Phenomenological and molecular-level Petri net modeling and simulation of long-term potentiation

Petri net-based modeling methods have been used in many research projects to represent biological systems. Among these, the hybrid functional Petri net (HFPN) was developed especially for biological modeling in order to provide biologists with a more intuitive Petri net-based method. In the literature, HFPNs are used to represent kinetic models at the molecular level. We present two models of long-term potentiation previously represented by differential equations which we have transformed into HFPN models: a phenomenological synapse model and a molecular-level model of the CaMKII regulation pathway. Through simulation, we obtained results similar to those of previous studies using these models. Our results open the way to a new type of modeling for systems biology where HFPNs are used to combine different levels of abstraction within one model. This approach can be useful in fully modeling a system at the molecular level when kinetic data is missing or when a full study of a system at the molecular level it is not within the scope of the research.     

Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber

MOTIVATION: Because of the complexity of metabolic networks and their regulation, formal modelling is a useful method to improve the understanding of these systems. An essential step in network modelling is to validate the network model. Petri net theory provides algorithms and methods, which can be applied directly to metabolic network modelling and analysis in order to validate the model. The metabolism between sucrose and starch in the potato tuber is of great research interest. Even if the metabolism is one of the best studied in sink organs, it is not yet fully understood. RESULTS: We provide an approach for model validation of metabolic networks using Petri net theory, which we demonstrate for the sucrose breakdown pathway in the potato tuber. We start with hierarchical modelling of the metabolic network as a Petri net and continue with the analysis of qualitative properties of the network. The results characterize the net structure and give insights into the complex net behaviour.     

Modeling of signaling networks

Biochemical networks, including those containing signaling pathways, display a wide range of regulatory properties. These include the ability to propagate information across different time scales and to function as switches and oscillators. The mechanisms underlying these complex behaviors involve many interacting components and cannot be understood by experiments alone. The development of computational models and the integration of these models with experiments provide valuable insight into these complex systems-level behaviors. Here we review current approaches to the development of computational models of biochemical networks and describe the insights gained from models that integrate experimental data, using three examples that deal with ultrasensitivity, flexible bistability and oscillatory behavior. These types of complex behavior from relatively simple networks highlight the necessity of using theoretical approaches in understanding higher order biological functions.     

Dynamical and integrative cell signaling: challenges for the new biology

Years of careful experimental analysis have revealed that signaling molecules are organized into complex networks of biochemical reactions exquisitely regulated in time and space to provide a cell with high-fidelity information about an extremely noisy and volatile environment. A new view of signaling networks as systems consisting of multiple complex elements interacting in a multifarious fashion is emerging, a view that conflicts with the single-gene or protein-centric approach common in biological research. The postgenomic era has brought about a different, network-centric methodology of analysis, suddenly forcing researchers toward the opposite extreme of complexity, where the networks being explored are, to a certain extent, intractable and uninterpretable. Both the cartoons of simple pathways and the very large "hair-ball" diagrams of large intracellular networks are also representations of static worlds, superficially devoid of dynamics and chemistry. These representations are often viewed as being analogous to stably linked computer and neural networks rather than dynamically changing networks of chemical interactions, where the notions of concentration, compartmentalization, and diffusion may be the primary determinants of connectivity. Arguably, the systems biology approach, relying on computational modeling coupled with various experimental techniques and methodologies, will be an essential component of analysis of the behavior of signal transduction pathways. Combining the dynamical view of rapidly evolving responses and the structural view arising from high-throughput analyses of the interacting species will be the best approach toward efforts toward greater understanding of intracellular signaling processes.     

Functional alignment of regulatory networks: a study of temperate phages

The relationship between the design and functionality of molecular networks is now a key issue in biology. Comparison of regulatory networks performing similar tasks can provide insights into how network architecture is constrained by the functions it directs. Here, we discuss methods of network comparison based on network architecture and signaling logic. Introducing local and global signaling scores for the difference between two networks, we quantify similarities between evolutionarily closely and distantly related bacteriophages. Despite the large evolutionary separation between phage λ and 186, their networks are found to be similar when difference is measured in terms of global signaling. We finally discuss how network alignment can be used to pinpoint protein similarities viewed from the network perspective.     

