Truncation identities for the small polaron fusion hierarchy

We study a one-dimensional lattice model of interacting spinless fermions. This model is integrable for both periodic and open boundary conditions; the latter case includes the presence of Grassmann valued non-diagonal boundary fields breaking the bulk U(1) symmetry of the model. Starting from the embedding of this model into a graded Yang-Baxter algebra, an infinite hierarchy of commuting transfer matrices is constructed by means of a fusion procedure. For certain values of the coupling constant related to anisotropies of the underlying vertex model taken at roots of unity, this hierarchy is shown to truncate giving a finite set of functional equations for the spectrum of the transfer matrices. For generic coupling constants, the spectral problem is formulated in terms of a functional (or TQ-)equation which can be solved by Bethe ansatz methods for periodic and diagonal open boundary conditions. Possible approaches for the solution of the model with generic non-diagonal boundary fields are discussed.

Phospholipases and the network of auxin signal transduction with ABP1 and TIR1 as two receptors: a comprehensive and provocative model

Three types of phospholipases, phospholipase D, secreted phospholipase A2, and patatin-related phospholipase A (pPLA) have functions in auxin signal transduction. Potential linkage to auxin receptors ABP1 or TIR1, their rapid activation or post-translational activation mechanisms, and downstream functions regulated by these phospholipases is reviewed and discussed. Only for pPLA all aspects are known at least to some detail. Evidence is gathered that all these signal reactions are located in the cytosol and seem to merge on regulation of PIN-catalyzed auxin efflux transport proteins. As a consequence, auxin concentration in the nucleus is also affected and this regulates the E3 activity of this auxin receptor. We showed that ABP1, PIN2, and pPLA, all outside the nucleus, have an impact on regulation of auxin-induced genes within 30 min. We propose that regulation of PIN protein activities and of auxin efflux transport are the means to coordinate ABP1 and TIR1 activity and that no physical contact between components of the ABP1-triggered cytosolic pathways and TIR1-triggered nuclear pathways of signaling is necessary to perform this.