AbstractsFunctions of several variables, such as the electron density and the nuclear Born-Oppenheimer potential, may be analysed very effectively using orthogonal trajectories. In particular the behaviour of these trajectories at critical points of the functions is investigated in detail. The use of orthogonal trajectories in the virial partitioning of Bader and in the definition of reaction coordinates is extended. A chemical interpretation of the critical points is suggested. The relevance of catastrophe theory is illustrated.Des fonctions de plusieurs variables, comme par exemple la densitt tlectronique et le potentiel nucltaire de Born-Oppenheimer, peuvent Stre analystes tres effectivement avec des trajectoires orthogonales. En particulier le comportement de ces trajectoires B des points critiques des fonctions est etudit en dttail. L'emploi de trajectoires orthogonales dans le partitionnement viriel de Bader et dans la dtfinition de coordonntes de rtaction a ttf gtnkralist. On propose une interpritation chimique des points critiques. L'importance de la thtorie des catastrophes a t t t illustrte.Funktionen mehrerer Veranderlichen, wie die Elektronendichte und das Born-Oppenheimersche Kernpotential, konnen mittels orthogonaler Trajektorien sehr effektiv analysiert werden. Im besonderen wird das Auftreten dieser Trajektorien in kritischen Punkten der Funktionen ausfuhrlich untersucht. Die Anwendung von orthogonalen Trajektorien in der Baderschen Virialzerlegung und in der Definition von Reaktionskoordinaten wird verallgemeinert. Eine chemische Interpretation der kritischen Punkte wird vorgeschlagen. Die Bedeufung der Katastrophentheorie wird illustriert.

SummaryIn bacteria, the highly conserved RsmA/CsrA family of RNA-binding proteins functions as global posttranscriptional regulators acting on mRNA translation and stability. Through phenotypic complementation of an rsmA mutant in Pseudomonas aeruginosa, we discovered a family member, termed RsmN. Elucidation of the RsmN crystal structure and that of the complex with a hairpin from the sRNA, RsmZ, reveals a uniquely inserted α helix, which redirects the polypeptide chain to form a distinctly different protein fold to the domain-swapped dimeric structure of RsmA homologs. The overall β sheet structure required for RNA recognition is, however, preserved with compensatory sequence and structure differences, allowing the RsmN dimer to target binding motifs in both structured hairpin loops and flexible disordered RNAs. Phylogenetic analysis indicates that, although RsmN appears unique to P. aeruginosa, homologous proteins with the inserted α helix are more widespread and arose as a consequence of a gene duplication event.

The theory of wave functions which have the form of a single determinant, but without the restriction to doubly occupied orbitals, is developed in general terms. The unrestricted molecular orbitals, the natural spin orbitals, the natural orbitals and the corresponding orbitals are defined and some of their properties deduced. The use of annihilators and projection operators to produce eigenfunctions of spin is investigated. The role of molecular symmetry and of a truncated set of basic functions in forcing a single determinant to be an eigenfunction of spin is discussed. A theorem on the diagonalization of a rectangular matrix by two unitary matrices is proved and applied to density matrices.

Context. Regular observations of Jupiter by a large number of amateur astronomers have resulted in the serendipitous discovery of short bright flashes in its atmosphere, which have been proposed as being caused by impacts of small objects. Three flashes were detected: one on June 3, 2010, one on August 20, 2010, and one on September 10, 2012. Aims. We show that the flashes are caused by impacting objects that we characterize in terms of their size, and we study the flux of small impacts on Jupiter. Methods. We measured the light curves of these atmospheric airbursts to extract their luminous energy and computed the masses and sizes of the objects. We ran simulations of impacts and compared them with the light curves. We analyzed the statistical significance of these events in the large pool of Jupiter observations. Results. All three objects are in the 5−20 m size category depending on their density, and they released energy comparable to the recent Chelyabinsk airburst. Model simulations approximately agree with the interpretation of the limited observations. Biases in observations of Jupiter suggest a rate of 12−60 similar impacts per year and we provide software tools for amateurs to examine the faint signature of impacts in their data to increase the number of detected collisions. Conclusions. The impact rate agrees with dynamical models of comets. More massive objects (a few 100 m) should impact with Jupiter every few years leaving atmospheric dark debris features that could be detectable about once per decade.

Zymogen PK is activated to PKa and cleaves substrates kininogen and FXII contributing to bradykinin generation. Monomeric PKa and dimeric homologue FXI utilize the N‐terminal apple domains to recruit substrates. A high‐resolution 1.3 Å structure of full‐length PKa reveals an active conformation of the protease and apple domains. The PKa protease and four‐apple domain disc organization is 180° rotated compared to FXI. Summary BackgroundPlasma prekallikrein (PK) and factor XI (FXI) are apple domain‐containing serine proteases that when activated to PKa and FXIa cleave substrates kininogen, factor XII, and factor IX, respectively, directing plasma coagulation, bradykinin release, inflammation, and thrombosis pathways. ObjectiveTo investigate the three‐dimensional structure of full‐length PKa and perform a comparison with FXI. MethodsA series of recombinant full‐length PKa and FXI constructs and variants were developed and the crystal structures determined. Results and conclusionsA 1.3 Å structure of full‐length PKa reveals the protease domain positioned above a disc‐shaped assemblage of four apple domains in an active conformation. A comparison with the homologous FXI structure reveals the intramolecular disulfide and structural differences in the apple 4 domain that prevents dimer formation in PK as opposed to FXI. Two latchlike loops (LL1 and LL2) extend from the PKa protease domain to form interactions with the apple 1 and apple 3 domains, respectively. A major unexpected difference in the PKa structure compared to FXI is the 180° disc rotation of the apple domains relative to the protease domain. This results in a switched configuration of the latch loops such that LL2 interacts and buries portions of the apple 3 domain in the FXI zymogen whereas in PKa LL2 interacts with the apple 1 domain. Hydrogen‐deuterium exchange mass spectrometry on plasma purified human PK and PKa determined that regions of the apple 3 domain have increased surface exposure in PKa compared to the zymogen PK, suggesting conformational change upon activation.

An analysis of the ‘linear combination of atomic orbitals’ approximation using the accurate molecular orbital equations shows that it does not lead to equations of the form usually assumed in the semi-empirical molecular orbital method. A new semi-empirical method is proposed, therefore, in terms of equivalent orbitals. The equations obtained, which do have the usual form, are applicable to a large class of molecules and do not involve the approximations that were thought necessary. In this method the ionization potentials are calculated by treating certain integrals as semi-empirical parameters. The value of these parameters is discussed in terms of the localization of equivalent orbitals and some approximate rules are suggested. As an illustration the ionization potentials of the paraffin series are considered and good agreement between the observed and calculated values is found.

The case is argued that the rigorous use of expert systems and abstract data types for quantum chemical calculations can lead to a more open, more flexible program, which is easier for a novice to use but also, through the possibility of rapid prototyping and symbolic manipulation, for an expert to exploit as an important working tool. The ideas behind this program are, however, quite general and apply equally to many other scientific areas where experience and different numerical techniques have to be combined in a flexible way to produce useful results.

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