Coarse-graining the Dynamics of Ideal Branched Polymers

AbstractWe define a class of local stochastic rewrite rules on directed site trees. We give a compact presentation of (often countably infinite) coarse-grained differential systems describing the dynamics of these rules in the deterministic limit, and study in a simple case finite approximations based on truncations to a certain size. We show an application to the modelling of the dynamics of sugar polymers

On a thermodynamic approach to biomolecular interaction networks

We explore the direct and inverse problem of thermodynamics in the context of rule-based modelling. The direct problem can be concisely stated as obtaining a set of rewriting rules and their rates from the description of the energy landscape such that their asymptotic behaviour when t → ∞ coincide. To tackle this problem, we describe an energy function as a finite set of connected patterns P and an energy cost function e which associates real values to each of these energy patterns.We use a finite set of reversible graph rewriting rules G to define the qualitative dynamics by showing which transformations are possible. Given G and P, we construct a finite set of rules Gp which i) has the same qualitative transition system as G and ii) when equipped with rates according to e, defines a continuous-time Markov chain that has detailed balance with respect to the invariant probability distribution determined by the energy function. The construction relies on a technique for rule refinement described in earlier work and allows us to represent thermodynamically consistent models of biochemical interaction networks in a concise manner. The inverse problem, on the other hand, is to i) check whether a rule-based model has an energy function that describes its asymptotic behaviour and if so ii) obtain the energy function from the graph rewriting rules and their rates. Although this problem is known to be undecidable in the general case, we find two suitable subsets of Kappa, our rule-based modelling framework of choice, were this question can be answer positively and the form of their energy functions described analytically

Defining complex rule-based models in space and over time

Computational biology seeks to understand complex spatio-temporal phenomena across multiple levels of structural and functional organisation. However, questions raised in this context are difficult to answer without modelling methodologies that are intuitive and approachable for non-expert users. Stochastic rule-based modelling languages such as Kappa have been the focus of recent attention in developing complex biological models that are nevertheless concise, comprehensible, and easily extensible. We look at further developing Kappa, in terms of how we might define complex models in both the spatial and the temporal axes. In defining complex models in space, we address the assumption that the reaction mixture of a Kappa model is homogeneous and well-mixed. We propose evolutions of the current iteration of Spatial Kappa to streamline the process of defining spatial structures for different modelling purposes. We also verify the existing implementation against established results in diffusion and narrow escape, thus laying the foundations for querying a wider range of spatial systems with greater confidence in the accuracy of the results. In defining complex models over time, we draw attention to how non-modelling specialists might define, verify, and analyse rules throughout a rigorous model development process. We propose structured visual methodologies for developing and maintaining knowledge base data structures, incorporating the information needed to construct a Kappa rule-based model. We further extend these methodologies to deal with biological systems defined by the activity of synthetic genetic parts, with the hope of providing tractable operations that allow multiple users to contribute to their development over time according to their area of expertise. Throughout the thesis we pursue the aim of bridging the divide between information sources such as literature and bioinformatics databases and the abstracting decisions inherent in a model. We consider methodologies for automating the construction of spatial models, providing traceable links from source to model element, and updating a model via an iterative and collaborative development process. By providing frameworks for modellers from multiple domains of expertise to work with the language, we reduce the entry barrier and open the field to further questions and new research

Developing a framework for semi-automated rule-based modelling for neuroscience research

Dynamic modelling has significantly improved our understanding of the complex molecular mechanisms underpinning neurobiological processes. The detailed mechanistic insights these models offer depend on the availability of a diverse range of experimental observations. Despite the huge increase in biomolecular data generation from novel high-throughput technologies and extensive research in bioinformatics and dynamical modelling, efficient creation of accurate dynamical models remains highly challenging. To study this problem, three perspectives are considered: comparison of modelling methods, prioritisation of results and analysis of primary data sets. Firstly, I compare two models of the DARPP-32 signalling network: a classically defined model with ordinary differential equations (ODE) and its equivalent, defined using a novel rule-based (RB) paradigm. The RB model recapitulates the results of the ODE model, but offers a more expressive and flexible syntax that can efficiently handle the “combinatorial complexity” commonly found in signalling networks, and allows ready access to fine-grain details of the emerging system. RB modelling is particularly well suited to encoding protein-centred features such as domain information and post-translational modification sites. Secondly, I propose a new pipeline for prioritisation of molecular species that arise during model simulation using a recently developed algorithm based on multivariate mutual information (CorEx) coupled with global sensitivity analysis (GSA) using the RKappa package. To efficiently evaluate the importance of parameters, Hilber-Schmidt Independence Criterion (HSIC)-based indices are aggregated into a weighted network that allows compact analysis of the model across conditions. Finally, I describe an approach for the development of disease-specific dynamical models using genes known to be associated with Attention Deficit Hyperactivity Disorder (ADHD) as an exemplar. Candidate disease genes are mapped to a selection of datasets that are potentially relevant to the modelling process (e.g. interactions between proteins and domains, protein-domain and kinase-substrates mappings) and these are jointly analysed using network clustering and pathway enrichment analyses to evaluate their coverage and utility in developing rule-based models

Cooperative assembly systems

Several molecular systems form large-scale objects. One would like to understand their assembly and how this assembly is regulated. As a first step, we investigate the phase transition structure of a class of sim- ple cooperative assembly systems.We characterize which of these systems have a (probabilistic) equilibrium and find an explicit form for their lo- cal energy (§2).We obtain, under additional limitations on cooperativity, the average dynamics of some partial observables (§4). Combining both steps, we obtain conditions for the appearance of a large cluster (§5)