Supramolecular assembly of a phosphole-based moiety into nanostructures dictated by alkynylplatinum(II) terpyridine complexes through non-covalent Pt···Pt and π–π stacking interactions: synthesis, characterization, photophysics and self-assembly behaviors

published_or_final_versio

A Large k Asymptotics of Witten's Invariant of Seifert Manifolds

We calculate a large $k$ asymptotic expansion of the exact surgery formula for Witten's $SU(2)$ invariant of Seifert manifolds. The contributions of all flat connections are identified. An agreement with the 1-loop formula is checked. A contribution of the irreducible connections appears to contain only a finite number of terms in the asymptotic series. A 2-loop correction to the contribution of the trivial connection is found to be proportional to Casson's invariant.Comment: 51 pages (Some changes are made to the Discussion section. A surgery formula for perturbative corrections to the contribution of the trivial connection is suggested.

A Contribution of the Trivial Connection to Jones Polynomial and Witten's Invariant of 3d Manifolds I

We use the Chern-Simons quantum field theory in order to prove a recently conjectured limitation on the 1/K expansion of the Jones polynomial of a knot and its relation to the Alexander polynomial. This limitation allows us to derive a surgery formula for the loop corrections to the contribution of the trivial connection to Witten's invariant. The 2-loop part of this formula coincides with Walker's surgery formula for Casson-Walker invariant. This proves a conjecture that Casson-Walker invariant is a 2-loop correction to the trivial connection contribution to Witten's invariant of a rational homology sphere. A contribution of the trivial connection to Witten's invariant of a manifold with nontrivial rational homology is calculated for the case of Seifert manifolds.Comment: 28 page

A TQFT associated to the LMO invariant of three-dimensional manifolds

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant.Comment: 28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.

Exchange Interaction in Binuclear Complexes with Rare Earth and Copper Ions: A Many-Body Model Study

We have used a many-body model Hamiltonian to study the nature of the magnetic ground state of hetero-binuclear complexes involving rare-earth and copper ions. We have taken into account all diagonal repulsions involving the rare-earth 4f and 5d orbitals and the copper 3d orbital. Besides, we have included direct exchange interaction, crystal field splitting of the rare-earth atomic levels and spin-orbit interaction in the 4f orbitals. We have identified the inter-orbital $4f$ repulsion, U$_{ff}$ and crystal field parameter, $\Delta_f$ as the key parameters involved in controlling the type of exchange interaction between the rare earth $4f$ and copper 3d spins. We have explored the nature of the ground state in the parameter space of U$_{ff}$, $\Delta_f$, spin-orbit interaction strength $\lambda$ and the $4f$ filling n$_f$. We find that these systems show low-spin or high-spin ground state depending on the filling of the $4f$ levels of the rare-earth ion and ground state spin is critically dependent on U$_{ff}$ and $\Delta_f$. In case of half-filling (Gd(III)) we find a reentrant low-spin state as U$_{ff}$ is increased, for small values of $\Delta_f$, which explains the recently reported apparent anomalous anti-ferromagnetic behaviour of Gd(III)-radical complexes. By varying U$_{ff}$ we also observe a switch over in the ground state spin for other fillings . We have introduced a spin-orbit coupling scheme which goes beyond L-S or j-j coupling scheme and we find that spin-orbit coupling does not significantly alter the basic picture.Comment: 22 pages, 11 ps figure

High dimensional and high resolution pulse sequences for backbone resonance assignment of intrinsically disordered proteins

Four novel 5D (HACA(N)CONH, HNCOCACB, (HACA)CON(CA)CONH, (H)NCO(NCA)CONH), and one 6D ((H)NCO(N)CACONH) NMR pulse sequences are proposed. The new experiments employ non-uniform sampling that enables achieving high resolution in indirectly detected dimensions. The experiments facilitate resonance assignment of intrinsically disordered proteins. The novel pulse sequences were successfully tested using δ subunit (20 kDa) of Bacillus subtilis RNA polymerase that has an 81-amino acid disordered part containing various repetitive sequences

Mechanism of subunit interaction at ketosynthase-dehydratase junctions in trans-AT polyketide synthases

Modular polyketide synthases (PKSs) produce numerous structurally complex natural products with diverse applications in medicine and agriculture. They typically consist of several multienzyme subunits that utilize structurally-defined docking domains (DDs) at their N- and C-termini to ensure correct assembly into functional multi-protein complexes. Here we report a fundamentally different mechanism for subunit assembly in trans-AT modular PKSs at the junction between ketosynthase (KS) and dehydratase (DH) domains. This involves direct interaction of a largely unstructured docking domain (DD) at the C-terminus of the KS with the surface of the downstream DH. Acyl transfer assays and mechanism-based cross-linking established that the DD is required for the KS to communicate with the acyl carrier protein appended to the DH. Two distinct regions for binding of the DD to the DH were identified using NMR spectroscopy, carbene foot-printing and mutagenesis, providing a foundation for future elucidation of the molecular basis for interaction specificity

Structure of S. aureus HPPK and the Discovery of a New Substrate Site Inhibitor

The first structural and biophysical data on the folate biosynthesis pathway enzyme and drug target, 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (SaHPPK), from the pathogen Staphylococcus aureus is presented. HPPK is the second essential enzyme in the pathway catalysing the pyrophosphoryl transfer from cofactor (ATP) to the substrate (6-hydroxymethyl-7,8-dihydropterin, HMDP). In-silico screening identified 8-mercaptoguanine which was shown to bind with an equilibrium dissociation constant, Kd, of ∼13 µM as measured by isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR). An IC50 of ∼41 µM was determined by means of a luminescent kinase assay. In contrast to the biological substrate, the inhibitor has no requirement for magnesium or the ATP cofactor for competitive binding to the substrate site. The 1.65 Å resolution crystal structure of the inhibited complex showed that it binds in the pterin site and shares many of the key intermolecular interactions of the substrate. Chemical shift and 15N heteronuclear NMR measurements reveal that the fast motion of the pterin-binding loop (L2) is partially dampened in the SaHPPK/HMDP/α,β-methylene adenosine 5′-triphosphate (AMPCPP) ternary complex, but the ATP loop (L3) remains mobile on the µs-ms timescale. In contrast, for the SaHPPK/8-mercaptoguanine/AMPCPP ternary complex, the loop L2 becomes rigid on the fast timescale and the L3 loop also becomes more ordered – an observation that correlates with the large entropic penalty associated with inhibitor binding as revealed by ITC. NMR data, including 15N-1H residual dipolar coupling measurements, indicate that the sulfur atom in the inhibitor is important for stabilizing and restricting important motions of the L2 and L3 catalytic loops in the inhibited ternary complex. This work describes a comprehensive analysis of a new HPPK inhibitor, and may provide a foundation for the development of novel antimicrobials targeting the folate biosynthetic pathway