@phdthesis{Assaf, author = {Assaf, George}, title = {Fuzzy coloured Petri nets for modelling biological systems with uncertain kinetic parameters}, publisher = {BTU}, address = {Cottbus}, doi = {10.26127/BTUOpen-5851}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-58516}, pages = {185}, abstract = {Over the last twenty years, Petri nets have been increasingly adopted for modelling and simulating biological systems, as they offer an intuitive and graphical approach for this purpose. Their usability convenience comes from the fact that they offer many types of elements to describe systems in a qualitative and quantitative way. Coloured Petri nets are particularly useful to model systems with repeated components in a compact fashion. Our tool Snoopy for modelling and simulating Petri nets is one of the most well-known tools supporting a family of related Petri net classes comprising stochastic, continuous and hybrid Petri nets, and covering uncoloured and coloured Petri nets alike. However, kinetic information of a biological system, i.e. kinetic parameters may be uncertain, due to many reasons, e.g. environmental factors. Besides, coloured Petri nets as they were previously supported in Snoopy suffered from some inconsistencies. Due to these inconsistencies, exploring the model behaviour using different sizes (scaleability) was not feasible. Both challenges call for a new and more powerful approach integrating the modelling of uncertainties together with modelling features supporting repeated structures in a compact and scalable way. This thesis comprises two major contributions: Firstly, we introduce the definition and present the simulation algorithm for both uncoloured and coloured fuzzy Petri nets, by extending the existing quantitative uncoloured and coloured Petri nets in Snoopy. This includes discretising the uncertain kinetic parameters to crisp values by using sampling strategies. Secondly, we harmonise coloured Petri nets in Snoopy with their uncoloured counterparts and we extend the Snoopy's coloured Petri nets by all the features, which are supported by the coloured abstract net description language - an exchange format of coloured Petri nets in our PetriNuts tool family. By performing fuzzy simulation, one can obtain two kinds of output: fuzzy bands of each output variable and their corresponding timed-membership functions. Each fuzzy band describes the uncertainties associated with the input, whereas membership functions give more accurate information about the associated uncertainties. The most important features that we obtain by harmonising coloured Petri nets are to develop scaleable models, by defining scaling factors as constants and unifying the usage of coloured Petri nets with the other tools in our PetriNuts tool family.}, language = {en} } @misc{LiuSunHeineretal., author = {Liu, Fei and Sun, Wujie and Heiner, Monika and Gilbert, David}, title = {Hybrid modelling of biological systems using fuzzy continuous Petri nets}, series = {Briefings in Bioinformatics}, volume = {22(2021)}, journal = {Briefings in Bioinformatics}, doi = {10.1093/bib/bbz114}, pages = {438 -- 450}, abstract = {Integrated modelling of biological systems is challenged by composing components with sufficient kinetic data and components with insufficient kinetic data or components built only using experts' experience and knowledge. Fuzzy continuous Petri nets (FCPNs) combine continuous Petri nets with fuzzy inference systems, and thus offer an hybrid uncertain/certain approach to integrated modelling of such biological systems with uncertainties. In this paper, we give a formal definition and a corresponding simulation algorithm of FCPNs, and briefly introduce the FCPN tool that we have developed for implementing FCPNs. We then present a methodology and workflow utilizing FCPNs to achieve hybrid (uncertain/certain) modelling of biological systems illustrated with a case study of the Mercaptopurine metabolic pathway. We hope this research will promote the wider application of FCPNs and address the uncertain/certain integrated modelling challenge in the systems biology area.}, language = {en} } @misc{PretschnerPabelHaasetal., author = {Pretschner, Anna and Pabel, Sophie and Haas, Markus and Heiner, Monika and Marwan, Wolfgang}, title = {Regulatory dynamics of cell differentiation revealed by true time series from multinucleate single cells}, series = {Frontiers in Genetics}, journal = {Frontiers in Genetics}, number = {11}, issn = {1664-8021}, doi = {10.3389/fgene.2020.612256}, pages = {17}, abstract = {Dynamics of cell fate decisions are commonly investigated by inferring temporal sequences of gene expression states by assembling snapshots of individual cells where each cell is measured once. Ordering cells according to minimal differences in expression patterns and assuming that differentiation occurs by a sequence of irreversible steps, yields unidirectional, eventually branching Markov chains with a single source node. In an alternative approach, we used multi-nucleate cells to follow gene expression taking true time series. Assembling state machines, each made from single-cell trajectories, gives a network of highly structured Markov chains of states with different source and sink nodes including cycles, revealing essential information on the dynamics of regulatory events. We argue that the obtained networks depict aspects of the Waddington landscape of cell differentiation and characterize them as reachability graphs that provide the basis for the reconstruction of the underlying gene regulatory network.}, language = {en} }