Petri nets are a discrete event simulation approach developed for system representation, in particular for their concurrency and synchronization properties. Various extensions to the original theory of Petri nets have been used for modeling molecular biology systems and metabolic networks. These extensions are stochastic, colored, hybrid and functional. This paper carries out an initial review of the various modeling approaches based on Petri net found in the literature, and of the biological systems that have been successfully modeled with these approaches. Moreover, the modeling goals and possibilities of qualitative analysis and system simulation of each approach are discussed.

Podocytes are kidney cells with specialized morphology that is required for glomerular filtration. Diseases, such as diabetes, or drug exposure that causes disruption of the podocyte foot process morphology results in kidney pathophysiology. Proteomic analysis of glomeruli isolated from rats with puromycin-induced kidney disease and control rats indicated that protein kinase A (PKA), which is activated by adenosine 3′,5′-monophosphate (cAMP), is a key regulator of podocyte morphology and function. In podocytes, cAMP signaling activates cAMP response element–binding protein (CREB) to enhance expression of the gene encoding a differentiation marker, synaptopodin, a protein that associates with actin and promotes its bundling. We constructed and experimentally verified a β-adrenergic receptor–driven network with multiple feedback and feedforward motifs that controls CREB activity. To determine how the motifs interacted to regulate gene expression, we mapped multicompartment dynamical models, including information about protein subcellular localization, onto the network topology using Petri net formalisms. These computational analyses indicated that the juxtaposition of multiple feedback and feedforward motifs enabled the prolonged CREB activation necessary for synaptopodin expression and actin bundling. Drug-induced modulation of these motifs in diseased rats led to recovery of normal morphology and physiological function in vivo. Thus, analysis of regulatory motifs using network dynamics can provide insights into pathophysiology that enable predictions for drug intervention strategies to treat kidney disease.

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This article introduces a new method for analyzing the dynamics of signal propagation in signaling pathways using Petri net theory. The method is demonstrated with the Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) regulation network. The results constitute temporal information about signal propagation in the network, a simplified graphical representation of the network and of the signal propagation dynamics and a characterization of some signaling routes as regulation motifs.

Diatoms are major primary producers in polar environments where they can actively grow under extremely variable conditions. Integrative modeling using a genome-scale model (GSM) is a powerful approach to decipher the complex interactions between components of diatom metabolism and can provide insights into metabolic mechanisms underlying their evolutionary success in polar ecosystems. We developed the first GSM for a polar diatom, Fragilariopsis cylindrus, which enabled us to study its metabolic robustness using sensitivity analysis. We find that the predicted growth rate was robust to changes in all model parameters (i.e., cell biochemical composition) except the carbon uptake rate. Constraints on total cellular carbon buffer the effect of changes in the input parameters on reaction fluxes and growth rate. We also show that single reaction deletion of 20% to 32% of active (nonzero flux) reactions and single gene deletion of 44% to 55% of genes associated with active reactions affected the growth rate, as well as the production fluxes of total protein, lipid, carbohydrate, DNA, RNA, and pigments by less than 1%, which was due to the activation of compensatory reactions (e.g., analogous enzymes and alternative pathways) with more highly connected metabolites involved in the reactions that were robust to deletion. Interestingly, including highly divergent alleles unique for F. cylindrus increased its metabolic robustness to cellular perturbations even more. Overall, our results underscore the high robustness of metabolism in F. cylindrus, a feature that likely helps to maintain cell homeostasis under polar conditions.