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.

Differential Expression and Functions of Cortical Myosin IIA and IIB Isotypes during Meiotic Maturation, Fertilization, and Mitosis in Mouse Oocytes and Embryos

To explore the role of nonmuscle myosin II isoforms during mouse gametogenesis, fertilization, and early development, localization and microinjection studies were performed using monospecific antibodies to myosin IIA and IIB isotypes. Each myosin II antibody recognizes a 205-kDa protein in oocytes, but not mature sperm. Myosin IIA and IIB demonstrate differential expression during meiotic maturation and following fertilization: only the IIA isoform detects metaphase spindles or accumulates in the mitotic cleavage furrow. In the unfertilized oocyte, both myosin isoforms are polarized in the cortex directly overlying the metaphase-arrested second meiotic spindle. Cortical polarization is altered after spindle disassembly with Colcemid: the scattered meiotic chromosomes initiate myosin IIA and microfilament assemble in the vicinity of each chromosome mass. During sperm incorporation, both myosin II isotypes concentrate in the second polar body cleavage furrow and the sperm incorporation cone. In functional experiments, the microinjection of myosin IIA antibody disrupts meiotic maturation to metaphase II arrest, probably through depletion of spindle-associated myosin IIA protein and antibody binding to chromosome surfaces. Conversely, the microinjection of myosin IIB antibody blocks microfilament-directed chromosome scattering in Colcemid-treated mature oocytes, suggesting a role in mediating chromosome–cortical actomyosin interactions. Neither myosin II antibody, alone or coinjected, blocks second polar body formation, in vitro fertilization, or cytokinesis. Finally, microinjection of a nonphosphorylatable 20-kDa regulatory myosin light chain specifically blocks sperm incorporation cone disassembly and impedes cell cycle progression, suggesting that interference with myosin II phosphorylation influences fertilization. Thus, conventional myosins break cortical symmetry in oocytes by participating in eccentric meiotic spindle positioning, sperm incorporation cone dynamics, and cytokinesis. Although murine sperm do not express myosin II, different myosin II isotypes may have distinct roles during early embryonic development.

Generalized flows, intrinsic stochasticity, and turbulent transport

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to the associated ordinary differential equations which no longer satisfy the uniqueness theorem for ordinary differential equations. Two most natural regularizations of this problem, namely the regularization via adding small molecular diffusion and the regularization via smoothing out the velocity field, are considered. White-in-time random velocity fields are used as an example to examine the variety of phenomena that take place when the velocity field is not spatially regular. Three different regimes, characterized by their degrees of compressibility, are isolated in the parameter space. In the regime of intermediate compressibility, the two different regularizations give rise to two different scaling behaviors for the structure functions of the passive scalar. Physically, this means that the scaling depends on Prandtl number. In the other two regimes, the two different regularizations give rise to the same generalized flows even though the sense of convergence can be very different. The “one force, one solution” principle is established for the scalar field in the weakly compressible regime, and for the difference of the scalar in the strongly compressible regime, which is the regime of inverse cascade. Existence and uniqueness of an invariant measure are also proved in these regimes when the transport equation is suitably forced. Finally incomplete self similarity in the sense of Barenblatt and Chorin is established.

Fluorescence and photobleaching dynamics of single light-harvesting complexes

Single light-harvesting complexes LH-2 from Rhodopseudomonas acidophila were immobilized on various charged surfaces under physiological conditions. Polarized light experiments showed that the complexes were situated on the surface as nearly upright cylinders. Their fluorescence lifetimes and photobleaching properties were obtained by using a confocal fluorescence microscope with picosecond time resolution. Initially all molecules fluoresced with a lifetime of 1 ± 0.2 ns, similar to the bulk value. The photobleaching of one bacteriochlorophyll molecule from the 18-member assembly caused the fluorescence to switch off completely, because of trapping of the mobile excitations by energy transfer. This process was linear in light intensity. On continued irradiation the fluorescence often reappeared, but all molecules did not show the same behavior. Some LH-2 complexes displayed a variation of their quantum yields that was attributed to photoinduced confinement of the excited states and thereby a diminution of the superradiance. Others showed much shorter lifetimes caused by excitation energy traps that are only ≈3% efficient. On repeated excitation some molecules entered a noisy state where the fluorescence switched on and off with a correlation time of ≈0.1 s. About 490 molecules were examined.

