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.

Evolutionary conservation of human TATA-binding-polypeptide-associated factors TAFII31 and TAFII80 and interactions of TAFII80 with other TAFs and with general transcription factors.

Human transcription initiation factor TFIID is composed of the TATA-binding polypeptide (TBP) and at least 13 TBP-associated factors (TAFs) that collectively or individually are involved in activator-dependent transcription. To investigate protein-protein interactions involved in TFIID assembly and in TAF-mediated activator functions, we have cloned and expressed cDNAs encoding human TAFII80 and TAFII31. Coimmunoprecipitation assays showed that TAFII80 interacted with TAFII250, TAFII31, TAFII20, and TBP, but not with TAFII55. Similar assays showed that TAFII80 interacted with TFIIE alpha and with TFIIF alpha (RAP74) but not with TFIIB, TFIIE beta, or TFIIF beta (RAP30). Further studies with TAFII80 mutations revealed three distinct interaction domains which fall within regions conserved in human TAFII80, Drosophila TAFII60, and yeast TAFII60. The N terminus of TAFII80 (residues 1-100) interacts with both TAFII31 and TAFII20, while two C-terminal regions are involved, respectively, in interactions with TAFII250 and TFIIF alpha (RAP74) (residues 203-276) and with TBP and TFIIE alpha (residues 377-505). The interactions between TAFII80 and general factors TFIIE alpha and TFIIF alpha (RAP74) could be important for recruitment of GTFs during activator-dependent transcription. Because TAFs 80, 31, and 20 show sequence similarities to histones H4, H3, and H2B, as well as some parallel interactions, this subset of TAFs may form a related core structure within TFIID.

A Mutational Analysis Identifies Three Functional Regions of the Spindle Pole Component Spc110p in Saccharomyces cerevisiae

The central coiled coil of the essential spindle pole component Spc110p spans the distance between the central and inner plaques of the Saccharomyces cerevisiae spindle pole body (SPB). The carboxy terminus of Spc110p, which binds calmodulin, resides at the central plaque, and the amino terminus resides at the inner plaque from which nuclear microtubules originate. To dissect the functions of Spc110p, we created temperature-sensitive mutations in the amino and carboxy termini. Analysis of the temperature-sensitive spc110 mutations and intragenic complementation analysis of the spc110 alleles defined three functional regions of Spc110p. Region I is located at the amino terminus. Region II is located at the carboxy-terminal end of the coiled coil, and region III is the previously defined calmodulin-binding site. Overexpression of SPC98 suppresses the temperature sensitivity conferred by mutations in region I but not the phenotypes conferred by mutations in the other two regions, suggesting that the amino terminus of Spc110p is involved in an interaction with the γ-tubulin complex composed of Spc97p, Spc98p, and Tub4p. Mutations in region II lead to loss of SPB integrity during mitosis, suggesting that this region is required for the stable attachment of Spc110p to the central plaque. Our results strongly argue that Spc110p links the γ-tubulin complex to the central plaque of the SPB.

Three-dimensional image reconstruction of dephosphorylated smooth muscle heavy meromyosin reveals asymmetry in the interaction between myosin heads and placement of subfragment 2

Regulation of the actin-activated ATPase of smooth muscle myosin II is known to involve an interaction between the two heads that is controlled by phosphorylation of the regulatory light chain. However, the three-dimensional structure of this inactivated form has been unknown. We have used a lipid monolayer to obtain two-dimensional crystalline arrays of the unphosphorylated inactive form of smooth muscle heavy meromyosin suitable for structural studies by electron cryomicroscopy of unstained, frozen-hydrated specimens. The three-dimensional structure reveals an asymmetric interaction between the two myosin heads. The ATPase activity of one head is sterically “blocked” because part of its actin-binding interface is positioned onto the converter domain of the second head. ATPase activity of the second head, which can bind actin, appears to be inhibited through stabilization of converter domain movements needed to release phosphate and achieve strong actin binding. When the subfragment 2 domain of heavy meromyosin is oriented as it would be in an actomyosin filament lattice, the position of the heads is very different from that needed to bind actin, suggesting an additional contribution to ATPase inhibition in situ.