Tools for visualization and analysis of molecular networks, pathways, and -omics data.

Biological pathways have become the standard way to represent the coordinated reactions and actions of a series of molecules in a cell. A series of interconnected pathways is referred to as a biological network, which denotes a more holistic view on the entanglement of cellular reactions. Biological pathways and networks are not only an appropriate approach to visualize molecular reactions. They have also become one leading method in -omics data analysis and visualization. Here, we review a set of pathway and network visualization and analysis methods and take a look at potential future developments in the field

Gene expression patterns following unilateral traumatic brain injury reveals a local pro-inflammatory and remote anti-inflammatory response.

BackgroundTraumatic brain injury (TBI) results in irreversible damage at the site of impact and initiates cellular and molecular processes that lead to secondary neural injury in the surrounding tissue. We used microarray analysis to determine which genes, pathways and networks were significantly altered using a rat model of TBI. Adult rats received a unilateral controlled cortical impact (CCI) and were sacrificed 24 h post-injury. The ipsilateral hemi-brain tissue at the site of the injury, the corresponding contralateral hemi-brain tissue, and naïve (control) brain tissue were used for microarray analysis. Ingenuity Pathway Analysis (IPA) software was used to identify molecular pathways and networks that were associated with the altered gene expression in brain tissues following TBI.ResultsInspection of the top fifteen biological functions in IPA associated with TBI in the ipsilateral tissues revealed that all had an inflammatory component. IPA analysis also indicated that inflammatory genes were altered on the contralateral side, but many of the genes were inversely expressed compared to the ipsilateral side. The contralateral gene expression pattern suggests a remote anti-inflammatory molecular response. We created a network of the inversely expressed common (i.e., same gene changed on both sides of the brain) inflammatory response (IR) genes and those IR genes included in pathways and networks identified by IPA that changed on only one side. We ranked the genes by the number of direct connections each had in the network, creating a gene interaction hierarchy (GIH). Two well characterized signaling pathways, toll-like receptor/NF-kappaB signaling and JAK/STAT signaling, were prominent in our GIH.ConclusionsBioinformatic analysis of microarray data following TBI identified key molecular pathways and networks associated with neural injury following TBI. The GIH created here provides a starting point for investigating therapeutic targets in a ranked order that is somewhat different than what has been presented previously. In addition to being a vehicle for identifying potential targets for post-TBI therapeutic strategies, our findings can also provide a context for evaluating the potential of therapeutic agents currently in development

Statistical analysis of network data and evolution on GPUs: High-performance statistical computing

Network analysis typically involves as set of repetitive tasks that are particularly amenable to poor-man's parallelization. This is therefore an ideal application are for GPU architectures, which help to alleviate the tedium inherent to statistically sound analysis of network data. Here we will illustrate the use of GPUs in a range of applications, which include percolation processes on networks, the evolution of protein-protein interaction networks, and the fusion of different types of biomedical and disease data in the context of molecular interaction networks. We will pay particular attention to the numerical performance of different routines that are frequently invoked in network analysis problems. We conclude with a review over recent developments in the generation of random numbers that address the specific requirements posed by GPUs and high-performance computing needs

Robust Stochastic Chemical Reaction Networks and Bounded Tau-Leaping

The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection between robustness and efficiency of simulation. Without robustness guarantees, stochastic simulation seems to require computational time proportional to the total number of reaction events. Even if the concentration (molecular count per volume) stays bounded, the number of reaction events can be linear in the duration of simulated time and total molecular count. We show that the behavior of robust systems can be predicted such that the computational work scales linearly with the duration of simulated time and concentration, and only polylogarithmically in the total molecular count. Thus our asymptotic analysis captures the dramatic speedup when molecular counts are large, and shows that for bounded concentrations the computation time is essentially invariant with molecular count. Finally, by noticing that even robust stochastic chemical reaction networks are capable of embedding complex computational problems, we argue that the linear dependence on simulated time and concentration is likely optimal

Defining a robust biological prior from Pathway Analysis to drive Network Inference

Inferring genetic networks from gene expression data is one of the most challenging work in the post-genomic era, partly due to the vast space of possible networks and the relatively small amount of data available. In this field, Gaussian Graphical Model (GGM) provides a convenient framework for the discovery of biological networks. In this paper, we propose an original approach for inferring gene regulation networks using a robust biological prior on their structure in order to limit the set of candidate networks. Pathways, that represent biological knowledge on the regulatory networks, will be used as an informative prior knowledge to drive Network Inference. This approach is based on the selection of a relevant set of genes, called the "molecular signature", associated with a condition of interest (for instance, the genes involved in disease development). In this context, differential expression analysis is a well established strategy. However outcome signatures are often not consistent and show little overlap between studies. Thus, we will dedicate the first part of our work to the improvement of the standard process of biomarker identification to guarantee the robustness and reproducibility of the molecular signature. Our approach enables to compare the networks inferred between two conditions of interest (for instance case and control networks) and help along the biological interpretation of results. Thus it allows to identify differential regulations that occur in these conditions. We illustrate the proposed approach by applying our method to a study of breast cancer's response to treatment

Complex-linear invariants of biochemical networks

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gr\"obner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency.Comment: 36 pages, 6 figure