Allostery is the process whereby binding of a substrate at a site other than the active site modulates the function of a protein. Allostery is thus one of the myriad of biological processes that keeps cells under tight regulatory control, specifically one that acts at the level of the protein rather than through changes in gene transciption or translation of mRNA. Despite over 50 years of investigation, allostery has remained a difficult phenomenon to elucidate. Structural changes are often too subtle for many experimental methods to capture and it has become increasingly obvious that a range of timescales are involved, from extremely fast pico- to nanosecond local fluctuations all the way up to the millisecond or even second timescales over which the biological effects of allostery are observed. As a result, computational methods have arisen to become a powerful means of studying allostery, aided greatly by the staggering increases in computational power over the last 70 years.

A field that has experienced a surge in interest over the last 20 years or so is \emph{network theory}, perhaps stimulated by the development of the internet and the Web, two examples of immensely important networks in our everyday life. One of the reasons for the popularity of networks in modelling is their comparative simplicity: a network consists of \emph{nodes}, representing a set of objects in a system, and \emph{edges}, that capture the relations between them.

In this thesis, we both apply existing ideas and methods from network theory and develop new computational network methods to study allostery in proteins. We attempt to tackle this problem in three distinct ways, each representing a protein using a different form of a network. Our initial work follows on logically from previous work in the group, representing proteins as \emph{graphs} where atoms are nodes and bonds are energy weighted edges. In effect we disregard the 3-dimensional structure of the protein and instead focus on how the bond \emph{connectivity} can be used to explain potential long range communication between allosteric and active sites in a multimeric protein. We then focus on a class of protein models known as \emph{elastic network models}, in which our edges now correspond to mechanical Hooke springs between either atoms or residues, in order to attempt to understand the physical, mechanistic basis of allostery.