A phenomenal basis for hybrid modelling

This work in progress extends the new mechanical philosophy from science to engineering. Engineering is the practice of organising the design and construction of artifices that satisfy needs in real-world contexts. This work shows how artifices can be described in terms of their mechanisms and composed through their observable phenomena. Typically, the engineering of real system requires descrip- tions in many different languages: software components will be described in code; sensors and actuators in terms of their physical and electronic characteristics; plant in terms of differ- ential equations, perhaps. Another aspect of this work, then, to construct a formal framework so that diverse description languages can be used to characterise sub-mechanisms. The work is situated in Problem Oriented Engineering, a design theoretic framework engineering defined by the first two authors

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

A critical review on modelling formalisms and simulation tools in computational biosystems

Integration of different kinds of biological processes is an ultimate goal for whole-cell modelling. We briefly review modelling formalisms that have been used in Systems Biology and identify the criteria that must be addressed by an integrating framework capable of modelling, analysing and simulating different biological networks. Aware that no formalism can fit all purposes we realize Petri nets as a suitable model for Metabolic Engineering and take a deeper perspective on the role of this formalism as an integrating framework for regulatory and metabolic networks.Research supported by PhD grant SFRH/BD/35215/2007 from the Fundacao para a Ciencia e a Tecnologia (FCT) and the MIT-Portugal program

Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

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

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