Inferring Boolean network structure via correlation

Leveraging quantum computing for dynamic analyses of logical networks in systems biology

The dynamics of cellular mechanisms can be investigated through the analysis of networks. One of the simplest but most popular modeling strategies involves logic-based models. However, these models still face exponential growth in simulation complexity compared with a linear increase in nodes. We transfer this modeling approach to quantum computing and use the upcoming technique in the field to simulate the resulting networks. Leveraging logic modeling in quantum computing has many benefits, including complexity reduction and quantum algorithms for systems biology tasks. To showcase the applicability of our approach to systems biology tasks, we implemented a model of mammalian cortical development. Here, we applied a quantum algorithm to estimate the tendency of the model to reach particular stable conditions and further revert dynamics. Results from two actual quantum processing units and a noisy simulator are presented, and current technical challenges are discussed.

CANTATA - prediction of missing links in Boolean networks using genetic programming

Motivation

Biological processes are complex systems with distinct behaviour. Despite the growing amount of available data, knowledge is sparse and often insufficient to investigate the complex regulatory behaviour of these systems. Moreover, different cellular phenotypes are possible under varying conditions. Mathematical models attempt to unravel these mechanisms by investigating the dynamics of regulatory networks. Therefore, a major challenge is to combine regulations and phenotypical information as well as the underlying mechanisms. To predict regulatory links in these models, we established an approach called CANTATA to support the integration of information into regulatory networks and retrieve potential underlying regulations. This is achieved by optimizing both static and dynamic properties of these networks.

Results

Initial results show that the algorithm predicts missing interactions by recapitulating the known phenotypes while preserving the original topology and optimizing the robustness of the model. The resulting models allow for hypothesizing about the biological impact of certain regulatory dependencies.

Availability and implementation

Source code of the application, example files and results are available at https://github.com/sysbio-bioinf/Cantata.

Supplementary information

Supplementary data are available at Bioinformatics online.

Review and assessment of Boolean approaches for inference of gene regulatory networks

Boolean descriptions of gene regulatory networks can provide an insight into interactions between genes. Boolean networks hold predictive power, are easy to understand, and can be used to simulate the observed networks in different scenarios. We review fundamental and state-of-the-art methods for inference of Boolean networks. We introduce a methodology for a straightforward evaluation of Boolean inference approaches based on the generation of evaluation datasets, application of selected inference methods, and evaluation of performance measures to guide the selection of the best method for a given inference problem. We demonstrate this procedure on inference methods REVEAL (REVerse Engineering ALgorithm), Best-Fit Extension, MIBNI (Mutual Information-based Boolean Network Inference), GABNI (Genetic Algorithm-based Boolean Network Inference) and ATEN (AND/OR Tree ENsemble algorithm), which infers Boolean descriptions of gene regulatory networks from discretised time series data. Boolean inference approaches tend to perform better in terms of dynamic accuracy, and slightly worse in terms of structural correctness. We believe that the proposed methodology and provided guidelines will help researchers to develop Boolean inference approaches with a good predictive capability while maintaining structural correctness and biological relevance.

Bacillus velezensis SYL-3 suppresses Alternaria alternata and tobacco mosaic virus infecting Nicotiana tabacum by regulating the phyllosphere microbial community

The occurrence of plant diseases is closely associated with the imbalance of plant tissue microecological environment. The regulation of the phyllosphere microbial communities has become a new and alternative approach to the biological control of foliar diseases. In this study, Bacillus velezensis SYL-3 isolated from Luzhou exhibited an effective inhibitory effect against Alternaria alternata and tobacco mosaic virus (TMV). The analysis of phyllosphere microbiome by PacBio sequencing indicated that SYL-3 treatment significantly altered fungal and bacterial communities on the leaves of Nicotiana tabacum plants and reduced the disease index caused by A. alternata and TMV. Specifically, the abundance of P. seudomo, Sphingomonas, Massilia, and Cladosporium in the SYL-3 treatment group increased by 19.00, 9.49, 3.34, and 12.29%, respectively, while the abundances of Pantoea, Enterobacter, Sampaiozyma, and Rachicladosporium were reduced. Moreover, the abundance of beneficial bacteria, such as Pseudomonas and Sphingomonas, was negatively correlated with the disease indexes of A. alternata and TMV. The PICRUSt data also predicted the composition of functional genes, with significant differences being apparent between SYL-3 and the control treatment group. Further functional analysis of the microbiome also showed that SYL-3 may induce host disease resistance by motivating host defense-related pathways. These results collectively indicate that SYL-3 may suppress disease progression caused by A. alternata or TMV by improving the microbial community composition on tobacco leaves.

