Manifolds and graphs with slow heat kernel decay

We give upper estimates on the long time behavior of the heat kernel on non-compact Riemannian manifolds and infinite graphs, which only depend on a lower bound of the volume growth. We also show that these estimates are sharp. Oblatum 23-VIII-1999 & 21-XII-2000?Published online: 5 March 2001     

Multivariate analysis of extremely large ToFSIMS imaging datasets by a rapid PCA method

Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth profiles in X‐ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES) and secondary ion mass spectrometry (SIMS). These methods have proved equally useful in fundamental studies as in applied work where speed of interpretation is very valuable. Until now these methods have been difficult to apply to very large datasets such as spectra associated with 2D images or 3D depth‐profiles. Existing algorithms for computing PCA matrices have been either too slow or demanded more memory than is available on desktop PCs. This often forces analysts to ‘bin’ spectra on much more coarse a grid than they would like, perhaps even to unity mass bins even though much higher resolution is available, or select only part of an image for PCA analysis, even though PCA of the full data would be preferred. We apply the new ‘random vectors’ method of singular value decomposition proposed by Halko and co‐authors to time‐of‐flight (ToF)SIMS data for the first time. This increases the speed of calculation by a factor of several hundred, making PCA of these datasets practical on desktop PCs for the first time. For large images or 3D depth profiles we have implemented a version of this algorithm which minimises memory needs, so that even datasets too large to store in memory can be processed into PCA results on an ordinary PC with a few gigabytes of memory in a few hours. We present results from ToFSIMS imaging of a citrate crystal and a basalt rock sample, the largest of which is 134GB in file size corresponding to 67 111 mass values at each of 512 × 512 pixels. This was processed into 100 PCA components in six hours on a conventional Windows desktop PC. © 2015 The Authors. Surface and Interface Analysis published by John Wiley & Sons Ltd.     

Linked Supramolecular Building Blocks for Enhanced Cluster Formation

Methylene‐bridged calix[4]arenes have emerged as extremely versatile ligand supports in the formation of new polymetallic clusters possessing fascinating magnetic properties. Metal ion binding rules established for this building block allow one to partially rationalise the complex assembly process. The ability to covalently link calix[4]arenes at the methylene bridge provides significantly improved control over the introduction of different metal centres to resulting cluster motifs. Clusters assembled from bis‐calix[4]arenes and transition metal ions or 3d‐4f combinations display characteristic features of the analogous calix[4]arene supported clusters, thereby demonstrating an enhanced and rational approach towards the targeted synthesis of complex and challenging structures.     

Facile Interchange of 3d and 4f Ions in Single‐Molecule Magnets: Stepwise Assembly of [Mn4], [Mn3Ln] and [Mn2Ln2] Cages within Calix[4]arene Scaffolds

The central Mn^II ions in a series of calix[4]arene‐stabilised butterflies can be sequentially replaced with Ln^III ions, maintaining the structural integrity of the molecule but transforming its magnetic properties. The replacement of Mn^II for Gd^III allows for the examination of the transferability of spin‐Hamiltonian parameters within the family as well as permitting their reliable determination. The introduction of the 4f ions results in weaker intramolecular magnetic exchange, an increase in the number of low‐lying excited states, and an increase in magnetisation relaxation, highlighting the importance of exchange over single‐ion anisotropy for the observation of SMM behaviour in this family of complexes. The presence of the [TM^II/III(TBC[4])(OH)(solvent)] metalloligand (TM=transition metal, TBC=p‐tBu‐calix[4]arene) suggests that magnetic calix[n]arene building blocks can be employed to encapsulate a range of different “guests” within structurally robust “hosts”.     

Mapping a Noncovalent Protein–Peptide Interface by Top-Down FTICR Mass Spectrometry Using Electron Capture Dissociation

Noncovalent protein–ligand and protein–protein complexes are readily detected using electrospray ionization mass spectrometry (ESI MS). Furthermore, recent reports have demonstrated that careful use of electron capture dissociation (ECD) fragmentation allows covalent backbone bonds of protein complexes to be dissociated without disruption of noncovalent protein–ligand interactions. In this way the site of protein–ligand interfaces can be identified. To date, protein–ligand complexes, which have proven tractable to this technique, have been mediated by ionic electrostatic interactions, i.e., ion pair interactions or salt bridging. Here we extend this methodology by applying ECD to study a protein–peptide complex that contains no electrostatics interactions. We analyzed the complex between the 21 kDa p53-inhibitor protein anterior gradient-2 and its hexapeptide binding ligand (PTTIYY). ECD fragmentation of the 1:1 complex occurs with retention of protein–peptide binding and analysis of the resulting fragments allows the binding interface to be localized to a C-terminal region between residues 109 and 175. These finding are supported by a solution-phase competition assay, which implicates the region between residues 108 and 122 within AGR2 as the PTTIYY binding interface. Our study expands previous findings by demonstrating that top-down ECD mass spectrometry can be used to determine directly the sites of peptide–protein interfaces. This highlights the growing potential of using ECD and related top-down fragmentation techniques for interrogation of protein–protein interfaces.