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The fatgraph models of proteins and their applications in the protein folding problem

Research output: Book/anthology/dissertation/reportPh.D. thesis

This thesis presents the results from my PhD studies at Aarhus University,
supervised by Professor Jørgen Ellegaard Andersen. The main focus of the PhD
project was to investigate applications of the fatgraph model of proteins, which
was first proposed by Andersen and others [66]. The studies are exploratory
in nature, but are designed with a goal of tackling the protein folding problem
using the fatgraph model.
In the first part of the thesis, a review of mathematical objects and theories
related to the project is presented. It is followed by a review of the works
utilising fatgraphs in the study of another biological macromolecule, RNA. We
review the recursion relations obtained by the so-called cut and join method,
and by topological recursion.
In the second part of the thesis, we present new results in relation to the
study of protein structures. First the basic fatgraph model of proteins is in-
troduced, and a recursion relations for the protein diagrams, obtained by cut
and join method, are presented. We then discuss three experimental studies in
applications of fatgraph models. In the first project, we introduce a novel model
of proteins, which we call protein metastructures, and an associated topological
model, which is a modification of the basic fatgraph model. These are used to
study β-sheet topology of proteins, which is the configuration of β-strands in
β-sheets. We show that the proteins favour less complex β-sheet topologies by
comparing the data from the actual and simulated proteins. Some applications
of the models are presented, including an example for combining the method
with an existing program for predicting β-sheet topology. The second project
takes inspiration from CASP assessment of model quality, and attempts to select
the best structure from a set of candidate structures, which aim to reproduce
the target protein structure from its primary sequence. We show the topolog-
ical information contained in our model is enough to predict, if not the best,
a structure close to the best candidate structure. The third project aims to
predict local geometry of the proteins, expressed as a rotation between peptide
units (expressed as an element in the rotation group SO(3)) that are connected
by a hydrogen bond, from their topology. The topological information is ex-
pressed as a pattern of other hydrogen bonds around the bond in question. We
show that the rotation can be predicted to a high accuracy; close to 90% of the
predictions lie within a ball centred at the true rotation occupying 1% of the
SO(3) space. We conclude the thesis by a brief discussion of potential future
challenges and benefits of the use of fatgraph models in the protein structure
Original languageEnglish
PublisherAarhus Universitet
Number of pages143
Publication statusPublished - Mar 2021

Note re. dissertation

Termination date: 22.03.2021

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