Stable Maps in Higher Dimensions

We formulate a notion of stability for maps between polarised varieties which generalises Kontsevich's definition when the domain is a curve and Tian-Donaldson's definition of K-stability when the target is a point. We give some examples, such as Kodaira embeddings and fibrations. We prove the existence of a projective moduli space of canonically polarised stable maps, generalising the Kontsevich-Alexeev moduli space of stable maps in dimensions one and two. We also state an analogue of the Yau-Tian-Donaldson conjecture in this setting, relating stability of maps to the existence of certain canonical Kähler metric

A finite dimensional approach to Donaldson's J-flow

Consider a projective manifold with two distinct polarisations $L_1$ and $L_2$. From this data, Donaldson has defined a natural flow on the space of Kähler metrics in $c_1$($L_1$), called the J-flow. The existence of a critical point of this flow is closely related to the existence of a constant scalar curvature Kähler metric in $c_1$($L_1$) for certain polarisations $L_2$. Associated to a quantum parameter $k$ $\gg$ 0, we define a flow over Bergman type metrics, which we call the J-balancing flow. We show that in the quantum limit $k$ → +∞, the rescaled J-balancing flow converges towards the J-flow. As corollaries, we obtain new proofs of uniqueness of critical points of the J-flow and also that these critical points achieve the absolute minimum of an associated energy functional. We show that the existence of a critical point of the J-flow implies the existence of J-balanced metrics for $k$ $\gg$ 0. Defining a notion of Chow stability for linear systems, we show that this in turn implies the linear system |$L_2$| is asymptotically Chow stable. Asymptotic Chow stability of |$L_2$| implies an analogue of K-semistability for the J-flow introduced by Lejmi-Székelyhidi, which we call J-semistability. We prove also that Jstability holds automatically in a certain numerical cone around $L_2$, and that if $L_2$ is the canonical class of the manifold that J-semistability implies K-stability. Eventually, this leads to new K-stable polarisations of surfaces of general type.The first author was funded by a studentship associated to an EPSRC Career Acceleration Fellowship (EP/J002062/1). The work of the second author has been carried out in the framework of the Labex Archimede (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX- 0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR). The second author was also partially supported by supported by the ANR project EMARKS, decision No ANR-14-CE25-0010

DNA crosslinking and biological activity of a hairpin polyamide–chlorambucil conjugate

A prototype of a novel class of DNA alkylating agents, which combines the DNA crosslinking moiety chlorambucil (Chl) with a sequence-selective hairpin pyrrole-imidazole polyamide ImPy-beta-ImPy-gamma-ImPy-beta-Dp (polyamide 1), was evaluated for its ability to damage DNA and induce biological responses. Polyamide 1-Chl conjugate (1-Chl) alkylates and interstrand crosslinks DNA in cell-free systems. The alkylation occurs predominantly at 5'-AGCTGCA-3' sequence, which represents the polyamide binding site. Conjugate-induced lesions were first detected on DNA treated for 1 h with 0.1 muM 1-Chl, indicating that the conjugate is at least 100-fold more potent than Chl. Prolonged incubation allowed for DNA damage detection even at 0.01 muM concentration. Treatment with 1-Chl decreased DNA template activity in simian virus 40 (SV40) in vitro replication assays. 1-Chl inhibited mammalian cell growth, genomic DNA replication and cell cycle progression, and arrested cells in the G(2)/M phase. Moreover, cellular effects were observed at 1-Chl concentrations similar to those needed for DNA damage in cell-free systems. Neither of the parent compounds, unconjugated Chl or polyamide 1, demonstrated any cellular activity in the same concentration range. The conjugate molecule 1-Chl possesses the sequence-selectivity of a polyamide and the enhanced DNA reactivity of Chl

Upgrade to the Birmingham Irradiation Facility

The Birmingham Irradiation Facility was developed in 2013 at the University of Birmingham using the Medical Physics MC40 cyclotron. It can achieve High Luminosity LHC (HL-LHC) fluences of 1015 (1 MeV neutron equivalent (neq)) cm-2 in 80 s with proton beam currents of 1 μA and so can evaluate effectively the performance and durability of detector technologies and new components to be used for the HL-LHC. Irradiations of silicon sensors and passive materials can be carried out in a temperature controlled cold box which moves continuously through the homogenous beamspot. This movement is provided by a pre-configured XY-axis Cartesian robot scanning system. In 2014 the cooling system and cold box were upgraded from a recirculating glycol chiller system to a liquid nitrogen evaporative system. The new cooling system achieves a stable temperature of -50 °C in 30 min and aims to maintain sub-0 °C temperatures on the sensors during irradiations. This paper reviews the design, development, commissioning and performance of the new cooling system