Data-Driven Boolean Network Inference Using a Genetic Algorithm With Marker-Based Encoding

The inference of Boolean networks is crucial for analyzing the topology and dynamics of gene regulatory networks. Many data-driven approaches using evolutionary algorithms have been proposed based on time-series data. However, the ability to infer both network topology and dynamics is restricted by their inflexible encoding schemes. To address this problem, we propose a novel Boolean network inference algorithm for inferring both network topology and dynamics simultaneously. The main idea is that, we use a marker-based genetic algorithm to encode both regulatory nodes and logical operators in a chromosome. By using the markers and introducing more logical operators, the proposed algorithm can infer more diverse candidate Boolean functions. The proposed algorithm is applied to five networks, including two artificial Boolean networks and three real-world gene regulatory networks. Compared with other algorithms, the experimental results demonstrate that our proposed algorithm infers more accurate topology and dynamics.

Discrete Logic Modeling of Cell Signaling Pathways

Cell signaling pathways often crosstalk generating complex biological behaviors observed in different cellular contexts. Frequently, laboratory experiments focus on a few putative regulators, alone unable to predict the molecular mechanisms behind the observed phenotypes. Here, systems biology complements these approaches by giving a holistic picture to complex signaling crosstalk. In particular, Boolean network models are a meaningful tool to study large network behaviors and can cope with incomplete kinetic information. By introducing a model describing pathways involved in hematopoietic stem cell maintenance, we present a general approach on how to model cell signaling pathways with Boolean network models.

Reconstructing Boolean network ensembles from single-cell data for unraveling dynamics in the aging of human hematopoietic stem cells

Regulatory dependencies in molecular networks are the basis of dynamic behaviors affecting the phenotypical landscape. With the advance of high throughput technologies, the detail of omics data has arrived at the single-cell level. Nevertheless, new strategies are required to reconstruct regulatory networks based on populations of single-cell data. Here, we present a new approach to generate populations of gene regulatory networks from single-cell RNA-sequencing (scRNA-seq) data. Our approach exploits the heterogeneity of single-cell populations to generate pseudo-timepoints. This allows for the first time to uncouple network reconstruction from a direct dependency on time series measurements. The generated time series are then fed to a combined reconstruction algorithm. The latter allows a fast and efficient reconstruction of ensembles of gene regulatory networks. Since this approach does not require knowledge on time-related trajectories, it allows us to model heterogeneous processes such as aging. Applying the approach to the aging-associated NF-κB signaling pathway-based scRNA-seq data of human hematopoietic stem cells (HSCs), we were able to reconstruct eight ensembles, and evaluate their dynamic behavior. Moreover, we propose a strategy to evaluate the resulting attractor patterns. Interaction graph-based features and dynamic investigations of our model ensembles provide a new perspective on the heterogeneity and mechanisms related to human HSCs aging.

A novel constrained genetic algorithm-based Boolean network inference method from steady-state gene expression data

MOTIVATION

It is a challenging problem in systems biology to infer both the network structure and dynamics of a gene regulatory network from steady-state gene expression data. Some methods based on Boolean or differential equation models have been proposed but they were not efficient in inference of large-scale networks. Therefore, it is necessary to develop a method to infer the network structure and dynamics accurately on large-scale networks using steady-state expression.

RESULTS

In this study, we propose a novel constrained genetic algorithm-based Boolean network inference (CGA-BNI) method where a Boolean canalyzing update rule scheme was employed to capture coarse-grained dynamics. Given steady-state gene expression data as an input, CGA-BNI identifies a set of path consistency-based constraints by comparing the gene expression level between the wild-type and the mutant experiments. It then searches Boolean networks which satisfy the constraints and induce attractors most similar to steady-state expressions. We devised a heuristic mutation operation for faster convergence and implemented a parallel evaluation routine for execution time reduction. Through extensive simulations on the artificial and the real gene expression datasets, CGA-BNI showed better performance than four other existing methods in terms of both structural and dynamics prediction accuracies. Taken together, CGA-BNI is a promising tool to predict both the structure and the dynamics of a gene regulatory network when a highest accuracy is needed at the cost of sacrificing the execution time.