The statistical mechanics of complex signaling networks: nerve growth factor signaling

The inherent complexity of cellular signaling networks and their importance to a wide range of cellular functions necessitates the development of modeling methods that can be applied toward making predictions and highlighting the appropriate experiments to test our understanding of how these systems are designed and function. We use methods of statistical mechanics to extract useful predictions for complex cellular signaling networks. A key difficulty with signaling models is that, while significant effort is being made to experimentally measure the rate constants for individual steps in these networks, many of the parameters required to describe their behavior remain unknown or at best represent estimates. To establish the usefulness of our approach, we have applied our methods toward modeling the nerve growth factor (NGF)-induced differentiation of neuronal cells. In particular, we study the actions of NGF and mitogenic epidermal growth factor (EGF) in rat pheochromocytoma (PC12) cells. Through a network of intermediate signaling proteins, each of these growth factors stimulates extracellular regulated kinase (Erk) phosphorylation with distinct dynamical profiles. Using our modeling approach, we are able to predict the influence of specific signaling modules in determining the integrated cellular response to the two growth factors. Our methods also raise some interesting insights into the design and possible evolution of cellular systems, highlighting an inherent property of these systems that we call 'sloppiness.'     

Petri net modelling of biological networks

Mathematical modelling is increasingly used to get insights into the functioning of complex biological networks. In this context, Petri nets (PNs) have recently emerged as a promising tool among the various methods employed for the modelling and analysis of molecular networks. PNs come with a series of extensions, which allow different abstraction levels, from purely qualitative to more complex quantitative models. Noteworthily, each of these models preserves the underlying graph, which depicts the interactions between the biological components. This article intends to present the basics of the approach and to foster the potential role PNs could play in the development of the computational systems biology.     

BioNetSim: a Petri net-based modeling tool for simulations of biochemical processes

BioNetSim, a Petri net-based software for modeling and simulating biochemistry processes, is developed, whose design and implement are presented in this paper, including logic construction, real-time access to KEGG (Kyoto Encyclopedia of Genes and Genomes), and BioModel database. Furthermore, glycolysis is simulated as an example of its application. BioNetSim is a helpful tool for researchers to download data, model biological network, and simulate complicated biochemistry processes. Gene regulatory networks, metabolic pathways, signaling pathways, and kinetics of cell interaction are all available in BioNetSim, which makes modeling more efficient and effective. Similar to other Petri net-based softwares, BioNetSim does well in graphic application and mathematic construction. Moreover, it shows several powerful predominances. (1) It creates models in database. (2) It realizes the real-time access to KEGG and BioModel and transfers data to Petri net. (3) It provides qualitative analysis, such as computation of constants. (4) It generates graphs for tracing the concentration of every molecule during the simulation processes.     

Quantitative phosphoproteomic analysis of signaling network dynamics

Protein phosphorylation mediated cellular signaling is a highly regulated, dynamic process that controls many aspects of cellular biology. Over the past few years many methods have been developed to quantify temporal dynamics of protein phosphorylation, including mass spectrometry, which can be applied in both an unbiased, discovery mode and in a targeted mode to monitor specific phosphorylation sites. Other methods, such as kinase activity assays and antibody microarrays, have been applied to quantify central nodes in the signaling network, yielding intriguing biological insights. This review provides a concise overview of the latest advances in the quantitative analysis of signaling dynamics including a brief commentary on the future of the field.     

Dose-response aligned circuits in signaling systems

Cells use biological signal transduction pathways to respond to environmental stimuli and the behavior of many cell types depends on precise sensing and transmission of external information. A notable property of signal transduction that was characterized in the Saccharomyces cerevisiae yeast cell and many mammalian cells is the alignment of dose-response curves. It was found that the dose response of the receptor matches closely the dose responses of the downstream. This dose-response alignment (DoRA) renders equal sensitivities and concordant responses in different parts of signaling system and guarantees a faithful information transmission. The experimental observations raise interesting questions about the nature of the information transmission through DoRA signaling networks and design principles of signaling systems with this function. Here, we performed an exhaustive computational analysis on network architectures that underlie the DoRA function in simple regulatory networks composed of two and three enzymes. The minimal circuits capable of DoRA were examined with Michaelis-Menten kinetics. Several motifs that are essential for the dynamical function of DoRA were identified. Systematic analysis of the topology space of robust DoRA circuits revealed that, rather than fine-tuning the network's parameters, the function is primarily realized by enzymatic regulations on the controlled node that are constrained in limiting regions of saturation or linearity.     

