Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks

Large-scale computational modelling of the M1 and M2 synovial macrophages in rheumatoid arthritis

Macrophages play an essential role in rheumatoid arthritis. Depending on their phenotype (M1 or M2), they can play a role in the initiation or resolution of inflammation. The M1/M2 ratio in rheumatoid arthritis is higher than in healthy controls. Despite this, no treatment targeting specifically macrophages is currently used in clinics. Thus, devising strategies to selectively deplete proinflammatory macrophages and promote anti-inflammatory macrophages could be a promising therapeutic approach. State-of-the-art molecular interaction maps of M1 and M2 macrophages in rheumatoid arthritis are available and represent a dense source of knowledge; however, these maps remain limited by their static nature. Discrete dynamic modelling can be employed to study the emergent behaviours of these systems. Nevertheless, handling such large-scale models is challenging. Due to their massive size, it is computationally demanding to identify biologically relevant states in a cell- and disease-specific context. In this work, we developed an efficient computational framework that converts molecular interaction maps into Boolean models using the CaSQ tool. Next, we used a newly developed version of the BMA tool deployed to a high-performance computing cluster to identify the models' steady states. The identified attractors are then validated using gene expression data sets and prior knowledge. We successfully applied our framework to generate and calibrate the M1 and M2 macrophage Boolean models for rheumatoid arthritis. Using KO simulations, we identified NFkB, JAK1/JAK2, and ERK1/Notch1 as potential targets that could selectively suppress proinflammatory macrophages and GSK3B as a promising target that could promote anti-inflammatory macrophages in rheumatoid arthritis.

Searching for significant reactions and subprocesses in models of biological systems based on Petri nets

The primary aim of this research was to propose algorithms enabling the identification of significant reactions and subprocesses within models of biological systems constructed using classical Petri nets. These solutions allow to performance of two analysis methods: an importance analysis for identifying individual reactions critical to the functioning of the model and an occurrence analysis for finding essential subprocesses. To demonstrate the utility of these methods, analyses of an example model have been performed. In this case, it was a model related to the DNA damage response mechanism. It is worth noting that the proposed analyses can be applied to any biological phenomenon represented using the Petri net formalism. The presented analysis methods represent an extension of classical Petri net-based analyses. Their utility lies in their potential to enhance our comprehension of the biological phenomena under investigation. Furthermore, they can lead to the development of more effective medical therapies, as they can aid in the identification of potential molecular targets for drugs.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Transducer Cascades for Biological Literature-Based Discovery

G protein-coupled receptors (GPCRs) control the response of cells to many signals, and as such, are involved in most cellular processes. As membrane receptors, they are accessible at the surface of the cell. GPCRs are also the largest family of membrane receptors, with more than 800 representatives in mammal genomes. For this reason, they are ideal targets for drugs. Although about one third of approved drugs target GPCRs, only about 16% of GPCRs are targeted by drugs. One of the difficulties comes from the lack of knowledge on the intra-cellular events triggered by these molecules. In the last two decades, scientists have started mapping the signaling networks triggered by GPCRs. However, it soon appeared that the system is very complex, which led to the publication of more than 320,000 scientific papers. Clearly, a human cannot take into account such massive sources of information. These papers represent a mine of information about both ontological knowledge and experimental results related to GPCRs, which have to be exploited in order to build signaling networks. The ABLISS project aims at the automatic building of GPCRs networks using automated deductive reasoning, allowing to integrate all available data. Therefore, we processed the automatic extraction of network information from the literature using Natural Language Processing (NLP). We mainly focused on the experimental results about GPCRs reported in the scientific papers, as so far there is no source gathering all these experimental results. We designed a relational database in order to make them available to the scientific community later. After introducing the more general objectives of the ABLISS project, we describe the formalism in detail. We then explain the NLP program using the finite state methods (Unitex graph cascades) we implemented and discuss the extracted facts obtained. Finally, we present the design of the relational database that stores the facts extracted from the selected papers.

Chemical data intelligence for sustainable chemistry

This study highlights new opportunities for optimal reaction route selection from large chemical databases brought about by the rapid digitalisation of chemical data. The chemical industry requires a transformation towards more sustainable practices, eliminating its dependencies on fossil fuels and limiting its impact on the environment. However, identifying more sustainable process alternatives is, at present, a cumbersome, manual, iterative process, based on chemical intuition and modelling. We give a perspective on methods for automated discovery and assessment of competitive sustainable reaction routes based on renewable or waste feedstocks. Three key areas of transition are outlined and reviewed based on their state-of-the-art as well as bottlenecks: (i) data, (ii) evaluation metrics, and (iii) decision-making. We elucidate their synergies and interfaces since only together these areas can bring about the most benefit. The field of chemical data intelligence offers the opportunity to identify the inherently more sustainable reaction pathways and to identify opportunities for a circular chemical economy. Our review shows that at present the field of data brings about most bottlenecks, such as data completion and data linkage, but also offers the principal opportunity for advancement.

Identifying all moiety conservation laws in genome-scale metabolic networks

The stoichiometry of a metabolic network gives rise to a set of conservation laws for the aggregate level of specific pools of metabolites, which, on one hand, pose dynamical constraints that cross-link the variations of metabolite concentrations and, on the other, provide key insight into a cell's metabolic production capabilities. When the conserved quantity identifies with a chemical moiety, extracting all such conservation laws from the stoichiometry amounts to finding all non-negative integer solutions of a linear system, a programming problem known to be NP-hard. We present an efficient strategy to compute the complete set of integer conservation laws of a genome-scale stoichiometric matrix, also providing a certificate for correctness and maximality of the solution. Our method is deployed for the analysis of moiety conservation relationships in two large-scale reconstructions of the metabolism of the bacterium E. coli, in six tissue-specific human metabolic networks, and, finally, in the human reactome as a whole, revealing that bacterial metabolism could be evolutionarily designed to cover broader production spectra than human metabolism. Convergence to the full set of moiety conservation laws in each case is achieved in extremely reduced computing times. In addition, we uncover a scaling relation that links the size of the independent pool basis to the number of metabolites, for which we present an analytical explanation.

Stochastic flux analysis of chemical reaction networks

Background

Chemical reaction networks provide an abstraction scheme for a broad range of models in biology and ecology. The two common means for simulating these networks are the deterministic and the stochastic approaches. The traditional deterministic approach, based on differential equations, enjoys a rich set of analysis techniques, including a treatment of reaction fluxes. However, the discrete stochastic simulations, which provide advantages in some cases, lack a quantitative treatment of network fluxes.

Results

We describe a method for flux analysis of chemical reaction networks, where flux is given by the flow of species between reactions in stochastic simulations of the network. Extending discrete event simulation algorithms, our method constructs several data structures, and thereby reveals a variety of statistics about resource creation and consumption during the simulation. We use these structures to quantify the causal interdependence and relative importance of the reactions at arbitrary time intervals with respect to the network fluxes. This allows us to construct reduced networks that have the same flux-behavior, and compare these networks, also with respect to their time series. We demonstrate our approach on an extended example based on a published ODE model of the same network, that is, Rho GTP-binding proteins, and on other models from biology and ecology.

Conclusions

We provide a fully stochastic treatment of flux analysis. As in deterministic analysis, our method delivers the network behavior in terms of species transformations. Moreover, our stochastic analysis can be applied, not only at steady state, but at arbitrary time intervals, and used to identify the flow of specific species between specific reactions. Our cases study of Rho GTP-binding proteins reveals the role played by the cyclic reverse fluxes in tuning the behavior of this network.