AVAILABILITY AND IMPLEMENTATION

Source code and data are freely available at https://github.com/csclab/CGA-BNI.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A Cytokine Network Balance Influences the Fate of Leishmania (Viannia) braziliensis Infection in a Cutaneous Leishmaniasis Hamster Model

The golden hamster is a suitable model for studying cutaneous leishmaniasis (CL) due to Leishmania (Viannia) braziliensis. Immunopathological mechanisms are well established in the L. (L.) major-mouse model, in which IL-4 instructs a Th2 response towards progressive infection. In the present study, we evaluated the natural history of L. braziliensis infection from its first stages up to lesion establishment, with the aim of identifying immunological parameters associated with the disease outcome and parasitism fate. To this end, hamsters infected with 10⁴, 10⁵, or 10⁶ promastigotes were monitored during the first hours (4h, 24h), early (15 days, 30 days) and late (50 days) post-infection (pi) phases. Cytokines, iNOS and arginase gene expression were quantified in the established lesions by reverse transcription-quantitative PCR. Compared to the 10⁵ or 10⁶ groups, 10⁴ animals presented lower lesions sizes, less tissue damage, and lower IgG levels. Basal gene expression in normal skin was high for TGF-β, and intermediary for TNF, IL-6, and IL-4. At 4hpi, no cytokine induction was observed in the 10⁴ group, while an upregulation of IL-6, IL-10, and IL-4 was observed in the 10⁶ group. At 15dpi, lesion appearance was accompanied by an increased expression of all assessed cytokines, markedly in the 10⁵ and 10⁶ groups. Upregulation of all investigated cytokines was observed in the late phase, although less expressive in the 10⁴ group. IFN-γ was the depending variable influencing tissue damage, while IL-6 was associated to parasite load. The network correlating gene expression and clinical and laboratorial parameters indicated inoculum-independent associations at 15 and 30dpi. A strong positive network correlation was observed in the 10⁴ group, but not in the 10⁵ or 10⁶ groups. In conclusion, IL-4, IL-6, IL-10, and TGF-β are linked o L. braziliensis progression. However, a balanced cytokine network is the key for an immune response able to reduce the ongoing infection and reduce pathological damage.

Capturing dynamic relevance in Boolean networks using graph theoretical measures

Motivation

Interaction graphs are able to describe regulatory dependencies between compounds without capturing dynamics. In contrast, mathematical models that are based on interaction graphs allow to investigate the dynamics of biological systems. However, since dynamic complexity of these models grows exponentially with their size, exhaustive analyses of the dynamics and consequently screening all possible interventions eventually becomes infeasible. Thus, we designed an approach to identify dynamically relevant compounds based on the static network topology.

Results

Here, we present a method only based on static properties to identify dynamically influencing nodes. Coupling vertex betweenness and determinative power, we could capture relevant nodes for changing dynamics with an accuracy of 75% in a set of 35 published logical models. Further analyses of the selected compounds’ connectivity unravelled a new class of not highly connected nodes with high impact on the networks’ dynamics, which we call gatekeepers. We validated our method’s working concept on logical models, which can be readily scaled up to complex interaction networks, where dynamic analyses are not even feasible.

Availability and implementation

Code is freely available at https://github.com/sysbio-bioinf/BNStatic.

Supplementary information

Supplementary data are available at Bioinformatics online.

ATEN: And/Or tree ensemble for inferring accurate Boolean network topology and dynamics

MOTIVATION

Inferring gene regulatory networks from gene expression time series data is important for gaining insights into the complex processes of cell life. A popular approach is to infer Boolean networks. However, it is still a pressing open problem to infer accurate Boolean networks from experimental data that are typically short and noisy.

RESULTS

To address the problem, we propose a Boolean network inference algorithm which is able to infer accurate Boolean network topology and dynamics from short and noisy time series data. The main idea is that, for each target gene, we use an And/Or tree ensemble algorithm to select prime implicants of which each is a conjunction of a set of input genes. The selected prime implicants are important features for predicting the states of the target gene. Using these important features we then infer the Boolean function of the target gene. Finally, the Boolean functions of all target genes are combined as a Boolean network. Using the data generated from artificial and real-world gene regulatory networks, we show that our algorithm can infer more accurate Boolean network topology and dynamics from short and noisy time series data than other algorithms. Our algorithm enables us to gain better insights into complex regulatory mechanisms of cell life.