ETS target genes: Identification of Egr1 as a target by RNA differential display and whole genome PCR techniques

ETS transcription factors play important roles in hematopoiesis, angiogenesis, and organogenesis during murine development. The ETS genes also have a role in neoplasia, for example in Ewing’s sarcomas and retrovirally induced cancers. The ETS genes encode transcription factors that bind to specific DNA sequences and activate transcription of various cellular and viral genes. To isolate novel ETS target genes, we used two approaches. In the first approach, we isolated genes by the RNA differential display technique. Previously, we have shown that the overexpression of ETS1 and ETS2 genes effects transformation of NIH 3T3 cells and specific transformants produce high levels of the ETS proteins. To isolate ETS1 and ETS2 responsive genes in these transformed cells, we prepared RNA from ETS1, ETS2 transformants, and normal NIH 3T3 cell lines and converted it into cDNA. This cDNA was amplified by PCR and displayed on sequencing gels. The differentially displayed bands were subcloned into plasmid vectors. By Northern blot analysis, several clones showed differential patterns of mRNA expression in the NIH 3T3-, ETS1-, and ETS2-expressing cell lines. Sixteen clones were analyzed by DNA sequence analysis, and 13 of them appeared to be unique because their DNA sequences did not match with any of the known genes present in the gene bank. Three known genes were found to be identical to the CArG box binding factor, phospholipase A2-activating protein, and early growth response 1 (Egr1) genes. In the second approach, to isolate ETS target promoters directly, we performed ETS1 binding with MboI-cleaved genomic DNA in the presence of a specific mAb followed by whole genome PCR. The immune complex-bound ETS binding sites containing DNA fragments were amplified and subcloned into pBluescript and subjected to DNA sequence and computer analysis. We found that, of a large number of clones isolated, 43 represented unique sequences not previously identified. Three clones turned out to contain regulatory sequences derived from human serglycin, preproapolipoprotein C II, and Egr1 genes. The ETS binding sites derived from these three regulatory sequences showed specific binding with recombinant ETS proteins. Of interest, Egr1 was identified by both of these techniques, suggesting strongly that it is indeed an ETS target gene.

Regular and stochastic dynamics in the real quadratic family

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c ∈ [−2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.

Vibrational population relaxation of carbon monoxide in the heme pocket of photolyzed carbonmonoxy myoglobin: Comparison of time-resolved mid-IR absorbance experiments and molecular dynamics simulations

The vibrational energy relaxation of carbon monoxide in the heme pocket of sperm whale myoglobin was studied by using molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300 K for both the δ- and ɛ-tautomers of the distal His-64. Vibrational population relaxation times of 335 ± 115 ps for the δ-tautomer and 640 ± 185 ps for the ɛ-tautomer were estimated by using the Landau–Teller model. Normal mode analysis was used to identify those protein residues that act as the primary “doorway” modes in the vibrational relaxation of the oscillator. Although the CO relaxation rates in both the ɛ- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer with the distal His playing an important role in the energy relaxation mechanism. Time-resolved mid-IR absorbance measurements were performed on photolyzed carbonmonoxy hemoglobin (Hb13CO). From these measurements, a T1 time of 600 ± 150 ps was determined. The simulation and experimental estimates are compared and discussed.

Multiple imprinted sense and antisense transcripts, differential methylation and tandem repeats in a putative imprinting control region upstream of mouse Igf2

The mouse insulin-like growth factor 2 (Igf2) locus is a complex genomic region that produces multiple transcripts from alternative promoters. Expression at this locus is regulated by parental imprinting. However, despite the existence of putative imprinting control elements in the Igf2 upstream region, imprinted transcriptional repression is abolished by null mutations at the linked H19 locus. To clarify the extent to which the Igf2 upstream region contains autonomous imprinting control elements we have performed functional and comparative analyses of the region in the mouse and human. Here we report the existence of multiple, overlapping imprinted (maternally repressed) sense and antisense transcripts that are associated with a tandem repeat in the mouse Igf2 upstream region. Regions flanking the repeat exhibit tissue-specific parental allelic methylation patterns, suggesting the existence of tissue-specific control elements in the upstream region. Studies in H19 null mice indicate that both parental allelic methylation and monoallelic expression of the upstream transcripts depends on an intact H19 gene acting in cis. The homologous region in human IGF2 is structurally conserved, with the significant exception that it does not contain a tandem repeat. Our results support the proposal that tandem repeats act to target methylation to imprinted genetic loci.

