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D.: How Might Petri Nets Enhance Your Systems Biology Toolkit
 In: Proc. PETRI NETS
, 2011
"... Abstract. “How might Petri nets enhance my Systems Biology toolkit?” – this is one of the questions that we get on a regular basis, which motivated us to write an answer in the form of this paper. We discuss the extent to which the Petri net approach can be used as an umbrella formalism to support ..."
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Abstract. “How might Petri nets enhance my Systems Biology toolkit?” – this is one of the questions that we get on a regular basis, which motivated us to write an answer in the form of this paper. We discuss the extent to which the Petri net approach can be used as an umbrella formalism to support the process of BioModel Engineering. This includes the facilitation of an active and productive interaction between biomodellers and bioscientists during the construction and analysis of dynamic models of biological systems. These models play a crucial role in both Systems Biology, where they can be explanatory and predictive, and synthetic biology, where they are effectively design templates. In this paper we give an overview of the tools and techniques which have been shown to be useful so far, and describe some of the current open challenges.
Simulative Model Checking of Steady State and TimeUnbounded Temporal Operators
"... Abstract. When working with large stochastic models simulation remains the only possible analysis technique. Therefore, simulative model checking is the way to go. While finite time horizon algorithms are well known for probabilistic lineartime temporal logic, we provide an infinite time horizon pr ..."
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Abstract. When working with large stochastic models simulation remains the only possible analysis technique. Therefore, simulative model checking is the way to go. While finite time horizon algorithms are well known for probabilistic lineartime temporal logic, we provide an infinite time horizon procedure as well as steady state computation, based on exact stochastic simulation algorithms. We demonstrate the approach on models of the RKIP inhibited ERK pathway and angiogenetic process.
Lumpings of Markov chains, entropy rate preservation, and higherorder lumpability
"... A lumping of a Markov chain is a coordinatewise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finitelength traject ..."
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A lumping of a Markov chain is a coordinatewise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finitelength trajectory of the lumped chain and by the information needed to reconstruct original trajectories from their lumped images. Both are purely combinatorial criteria, depending only on the transition graph of the Markov chain and the lumping function. A lumping is strongly klumpable, iff the lumped process is a kth order Markov chain for each starting distribution of the original Markov chain. We characterise strong klumpability via tightness of stationary entropic bounds. In the sparse setting, we give sufficient conditions on the lumping to both preserve the
Stochastic Modelling and Simulation of Biochemical Networks
"... Biochemical systems are inherently governed by stochastic laws. Consequently, stochastic models are an adequate choice for their thorough investigation. But due to the computational expense for their analysis, the considerations are often restricted to the averaged case and continuous models are ..."
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Biochemical systems are inherently governed by stochastic laws. Consequently, stochastic models are an adequate choice for their thorough investigation. But due to the computational expense for their analysis, the considerations are often restricted to the averaged case and continuous models are
of Generalized Stochastic Petri Nets. Its capabilities range from
"... Abstract—MARCIE is a multithreaded tool for the analysis ..."
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