On functional module detection in metabolic networks

Graphlets in comparison of Petri net-based models of biological systems

Capability to compare biological models is a crucial step needed in an analysis of complex organisms. Petri nets as a popular modelling technique, needs a possibility to determine the degree of structural similarities (e.g., comparison of metabolic or signaling pathways). However, existing comparison methods use matching invariants approach for establishing a degree of similarity, and because of that are vulnerable to the state explosion problem which may appear during calculation of a minimal invariants set. Its occurrence will block usage of existing methods. To find an alternative for this situation, we decided to adapt and tests in a Petri net environment a method based on finding a distribution of graphlets. First, we focused on adapting the original graphlets for notation of bipartite, directed graphs. As a result, 151 new graphlets with 592 orbits were created. The next step focused on evaluating a performance of the popular Graphlet Degree Distribution Agreement (GDDA) metric in the new environment. To do that, we decided to use randomly generated networks that share typical characteristics of biological models represented in Petri nets. Our results confirmed the usefulness of graphlets and GDDA in Petri net comparison and discovered its limitations.

Comparing Petri net-based models of biological systems using Holmes

MOTIVATION

The first and necessary step in systems approach to study biological phenomena is building a formal model. One of the possibilities is to construct a model based on Petri nets. They have an intuitive graphical representation on one hand, and on the other, can be analyzed using formal mathematical methods. Finding homologies or conserved processes playing important roles in various biological systems can be done by comparing models. The ones expressed as Petri nets are especially well-suited for such a comparison, but there is a lack of software tools for this task.

RESULTS

To resolve this problem, a new analytical tool has been implemented in Holmes application and described in this article. It offers four different comparison methods, i.e. the ones based on t-invariants, decomposition, graphlets and branching vertices.

AVAILABILITY AND IMPLEMENTATION

Available at http://www.cs.put.poznan.pl/mradom/Holmes/holmes.html.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Unsupervised Learning and Multipartite Network Models: A Promising Approach for Understanding Traditional Medicine

The ultimate goal of precision medicine is to determine right treatment for right patients based on precise diagnosis. To achieve this goal, correct stratification of patients using molecular features and clinical phenotypes is crucial. During the long history of medical science, our understanding on disease classification has been improved greatly by chemistry and molecular biology. Nowadays, we gain access to large scale patient-derived data by high-throughput technologies, generating a greater need for data science including unsupervised learning and network modeling. Unsupervised learning methods such as clustering could be a better solution to stratify patients when there is a lack of predefined classifiers. In network modularity analysis, clustering methods can be also applied to elucidate the complex structure of biological and disease networks at the systems level. In this review, we went over the main points of clustering analysis and network modeling, particularly in the context of Traditional Chinese medicine (TCM). We showed that this approach can provide novel insights on the rationale of classification for TCM herbs. In a case study, using a modularity analysis of multipartite networks, we illustrated that the TCM classifications are associated with the chemical properties of the herb ingredients. We concluded that multipartite network modeling may become a suitable data integration tool for understanding the mechanisms of actions of traditional medicine.

Petri net-based model of the human DNA base excision repair pathway

Cellular DNA is daily exposed to several damaging agents causing a plethora of DNA lesions. As a first aid to restore DNA integrity, several enzymes got specialized in damage recognition and lesion removal during the process called base excision repair (BER). A large number of DNA damage types and several different readers of nucleic acids lesions during BER pathway as well as two sub-pathways were considered in the definition of a model using the Petri net framework. The intuitive graphical representation in combination with precise mathematical analysis methods are the strong advantages of the Petri net-based representation of biological processes and make Petri nets a promising approach for modeling and analysis of human BER. The reported results provide new information that will aid efforts to characterize in silico knockouts as well as help to predict the sensitivity of the cell with inactivated repair proteins to different types of DNA damage. The results can also help in identifying the by-passing pathways that may lead to lack of pronounced phenotypes associated with mutations in some of the proteins. This knowledge is very useful when DNA damage-inducing drugs are introduced for cancer therapy, and lack of DNA repair is desirable for tumor cell death.

Comparison of different approaches for identifying subnetworks in metabolic networks

A metabolic network model provides a computational framework for studying the metabolism of a cell at the system level. The organization of metabolic networks has been investigated in different studies. One of the organization aspects considered in these studies is the decomposition of a metabolic network. The decompositions produced by different methods are very different and there is no comprehensive evaluation framework to compare the results with each other. In this study, these methods are reviewed and compared in the first place. Then they are applied to six different metabolic network models and the results are evaluated and compared based on two existing and two newly proposed criteria. Results show that no single method can beat others in all criteria but it seems that the methods introduced by Guimera and Amaral and Verwoerd do better on among metabolite-based methods and the method introduced by Sridharan et al. does better among reaction-based ones. Also, the methods are applied to several artificial networks, each constructed from merging a few KEGG pathways. Then, their capability to recover those pathways are compared. Results show that among metabolite-based methods, the method of Guimera and Amaral does better again, however, no notable difference between the performances of reaction-based methods was detected.

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

Motivation:Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models.

MONALISA for stochastic simulations of Petri net models of biochemical systems

BACKGROUND

The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology.

RESULTS

Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study.

CONCLUSIONS

We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0.

FCDECOMP: Decomposition of metabolic networks based on flux coupling relations

A metabolic network model provides a computational framework to study the metabolism of a cell at the system level. Due to their large sizes and complexity, rational decomposition of these networks into subsystems is a strategy to obtain better insight into the metabolic functions. Additionally, decomposing metabolic networks paves the way to use computational methods that will be otherwise very slow when run on the original genome-scale network. In the present study, we propose FCDECOMP decomposition method based on flux coupling relations (FCRs) between pairs of reaction fluxes. This approach utilizes a genetic algorithm (GA) to obtain subsystems that can be analyzed in isolation, i.e. without considering the reactions of the original network in the analysis. Therefore, we propose that our method is useful for discovering biologically meaningful modules in metabolic networks. As a case study, we show that when this method is applied to the metabolic networks of barley seeds and yeast, the modules are in good agreement with the biological compartments of these networks.