Simulation of a Petri net-based Model of the Terpenoid Biosynthesis Pathway

<p>Abstract</p> <p>Background</p> <p>The development and simulation of dynamic models of terpenoid biosynthesis has yielded a systems perspective that provides new insights into how the structure of this biochemical pathway affects compound synthesis. These insights may eventually help identify reactions that could be experimentally manipulated to amplify terpenoid production. In this study, a dynamic model of the terpenoid biosynthesis pathway was constructed based on the Hybrid Functional Petri Net (HFPN) technique. This technique is a fusion of three other extended Petri net techniques, namely Hybrid Petri Net (HPN), Dynamic Petri Net (HDN) and Functional Petri Net (FPN).</p> <p>Results</p> <p>The biological data needed to construct the terpenoid metabolic model were gathered from the literature and from biological databases. These data were used as building blocks to create an HFPNe model and to generate parameters that govern the global behaviour of the model. The dynamic model was simulated and validated against known experimental data obtained from extensive literature searches. The model successfully simulated metabolite concentration changes over time (pt) and the observations correlated with known data. Interactions between the intermediates that affect the production of terpenes could be observed through the introduction of inhibitors that established feedback loops within and crosstalk between the pathways.</p> <p>Conclusions</p> <p>Although this metabolic model is only preliminary, it will provide a platform for analysing various high-throughput data, and it should lead to a more holistic understanding of terpenoid biosynthesis.</p

Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Petri Nets with Fuzzy Logic (PNFL): Reverse Engineering and Parametrization

Background: The recent DREAM4 blind assessment provided a particularly realistic and challenging setting for network reverse engineering methods. The in silico part of DREAM4 solicited the inference of cycle-rich gene regulatory networks from heterogeneous, noisy expression data including time courses as well as knockout, knockdown and multifactorial perturbations. Methodology and Principal Findings: We inferred and parametrized simulation models based on Petri Nets with Fuzzy Logic (PNFL). This completely automated approach correctly reconstructed networks with cycles as well as oscillating network motifs. PNFL was evaluated as the best performer on DREAM4 in silico networks of size 10 with an area under the precision-recall curve (AUPR) of 81%. Besides topology, we inferred a range of additional mechanistic details with good reliability, e.g. distinguishing activation from inhibition as well as dependent from independent regulation. Our models also performed well on new experimental conditions such as double knockout mutations that were not included in the provided datasets. Conclusions: The inference of biological networks substantially benefits from methods that are expressive enough to deal with diverse datasets in a unified way. At the same time, overly complex approaches could generate multiple different models that explain the data equally well. PNFL appears to strike the balance between expressive power and complexity. This also applies to the intuitive representation of PNFL models combining a straightforward graphical notation with colloquial fuzzy parameters

An efficient biological pathway layout algorithm combining grid-layout and spring embedder for complicated cellular location information

<p>Abstract</p> <p>Background</p> <p>Graph drawing is one of the important techniques for understanding biological regulations in a cell or among cells at the pathway level. Among many available layout algorithms, the spring embedder algorithm is widely used not only for pathway drawing but also for circuit placement and www visualization and so on because of the harmonized appearance of its results. For pathway drawing, location information is essential for its comprehension. However, complex shapes need to be taken into account when torus-shaped location information such as nuclear inner membrane, nuclear outer membrane, and plasma membrane is considered. Unfortunately, the spring embedder algorithm cannot easily handle such information. In addition, crossings between edges and nodes are usually not considered explicitly.</p> <p>Results</p> <p>We proposed a new grid-layout algorithm based on the spring embedder algorithm that can handle location information and provide layouts with harmonized appearance. In grid-layout algorithms, the mapping of nodes to grid points that minimizes a cost function is searched. By imposing positional constraints on grid points, location information including complex shapes can be easily considered. Our layout algorithm includes the spring embedder cost as a component of the cost function. We further extend the layout algorithm to enable dynamic update of the positions and sizes of compartments at each step.</p> <p>Conclusions</p> <p>The new spring embedder-based grid-layout algorithm and a spring embedder algorithm are applied to three biological pathways; endothelial cell model, Fas-induced apoptosis model, and <it>C. elegans </it>cell fate simulation model. From the positional constraints, all the results of our algorithm satisfy location information, and hence, more comprehensible layouts are obtained as compared to the spring embedder algorithm. From the comparison of the number of crossings, the results of the grid-layout-based algorithm tend to contain more crossings than those of the spring embedder algorithm due to the positional constraints. For a fair comparison, we also apply our proposed method without positional constraints. This comparison shows that these results contain less crossings than those of the spring embedder algorithm. We also compared layouts of the proposed algorithm with and without compartment update and verified that latter can reach better local optima.</p

