Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA

This paper examines the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway [5] through modelling in a Markovian process algebra, PEPA [11]. Two models of the system are presented, a reagent-centric view and a pathway-centric view. The models capture functionality at the level of subpathway, rather than at a molecular level. Each model affords a different perspective of the pathway and analysis. We demonstrate the two models to be formally equivalent using the timing-aware bisimulation defined over PEPA models and discuss the biological significance

From Epidemic to Pandemic Modelling

We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. This method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All the models are available as supplementary material, ensuring reproducibility.Comment: 79 pages (with Appendix), 23 figures, 7 table

Application of bio-model engineering to model abstract biological behaviours

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonLife in nature is defined by many characteristics. Whether something can move, communicate, response to the others, reproduce or die, indicate if it is alive or not. Among these features, communication can be considered the most basic and yet the most important as it happens both inside and outside an organism; between every molecule and every cell there are signals to be passed and to be responded to. Communication defines biology. A network of molecules or a society of organisms are both complex systems. The smallest change in this snarled network affects the whole system and changes the output significantly. Comprehending and manipulating them in detail is time and resources consuming and involves human error. But there is a way to simplify the process of inspecting the living creatures. Bio-model engineering lies at the crossroads of biology, mathematics, computer science, engineering and is a branch of systems biology. In this field of science, biological models are created and/or re-designed for simplification, abstraction and description of biological networks. Modelling these networks based on past experimental observations in silico with a set of pre-designed models and a collection of components would make this process faster and simpler. This thesis contributes to science by providing a collection of model components built in Petri nets with Snoopy. These components each describe a specific behaviour and they can be used individually or as a combination. The set of behaviours in this collection include chemotaxis, reproduction, death, communication and response. These are a few of the most basic behaviours in nature that mark something as alive. These basic behaviours choose that a piece of stone is not alive but the small microscopic bacteria on it are. Starting with small achievable steps, these components are modelled in abstract, meaning they demonstrate only the critical parts of the behaviours. Not only the models, but also the process of modelling and combining the components is provided from the adaptation and manipulation of a general protocol. The components in this library are categorised based on their complexity. In this categorisation, the models have four levels, with each level more complex than the former. The more complex levels, are built from the simpler ones in a hierarchical manner. There are two application of the models to two different microorganisms, each from one of the main biological superkingdoms to demonstrate the practicality of this collection. The chosen microorganisms are from: the domain of Prokaryotes E. coli and Eukaryotes Dictyostelium a.k.a slime mould. Each model contains a set of rate constants that define the speed of the reactions. A set of expected behaviours based on biological literature is defined for these models to be compared with the outcome result of the analysis of the models. The models are simulated by Spike, a command line programme for simulation of models built in Snoopy, and are analysed with R and Python. To achieve the expected results, optimisation methods are used to find the best rates possible in the models in order to achieve a defined behaviour. In this thesis the optimisation is applied to Dictyostelium model to achieve the best rates for the accumulation of Dictyostelium cells in one location to create fruiting bodies. Random Restart Hill Climbing and Simulated Annealing are the chosen methods for optimisation

Using hypergraph theory to model coexistence management and coordinated spectrum allocation for heterogeneous wireless networks operating in shared spectrum

