High performance hybrid functional Petri net simulations of biological pathway models on CUDA

Hybrid functional Petri nets are a wide-spread tool for representing and simulating biological models. Due to their potential of providing virtual drug testing environments, biological simulations have a growing impact on pharmaceutical research. Continuous research advancements in biology and medicine lead to exponentially increasing simulation times, thus raising the demand for performance accelerations by efficient and inexpensive parallel computation solutions. Recent developments in the field of general-purpose computation on graphics processing units (GPGPU) enabled the scientific community to port a variety of compute intensive algorithms onto the graphics processing unit (GPU). This work presents the first scheme for mapping biological hybrid functional Petri net models, which can handle both discrete and continuous entities, onto compute unified device architecture (CUDA) enabled GPUs. GPU accelerated simulations are observed to run up to 18 times faster than sequential implementations. Simulating the cell boundary formation by Delta-Notch signaling on a CUDA enabled GPU results in a speedup of approximately 7x for a model containing 1,600 cells.     

Quantitative Petri net model of gene regulated metabolic networks in the cell

A method to exploit hybrid Petri nets (HPN) for quantitatively modeling and simulating gene regulated metabolic networks is demonstrated. A global kinetic modeling strategy and Petri net modeling algorithm are applied to perform the bioprocess functioning and model analysis. With the model, the interrelations between pathway analysis and metabolic control mechanism are outlined. Diagrammatical results of the dynamics of metabolites are simulated and observed by implementing a HPN tool, Visual Object Net ++. An explanation of the observed behavior of the urea cycle is proposed to indicate possibilities for metabolic engineering and medical care. Finally, the perspective of Petri nets on modeling and simulation of metabolic networks is discussed.     

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.     

Biopathways representation and simulation on hybrid functional Petri net

The following two matters should be resolved in order for biosimulation tools to be accepted by users in biology/medicine: (1) remove issues which are irrelevant to biological importance, and (2) allow users to represent biopathways intuitively and understand/manage easily the details of representation and simulation mechanism. From these criteria, we firstly define a novel notion of Petri net called Hybrid Functional Petri Net (HFPN). Then, we introduce a software tool, Genomic Object Net, for representing and simulating biopathways, which we have developed by employing the architecture of HFPN. In order to show the usefulness of Genomic Object Net for representing and simulating biopathways, we show two HFPN representations of gene regulation mechanisms of Drosophila melanogaster (fruit fly) circadian rhythm and apoptosis induced by Fas ligand. The simulation results of these biopathways are also correlated with biological observations. The software is available to academic users from http://www.GenomicObject.Net/.     

Topological analysis of metabolic networks based on Petri net theory

Petri net concepts provide additional tools for the modelling of metabolic networks. Here, the similarities between the counterparts in traditional biochemical modelling and Petri net theory are discussed. For example the stoichiometry matrix of a metabolic network corresponds to the incidence matrix of the Petri net. The flux modes and conservation relations have the T-invariants, respectively, P-invariants as counterparts. We reveal the biological meaning of some notions specific to the Petri net framework (traps, siphons, deadlocks, liveness). We focus on the topological analysis rather than on the analysis of the dynamic behaviour. The treatment of external metabolites is discussed. Some simple theoretical examples are presented for illustration. Also the Petri nets corresponding to some biochemical networks are built to support our results. For example, the role of triose phosphate isomerase (TPI) in Trypanosoma brucei metabolism is evaluated by detecting siphons and traps. All Petri net properties treated in this contribution are exemplified on a system extracted from nucleotide metabolism.     

Ontology based standardization of Petri net modeling for signaling pathways

Taking account of the great availability of Petri nets in modeling and analyzing large complicated signaling networks, semantics of Petri nets is in need of systematization for the purpose of consistency and reusability of the models. This paper reports on standardization of units of Petri nets on the basis of an ontology that gives an intrinsic definition to the process of signaling in signaling pathways.     

Petri net modeling of high-order genetic systems using grammatical evolution

Understanding how DNA sequence variations impact human health through a hierarchy of biochemical and physiological systems is expected to improve the diagnosis, prevention, and treatment of common, complex human diseases. We have previously developed a hierarchical dynamic systems approach based on Petri nets for generating biochemical network models that are consistent with genetic models of disease susceptibility. This modeling approach uses an evolutionary computation approach called grammatical evolution as a search strategy for optimal Petri net models. We have previously demonstrated that this approach routinely identifies biochemical network models that are consistent with a variety of genetic models in which disease susceptibility is determined by nonlinear interactions between two DNA sequence variations. In the present study, we evaluate whether the Petri net approach is capable of identifying biochemical networks that are consistent with disease susceptibility due to higher order nonlinear interactions between three DNA sequence variations. The results indicate that our model-building approach is capable of routinely identifying good, but not perfect, Petri net models. Ideas for improving the algorithm for this high-dimensional problem are presented.     

Colored Petri net modeling and simulation of signal transduction pathways

Presented herein is a methodology for quantitatively analyzing the complex signaling network by resorting to colored Petri nets (CPN). The mathematical as well as Petri net models for two basic reaction types were established, followed by the extension to a large signal transduction system stimulated by epidermal growth factor (EGF) in an application study. The CPN models based on the Petri net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the EGF signaling pathway. The usefulness of Petri nets is demonstrated for the quantitative analysis of the signal transduction pathway. Moreover, the trade-offs between modeling capability and simulation efficiency of this pathway are explored, suggesting that the Petri net model can be invaluable in the initial stage of building a dynamic model.     

