One of the first steps in understanding a protein's function is to determine its localization; however, the methods for localizing proteins in some systems have not kept pace with the developments in other fields, creating a bottleneck in the analysis of the large datasets that are generated in the post-genomic era. To address this, we developed tools for tagging proteins in trypanosomatids. We made a plasmid that, when coupled with long primer PCR, can be used to produce transgenes at their endogenous loci encoding proteins tagged at either terminus or within the protein coding sequence. This system can also be used to generate deletion mutants to investigate the function of different protein domains. We show that the length of homology required for successful integration precluded long primer PCR tagging in Leishmania mexicana. Hence, we developed plasmids and a fusion PCR approach to create gene tagging amplicons with sufficiently long homologous regions for targeted integration, suitable for use in trypanosomatids with less efficient homologous recombination than Trypanosoma brucei. Importantly, we have automated the primer design, developed universal PCR conditions and optimized the workflow to make this system reliable, efficient and scalable such that whole genome tagging is now an achievable goal.

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We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any ω-stable ω-categorical structure, and (ii) the random graph has the small index property. We also show that the automorphism group of such a structure is not the union of a countable chain of proper subgroups.

A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any fixed dimension (at least 3) are elementary.

We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques—thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF.