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Reproducibility of simulation experiments is still a significant challenge and has attracted considerable attention in recent years. One cause of this situation is bad habits of the scientific community. Many results are published without data or source code, and only a textual description of the simulation set-up is provided. Other causes are: no complete simulation set-up, no proper output data analysis and inconsistency of published data, which makes it impossible to compare results.
The progress of computational modelling, amount of data and complexity of models requires designing experiments in such a way that ensures reproducibility. A textual description does not provide all the needed details. A computer code is more reliable than a textual description. It is the precise specification that describes a simulation configuration, model, etc. When computer code, data, models and all parameters are provided, the simulation results become reproducible.
The main goal of this thesis is to develop a tool that ensures reproducibility and efficient execution of simulation experiments, often involving many individual simulation runs. The tool should support a wide range of application scenarios, where the typical scenario is simulation of biochemical reaction networks, which are represented as (coloured) Petri nets interpreted in the stochastic, continuous or hybrid paradigm. The model to be simulated can be given in various formats, including SBML.
The result is a command line tool called Spike, which can be used for various scenarios, including benchmarking, simulation of adaptive models and parameter optimization. It builds on a human-readable configuration script SPC, supporting the efficient specification of multiple model configurations as well as multiple simulator configurations in a single configuration file.
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.
Hybrid simulation of biological processes becomes widely used to overcome the limitations of the pure stochastic or the complete deterministic simulation. In this manual, we present easy-to-follow steps for constructing and executing hybrid models via Snoopy [HHL+12]. Snoopy is a tool to design and animate or simulate hierarchical graphs, i.e., qualitative, stochastic, continuous, and hybrid Petri nets. This manual is concerned with hybrid Petri nets (HPN) [HH12] as well as their coloured counterpart (HPNC) [HLR14]. HPN combine the merits of stochastic and continuous Petri nets into one single class. Moreover, HPN in Snoopy supports state of the art hybrid simulation algorithms (e.g., [HH16]) to execute the constructed HPN models. Simulating a model using Snoopy's hybrid simulation involves first constructing the reaction network via HPN notations and afterwards executing such model.
Stochastic modelling of biochemical reaction networks is getting more and more popular. Throughout the past decades typical biological models increased in their size and complexity, because of advances in systems and molecular biology, in particular through the high-throughput omic technologies. Here biochemical networks of different levels of detail are modelled, starting with simple chemical reactions and signal transduction networks, up to individual cells and entire organisms. This increases the demand for efficient analysis methods.
A Petri net is a mathematical modelling language for the description of concurrent behaviour of distributed systems. Its advantage is the ease of scalability of the models, which relates to the network’s state space, as well as the structure of the network itself.
In this work, we recall several stochastic simulation algorithms, e.g., exact as well as approximate methods. Furthermore, we introduce an approach to improve the efficiency of stochastic simulation for large and dense networks by a new approximate stochastic simulation algorithm called discrete-time leap method. We depict the wide range of simulative analyses of complex stochastic systems ranging from trace generation to the computation of transient solutions and steady state distributions. We set forth advanced analysis of stochastic models by means of simulative model checking. For the use of simulative model checking, we integrate the continuous stochastic (reward) logic (CS(R)L) and the probabilistic linear-time temporal logic with constraints (PLTLc). Simulative model checking has some limitations compared to the numerical methods, e.g., in principle it is possible to consider nested probabilistic formulas in CS(R)L, but not practical, since the calculation is not feasible in a reasonable period of time. In addition to the transient analysis, the steady state analysis is often of interest; therefore we have implemented two on-the-fly steady state detection methods. The first one is based on a “sample batch means” algorithm and is used in the linear-time temporal logic. The second approximates the steady state distribution and checks for convergence. We apply the aforementioned techniques to several case studies from systems biology and technical systems.
The main contributions of this thesis to scientific knowledge are the development of the discrete-time leap method for the simulation of stochastic models, the approximations of transient solutions and steady state distributions by use of stochastic simulation for stochastic models and Markov reward models, the development of an infinite time horizon model checking algorithm exploiting the steady state property for PLTLc and CSL, and the first simulative model checking algorithm for CSRL incorporating state and impulse rewards. All presented algorithms and methods are implemented in the advanced analysis tool MARCIE.