AVAILABILITY AND IMPLEMENTATION

Package ATEN is freely available at https://github.com/ningshi/ATEN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Concepts in Boolean network modeling: What do they all mean?

Boolean network models are one of the simplest models to study complex dynamic behavior in biological systems. They can be applied to unravel the mechanisms regulating the properties of the system or to identify promising intervention targets. Since its introduction by Stuart Kauffman in 1969 for describing gene regulatory networks, various biologically based networks and tools for their analysis were developed. Here, we summarize and explain the concepts for Boolean network modeling. We also present application examples and guidelines to work with and analyze Boolean network models.

Using extremal events to characterize noisy time series

Experimental time series provide an informative window into the underlying dynamical system, and the timing of the extrema of a time series (or its derivative) contains information about its structure. However, the time series often contain significant measurement errors. We describe a method for characterizing a time series for any assumed level of measurement error [Formula: see text] by a sequence of intervals, each of which is guaranteed to contain an extremum for any function that [Formula: see text]-approximates the time series. Based on the merge tree of a continuous function, we define a new object called the normalized branch decomposition, which allows us to compute intervals for any level [Formula: see text]. We show that there is a well-defined total order on these intervals for a single time series, and that it is naturally extended to a partial order across a collection of time series comprising a dataset. We use the order of the extracted intervals in two applications. First, the partial order describing a single dataset can be used to pattern match against switching model output (Cummins et al. in SIAM J Appl Dyn Syst 17(2):1589-1616, 2018), which allows the rejection of a network model. Second, the comparison between graph distances of the partial orders of different datasets can be used to quantify similarity between biological replicates.

Representing dynamic biological networks with multi-scale probabilistic models

Dynamic models analyzing gene regulation and metabolism face challenges when adapted to modeling signal transduction networks. During signal transduction, molecular reactions and mechanisms occur in different spatial and temporal frames and involve feedbacks. This impedes the straight-forward use of methods based on Boolean networks, Bayesian approaches, and differential equations. We propose a new approach, ProbRules, that combines probabilities and logical rules to represent the dynamics of a system across multiple scales. We demonstrate that ProbRules models can represent various network motifs of biological systems. As an example of a comprehensive model of signal transduction, we provide a Wnt network that shows remarkable robustness under a range of phenotypical and pathological conditions. Its simulation allows the clarification of controversially discussed molecular mechanisms of Wnt signaling by predicting wet-lab measurements. ProbRules provides an avenue in current computational modeling by enabling systems biologists to integrate vast amounts of available data on different scales.

Automatic Screening for Perturbations in Boolean Networks

A common approach to address biological questions in systems biology is to simulate regulatory mechanisms using dynamic models. Among others, Boolean networks can be used to model the dynamics of regulatory processes in biology. Boolean network models allow simulating the qualitative behavior of the modeled processes. A central objective in the simulation of Boolean networks is the computation of their long-term behavior—so-called attractors. These attractors are of special interest as they can often be linked to biologically relevant behaviors. Changing internal and external conditions can influence the long-term behavior of the Boolean network model. Perturbation of a Boolean network by stripping a component of the system or simulating a surplus of another element can lead to different attractors. Apparently, the number of possible perturbations and combinations of perturbations increases exponentially with the size of the network. Manually screening a set of possible components for combinations that have a desired effect on the long-term behavior can be very time consuming if not impossible. We developed a method to automatically screen for perturbations that lead to a user-specified change in the network's functioning. This method is implemented in the visual simulation framework ViSiBool utilizing satisfiability (SAT) solvers for fast exhaustive attractor search.

PyBoolNet: a python package for the generation, analysis and visualization of boolean networks

Motivation

The goal of this project is to provide a simple interface to working with Boolean networks. Emphasis is put on easy access to a large number of common tasks including the generation and manipulation of networks, attractor and basin computation, model checking and trap space computation, execution of established graph algorithms as well as graph drawing and layouts.