Expanding the Repertoire of Natural Product-Inspired Ring Pairs for Molecular Recognition of DNA

A furan amino acid, inspired by the recently discovered proximicin natural products, was incorporated into the scaffold of a DNA-binding hairpin polyamide. While unpaired oligomers of 2,4-disubstituted furan amino acids show poor DNA-binding activity, furan (Fn) carboxamides paired with N-methylpyrrole (Py) and N-methylimidazole (Im) rings demonstrate excellent stabilization of duplex DNA as well as discrimination of noncognate sequences, consistent with function as a Py mimic according to the Py/Im polyamide pairing rules

Fmoc solid phase synthesis of polyamides containing pyrrole and imidazole amino acids

Polyamides containing N-methylimidazole (Im) and N-methylpyrrole (Py) amino acids are synthetic ligands that have an affinity and specificity for DNA comparable to those of many naturally occurring DNA binding proteins. A machine-assisted Fmoc solid phase synthesis of polyamides has been optimized to afford high stepwise coupling yields (>99%). Two monomer building blocks, Fmoc-Py acid and Fmoc-Im acid, were prepared in multigram scale. Cleavage by aminolysis followed by HPLC purification affords up to 200 mg quantities of polyamide with purities and yields greater than or equal to those reported using Boc chemistry. A broader set of reaction conditions will increase the number and complexity of minor groove binding polyamides which may be prepared and help ensure compatibility with many commercially available peptide synthesizers

K-stability for Kähler manifolds

We formulate a notion of K-stability for Kähler manifolds, and prove one direction of the Yau–Tian–Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies K-semistability (resp. uniformly K-stable). In particular this shows that the existence of a constant scalar curvature Kähler metric implies K-semistability, and K-stability if one assumes the automorphism group is discrete. We also show how Stoppa’s argument holds in the Kähler case, giving a simpler proof of this K-stability statement.JR is supported by an EPSRC Career Accelleration Grant (EP/J002062/1) which also provides RD’s studentship. RD has received additional support from a Fondation Wiener-Anspach scholarship

A pyrrole-imidazole polyamide is active against enzalutamide-resistant prostate cancer

The LREX' prostate cancer model is resistant to the antiandrogen enzalutamide via activation of an alternative nuclear hormone receptor (NHR), glucocorticoid receptor (GR), which has similar DNA binding specificity to the androgen receptor (AR). Small molecules that target DNA to interfere with protein-DNA interactions may retain activity against enzalutamide-resistant prostate cancers where ligand binding domain antagonists are ineffective. We reported previously that a pyrrole-imidazole (Py-Im) polyamide designed to bind the consensus androgen response element half-site has antitumor activity against hormone-sensitive prostate cancer. In enzalutamide-resistant LREX' cells, Py-Im polyamide interfered with both androgen receptor- and glucocorticoid receptor-driven gene expression, while enzalutamide interfered with only that of androgen receptor. Genomic analyses indicated immediate interference with the androgen receptor transcriptional pathway. Long-term treatment with Py-Im polyamide demonstrated a global decrease in RNA levels consistent with inhibition of transcription. The polyamide was active against two enzalutamide-resistant xenografts with minimal toxicity. Overall, our results identify Py-Im polyamide as a promising therapeutic strategy in enzalutamide-resistant prostate cancer

Microwave Assisted Synthesis of Py-Im Polyamides

Microwave synthesis was utilized to rapidly build Py-Im polyamides in high yields and purity using Boc-protection chemistry on Kaiser oxime resin. A representative polyamide targeting the 5′-WGWWCW-3′ (W = A or T) subset of the consensus Androgen and Glucocorticoid Response Elements was synthesized in 56% yield after 20 linear steps and HPLC purification. It was confirmed by Mosher amide derivatization of the polyamide that a chiral α-amino acid does not racemize after several additional coupling steps