Computational modeling with forward and reverse engineering links signaling network and genomic regulatory responses: NF-κB signaling-induced gene expression responses in inflammation

<p>Abstract</p> <p>Background</p> <p>Signal transduction is the major mechanism through which cells transmit external stimuli to evoke intracellular biochemical responses. Diverse cellular stimuli create a wide variety of transcription factor activities through signal transduction pathways, resulting in different gene expression patterns. Understanding the relationship between external stimuli and the corresponding cellular responses, as well as the subsequent effects on downstream genes, is a major challenge in systems biology. Thus, a systematic approach is needed to integrate experimental data and theoretical hypotheses to identify the physiological consequences of environmental stimuli.</p> <p>Results</p> <p>We proposed a systematic approach that combines forward and reverse engineering to link the signal transduction cascade with the gene responses. To demonstrate the feasibility of our strategy, we focused on linking the NF-κB signaling pathway with the inflammatory gene regulatory responses because NF-κB has long been recognized to play a crucial role in inflammation. We first utilized forward engineering (Hybrid Functional Petri Nets) to construct the NF-κB signaling pathway and reverse engineering (Network Components Analysis) to build a gene regulatory network (GRN). Then, we demonstrated that the corresponding IKK profiles can be identified in the GRN and are consistent with the experimental validation of the IKK kinase assay. We found that the time-lapse gene expression of several cytokines and chemokines (TNF-α, IL-1, IL-6, CXCL1, CXCL2 and CCL3) is concordant with the NF-κB activity profile, and these genes have stronger influence strength within the GRN. Such regulatory effects have highlighted the crucial roles of NF-κB signaling in the acute inflammatory response and enhance our understanding of the systemic inflammatory response syndrome.</p> <p>Conclusion</p> <p>We successfully identified and distinguished the corresponding signaling profiles among three microarray datasets with different stimuli strengths. In our model, the crucial genes of the NF-κB regulatory network were also identified to reflect the biological consequences of inflammation. With the experimental validation, our strategy is thus an effective solution to decipher cross-talk effects when attempting to integrate new kinetic parameters from other signal transduction pathways. The strategy also provides new insight for systems biology modeling to link any signal transduction pathways with the responses of downstream genes of interest.</p

Time-dependent structural transformation analysis to high-level Petri net model with active state transition diagram

<p>Abstract</p> <p>Background</p> <p>With an accumulation of <it>in silico </it>data obtained by simulating large-scale biological networks, a new interest of research is emerging for elucidating how living organism functions over time in cells.</p> <p>Investigating the dynamic features of current computational models promises a deeper understanding of complex cellular processes. This leads us to develop a method that utilizes structural properties of the model over all simulation time steps. Further, user-friendly overviews of dynamic behaviors can be considered to provide a great help in understanding the variations of system mechanisms.</p> <p>Results</p> <p>We propose a novel method for constructing and analyzing a so-called <it>active state transition diagram </it>(ASTD) by using time-course simulation data of a high-level Petri net. Our method includes two new algorithms. The first algorithm extracts a series of subnets (called <it>temporal subnets</it>) reflecting biological components contributing to the dynamics, while retaining positive mathematical qualities. The second one creates an ASTD composed of unique temporal subnets. ASTD provides users with concise information allowing them to grasp and trace how a key regulatory subnet and/or a network changes with time. The applicability of our method is demonstrated by the analysis of the underlying model for circadian rhythms in <it>Drosophila</it>.</p> <p>Conclusions</p> <p>Building ASTD is a useful means to convert a hybrid model dealing with discrete, continuous and more complicated events to finite time-dependent states. Based on ASTD, various analytical approaches can be applied to obtain new insights into not only systematic mechanisms but also dynamics.</p