Allergy is an IgE-mediated hypersensitivity that is triggered by allergens, leading to various
physical symptoms including eczema, asthma, diarrhoea and cardiac arrest. The molecular
mechanism for allergenicity elicitation with critical disease symptoms is yet beyond understanding,
despite the development in knowledge of crystallographic structures of various protein
allergens, and the identification of immunoglobin-binding protein fragments, which are
usually called epitopes. We also lack a robust prediction methodology for a new protein’s
potential to trigger allergic reactions, which leads to an equally important question of differentiating
structurally similar proteins and identify their own capability to trigger allergic reaction.
It is clear that we are in need of efficient multi-scale methods for understanding the dynamical
properties of allergen proteins in a whole at the molecular level, but traditional computational
methods are restricted not only by the coupling of protein dynamics across time scales, but
also their demanding cost to extract multi-scale information if an efficient new representation
of the same protein system cannot be established.

We try to solve these problems by taking a graph-theoretical approach. By representing the
atomic level description of an allergen structure using a mathematical abstraction called graph,
we extract the physical-chemical details and map them into a weighted graph which then is
explored by Markov random explorers. Three graph-based methods, namely, Markov Stability,
Markov Transient and the bond-bond Propensity have been proposed and applied in our cases,
to extract dynamical information for understanding the allergenicity problem. These methods
are linear or sub-linear with respect to the number of nodes in a protein graph, so they are far
more efficient than the previous methods.

Two allergen protein families have been studied in this thesis: the bi-cupin super-family proteins,
exemplified by the peanut allergen proteins Ara h 1, 2 and 6; and the PR-10 super-family
including the pollen allergens Bet v 1 and 2. The hierarchical structural properties as well as
their inherent correlation between the immunoglobulin-binding sites and the the active sites are
studied and compared. Also the difference between allergens and their negative controls are
discussed. In parallel, theoretical mutagenesis is taken to identify hot spots which contribute
to the changes in the physical-chemical properties of an allergen protein. Through these attempts,
we are able to find a series of amino acid residues that can be potential targets for
designing targeted-drugs, as well as full comprehension of the allergenicity problem.

Since the protein-protein interaction of an allergen and the immunoglobulin has not been
looked at, and that we are in lack of full, feasible crystal structures to critically study the
effects of an allergen before and after binding to an immunoglobulin such as type E, we study
human cell-cycle cyclin-dependent kinase 2 (Cdk2) and its various structures along with binding
counter-parties using our graph-theoretical suite. Our results indicate that hidden information
propagation pathway between the kinase and its binding parties can be exposed, and the
identified amino acid residues are being considered as possible targets for further research.