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.

Proper sorting of the cation-dependent mannose 6-phosphate receptor in endosomes depends on a pair of aromatic amino acids in its cytoplasmic tail

The 67-amino acid cytoplasmic tail of the cation-dependent mannose 6-phosphate receptor (CD-MPR) contains a signal(s) that prevents the receptor from entering lysosomes where it would be degraded. To identify the key residues required for proper endosomal sorting, we analyzed the intracellular distribution of mutant forms of the receptor by Percoll density gradients. A receptor with a Trp19 → Ala substitution in the cytoplasmic tail was highly missorted to lysosomes whereas receptors with either Phe18 → Ala or Phe13 → Ala mutations were partially defective in avoiding transport to lysosomes. Analysis of double and triple mutants confirmed the key role of Trp19 for sorting of the CD-MPR in endosomes, with Phe18, Phe13, and several neighboring residues contributing to this function. The addition of the Phe18-Trp19 motif of the CD-MPR to the cytoplasmic tail of the lysosomal membrane protein Lamp1 was sufficient to partially impair its delivery to lysosomes. Replacing Phe18 and Trp19 with other aromatic amino acids did not impair endosomal sorting of the CD-MPR, indicating that two aromatic residues located at these positions are sufficient to prevent the receptor from trafficking to lysosomes. However, alterations in the spacing of the diaromatic amino acid sequence relative to the transmembrane domain resulted in receptor accumulation in lysosomes. These findings indicate that the endosomal sorting of the CD-MPR depends on the correct presentation of a diaromatic amino acid-containing motif in its cytoplasmic tail. Because a diaromatic amino acid sequence is also present in the cytoplasmic tail of other receptors known to be internalized from the plasma membrane, this feature may prove to be a general determinant for endosomal sorting.

Identification of Darlin, a Dictyostelium Protein with Armadillo-like Repeats that Binds to Small GTPases and Is Important for the Proper Aggregation of Developing Cells

We purified from Dictyostelium lysates an 88-kDa protein that bound to a subset of small GTPases, including racE, racC, cdc42Hs, and TC4ran, but did not bind to R-ras or rabB. Cloning of the gene encoding this 88-kDa protein revealed that it contained multiple armadillo-like repeats most closely related to the mammalian GTP exchange factor smgGDS. We named this protein darlin (Dictyostelium armadillo-like protein). Disruption of the gene encoding darlin demonstrated that this protein is not essential for cytokinesis, pinocytosis, phagocytosis, or development. However, the ability of darlin null cells to aggregate in response to starvation is severely affected. When starved under liquid medium, the mutant cells were unable to form aggregation centers and streams, possibly because of a defect in cAMP relay signaling. This defect was not due to an inability of the darlin mutants to activate adenylate cyclase in response to G protein stimulation. These results suggest that the darlin protein is involved in a signaling pathway that may modulate the chemotactic response during early development.

Proper placement of the Escherichia coli division site requires two functions that are associated with different domains of the MinE protein.

The proper placement of the Escherichia coli division septum requires the MinE protein. MinE accomplishes this by imparting topological specificity to a division inhibitor coded by the minC and minD genes. As a result, the division inhibitor prevents septation at potential division sites that exist at the cell poles but permits septation at the normal division site at midcell. In this paper, we define two functions of MinE that are required for this effect and present evidence that different domains within the 88-amino acid MinE protein are responsible for each of these two functions. The first domain, responsible for the ability of MinE to counteract the activity of the MinCD division inhibitor, is located in a small region near the N terminus of the protein. The second domain, required for the topological specificity of MinE function, is located in the more distal region of the protein and affects the site specificity of placement of the division septum even when separated from the domain responsible for suppression of the activity of the division inhibitor.

Shift in speed selectivity of visual cortical neurons: A neural basis of perceived motion contrast

The perceived speed of motion in one part of the visual field is influenced by the speed of motion in its surrounding fields. Little is known about the cellular mechanisms causing this phenomenon. Recordings from mammalian visual cortex revealed that speed preference of the cortical cells could be changed by displaying a contrast speed in the field surrounding the cell’s classical receptive field. The neuron’s selectivity shifted to prefer faster speed if the contextual surround motion was set at a relatively lower speed, and vice versa. These specific center–surround interactions may underlie the perceptual enhancement of speed contrast between adjacent fields.

Neural systems underlying learning and representation of global motion

We demonstrate performance-related changes in cortical and cerebellar activity. The largest learning-dependent changes were observed in the anterior lateral cerebellum, where the extent and intensity of activation correlated inversely with psychophysical performance. After learning had occurred (a few minutes), the cerebellar activation almost disappeared; however, it was restored when the subjects were presented with a novel, untrained direction of motion for which psychophysical performance also reverted to chance level. Similar reductions in the extent and intensity of brain activations in relation to learning occurred in the superior colliculus, anterior cingulate, and parts of the extrastriate cortex. The motion direction-sensitive middle temporal visual complex was a notable exception, where there was an expansion of the cortical territory activated by the trained stimulus. Together, these results indicate that the learning and representation of visual motion discrimination are mediated by different, but probably interacting, neuronal subsystems.

Origin of nanomechanical cantilever motion generated from biomolecular interactions

Generation of nanomechanical cantilever motion from biomolecular interactions can have wide applications, ranging from high-throughput biomolecular detection to bioactuation. Although it has been suggested that such motion is caused by changes in surface stress of a cantilever beam, the origin of the surface-stress change has so far not been elucidated. By using DNA hybridization experiments, we show that the origin of motion lies in the interplay between changes in configurational entropy and intermolecular energetics induced by specific biomolecular interactions. By controlling entropy change during DNA hybridization, the direction of cantilever motion can be manipulated. These thermodynamic principles were also used to explain the origin of motion generated from protein–ligand binding.