The combinatorial game Nofil played on Steiner triple systems

We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions.     

Synthesis of stable and cell-type selective analogues of cyclic ADP-ribose, a Ca(2+)-mobilizing second messenger. Structure--activity relationship of the N1-ribose moiety

We previously developed cyclic ADP-carbocyclic ribose (cADPcR, 2) as a stable mimic of cyclic ADP-ribose (cADPR, 1), a Ca(2+)-mobilizing second messenger. A series of the N1-ribose modified cADPcR analogues, designed as novel stable mimics of cADPR, which were the 2"-deoxy analogue 3, the 3"-deoxy analogue 4, the 3"-deoxy-2"-O-(methoxymethyl) analogue 5, the 3"-O-methyl analogue 6, the 2",3"-dideoxy analogue 7, and the 2",3"-dideoxydidehydro analogue 8, were successfully synthesized using the key intramolecular condensation reaction with phenylthiophosphate-type substrates. We investigated the conformations of these analogues and of cADPR and found that steric repulsion between both the adenine and N9-ribose moieties and between the adenine and N1-ribose moieties was a determinant of the conformation. The Ca(2+)-mobilizing effects were evaluated systematically using three different biological systems, i.e., sea urchin eggs, NG108-15 neuronal cells, and Jurkat T-lymphocytes. The relative potency of Ca(2+)-mobilization by these cADPR analogues varies depending on the cell-type used: e.g., 3"-deoxy-cADPcR (4) > cADPcR (2) > cADPR (1) in sea urchin eggs; cADPR (1) > cADPcR (2) approximately 3"-deoxy-cADPcR (4) in T-cells; and cADPcR (2) > cADPR (1) > 3"-deoxy-cADPcR (4) in neuronal cells, respectively. These indicated that the target proteins and/or the mechanism of action of cADPR in sea urchin eggs, T-cells, and neuronal cells are different. Thus, this study represents an entry to cell-type selective cADPR analogues, which can be used as biological tools and/or novel drug leads.     

Subunit rotation models activation of serotonin 5-HT<Subscript>3AB</Subscript> receptors by agonists

The N-terminal extracellular regions of heterooligomeric 3AB-type human 5-hydroxytryptamine receptors (5-HT3ABR) were modelled based on the crystal structure of snail acetylcholine binding protein AChBP. Stepwise rotation of subunit A by 5 degrees was performed between -10 degrees and 15 degrees to mimic agonist binding and receptor activation. Anticlockwise rotation reduced the size of the binding cavity in interface AB and reorganised the network of hydrogen bonds along the interface. AB subunit dimers with different rotations were applied for docking of ligands with different efficacies: 5-HT, m-chlorophenylbiguanide, SR 57227, quinolinyl piperazine and lerisetron derivatives. All ligands were docked into the dimer with -10 degrees rotation representing ligand-free, open binding cavities similarly, without pharmacological discrimination. Their ammonium ions were in hydrogen bonding distance to the backbone carbonyl of W183. Anticlockwise rotation and contraction of the binding cavity led to distinctive docking interactions of agonists with E129 and cation-pi interactions of their ammonium ions. Side chains of several further amino acids participating in docking (Y143, Y153, Y234 and E236) are in agreement with the effects of point mutations in the binding loops. Our model postulates that 5-HT binds to W183 in a hydrophobic cleft as well as to E236 in a hydrophilic vestibule. Then it elicits anticlockwise rotation to draw in loop C via pi-cation-pi interactions of its ammonium ion with W183 and Y234. Finally, closure of the binding cavity might end in rebinding of 5-HT to E129 in the hydrophilic vestibule.     

Graph Pairs and their Entropies: Modularity Problems

Received June 24, 1997