Bessel functions and equations of mathematical physics

The aim of this dissertation is to introduce Bessel functions to the reader, as well as studying some of their properties. Moreover, the final goal of this document is to present the most well- known applications of Bessel functions in physics.

Structure-function analysis of USP1: insights into the role of Ser313 phosphorylation site and the effect of cancer-associated mutations on autocleavage

Background: In complex with its cofactor UAF1, the USP1 deubiquitinase plays an important role in cellular processes related to cancer, including the response to DNA damage. The USP1/UAF1 complex is emerging as a novel target in cancer therapy, but several aspects of its function and regulation remain to be further clarified. These include the role of the serine 313 phosphorylation site, the relative contribution of different USP1 sequence motifs to UAF1 binding, and the potential effect of cancer-associated mutations on USP1 regulation by autocleavage. Methods: We have generated a large set of USP1 structural variants, including a catalytically inactive form (C90S), non-phosphorylatable (S313A) and phosphomimetic (S313D) mutants, deletion mutants lacking potential UAF1 binding sites, a mutant (GG/AA) unable to undergo autocleavage at the well-characterized G670/G671 diglycine motif, and four USP1 mutants identified in tumor samples that cluster around this cleavage site (G667A, L669P, K673T and A676T). Using cell-based assays, we have determined the ability of these mutants to bind UAF1, to reverse DNA damage-induced monoubiquitination of PCNA, and to undergo autocleavage. Results: A non-phosphorylatable S313A mutant of USP1 retained the ability to bind UAF1 and to reverse PCNA ubiquitination in cell-based assays. Regardless of the presence of a phosphomimetic S313D mutation, deletion of USP1 fragment 420-520 disrupted UAF1 binding, as determined using a nuclear relocation assay. The UAF1 binding site in a second UAF1-interacting DUB, USP46, was mapped to a region homologous to USP1(420-520). Regarding USP1 autocleavage, co-expression of the C90S and GG/AA mutants did not result in cleavage, while the cancer-associated mutation L669P was found to reduce cleavage efficiency. Conclusions: USP1 phosphorylation at S313 is not critical for PCNA deubiquitination, neither for binding to UAF1 in a cellular environment. In this context, USP1 amino acid motif 420-520 is necessary and sufficient for UAF1 binding. This motif, and a homologous amino acid segment that mediates USP46 binding to UAF1, map to the Fingers sub-domain of these DUBs. On the other hand, our results support the view that USP1 autocleavage may occur in cis, and can be altered by a cancer-associated mutation.

Ecosystem function and biodiversity on coral reefs

The article highlights a workshop held in Key West, Florida in November 1993 attended by a group of 35 international scientists where topics of ecosystem function and biodiversity on coral reefs were discussed.

Food conversion efficiency and the von Bertalanffy growth function 1: a modification of Pauly's model

A simple modification of Pauly's model for relating food conversion efficiency (K sub(1)) and body weight is proposed. The key parameter is an index to how efficiently food can be absorbed; the other parameter is related to the surface-limiting growth, an important component of von Bertalanff's and Pauly's theories of fish growth.

Food conversion efficiency and the von Bertalanffy growth function. Part II and conclusion: Extension of the new model to the generalized von Bertalanffy growth function

The simple model relating food conversion efficiency (K sub(1)) to body weight derived from the theoretical concepts behind von Bertalanffy's growth model, is extended here in the context of Pauly's generalization of that model. The exponent, which was fixed to 1/3 in the simple model, is in the extended model equivalent to 1-d, with d being the weight exponent of the anabolism term in Pauly's growth model. This makes the model applicable to fish for which the assumptions of the original (special) version of von Bertalanffy's growth model are violated.