Counting and enumerating partial Latin rectangles by means of computer algebra systems and CSP solvers

This paper provides an in-depth analysis of how computer algebra systems and CSP solvers can be used to deal with the problem of enumerating and distributing the set of $r\times s$ partial Latin rectangles based on $n$ symbols according to their weight, shape, type or structure. The computation of Hilbert functions and triangular systems of radical ideals enables us to solve this problem for all $r,s,n\leq 6$. As a by-product, explicit formulas are determined for the number of partial Latin rectangles of weight up to six. Further, in order to illustrate the effectiveness of the computational method, we focus on the enumeration of three subsets: (a) non-compressible and regular, (b) totally symmetric, and (c) totally conjugate orthogonal partial Latin squares. In particular, the former enables us to enumerate the set of seminets of point rank up to eight and to prove the existence of two new configurations of point rank eight. Finally, as an illustrative application, it is also exposed a method to construct totally symmetric partial Latin squares that gives rise, under certain conditions, to new families of Lie partial quasigroup rings

Requirement for O-linked N-acetylglucosaminyltransferase in lymphocytes activation

The dynamic modification of nuclear and cytoplasmic proteins with O-linked β-N-acetylglucosamine (O-GlcNAc) by the O-linked N-acetylglucosaminyltransferase (OGT) is a regulatory post-translational modification that is responsive to various stimuli. Here, we demonstrate that OGT is a central factor for T- and B-lymphocytes activation. SiRNA-mediated knockdown of OGT in T cells leads to an impaired activation of the transcription factors NFAT and NFκB. This results in a reduction of IL-2 production consistent with prevention of T-cell activation. OGT is also required for the early activation of B cells mediated by stimulation of the B-cell receptor. Mechanistically, we demonstrate that NFκB as well as NFAT are glycosylated with O-GlcNAc after direct binding to OGT. Moreover, kinetic experiments show that O-GlcNAc modification prominently increased shortly after activation of lymphoid cells and it might be required for nuclear translocation of the transcription factors NFκB and NFAT

Computational Modeling of Photoexcitation in DNA Single and Double Strands

The photoexcitation of DNA strands triggers extremely complex photoinduced processes, which cannot be understood solely on the basis of the behavior of the nucleobase building blocks. Decisive factors in DNA oligomers and polymers include collective electronic effects, excitonic coupling, hydrogen-bonding interactions, local steric hindrance, charge transfer, and environmental and solvent effects. This chapter surveys recent theoretical and computational efforts to model real-world excited-state DNA strands using a variety of established and emerging theoretical methods. One central issue is the role of localized vs delocalized excitations and the extent to which they determine the nature and the temporal evolution of the initial photoexcitation in DNA strands