Electromagnetic waves in the Radio Frequency (RF) spectrum are used to convey wireless transmissions from one radio antenna to another. Spectrum utilisation factor, which refers to how readily a given spectrum can be reused across space and time while maintaining an acceptable level of transmission errors, is used to measure how efficiently a unit of frequency spectrum can be allocated to a specified number of users. The demand for wireless applications is increasing exponentially, hence there is a need for efficient management of the RF spectrum. However, spectrum usage studies have shown that the spectrum is under-utilised in space and time. A regulatory shift from static spectrum assignment to DSA is one way of addressing this. Licence exemption policy has also been advanced in Dynamic Spectrum Access (DSA) systems to spur wireless innovation and universal access to the internet. Furthermore, there is a shift from homogeneous to heterogeneous radio access and usage of the same spectrum band. These three shifts from traditional spectrum management have led to the challenge of coexistence among heterogeneous wireless networks which access the spectrum using DSA techniques. Cognitive radios have the ability for spectrum agility based on spectrum conditions. However, in the presence of multiple heterogeneous networks and without spectrum coordination, there is a challenge related to switching between available channels to minimise interference and maximise spectrum allocation. This thesis therefore focuses on the design of a framework for coexistence management and spectrum coordination, with the objective of maximising spectrum utilisation across geographical space and across time. The amount of geographical coverage in which a frequency can be used is optimised through frequency reuse while ensuring that harmful interference is minimised. The time during which spectrum is occupied is increased through time-sharing of the same spectrum by two or more networks, while ensuring that spectrum is shared by networks that can coexist in the same spectrum and that the total channel load is not excessive to prevent spectrum starvation. Conventionally, a graph is used to model relationships between entities such as interference relationships among networks. However, the concept of an edge in a graph is not sufficient to model relationships that involve more than two entities, such as more than two networks that are able to share the same channel in the time domain, because an edge can only connect two entities. On the other hand, a hypergraph is a generalisation of an undirected graph in which a hyperedge can connect more than two entities. Therefore, this thesis investigates the use of hypergraph theory to model the RF environment and the spectrum allocation scheme. The hypergraph model was applied to an algorithm for spectrum sharing among 100 heterogeneous wireless networks, whose geo-locations were randomly and independently generated in a 50 km by 50 km area. Simulation results for spectrum utilisation performance have shown that the hypergraph-based model allocated channels, on average, to 8% more networks than the graph-based model. The results also show that, for the same RF environment, the hypergraph model requires up to 36% fewer channels to achieve, on average, 100% operational networks, than the graph model. The rate of growth of the running time of the hypergraph-based algorithm with respect to the input size is equal to the square of the input size, like the graph-based algorithm. Thus, the model achieved better performance at no additional time complexity.Electromagnetic waves in the Radio Frequency (RF) spectrum are used to convey wireless transmissions from one radio antenna to another. Spectrum utilisation factor, which refers to how readily a given spectrum can be reused across space and time while maintaining an acceptable level of transmission errors, is used to measure how efficiently a unit of frequency spectrum can be allocated to a specified number of users. The demand for wireless applications is increasing exponentially, hence there is a need for efficient management of the RF spectrum. However, spectrum usage studies have shown that the spectrum is under-utilised in space and time. A regulatory shift from static spectrum assignment to DSA is one way of addressing this. Licence exemption policy has also been advanced in Dynamic Spectrum Access (DSA) systems to spur wireless innovation and universal access to the internet. Furthermore, there is a shift from homogeneous to heterogeneous radio access and usage of the same spectrum band. These three shifts from traditional spectrum management have led to the challenge of coexistence among heterogeneous wireless networks which access the spectrum using DSA techniques. Cognitive radios have the ability for spectrum agility based on spectrum conditions. However, in the presence of multiple heterogeneous networks and without spectrum coordination, there is a challenge related to switching between available channels to minimise interference and maximise spectrum allocation. This thesis therefore focuses on the design of a framework for coexistence management and spectrum coordination, with the objective of maximising spectrum utilisation across geographical space and across time. The amount of geographical coverage in which a frequency can be used is optimised through frequency reuse while ensuring that harmful interference is minimised. The time during which spectrum is occupied is increased through time-sharing of the same spectrum by two or more networks, while ensuring that spectrum is shared by networks that can coexist in the same spectrum and that the total channel load is not excessive to prevent spectrum starvation. Conventionally, a graph is used to model relationships between entities such as interference relationships among networks. However, the concept of an edge in a graph is not sufficient to model relationships that involve more than two entities, such as more than two networks that are able to share the same channel in the time domain, because an edge can only connect two entities. On the other hand, a hypergraph is a generalisation of an undirected graph in which a hyperedge can connect more than two entities. Therefore, this thesis investigates the use of hypergraph theory to model the RF environment and the spectrum allocation scheme. The hypergraph model was applied to an algorithm for spectrum sharing among 100 heterogeneous wireless networks, whose geo-locations were randomly and independently generated in a 50 km by 50 km area. Simulation results for spectrum utilisation performance have shown that the hypergraph-based model allocated channels, on average, to 8% more networks than the graph-based model. The results also show that, for the same RF environment, the hypergraph model requires up to 36% fewer channels to achieve, on average, 100% operational networks, than the graph model. The rate of growth of the running time of the hypergraph-based algorithm with respect to the input size is equal to the square of the input size, like the graph-based algorithm. Thus, the model achieved better performance at no additional time complexity

Steering in computational science: mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.Comment: 40 pages, 11 figures. Accepted for publication in Contemporary Physic

From Epidemic to Pandemic Modelling

We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. The epidemic components and the spatial and stratification data are combined together in these coloured models and built in to the underlying expanded models. As a consequence this method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All models are available as Supplementary Material, ensuring reproducibility. All uncoloured Petri nets can be animated within a web browser at https://www-dssz.informatik.tu-cottbus.de/DSSZ/Research/ModellingEpidemics, assisting the comprehension of those models. We aim to enable modellers and planners to construct clear and robust models by themselves

Complex network analysis and nonlinear dynamics

This chapter aims at reviewing complex network and nonlinear dynamical models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the field of complex networks, the present summary introduces some applications of complex networks to economics, finance, epidemic spreading of innovations, and regional trade and developments. The chapter also reviews results involving applications of complex networks to other relevant socioeconomic issue

Clusters in randomly-coloured spatial networks

The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related individuals. Here we study the properties of clusters in spatially-embedded networks where nodes are coloured according to a given colouring process. This characterisation will allow us to use spatial networks with uniformly-coloured nodes as a null-model against which the importance, relevance, and significance of clusters of related units in a given real-world system can be assessed. We show that even a uniform and uncorrelated random colouring process can generate coloured clusters of substantial size and interesting shapes, which can be distinguished by using some simple dynamical measures, like the average time needed for a random walk to escape from the cluster. We provide a mean-field approach to study the properties of those clusters in large two-dimensional lattices, and we show that the analytical treatment agrees very well with the numerical results.Comment: 21 pages, 11 figure

Coloured noise from stochastic inflows in reaction-diffusion systems

In this paper we present a framework for investigating coloured noise in reaction-diffusion systems. We start by considering a deterministic reaction-diffusion equation and show how external forcing can cause temporally correlated or coloured noise. Here, the main source of external noise is considered to be fluctuations in the parameter values representing the in flow of particles to the system. First, we determine which reaction systems, driven by extrinsic noise, can admit only one steady state, so that effects, such as stochastic switching, are precluded from our analysis. To analyse the steady state behaviour of reaction systems, even if the parameter values are changing, necessitates a parameter-free approach, which has been central to algebraic analysis in chemical reaction network theory. To identify suitable models we use tools from real algebraic geometry that link the network structure to its dynamical properties. We then make a connection to internal noise models and show how power spectral methods can be used to predict stochastically driven patterns in systems with coloured noise. In simple cases we show that the power spectrum of the coloured noise process and the power spectrum of the reaction-diffusion system modelled with white noise multiply to give the power spectrum of the coloured noise reaction-diffusion system