Scalable methods for modelling complex biochemical networks

In cells, complex networks of interacting biomolecules process both environmental and endogenous signals to control gene expression and other cellular processes. This poses a challenge to researchers who attempt to develop mathematical and computational models of biochemical networks that reflect this complexity. In this thesis, I propose methods that help manage complexity by exploiting the finding that, as for other biological systems, cellular networks are characterized by a modularity that appears at all levels of organization.The first part of this work focuses on the modular properties of proteins and how their function can be characterized through their structure and allosteric properties. I develop a modular rule-based framework and formal modelling language that describes the computations performed by allosteric proteins and that is rooted in biophysical principles. Rule-based modelling conventionally addresses the problem of combinatorial complexity, whereby protein interactions can generate a combinatorial explosion of protein complex states. However, I explore how these same interactions can potentially require a combinatorial number of parameters to describe them. I demonstrate that my rule-based framework effectively addresses this problem of regulatory complexity, and describes allosteric proteins and networks in a unified, consistent, and modular fashion. I use the framework in three applications. First, I show that allostery can make macromolecular assembly more efficacious when a protein that joins two separable parts of a complex is present in excessively high concentrations. Second, I demonstrate that I can straightforwardly analyze the complex cooperative interactions that arise when competitive ligands bind to a multimeric protein. Third, I analyze a new model of G protein-coupled receptor signalling and demonstrate that it explains the functional selectivity of these receptors while being parsimonious in the number of parameters used. Overall, I find that my rule-based modelling framework, implemented as the Allosteric Network Compiler software tool, can ease of modelling and analysis of complex allosteric interactions.If cellular networks are modular, this implies that small sub-systems can be studied in isolation, provided that external inputs and perturbations to the system can be modelled appropriately. However, cellular networks are subject to both intrinsic noise, which is endogenous to the system, but also extrinsic noise, arising from noisy inputs. Furthermore, many inputs may be dynamic, whether due to experimental protocols or perhaps reflecting the cyclic process of cell division. This motivates my development, in the second part of this work, of efficient stochastic simulation algorithms for biochemical networks that can accommodate time-varying biochemical parameters. Starting from Gillespie's well-known First Reaction Method and Gibson and Bruck's Next Reaction Method, I develop two new algorithms that allow time-varying inputs of arbitrary functional form while scaling well to systems comprising many biochemical reactions. I analyze their scaling properties and find that a modified First Reaction Method may scale better than a modified Next Reaction Method in some applications.The third and last part of this thesis introduces a new software tool, Facile, that eases the creation, update and simulation of biochemical network models. Models created through a simple and intuitive textual language are automatically converted into a form usable by downstream tools, for example ordinary differential equations for simulation by Matlab. Also, Facile conveniently accommodates mathematical and time-varying expressions in rate laws.

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