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One of the primary goals of combinatorial mathematics is to understand how an object's properties are influenced by the presence or multiplicity of a given substructure. Over time, it has become popular to highlight the asymptotic behaviour of objects by expressing results in terms of the density of substructures. In this thesis, we investigate three topics concerning combinatorial density: We study the interplay between the densities of cycles of length 3 and 4 in large tournaments, we characterise quasirandomness in permutations, and we solve two open problems about the inducibility of trees.

Background Studying proteins and enzymes involved in important biological processes in the Aedes aegypti mosquito is limited by the quantity that can be directly isolated from the mosquito. Adding to this difficulty, digestive enzymes (midgut proteases) involved in metabolizing blood meal proteins require a more oxidizing environment to allow proper folding of disulfide bonds. Therefore, recombinant techniques to express foreign proteins in Escherichia coli prove to be effective in producing milligram quantities of the expressed product. However, with the most commonly used strains having a reducing cytoplasm, soluble expression of recombinant proteases is hampered. Fortunately, new E. coli strains with a more oxidizing cytoplasm are now available to ensure proper folding of disulfide bonds. Results Utilizing an E. coli strain with a more oxidizing cytoplasm (SHuffle® T7, New England Biolabs) and changes in bacterial growth temperature has resulted in the soluble expression of the four most abundantly expressed Ae. aegypti midgut proteases (AaET, AaSPVI, AaSPVII, and AaLT). A previous attempt of solubly expressing the full-length zymogen forms of these proteases with the leader (signal) sequence and a modified pseudo propeptide with a heterologous enterokinase cleavage site led to insoluble recombinant protein expression. In combination with the more oxidizing cytoplasm, and changes in growth temperature, helped improve the solubility of the zymogen (no leader) native propeptide proteases in E. coli. Furthermore, the approach led to autocatalytic activation of the proteases during bacterial expression and observable BApNA activity. Different time-points after bacterial growth induction were tested to determine the time at which the inactive (zymogen) species is observed to transition to the active form. This helped with the purification and isolation of only the inactive zymogen forms using Nickel affinity. Conclusions The difficulty in solubly expressing recombinant proteases in E. coli is caused by the native reducing cytoplasm. However, with bacterial strains with a more oxidizing cytoplasm, recombinant soluble expression can be achieved, but only in concert with changes in bacterial growth temperature. The method described herein should provide a facile starting point to recombinantly expressing Ae. aegypti mosquito proteases or proteins dependent on disulfide bonds utilizing E. coli as a host. Electronic supplementary material The online version of this article (10.1186/s12858-018-0101-0) contains supplementary material, which is available to authorized users.

In recent years, awareness and concern has grown within the psychological and medical communities regarding “behavioral addictions”: these are defined as the compulsive performance of otherwise normal everyday activities such as sex, gambling, use of the Internet and online video games, and shopping. This chapter examines 3 such addictive disorders: gambling disorder, compulsive buying disorder (CBD), and Internet gaming disorder (IGD), exploring their definitions, prevalence, diagnoses, consequences, and treatment. All 3 disorders share similar neurobiological mechanisms, acting on the pleasure centers of the brain and having potentially severe social, mental, and psychological repercussions, including loss of interest in life and withdrawal symptoms as intense as those felt by substance abusers when quitting drugs. Certain pharmaceuticals, CBT, and treatment principles similar to those followed by substance abusers, as well as various non-traditional modalities such as acupuncture and yoga, all have shown promise in treating these disorders.