Molecular design of the N-methyl-D-aspartate receptor binding site for phencyclidine and dizolcipine.

The N-methyl-D-aspartate receptor (NMDAR), a pivotal entity for synaptic plasticity and excitotoxicity in the brain, is a target of psychotomimetic drugs such as phencyclidine (PCP) and dizolcipine (MK-801). In contrast, a related glutamate receptor, the alpha-amino-3-hydroxy-5-methyl-4-isoxazole propionate/kainate receptor GluR1, is weakly sensitive to these drugs. Three point mutations on GluR1, mimicking homologous residues on the NMDAR, confer the PCP and MK-801 blockade properties that are characteristic of the NMDAR--namely, high potency, voltage dependence, and use dependence. The molecular determinants that specify the PCP block appear confined to the putative M2 transmembrane segment, whereas the sensitivity to MK-801 requires an interplay between residues from M2 and M3. Given the plausible involvement of the NMDAR in the etiology of several neurodegenerative diseases and in excitotoxic neuronal cell death, tailored glutamate receptors with specific properties may be models for designing and screening new drugs targeted to prevent glutamate-mediated neural damage.

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.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.