Altered Functional Connectivity between Emotional and Cognitive Resting State Networks in Euthymic Bipolar I Disorder Patients

Bipolar disorder is characterized by a functional imbalance between hyperactive ventral/limbic areas and hypoactive dorsal/cognitive brain regions potentially contributing to affective and cognitive symptoms. Resting-state studies in bipolar disorder have identified abnormal functional connectivity between these brain regions. However, most of these studies used a seed-based approach, thus restricting the number of regions that were analyzed. Using data-driven approaches, researchers identified resting state networks whose spatial maps overlap with frontolimbic areas such as the default mode network, the frontoparietal networks, the salient network, and the meso/paralimbic network. These networks are specifically engaged during affective and cognitive tasks and preliminary evidence suggests that functional connectivity within and between some of these networks is impaired in bipolar disorder. The present study used independent component analysis and functional network connectivity approaches to investigate functional connectivity within and between these resting state networks in bipolar disorder. We compared 30 euthymic bipolar I disorder patients and 35 age- and gender-matched healthy controls. Inter-network connectivity analysis revealed increased functional connectivity between the meso/paralimbic and the right frontoparietal network in bipolar disorder. This abnormal connectivity pattern did not correlate with variables related to the clinical course of the disease. The present finding may reflect abnormal integration of affective and cognitive information in ventral-emotional and dorsal-cognitive networks in euthymic bipolar patients. Furthermore, the results provide novel insights into the role of the meso/paralimbic network in bipolar disorder.     

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network''s dynamics. The question that begs for an answer is how to identify the core that is representative of a network''s dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.     

The systems biology of signaling pathways

Signaling networks play the central role in the regulation of processes in a single cell and in the entire body. A recent breakthrough in technologies for systems biology, which combine experimental and mathematical methods, permits scientists to model signaling pathways in an individual cell and in cell populations. This approach provides new information on mechanisms that regulate a variety of biological processes. Here we discuss the mathematical formalisms that are applied to signaling pathway modeling and relevant experimental methods.     

Reconstruction of extended Petri nets from time-series data by using logical control functions

The aim of this work is to extend a previously presented algorithm (Durzinsky et al. 2008b in Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 328–346; Marwan et al. 2008 in Math Methods Oper Res 67:117–132) for the reconstruction of standard place/transition Petri nets from time-series of experimental data sets. This previously reported method finds provably all networks capable to reproduce the experimental observations. In this paper we enhance this approach to generate extended Petri nets involving mechanisms formally corresponding to catalytic or inhibitory dependencies that mediate the involved reactions. The new algorithm delivers the set of all extended Petri nets being consistent with the time-series data used for reconstruction. It is illustrated using the phosphate regulatory network of enterobacteria as a case study.     

Mathematical models of specificity in cell signaling

Cellular signaling pathways transduce extracellular signals into appropriate responses. These pathways are typically interconnected to form networks, often with different pathways sharing similar or identical components. A consequence of this connectedness is the potential for cross talk, some of which may be undesirable. Indeed, experimental evidence indicates that cells have evolved insulating mechanisms to partially suppress "leaking" between pathways. Here we characterize mathematical models of simple signaling networks and obtain exact analytical expressions for two measures of cross talk called specificity and fidelity. The performance of several insulating mechanisms--combinatorial signaling, compartmentalization, the inhibition of one pathway by another, and the selective activation of scaffold proteins--is evaluated with respect to the trade-off between the specificity they provide and the constraints they place on the network. The effects of noise are also examined. The insights gained from this analysis are applied to understanding specificity in the yeast mating and invasive growth MAP kinase signaling network.     

Learning genetic regulatory network connectivity from time series data

Recent experimental advances facilitate the collection of time series data that indicate which genes in a cell are expressed. This information can be used to understand the genetic regulatory network that generates the data. Typically, Bayesian analysis approaches are applied which neglect the time series nature of the experimental data, have difficulty in determining the direction of causality, and do not perform well on networks with tight feedback. To address these problems, this paper presents a method to learn genetic network connectivity which exploits the time series nature of experimental data to achieve better causal predictions. This method first breaks up the data into bins. Next, it determines an initial set of potential influence vectors for each gene based upon the probability of the gene's expression increasing in the next time step. These vectors are then combined to form new vectors with better scores. Finally, these influence vectors are competed against each other to determine the final influence vector for each gene. The result is a directed graph representation of the genetic network's repression and activation connections. Results are reported for several synthetic networks with tight feedback showing significant improvements in recall and runtime over Yu's dynamic Bayesian approach. Promising preliminary results are also reported for an analysis of experimental data for genes involved in the yeast cell cycle.     

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.