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.     

Usefulness and limitations of dK random graph models to predict interactions and functional homogeneity in biological networks under a pseudo-likelihood parameter estimation approach

Background  

Many aspects of biological functions can be modeled by biological networks, such as protein interaction networks, metabolic networks, and gene coexpression networks. Studying the statistical properties of these networks in turn allows us to infer biological function. Complex statistical network models can potentially more accurately describe the networks, but it is not clear whether such complex models are better suited to find biologically meaningful subnetworks.     

Increased entropy of signal transduction in the cancer metastasis phenotype

Background  

The statistical study of biological networks has led to important novel biological insights, such as the presence of hubs and hierarchical modularity. There is also a growing interest in studying the statistical properties of networks in the context of cancer genomics. However, relatively little is known as to what network features differ between the cancer and normal cell physiologies, or between different cancer cell phenotypes.     

Invariants and Other Structural Properties of Biochemical Models as a Constraint Satisfaction Problem

Background

We present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as resolution of a Constraint Satisfaction Problem. The use of Petri nets to manipulate Systems Biology models and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, for instance in the context of module decomposition.

Results

In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws, consistency checking, etc. thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri nets correspond to well-known techniques in constraint solving, like symmetry-breaking. Moreover, we show that the simple and natural encoding proposed is not only efficient but also flexible enough to encompass sub/sur-invariants, siphons/traps, etc., i.e., other Petri net structural properties that lead to supplementary insight on the dynamics of the biochemical system under study.

Conclusions

A simple implementation based on GNU-Prolog's finite domain solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment and in the independent tool Nicotine. Some illustrative examples and benchmarks are provided.     

Inverse bifurcation analysis: application to simple gene systems

Background  

Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional forward problem of determining the mapping from parameter space to the space of model behavior, the inverse problem of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties.     

Algorithms for effective querying of compound graph-based pathway databases

Background  

Graph-based pathway ontologies and databases are widely used to represent data about cellular processes. This representation makes it possible to programmatically integrate cellular networks and to investigate them using the well-understood concepts of graph theory in order to predict their structural and dynamic properties. An extension of this graph representation, namely hierarchically structured or compound graphs, in which a member of a biological network may recursively contain a sub-network of a somehow logically similar group of biological objects, provides many additional benefits for analysis of biological pathways, including reduction of complexity by decomposition into distinct components or modules. In this regard, it is essential to effectively query such integrated large compound networks to extract the sub-networks of interest with the help of efficient algorithms and software tools.     

KID - an algorithm for fast and efficient text mining used to automatically generate a database containing kinetic information of enzymes

Background  

The amount of available biological information is rapidly increasing and the focus of biological research has moved from single components to networks and even larger projects aiming at the analysis, modelling and simulation of biological networks as well as large scale comparison of cellular properties. It is therefore essential that biological knowledge is easily accessible. However, most information is contained in the written literature in an unstructured way, so that methods for the systematic extraction of knowledge directly from the primary literature have to be deployed.     

Incremental genetic K-means algorithm and its application in gene expression data analysis

Background  

In recent years, clustering algorithms have been effectively applied in molecular biology for gene expression data analysis. With the help of clustering algorithms such as K-means, hierarchical clustering, SOM, etc, genes are partitioned into groups based on the similarity between their expression profiles. In this way, functionally related genes are identified. As the amount of laboratory data in molecular biology grows exponentially each year due to advanced technologies such as Microarray, new efficient and effective methods for clustering must be developed to process this growing amount of biological data.     

Determining modular organization of protein interaction networks by maximizing modularity density

Background

With ever increasing amount of available data on biological networks, modeling and understanding the structure of these large networks is an important problem with profound biological implications. Cellular functions and biochemical events are coordinately carried out by groups of proteins interacting each other in biological modules. Identifying of such modules in protein interaction networks is very important for understanding the structure and function of these fundamental cellular networks. Therefore, developing an effective computational method to uncover biological modules should be highly challenging and indispensable.

Results

The purpose of this study is to introduce a new quantitative measure modularity density into the field of biomolecular networks and develop new algorithms for detecting functional modules in protein-protein interaction (PPI) networks. Specifically, we adopt the simulated annealing (SA) to maximize the modularity density and evaluate its efficiency on simulated networks. In order to address the computational complexity of SA procedure, we devise a spectral method for optimizing the index and apply it to a yeast PPI network.

Conclusions

Our analysis of detected modules by the present method suggests that most of these modules have well biological significance in context of protein complexes. Comparison with the MCL and the modularity based methods shows the efficiency of our method.

     

Inferring protein function by domain context similarities in protein-protein interaction networks

Background  

Genome sequencing projects generate massive amounts of sequence data but there are still many proteins whose functions remain unknown. The availability of large scale protein-protein interaction data sets makes it possible to develop new function prediction methods based on protein-protein interaction (PPI) networks. Although several existing methods combine multiple information resources, there is no study that integrates protein domain information and PPI networks to predict protein functions.     

A general strategy to determine the congruence between a hierarchical and a non-hierarchical classification

Background  

Classification procedures are widely used in phylogenetic inference, the analysis of expression profiles, the study of biological networks, etc. Many algorithms have been proposed to establish the similarity between two different classifications of the same elements. However, methods to determine significant coincidences between hierarchical and non-hierarchical partitions are still poorly developed, in spite of the fact that the search for such coincidences is implicit in many analyses of massive data.     

