All (connected) graphlets of sizes <i>k</i> = 3, 4, 5 nodes, and their automorphism orbits; within each graphlet, nodes of equal shading are in the same orbit.

<p>The numbering of these graphlets and orbits were created by hand [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181570#pone.0181570.ref008" target="_blank">8</a>] and do not correspond to the automatically generated numbering used in this paper. The figure is taken verbatim from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181570#pone.0181570.ref016" target="_blank">16</a>].</p

All the possible 3-graphettes.

<p>All the possible 3-graphettes.</p

For each value of <i>k</i>: The number of bits required to store the lower-triangle of the adjacency matrix for an undirected <i>k</i>-graphette; the number of such <i>k</i>-graphettes counting all isomorphs which is just 2^{<i>b</i>(<i>k</i>)}; the number of canonical <i>k</i>-graphettes (this will be the number of unique entries in the above lookup table [22], and up to <i>k</i> = 8, 14 bits is sufficient); and the total number of unique automorphism orbits (up to <i>k</i> = 8, 17 bits is sufficient) [27].

<p>Note that up to <i>k</i> = 8, together the lookup table for canonical graphettes and their canonical orbits fits into 31 bits, allowing storage as a single 4-byte integer, with 1 bit to store whether the graphette is connected (i.e., also a graphlet). The suffixes K, M, G, T, P, and E represent exactly 2¹⁰, 2²⁰, 2³⁰, 2⁴⁰, 2⁵⁰ and 2⁶⁰, respectively.</p

All 3-graphettes with exactly one edge; the <i>canonical</i> one is the one with lowest integer representation (the middle one in this case).

<p>Each of them is placed in a lookup table indexed by the bit vector representation of its adjacency matrix, pointing at the canonical one. In this way we can determine that it is the one-edge 3-graphette in constant time.</p

Three isomorphic representations of the Petersen graph.

<p>Three isomorphic representations of the Petersen graph.</p

Mutual complexation between p-p stacked molecular tweezers

Aromatic and heterocyclic molecules which form electronically complementary p-p stacked complexes have recently found extensive application in functional materials, molecular machines, and stimuli-responsive supra- molecular polymers. Here we describe the design and synthesis of model compounds that self-assemble through complemen- tary stacking motifs, paralleling those postulated to exist in high-molecular weight, healable, supramolecular polymer systems. Complexation studies using 1H NMR and UV-vis spectroscopy indicated formation of a complementary complex between a p-electron rich dipyrenyl tweezer-motif and a tweezer-like, p-electron deficient bis-diimide. The binding stoichiometry in solution between the chain-folding diimide and the pyrenyl derivative was equimolar with respect to the two binding motifs, and the resulting association constant was measured at Ka = 1200 ± 90 M-1. Single crystal X-ray analysis of this “tweezer- tweezer” complex showed a low-energy conformation of the triethylenedioxy linker within the bis-diimide chain-fold. Interplanar separations of 3.4-3.5 Å were found within the p-stacks, and supporting hydrogen bonds between pyrenyl amide NH groups and diimide carbonyl oxygens were identified

Two alignments of assemblies to the finished sequence of BAC GMEZ.

<p>The original Atlas assembly created a single scaffold. The UMD+Atlas assembly of GMEZ assembled a 26 Kb section from the middle of the bigger scaffold into a separate Scaffold 1. Note that the large scaffold gap in the Scaffold 2 is estimated correctly. This UMD+Atlas assembly used reliable overlaps. This was the BAC that gave UMD+Atlas the most trouble and the only case where UMD+Atas assembly had two scaffolds.</p

Illustration of the technique that identifies reliable overlaps: (a) a scenario where a genome contains two copies of a repeat region R.

<p>The correct positions of reads A, B, C and D are shown. (b) A “fork” in the overlaps. (c) a scenario where reads A and D have the same sequencing error at the same base.</p

Janus PEG-Based Dendrimers for Use in Combination Therapy: Controlled Multi-Drug Loading and Sequential Release

The increasing use of drug combinations to treat disease states, such as cancer, calls for improved delivery systems that are able to deliver multiple agents. Herein, we report a series of novel Janus dendrimers with potential for use in combination therapy. Different generations (first and second) of PEG-based dendrons containing two different “model drugs”, benzyl alcohol (BA) and 3-phenylpropionic acid (PPA), were synthesized. BA and PPA were attached via two different linkers (carbonate and ester, respectively) to promote differential drug release. The four dendrons were coupled together via (3 + 2) cycloaddition chemistries to afford four Janus dendrimers, which contained varying amounts and different ratios of BA and PPA, namely, <b>(BA)</b>_<b>2</b><b>-G1-G1-(PPA)</b>_<b>2</b>, <b>(BA)</b>_<b>4</b><b>-G2-G1-(PPA)</b>_<b>2</b>, <b>(BA)</b>_<b>2</b><b>-G1-G2-(PPA)</b>_<b>4</b>, and <b>(BA)</b>_<b>4</b><b>-G2-G2-(PPA)</b>_<b>4</b>. Release studies in plasma showed that the dendrimers provided sequential release of the two model drugs, with BA being released faster than PPA from all of the dendrons. The different dendrimers allowed delivery of increasing amounts (0.15–0.30 mM) and in exact molecular ratios (1:2; 2:1; 1:2; 2:2) of the two model drug compounds. The dendrimers were noncytotoxic (100% viability at 1 mg/mL) toward human umbilical vein endothelial cells (HUVEC) and nontoxic toward red blood cells, as confirmed by hemolysis studies. These studies demonstrate that these Janus PEG-based dendrimers offer great potential for the delivery of drugs via combination therapy

Two alignments of assemblies to the finished sequence of BAC GQQD.

<p>The original Atlas assembly created two scaffolds only covering 73.2% of the finished sequence. Note the misplaced 20 Kb segment in the Atlas assembly. The UMD+Atlas assembly of GQQD correctly places the 20 Kb section originally misplaced and creates a single scaffold of the BAC covering 93.3% of the finished sequence. This UMD+Atlas assembly used reliable overlaps. This was the BAC that gave Atlas the most trouble.</p