Results

P y B ool N et is a Python package for working with Boolean networks that supports simple access to model checking via N u SMV, standard graph algorithms via N etwork X and visualization via dot . In addition, state of the art attractor computation exploiting P otassco ASP is implemented. The package is function-based and uses only native Python and N etwork X data types.

Availability and Implementation

https://github.com/hklarner/PyBoolNet.

Contact

hannes.klarner@fu-berlin.de.

ViSiBooL-visualization and simulation of Boolean networks with temporal constraints

Summary

Mathematical models and their simulation are increasingly used to gain insights into cellular pathways and regulatory networks. Dynamics of regulatory factors can be modeled using Boolean networks (BNs), among others. Text-based representations of models are precise descriptions, but hard to understand and interpret. ViSiBooL aims at providing a graphical way of modeling and simulating networks. By providing visualizations of static and dynamic network properties simultaneously, it is possible to directly observe the effects of changes in the network structure on the behavior. In order to address the challenges of clear design and a user-friendly graphical user interface (GUI), ViSiBooL implements visual representations of BNs. Additionally temporal extensions of the BNs for the modeling of regulatory time delays are incorporated. The GUI of ViSiBooL allows to model, organize, simulate and visualize BNs as well as corresponding simulation results such as attractors. Attractor searches are performed in parallel to the modeling process. Hence, changes in the network behavior are visualized at the same time.

Availability and Implementation

ViSiBooL (Java 8) is freely available at http://sysbio.uni-ulm.de/?Software:ViSiBooL .

Contact

hans.kestler@uni-ulm.de.

Stability of Signaling Pathways during Aging-A Boolean Network Approach

Biological pathways are thought to be robust against a variety of internal and external perturbations. Fail-safe mechanisms allow for compensation of perturbations to maintain the characteristic function of a pathway. Pathways can undergo changes during aging, which may lead to changes in their stability. Less stable or less robust pathways may be consequential to or increase the susceptibility of the development of diseases. Among others, NF- κ B signaling is a crucial pathway in the process of aging. The NF- κ B system is involved in the immune response and dealing with various internal and external stresses. Boolean networks as models of biological pathways allow for simulation of signaling behavior. They can help to identify which proposed mechanisms are biologically representative and which ones function but do not mirror physical processes-for instance, changes of signaling pathways during the aging process. Boolean networks can be inferred from time-series of gene expression data. This allows us to get insights into the changes of behavior of pathways such as NF- κ B signaling in aged organisms in comparison to young ones.

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology

Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

A novel mutual information-based Boolean network inference method from time-series gene expression data

Background

Inferring a gene regulatory network from time-series gene expression data in systems biology is a challenging problem. Many methods have been suggested, most of which have a scalability limitation due to the combinatorial cost of searching a regulatory set of genes. In addition, they have focused on the accurate inference of a network structure only. Therefore, there is a pressing need to develop a network inference method to search regulatory genes efficiently and to predict the network dynamics accurately.

Results

In this study, we employed a Boolean network model with a restricted update rule scheme to capture coarse-grained dynamics, and propose a novel mutual information-based Boolean network inference (MIBNI) method. Given time-series gene expression data as an input, the method first identifies a set of initial regulatory genes using mutual information-based feature selection, and then improves the dynamics prediction accuracy by iteratively swapping a pair of genes between sets of the selected regulatory genes and the other genes. Through extensive simulations with artificial datasets, MIBNI showed consistently better performance than six well-known existing methods, REVEAL, Best-Fit, RelNet, CST, CLR, and BIBN in terms of both structural and dynamics prediction accuracy. We further tested the proposed method with two real gene expression datasets for an Escherichia coli gene regulatory network and a fission yeast cell cycle network, and also observed better results using MIBNI compared to the six other methods.

Conclusions

Taken together, MIBNI is a promising tool for predicting both the structure and the dynamics of a gene regulatory network.

Immuno-hybrid algorithm: a novel hybrid approach for GRN reconstruction

Bio-inspired algorithms are widely used to optimize the model parameters of GRN. In this paper, focus is given to develop improvised versions of bio-inspired algorithm for the specific problem of reconstruction of gene regulatory network. The approach is applied to the data set that was developed by the DNA microarray technology through biological experiments in the lab. This paper introduced a novel hybrid method, which combines the clonal selection algorithm and BFGS Quasi-Newton algorithm. The proposed approach implemented for real world E. coli data set and identified most of the relations. The results are also compared with the existing methods and proven to be efficient.