Induced fit DNA recognition by a minor groove binding analogue of Hoechst 33258: fluctuations in DNA A tract structure investigated by NMR and molecular dynamics simulations

NMR analysis and molecular dynamics simulations of d(GGTAATTACC)2 and its complex with a tetrahydropyrimidinium analogue of Hoechst 33258 suggest that DNA minor groove recognition in solution involves a combination of conformational selection and induced fit, rather than binding to a preorganised site. Analysis of structural fluctuations in the bound and unbound states suggests that the degree of induced fit observed is primarily a consequence of optimising van der Waals contacts with the walls of the minor groove resulting in groove narrowing through: (i) changes in base step parameters, including increased helical twist and propeller twist; (ii) changes to the sugar–phosphate backbone conformation to engulf the bound ligand; (iii) suppression of bending modes at the TpA steps. In contrast, the geometrical arrangement of hydrogen bond acceptors on the groove floor appears to be relatively insensitive to DNA conformation (helical twist and propeller twist). We suggest that effective recognition of DNA sequences (in this case an A tract structure) appears to depend to a significant extent on the sequence being flexible enough to be able to adopt the geometrically optimal conformation compatible with the various binding interactions, rather than involving ‘lock and key’ recognition.

Arp2/3 complex and actin dynamics are required for actin-based mitochondrial motility in yeast

The Arp2/3 complex is implicated in actin polymerization-driven movement of Listeria monocytogenes. Here, we find that Arp2p and Arc15p, two subunits of this complex, show tight, actin-independent association with isolated yeast mitochondria. Arp2p colocalizes with mitochondria. Consistent with this result, we detect Arp2p-dependent formation of actin clouds around mitochondria in intact yeast. Cells bearing mutations in ARP2 or ARC15 genes show decreased velocities of mitochondrial movement, loss of all directed movement and defects in mitochondrial morphology. Finally, we observe a decrease in the velocity and extent of mitochondrial movement in yeast in which actin dynamics are reduced but actin cytoskeletal structure is intact. These results support the idea that the movement of mitochondria in yeast is actin polymerization driven and that this movement requires Arp2/3 complex.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Differential Expression and Internal Feedback Regulation of 1-Aminocyclopropane-1-Carboxylate Synthase, 1-Aminocyclopropane-1-Carboxylate Oxidase, and Ethylene Receptor Genes in Tomato Fruit during Development and Ripening1

We investigated the feedback regulation of ethylene biosynthesis in tomato (Lycopersicon esculentum) fruit with respect to the transition from system 1 to system 2 ethylene production. The abundance of LE-ACS2, LE-ACS4, and NR mRNAs increased in the ripening fruit concomitant with a burst in ethylene production. These increases in mRNAs with ripening were prevented to a large extent by treatment with 1-methylcyclopropene (MCP), an ethylene action inhibitor. Transcripts for the LE-ACS6 gene, which accumulated in preclimacteric fruit but not in untreated ripening fruit, did accumulate in ripening fruit treated with MCP. Treatment of young fruit with propylene prevented the accumulation of transcripts for this gene. LE-ACS1A, LE-ACS3, and TAE1 genes were expressed constitutively in the fruit throughout development and ripening irrespective of whether the fruit was treated with MCP or propylene. The transcripts for LE-ACO1 and LE-ACO4 genes already existed in preclimacteric fruit and increased greatly when ripening commenced. These increases in LE-ACO mRNA with ripening were also prevented by treatment with MCP. The results suggest that in tomato fruit the preclimacteric system 1 ethylene is possibly mediated via constitutively expressed LE-ACS1A and LE-ACS3 and negatively feedback-regulated LE-ACS6 genes with preexisting LE-ACO1 and LE-ACO4 mRNAs. At the onset of the climacteric stage, it shifts to system 2 ethylene, with a large accumulation of LE-ACS2, LE-ACS4, LE-ACO1, and LE-ACO4 mRNAs as a result of a positive feedback regulation. This transition from system 1 to system 2 ethylene production might be related to the accumulated level of NR mRNA.