Dynamics of protein interaction subnetworks

Abstract

I show that in the generic situations where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger bulk network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. I use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation, respectively. Remarkably, in
the limit of low intrinsic copy-number noise such expressions can be obtained even for nonlinear dependences on the past. I illustrate the method with examples from a protein interaction network around epidermal growth factor receptor (EGFR), which is relevant to cancer signalling. These examples demonstrate that inclusion of memory terms is not only important conceptually but also leads to substantially higher quantitative accuracy in the predicted subnetwork dynamics.
I also study how the presence of Michaelis-Menten reactions affect the behaviour of the subnetwork. While such reactions do not directly t into our framework of unary and binary reactions, I demonstrate that our approach can be generalised to include them. This is done by first introducing enzyme and enzyme complex species and reactions, then constructing the projected equations, and finally taking the limit of fast enzyme reactions that gives back Michaelis-Menten dynamics. I show that this limit can be taken in closed form, leading to a simple procedure that allows the projected equations to be constructed without ever introducing the fast variables explicitly. I then apply projection methods to the analysis of the effects of perturbations in the bulk network, e.g. from gene regulation processes. I show that the resulting behaviour of the linear response can again be decomposed according to a boundary structure, so that the total linear response is split into the eect of the bulk perturbation on the subnetwork boundary and the propagation of the perturbation from there to the rest
of the subnetwork. I also use the projection method to find the steady states of the perturbed system in nonlinear response, which makes it possible to analyse biologically relevant scenarios such as knock-down experiments.
Finally, I look at the statistics of the random force. I propose a simple approximation of the random force made up of a persistent piece and a random change in the subnetwork initial conditions. I verify that this gives accurate predictions for both the linearised and nonlinear dynamics.

Date of Award	2015
Original language	English
Awarding Institution	King's College London
Supervisor	Peter Sollich (Supervisor) & Tony Ng (Supervisor)