LucidDraw: Efficiently visualizing complex biochemical networks within MATLAB

Background  

Biochemical networks play an essential role in systems biology. Rapidly growing network data and versatile research activities call for convenient visualization tools to aid intuitively perceiving abstract structures of networks and gaining insights into the functional implications of networks. There are various kinds of network visualization software, but they are usually not adequate for visual analysis of complex biological networks mainly because of the two reasons: 1) most existing drawing methods suitable for biochemical networks have high computation loads and can hardly achieve near real-time visualization; 2) available network visualization tools are designed for working in certain network modeling platforms, so they are not convenient for general analyses due to lack of broader range of readily accessible numerical utilities.     

Adaptive diffusion kernel learning from biological networks for protein function prediction

Background  

Machine-learning tools have gained considerable attention during the last few years for analyzing biological networks for protein function prediction. Kernel methods are suitable for learning from graph-based data such as biological networks, as they only require the abstraction of the similarities between objects into the kernel matrix. One key issue in kernel methods is the selection of a good kernel function. Diffusion kernels, the discretization of the familiar Gaussian kernel of Euclidean space, are commonly used for graph-based data.     

Spectral embedding finds meaningful (relevant) structure in image and microarray data

Background  

Accurate methods for extraction of meaningful patterns in high dimensional data have become increasingly important with the recent generation of data types containing measurements across thousands of variables. Principal components analysis (PCA) is a linear dimensionality reduction (DR) method that is unsupervised in that it relies only on the data; projections are calculated in Euclidean or a similar linear space and do not use tuning parameters for optimizing the fit to the data. However, relationships within sets of nonlinear data types, such as biological networks or images, are frequently mis-rendered into a low dimensional space by linear methods. Nonlinear methods, in contrast, attempt to model important aspects of the underlying data structure, often requiring parameter(s) fitting to the data type of interest. In many cases, the optimal parameter values vary when different classification algorithms are applied on the same rendered subspace, making the results of such methods highly dependent upon the type of classifier implemented.     

Applications of a formal approach to decipher discrete genetic networks

Background  

A growing demand for tools to assist the building and analysis of biological networks exists in systems biology. We argue that the use of a formal approach is relevant and applicable to address questions raised by biologists about such networks. The behaviour of these systems being complex, it is essential to exploit efficiently every bit of experimental information. In our approach, both the evolution rules and the partial knowledge about the structure and the behaviour of the network are formalized using a common constraint-based language.     

Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory

Background  

Large-scale sequencing of entire genomes has ushered in a new age in biology. One of the next grand challenges is to dissect the cellular networks consisting of many individual functional modules. Defining co-expression networks without ambiguity based on genome-wide microarray data is difficult and current methods are not robust and consistent with different data sets. This is particularly problematic for little understood organisms since not much existing biological knowledge can be exploited for determining the threshold to differentiate true correlation from random noise. Random matrix theory (RMT), which has been widely and successfully used in physics, is a powerful approach to distinguish system-specific, non-random properties embedded in complex systems from random noise. Here, we have hypothesized that the universal predictions of RMT are also applicable to biological systems and the correlation threshold can be determined by characterizing the correlation matrix of microarray profiles using random matrix theory.     

VANLO - Interactive visual exploration of aligned biological networks

Background  

Protein-protein interaction (PPI) is fundamental to many biological processes. In the course of evolution, biological networks such as protein-protein interaction networks have developed. Biological networks of different species can be aligned by finding instances (e.g. proteins) with the same common ancestor in the evolutionary process, so-called orthologs. For a better understanding of the evolution of biological networks, such aligned networks have to be explored. Visualization can play a key role in making the various relationships transparent.     

Identification of functional modules using network topology and high-throughput data

Background  

With the advent of systems biology, biological knowledge is often represented today by networks. These include regulatory and metabolic networks, protein-protein interaction networks, and many others. At the same time, high-throughput genomics and proteomics techniques generate very large data sets, which require sophisticated computational analysis. Usually, separate and different analysis methodologies are applied to each of the two data types. An integrated investigation of network and high-throughput information together can improve the quality of the analysis by accounting simultaneously for topological network properties alongside intrinsic features of the high-throughput data.     

Modeling biological systems with uncertain kinetic data using fuzzy continuous Petri nets

Background

Uncertainties exist in many biological systems, which can be classified as random uncertainties and fuzzy uncertainties. The former can usually be dealt with using stochastic methods, while the latter have to be handled with such approaches as fuzzy methods.

Results

In this paper, we focus on a special type of biological systems that can be described using ordinary differential equations or continuous Petri nets (CPNs), but some kinetic parameters are missing or inaccurate. For this, we propose a class of fuzzy continuous Petri nets (FCPNs) by combining CPNs and fuzzy logics. We also present and implement a simulation algorithm for FCPNs, and illustrate our method with the heat shock response system.

Conclusions

This approach can be used to model biological systems where some kinetic parameters are not available or their values vary due to some environmental factors.

     

Detecting causality from short time-series data based on prediction of topologically equivalent attractors

Background

Detecting causality for short time-series data such as gene regulation data is quite important but it is usually very difficult. This can be used in many fields especially in biological systems. Recently, several powerful methods have been set up to solve this problem. However, it usually needs very long time-series data or much more samples for the existing methods to detect causality among the given or observed data. In our real applications, such as for biological systems, the obtained data or samples are short or small. Since the data or samples are highly depended on experiment or limited resource.

Results

In order to overcome these limitations, here we propose a new method called topologically equivalent position method which can detect causality for very short time-series data or small samples. This method is mainly based on attractor embedding theory in nonlinear dynamical systems. By comparing with inner composition alignment, we use theoretical models and real gene expression data to show the effectiveness of our method.

Conclusions

As a result, it shows our method can be effectively used in biological systems. We hope our method can be useful in many other fields in near future such as complex networks, ecological systems and so on.