On a Subposet of the Tamari Lattice

We explore some of the properties of a subposet of the Tamari lattice introduced by Pallo, which we call the comb poset. We show that three binary functions that are not well-behaved in the Tamari lattice are remarkably well-behaved within an interval of the comb poset: rotation distance, meets and joins, and the common parse words function for a pair of trees. We relate this poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

A Survey of the Higher Stasheff-Tamari Orders

The Tamari lattice, thought as a poset on the set of triangulations of a convex polygon with n vertices, generalizes to the higher Stasheff-Tamari orders on the set of triangulations of a cyclic d-dimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them

Homology Modeling of Human c-Butyric Acid Transporters and the Binding of Pro-Drugs 5-Aminolevulinic Acid and Methyl Aminolevulinic Acid Used in Photodynamic Therapy

Photodynamic therapy (PDT) is a safe and effective method currently used in the treatment of skin cancer. In ALA-basedPDT, 5-aminolevulinic acid (ALA), or ALA esters, are used as pro-drugs to induce the formation of the potent photosensitizerprotoporphyrin IX (PpIX). Activation of PpIX by light causes the formation of reactive oxygen species (ROS) and toxicresponses. Studies have indicated that ALA and its methyl ester (MAL) are taken up into the cells via c-butyric acid (GABA)transporters (GATs). Uptake via GATs into peripheral sensory nerve endings may also account for one of the few adverseside effects of ALA-based PDT, namely pain. In the present study, homology models of the four human GAT subtypes wereconstructed using three x-ray crystal structures of the homologous leucine transporter (LeuT) as templates. Binding of thenative substrate GABA and the possible substrates ALA and MAL was investigated by molecular docking of the ligands intothe central putative substrate binding sites in the outward-occluded GAT models. Electrostatic potentials (ESPs) of theputative substrate translocation pathway of each subtype were calculated using the outward-open and inward-openhomology models. Our results suggested that ALA is a substrate of all four GATs and that MAL is a substrate of GAT-2, GAT-3and BGT-1. The ESP calculations indicated that differences likely exist in the entry pathway of the transporters (i.e. inoutward-open conformations). Such differences may be exploited for development of inhibitors that selectively targetspecific GAT subtypes and the homology models may hence provide tools for design of therapeutic inhibitors that can beused to reduce ALA-induced pain.<p><em>©</em>2013 Baglo et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.</p