Manchester Applied Mathematics and Numerical Analysis Seminars Winter 1999/2000

Simon Hubbard
Biomolecular Sciences, UMIST

Proteomics is an expanding field in bioscience research. By combining protein chemistry, genomics, mass spectrometry and bioinformatics, we are now able to identify proteins based from characteristic peptide mass patterns. This has applications in the study of many important biological processes such as disease, gene function, cell cycle and cell development. The informatics problems underlying proteomics will be discussed, along with some of the current solutions and ideas for future models and approaches.
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Robin Allaby
Biomolecular Sciences, UMIST

Domestication of wheat occurred 10,000 years ago in the Near East, although it is unclear whether this was a single event or which part of the Fertile Crescent was involved. Resolving this dispute using molecular phylogeny presents a great challenge - wheat is a genetically complex polyploid system and 10 000 years is an extremely short period of time in terms of evolution. We have used two approaches. The first examines a nuclear multigene family using cladistic tree building analysis to compare alleles. Common ancestors of alleles can be dated using genetic distance, and the biogeography of antiquated alleles can be mapped. The resulting picture is illuminating but limited in terms of resolution. The second approach uses a gene system that evolves rapidly but violates Hennig's cladistic assumptions and requires a novel approach to molecular phylogeny. In this case a network approach is taken which allows for multiple ancestry though recombination. The concept of genetic distance has to be abandoned and a concept of genetic similarity through recombination events is adopted. The emerging results from using this are exciting and informative, and show that we have a system that is biologically appropriate in its assumptions. However, network construction limits the size of the usable data set and represents an example of a system ripe for mathematical formalisation.
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Chris Taylor and Paul Higgs
Bioinformatics, University of Manchester

Our work concerns neutral change in genotype under stabilising selection on phenotype, the behaviour of quantitative traits, the rates at which species evolve, and some of the processes which drive populations to diverge and speciate.

Reductionist models constitute a powerful tool with which to understand, piece by piece, complex systems such as are found in the natural world. With the advent of faster computers, models become tractable which previously were not. While still only using a small subset of the features of the natural world, these models can provide a satisfying and useful approximation to it.

The MQT model represents organisms with Multiple Quantitative Traits, where fitness is a function of phenotype only. The model incorporates variable degrees of pleiotropy and epistasis for fitness. This presentation will deal with the properties of the fitness landscapes generated by the model, and some biological phenomena exhibited such as neutral drift in genotype space, and differential adaptation.
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M. Muldoon
Depts. of Mathematics and Optometry & Neuroscience, UMIST

One normally expects talks about DNA and evolution to involve deep time: a phylogenetic history of, say, whales, would span many millions of years and might draw evidence from the fossil record. By contrast, HIV evolves incredibly rapidly, with substantial genetic change occuring over the course of a single individual's illness. In this talk I will discuss a project that uses sequence data to estimate the date of the emergence of modern clades of the virus. The main technical innovation will be a generalisation of a model (originally due to Jeff Thorne and his collaborators) that permits one to estimate the ages of ancestral forms without having to assume a strict molecular clock.
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