Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets

Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways applying Petri net formalism and in silico knockout analysis

The paper describes a mathematical model of the molecular switches of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the literature, we constructed a Petri net model based on detailed molecular reactions of the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 edges. We verified the model by evaluating invariant properties of the system at steady state and by in silico knockout analysis. Applying Petri net analysis techniques, we found 279 pathways, which describe signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic and led to multiple possible outcomes. We investigated the in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction. Despite not knowing enough kinetic data of sufficient quality, we estimated system’s dynamics using a discrete, semi-quantitative Petri net model.

It is still a challenge to develop mechanistic models for big molecular systems without the knowledge of enough kinetic parameters of sufficient quality. At the same time, more qualitative and semi-quantitative data have been produced in increasing numbers, e.g., by new high-throughput technologies. This has generated demands for new concepts at appropriate abstraction levels. The Petri net formalism enables the integration of qualitative as well as quantitative data and provides algorithms and methods for model verification and model simulation. Moreover, Petri nets exhibit a clear and coherent visualization. Here, we modeled the molecular switches between cell survival, apoptosis, and necroptosis induced by tumor necrosis factor 1. We were interested not only in an exhaustive exploration of all possible signaling pathways, but also in finding the system’s checkpoints. Our Petri net model comprises 118 biochemical entities, 130 reactions, and 299 edges. We found 279 pathways that describe signal flows from receptor activation to cellular response.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic, leading to multiple possible outcomes. We applied in silico knockout analyses to the Petri net model and could identify important checkpoints of the tumor necrosis factor 1 signaling pathway.

Advances in flux balance analysis by integrating machine learning and mechanism-based models

The availability of multi-omics data sets and genome-scale metabolic models for various organisms provide a platform for modeling and analyzing genotype-to-phenotype relationships. Flux balance analysis is the main tool for predicting flux distributions in genome-scale metabolic models and various data-integrative approaches enable modeling context-specific network behavior. Due to its linear nature, this optimization framework is readily scalable to multi-tissue or -organ and even multi-organism models. However, both data and model size can hamper a straightforward biological interpretation of the estimated fluxes. Moreover, flux balance analysis simulates metabolism at steady-state and thus, in its most basic form, does not consider kinetics or regulatory events. The integration of flux balance analysis with complementary data analysis and modeling techniques offers the potential to overcome these challenges. In particular machine learning approaches have emerged as the tool of choice for data reduction and selection of most important variables in big data sets. Kinetic models and formal languages can be used to simulate dynamic behavior. This review article provides an overview of integrative studies that combine flux balance analysis with machine learning approaches, kinetic models, such as physiology-based pharmacokinetic models, and formal graphical modeling languages, such as Petri nets. We discuss the mathematical aspects and biological applications of these integrated approaches and outline challenges and future perspectives.

Integrative Modeling of Gene Expression and Metabolic Networks of Arabidopsis Embryos for Identification of Seed Oil Causal Genes

Fatty acids in crop seeds are a major source for both vegetable oils and industrial applications. Genetic improvement of fatty acid composition and oil content is critical to meet the current and future demands of plant-based renewable seed oils. Addressing this challenge can be approached by network modeling to capture key contributors of seed metabolism and to identify underpinning genetic targets for engineering the traits associated with seed oil composition and content. Here, we present a dynamic model, using an Ordinary Differential Equations model and integrated time-course gene expression data, to describe metabolic networks during Arabidopsis thaliana seed development. Through in silico perturbation of genes, targets were predicted in seed oil traits. Validation and supporting evidence were obtained for several of these predictions using published reports in the scientific literature. Furthermore, we investigated two predicted targets using omics datasets for both gene expression and metabolites from the seed embryo, and demonstrated the applicability of this network-based model. This work highlights that integration of dynamic gene expression atlases generates informative models which can be explored to dissect metabolic pathways and lead to the identification of causal genes associated with seed oil traits.

Challenges and Perspectives of Polyhydroxyalkanoate Production From Microalgae/Cyanobacteria and Bacteria as Microbial Factories: An Assessment of Hybrid Biological System

Polyhydroxyalkanoates (PHAs) are the biopolymer of choice if we look for a substitute of petroleum-based non-biodegradable plastics. Microbial production of PHAs as carbon reserves has been studied for decades and PHAs are gaining attention for a wide range of applications in various fields. Still, their uneconomical production is the major concern largely attributed to high cost of organic substrates for PHA producing heterotrophic bacteria. Therefore, microalgae/cyanobacteria, being photoautotrophic, prove to have an edge over heterotrophic bacteria. They have minimal metabolic requirements, such as inorganic nutrients (CO2, N, P, etc.) and light, and they can survive under adverse environmental conditions. PHA production under photoautotrophic conditions has been reported from cyanobacteria, the only candidate among prokaryotes, and few of the eukaryotic microalgae. However, an efficient cultivation system is still required for photoautotrophic PHA production to overcome the limitations associated with (1) stringent management of closed photobioreactors and (2) optimization of monoculture in open pond culture. Thus, a hybrid system is a necessity, involving the participation of microalgae/cyanobacteria and bacteria, i.e., both photoautotrophic and heterotrophic components having mutual interactive benefits for each other under different cultivation regime, e.g., mixotrophic, successive two modules, consortium based, etc. Along with this, further strategies like optimization of culture conditions (N, P, light exposure, CO2 dynamics, etc.), bioengineering, efficient downstream processes, and the application of mathematical/network modeling of metabolic pathways to improve PHA production are the key areas discussed here. Conclusively, this review aims to critically analyze cyanobacteria as PHA producers and proposes economically sustainable production of PHA from microbial autotrophs and heterotrophs in "hybrid biological system."

The outer membrane Omp85-like protein P39 influences metabolic homeostasis in mature Arabidopsis thaliana

The Omp85 proteins form a large membrane protein family in bacteria and eukaryotes. Omp85 proteins are composed of a C-terminal β-barrel-shaped membrane domain and one or more N-terminal polypeptide transport-associated (POTRA) domains. However, Arabidopsis thaliana contains two genes coding for Omp85 proteins without a POTRA domain. One gene is designated P39, according to the molecular weight of the encoded protein. The protein is targeted to plastids and it was established that p39 has electrophysiological properties similar to other Omp85 family members, particularly to that designated as Toc75V/Oep80. We analysed expression of the gene and characterised two T-DNA insertion mutants, focusing on alterations in photosynthetic activity, plastid ultrastructure, global expression profile and metabolome. We observed pronounced expression of P39, especially in veins. Mutants of P39 show growth aberrations, reduced photosynthetic activity and changes in plastid ultrastructure, particularly in the leaf tip. Further, they display global alteration of gene expression and metabolite content in leaves of mature plants. We conclude that the function of the plastid-localised and vein-specific Omp85 family protein p39 is important, but not essential, for maintenance of metabolic homeostasis of full-grown A. thaliana plants. Further, the function of p39 in veins influences the functionality of other plant tissues. The link connecting p39 function with metabolic regulation in mature A. thaliana is discussed.