Membrane Systems and Petri Net Synthesis

Automated synthesis from behavioural specifications is an attractive and powerful way of constructing concurrent systems. Here we focus on the problem of synthesising a membrane system from a behavioural specification given in the form of a transition system which specifies the desired state space of the system to be constructed. We demonstrate how a Petri net solution to this problem, based on the notion of region of a transition system, yields a method of automated synthesis of membrane systems from state spaces.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks a la Rene Thomas equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models

Additive Invariants of Open Petri Nets

We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems: one for open Petri nets and one for monically open Petri nets (i.e. open Petri nets whose interfaces are specified by monic maps). Our results can be summarized as follows. The additive invariants of open Petri nets are completely determined by their values on a particular class of single-transition Petri nets. However, for monically open Petri nets, the additive invariants are determined by their values on transitionless Petri nets and all single-transition Petri nets. Our results confirm a conjecture of John Baez (stated during the AMS' 2022 Mathematical Research Communities workshop).Comment: 20 page

Building Confidence in Quantitative Systems Pharmacology Models : An Engineer's Guide to Exploring the Rationale in Model Design and Development

This tutorial promotes good practice for exploring the rationale of systems pharmacology models. A safety systems engineering inspired notation approach provides much needed rigor and transparency in development and application of models for therapeutic discovery and design of intervention strategies. Structured arguments over a model's development, underpinning biological knowledge, and analyses of model behaviors are constructed to determine the confidence that a model is fit for the purpose for which it will be applied

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

<p>Abstract</p> <p>Background</p> <p>Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set.</p> <p>Results</p> <p>We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using <it>in silico</it>-generated time-series data sets on wild-type and <it>in silico </it>mutants.</p> <p>Conclusions</p> <p>The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model.</p

State Space Exploration of Spatially Organized Populations of Agents

Abstract-In this paper, we aim at modeling and analyzing the behavior of a spatial population of agents through an exploration of their state space. Agents are localized on a dynamic graph and they have internal states. They interact with an environment. The evolution of the agents and of the environment is specified by a set of rules. The framework is carefully designed to enable the construction of a global state space that can be automatically build and analyzed. The formalism, called IRNs for integrated regulatory networks, may be seen as an extension of logical regulatory networks (à la Thomas) developed in systems biology with spatial information and generalized to use arbitrary data values and update functions of this values. This thus allows to model systems with multiple agents that may be located on a varying spatial structure, may store and update local information, may depend on varying global information and may communicate in their neighborhood. A model of such a system can be defined as an IRN, and then analyzed using model-checking to asses its properties. This paper sketches the modeling framework and its semantics. We show how IRN may be used for the modeling of a population of simple agents, the automatic analysis of various reachability properties and the use of symmetries to reduce the size of the state space

Petri Nets for Biologically Motivated Computing

Petri nets are a general and well-established model of concurrent and distributed computation and behaviour, including that taking place in biological systems. In this survey paper, we are concerned with intrinsic relationships between Petri nets and two formal models inspired by aspects of the functioning of the living cell: membrane systems and reaction systems. In particular, we are interested in the benefits that can result from establishing strong semantical links between Petri nets and membrane systems and reaction systems. We first discuss Petri nets with localities reflecting the compartmentalisation modelled in membrane systems. Then special attention is given to set-nets, a new Petri net model for reaction systems and their qualitative approach to the investigation of the processes carried out by biochemical reactions taking place in the living cell

Dynamical modeling of uncertain interaction-based genomic networks

BACKGROUND: Most dynamical models for genomic networks are built upon two current methodologies, one process-based and the other based on Boolean-type networks. Both are problematic when it comes to experimental design purposes in the laboratory. The first approach requires a comprehensive knowledge of the parameters involved in all biological processes a priori, whereas the results from the second method may not have a biological correspondence and thus cannot be tested in the laboratory. Moreover, the current methods cannot readily utilize existing curated knowledge databases and do not consider uncertainty in the knowledge. Therefore, a new methodology is needed that can generate a dynamical model based on available biological data, assuming uncertainty, while the results from experimental design can be examined in the laboratory. RESULTS: We propose a new methodology for dynamical modeling of genomic networks that can utilize the interaction knowledge provided in public databases. The model assigns discrete states for physical entities, sets priorities among interactions based on information provided in the database, and updates each interaction based on associated node states. Whenever uncertainty in dynamics arises, it explores all possible outcomes. By using the proposed model, biologists can study regulation networks that are too complex for manual analysis. CONCLUSIONS: The proposed approach can be effectively used for constructing dynamical models of interaction-based genomic networks without requiring a complete knowledge of all parameters affecting the network dynamics, and thus based on a small set of available data

Modeling Biological Gradient Formation: Combining Partial Differential Equations and Petri Nets

Algorithms and the Foundations of Software technologyComputer Systems, Imagery and Medi