TY - GEN A1 - Pretschner, Anna A1 - Pabel, Sophie A1 - Haas, Markus A1 - Heiner, Monika A1 - Marwan, Wolfgang T1 - Regulatory dynamics of cell differentiation revealed by true time series from multinucleate single cells T2 - Frontiers in Genetics N2 - 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. KW - single cell time series KW - gene regulatory network KW - Petri net KW - Markov chain KW - systems biology KW - Waddington landscape Y1 - 2021 U6 - https://doi.org/10.3389/fgene.2020.612256 SN - 1664-8021 N1 - This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). IS - 11 ER - TY - RPRT A1 - Assaf, George A1 - Heiner, Monika A1 - Liu, Fei T1 - Fuzzy Petri nets N2 - This document explains the procedure of modelling and simulating FPN and FPNC in Snoopy; please compare Figure 1 . Please note that the same steps for one net class can be equally applied to the other classes, just differentiate between uncoloured Petri nets (PN) and coloured Petri nets (PNC). Furthermore, we give more details about Latin Hybercube Sampling strategies supported by Snoopy's FPN. KW - Fuzzy Petri Nets coloured fuzzy Petri nets Snoopy Y1 - 2021 UR - https://www-dssz.informatik.tu-cottbus.de/publications/btu-reports/fpn_manual.pdf ER - TY - RPRT A1 - Connolly, Shannon A1 - Gilbert, David A1 - Heiner, Monika T1 - From Epidemic to Pandemic Modelling N2 - 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. KW - SIR model KW - coloured Petri nets KW - stochastic Petri nets KW - continuous Petri nets KW - ODEs KW - simulation KW - geographic spatio-temporal 20 modelling KW - multiscale models Y1 - 2021 U6 - https://doi.org/10.48550/arXiv.2107.00835 PB - Cornell University CY - arXiv ER - TY - GEN A1 - Assaf, George A1 - Heiner, Monika A1 - Liu, Fei T1 - Colouring Fuzziness for Systems Biology T2 - Theoretical Computer Science N2 - Snoopy is a powerful modelling and simulation tool for various types of Petri nets, which have been applied to a wide range of biochemical reaction networks. We present an enhanced version of Snoopy, now supporting coloured and uncoloured stochastic, continuous and hybrid Petri Nets with fuzzy kinetic parameters. Colour helps to cope with modelling challenges imposed by larger and more complex networks. Fuzzy parameters are specifically useful when kinetic parameter values can not be precisely measured or estimated. By running fuzzy simulation we obtain output bands of the variables of interest induced by the effect of the fuzzy kinetic parameters. Simulation is always done on the uncoloured level. For this purpose, coloured fuzzy Petri nets are automatically unfolded to their corresponding uncoloured counterparts. Combining the power of fuzzy kinetic parameters with the modelling convenience of coloured Petri nets provides a new quality in user support with sophisticated modelling and analysis features. KW - fuzzy logic KW - Fuzzy kinetic parameters KW - Coloured fuzzy continuous, stochastic and hybrid Petri nets KW - Modelling and simulation KW - Modelling uncertainty Y1 - 2021 UR - https://www.sciencedirect.com/science/article/abs/pii/S0304397521002152?via%3Dihub U6 - https://doi.org/10.1016/j.tcs.2021.04.011 SN - 1879-2294 SN - 0304-3975 VL - 875 SP - 52 EP - 64 ER - TY - GEN A1 - Liu, Fei A1 - Assaf, George A1 - Chen, Ming A1 - Heiner, Monika T1 - A Petri nets-based framework for whole-cell modeling T2 - Biosystems N2 - Whole-cell modeling aims to incorporate all main genes and processes, and their interactions of a cell in one model. Whole-cell modeling has been regarded as the central aim of systems biology but also as a grand challenge, which plays essential roles in current and future systems biology. In this paper, we analyze whole-cell modeling challenges and requirements and classify them into three aspects (or dimensions): heterogeneous biochemical networks, uncertainties in components, and representation of cell structure. We then explore how to use different Petri net classes to address different aspects of whole-cell modeling requirements. Based on these analyses, we present a Petri nets-based framework for whole-cell modeling, which not only addresses many whole-cell modeling requirements, but also offers a graphical, modular, and hierarchical modeling tool. We think this framework can offer a feasible modeling approach for whole-cell model construction. KW - Whole-cell modeling KW - Systems biology KW - Petri nets KW - Modeling framework Y1 - 2021 UR - https://www.sciencedirect.com/science/article/abs/pii/S0303264721001738?via%3Dihub U6 - https://doi.org/10.1016/j.biosystems.2021.104533 SN - 0303-2647 SN - 1872-8324 VL - 210 ER -