Modularization of biochemical networks based on classification of Petri net t-invariants

Background  

Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.     

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 based analysis techniques to signal transduction pathways

Background  

Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed.     

Data-based identifiability analysis of non-linear dynamical models

MOTIVATION: Mathematical modelling of biological systems is becoming a standard approach to investigate complex dynamic, non-linear interaction mechanisms in cellular processes. However, models may comprise non-identifiable parameters which cannot be unambiguously determined. Non-identifiability manifests itself in functionally related parameters, which are difficult to detect. RESULTS: We present the method of mean optimal transformations, a non-parametric bootstrap-based algorithm for identifiability testing, capable of identifying linear and non-linear relations of arbitrarily many parameters, regardless of model size or complexity. This is performed with use of optimal transformations, estimated using the alternating conditional expectation algorithm (ACE). An initial guess or prior knowledge concerning the underlying relation of the parameters is not required. Independent, and hence identifiable parameters are determined as well. The quality of data at disposal is included in our approach, i.e. the non-linear model is fitted to data and estimated parameter values are investigated with respect to functional relations. We exemplify our approach on a realistic dynamical model and demonstrate that the variability of estimated parameter values decreases from 81 to 1% after detection and fixation of structural non-identifiabilities.     

Learning rule-based models of biological process from gene expression time profiles using gene ontology

MOTIVATION: Microarray technology enables large-scale inference of the participation of genes in biological process from similar expression profiles. Our aim is to induce classificatory models from expression data and biological knowledge that can automatically associate genes with novel hypotheses of biological process. RESULTS: We report a systematic supervised learning approach to predicting biological process from time series of gene expression data and biological knowledge. Biological knowledge is expressed using gene ontology and this knowledge is associated with discriminatory expression-based features to form minimal decision rules. The resulting rule model is first evaluated on genes coding for proteins with known biological process roles using cross validation. Then it is used to generate hypotheses for genes for which no knowledge of participation in biological process could be found. The theoretical foundation for the methodology based on rough sets is outlined in the paper, and its practical application demonstrated on a data set previously published by Cho et al. (Nat. Genet., 27, 48-54, 2001). AVAILABILITY: The Rosetta system is available at http://www.idi.ntnu.no/~aleks/rosetta. SUPPLEMENTARY INFORMATION: http://www.lcb.uu.se/~hvidsten/bioinf_cho/     

Angiogenesis gene expression profiling in xenograft models to study cellular interactions

The present study describes a method to simultaneously obtain the angiogenic expression profile in tumor cells and vascular cells of a single tumor. Human- and mouse-specific primers were used for quantitative real-time RT-PCR to determine the expression of vascular endothelial growth factors A, B, C, and D, vascular endothelial growth factor receptors 1, 2, and 3, neuropilin 1 and 2, angiopoietin 1, 2, 3/4, tyrosine kinase receptors 1 and 2, basic fibroblast growth factor (bFGF) in xenograft tumors obtained by injection of human ovarian carcinoma cells in nude mice. In addition, the effect of treatment with anginex and taxol on the expression profile was analyzed. Most factors were expressed higher in vascular cells as compared to tumor cells. In response to treatment, tumor cells significantly upregulated bFGF expression and downregulated VEGF receptor expression. This was accompanied by downregulation of VEGF-B and -D, and upregulation of angiopoietin-3 as well as angiopoetin receptors in nontumor cells. In conclusion, real-time qRT-PCR combined with xenograft tumor models presents a sensitive method to monitor angiogenesis and to analyze interactions between tumor cells and nontumor cells in vivo. The approach can be applied to different research fields in which xenograft models are used.     

Cyclic modes in neural net models

Neural network models with possible cross-coupling from every neuron to every other neuron are condisered. The all-or-none law is assumed for firing of neurons. A network is shown to have a set of latent cyclic modes. If the net is stimulated briefly, it will subsequently either return to quiescence or settle into periodic activity in one of its cyclic modes. Realization of cyclic modes and analysis of nets are discussed. A learning rule for adjustment of synaptic strengths is presented.     

On non-linear species response models in ordination

Ordination techniques are plagued by the non-linearity of vegetation data. The purpose of ordination is discussed and considered to be the process of arranging samples (or species) in relation to one or more environmental gradients or abstract axes that may represent such gradients, the arrangement to be ecologically significant. The appropriateness of various models of vegetation to current ordination techniques is considered, particularly the gaussian species response curve. Two alternatives are suggested based on -functions and an ecological response curve model incorporating competition between species.     

Computational models of signalling networks for non-linear control

Artificial signalling networks (ASNs) are a computational approach inspired by the signalling processes inside cells that decode outside environmental information. Using evolutionary algorithms to induce complex behaviours, we show how chaotic dynamics in a conservative dynamical system can be controlled. Such dynamics are of particular interest as they mimic the inherent complexity of non-linear physical systems in the real world. Considering the main biological interpretations of cellular signalling, in which complex behaviours and robust cellular responses emerge from the interaction of multiple pathways, we introduce two ASN representations: a stand-alone ASN and a coupled ASN. In particular we note how sophisticated cellular communication mechanisms can lead to effective controllers, where complicated problems can be divided into smaller and independent tasks.