria-turn was investigated in Sprague-Dawley rats. The neurotoxin 6-hydroxydopamine (6-OHDA) was used to induce DA deficiency on postnatal day 3 in rats, and the animals were killed at different postnatal time points until 35 days of age. The levels of ME and SP were determined by radioimmu-noassay, and the abundance of preproenkephalin (PPE) and preprotachykinin (PPT) mRNA in the striatum was assessed by Northern blot hybridization analysis. The concentrations of DA, 5-hydroxytryptamine (5-HT), and their acid metabolites were determined by HPLC with electrochemical detection. The postnatal development of the PPE-derived pep-tide ME and the PPT-derived peptide SP closely paralleled the appearance of the respective mRNAs coding for these peptides. The dopaminergic lesion with 6-OHDA led to a marked depletion of DA and its metabolites but produced an increase in content of 5-HT and its metabolite in the striatum. The lesion did not affect the ME and PPE mRNA levels in the striatum up to 25 days but increased the levels at 35 days. In contrast, a decreased developmental expression in SP and PPT mRNA was observed throughout the observation period. The lesion failed to influence the development of the mRNA coding for the structural protein β-actin. The results indicate that the normal development of enkephalin, tachy-kinin, and 5-HT systems of the striatum is dependent on the availability of DA, the integrity of dopaminergic neurons, or both. The studies provide evidence for an interrelationship and interdependence between the development of neurotransmitter and neuropeptide systems. It is suggested that an early developmental abnormality in the DA system could permanently alter the neuropeptide systems, which in turn could influence the progression and expression of the DA-deficiency state parkinsonism, Lesch-Nyhan disease, or both.

Notes: Abstract: Chinese hamster ovary cells expressing the N-glycosylated substance P (NK-1) receptor were treated with the glycosylation inhibitor tunicamycin and photolabeled with 125I-Bolton-Hunter-p-benzoyl-l-phenylalanine8-substance P. Two radioactive proteins of Mr 80,000 and 46,000, representing the glycosylated and nonglycosylated substance P (NK-1) receptor, respectively, were observed. The IC50 for the inhibition of photolabeling of both receptor forms was 0.3 ± 0.1 nM for substance P and 30 ± 5 nM for neurokinin A (substance K). Thus, glycosylation of the substance P (NK-1) receptor has no detectable effect on the affinity of the substance P (NK-1) receptor for substance P or neurokinin A (substance K).

Notes: Abstract: The aim of the study was to test whether the synthesis of substance P (SP) and that of its receptor (also known as NK1 receptor) are coordinately regulated after chronic pharmacologic intervention in two neural systems, the spinal cord and basal ganglia. In one set of experiments, capsaicin was administered subcutaneously during the early postnatal period (day 3 after birth) to induce degeneration of afferent sensory neurons in the spinal cord. In the other set of experiments, interruption of dopaminergic transmission was achieved by two methods: (a) The neurotoxin 6-hydroxydopamine was used to denervate dopaminergic neurons during the early postnatal period, and (b) haloperidol was used in adult animals to block dopaminergic transmission by receptor blockade. The spinal cord, striatum, or both were used for the quantification of tachykinin [SP and neurokinin A (NKA)] and opioid peptides [[Met5]-enkephalin (ME) and dynorphin A (1–8) (DYN)] by radioimmunoassays. The abundance of total SP-encoding preprotachykinin (PPT) mRNA and SP receptor (SPR) mRNA in spinal cord (C5 to T1 segments), striatum, or microdissected substantia nigra was determined by northern blot or solution hybridization analysis. Amines and their acid metabolites were quantified by HPLC. Capsaicin administration (subcutaneously) during the early postnatal period increased latency in a hot-plate test, decreased SP and NKA levels, increased levels of PPT mRNAs, and did not affect SPR mRNA levels in the spinal cord. Intraspinal SP systems may attempt to compensate for the loss of afferent SP input, whereas spinal cord receptor mRNA levels do not appear to be altered. Neonatal dopaminergic denervation or haloperidol blockade of dopamine receptors in adult rats decreased PPT mRNA levels in the striatum as previously reported but did not alter the abundance of SPR mRNA in the striatum or substantia nigra. The presence of SPR mRNA levels in microdissected substantia nigra and the lack of alteration in its levels as a consequence of dopamine denervation suggest that the receptor is expressed within nondopaminergic neurons, possibly GABAergic neurons. In both spinal cord and basal ganglia systems, regardless of increases or decreases in SP or SP-encoding mRNA levels, SPR mRNA levels were not altered. We conclude that the regulation of the presynaptic biosynthesis of SP and the postsynaptic regulation of the SPR mRNA can be modulated independently of each other in spinal cord and basal ganglia SP systems.

Notes: The canonical commutation relations of quantum mechanics are generalized to the case where appropriate dynamical variables are angular-momentum, rotation-angle, and rotation-axis observables. To this end, SU(2) is "quantized" on the compact group manifold, according to the standard procedure of non-Abelian quantum kinematics. Quantum-kinematic invariant operators are introduced, and their commutation relations with the rotation variables are found in an explicit manner. The quantum-kinematic invariants yield superselection rules in the form of eigenvalue equations of an isotopic structure (which one should solve in the applications, in order to get multiplets that carry the irreducible representations of the underlying quantum kinematic models). A wide range of applicability of SU(2) quantum kinematics is suggested. © 1998 American Institute of Physics.

Notes: A rather strong concept of symmetry is introduced in classical mechanics, in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey. Accordingly, a "complete symmetry group'' realization in mechanics must be endowed with the following two features: (1) the group acts freely and transitively on the manifold of all allowed motions of the system; (2) the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group. This program is applied successfully to the classical Kepler problem, since the complete symmetry group for this particular system is here obtained. The importance of this result for the quantum kinematic theory of the Kepler system is emphasized.