Inferring Weighted Directed Association Network from Multivariate Time Series with a Synthetic Method of Partial Symbolic Transfer Entropy Spectrum and Granger Causality

Complex network methodology is very useful for complex system explorer. However, the relationships among variables in complex system are usually not clear. Therefore, inferring association networks among variables from their observed data has been a popular research topic. We propose a synthetic method, named small-shuffle partial symbolic transfer entropy spectrum (SSPSTES), for inferring association network from multivariate time series. The method synthesizes surrogate data, partial symbolic transfer entropy (PSTE) and Granger causality. A proper threshold selection is crucial for common correlation identification methods and it is not easy for users. The proposed method can not only identify the strong correlation without selecting a threshold but also has the ability of correlation quantification, direction identification and temporal relation identification. The method can be divided into three layers, i.e. data layer, model layer and network layer. In the model layer, the method identifies all the possible pair-wise correlation. In the network layer, we introduce a filter algorithm to remove the indirect weak correlation and retain strong correlation. Finally, we build a weighted adjacency matrix, the value of each entry representing the correlation level between pair-wise variables, and then get the weighted directed association network. Two numerical simulated data from linear system and nonlinear system are illustrated to show the steps and performance of the proposed approach. The ability of the proposed method is approved by an application finally.

Boolean modeling techniques for protein co-expression networks in systems medicine

INTRODUCTION

Application of systems biology/systems medicine approaches is promising for proteomics/biomedical research, but requires selection of an adequate modeling type.

AREAS COVERED

This article reviews the existing Boolean network modeling approaches, which provide in comparison with alternative modeling techniques several advantages for the processing of proteomics data. Application of methods for inference, reduction and validation of protein co-expression networks that are derived from quantitative high-throughput proteomics measurements is presented. It's also shown how Boolean models can be used to derive system-theoretic characteristics that describe both the dynamical behavior of such networks as a whole and the properties of different cell states (e.g. healthy or diseased cell states). Furthermore, application of methods derived from control theory is proposed in order to simulate the effects of therapeutic interventions on such networks, which is a promising approach for the computer-assisted discovery of biomarkers and drug targets. Finally, the clinical application of Boolean modeling analyses is discussed. Expert commentary: Boolean modeling of proteomics data is still in its infancy. Progress in this field strongly depends on provision of a repository with public access to relevant reference models. Also required are community supported standards that facilitate input of both proteomics and patient related data (e.g. age, gender, laboratory results, etc.).

High-order dynamic Bayesian Network learning with hidden common causes for causal gene regulatory network

BACKGROUND

Inferring gene regulatory network (GRN) has been an important topic in Bioinformatics. Many computational methods infer the GRN from high-throughput expression data. Due to the presence of time delays in the regulatory relationships, High-Order Dynamic Bayesian Network (HO-DBN) is a good model of GRN. However, previous GRN inference methods assume causal sufficiency, i.e. no unobserved common cause. This assumption is convenient but unrealistic, because it is possible that relevant factors have not even been conceived of and therefore un-measured. Therefore an inference method that also handles hidden common cause(s) is highly desirable. Also, previous methods for discovering hidden common causes either do not handle multi-step time delays or restrict that the parents of hidden common causes are not observed genes.

RESULTS

We have developed a discrete HO-DBN learning algorithm that can infer also hidden common cause(s) from discrete time series expression data, with some assumptions on the conditional distribution, but is less restrictive than previous methods. We assume that each hidden variable has only observed variables as children and parents, with at least two children and possibly no parents. We also make the simplifying assumption that children of hidden variable(s) are not linked to each other. Moreover, our proposed algorithm can also utilize multiple short time series (not necessarily of the same length), as long time series are difficult to obtain.

CONCLUSIONS

We have performed extensive experiments using synthetic data on GRNs of size up to 100, with up to 10 hidden nodes. Experiment results show that our proposed algorithm can recover the causal GRNs adequately given the incomplete data. Using the limited real expression data and small subnetworks of the YEASTRACT network, we have also demonstrated the potential of our algorithm on real data, though more time series expression data is needed.

Time Delayed Causal Gene Regulatory Network Inference with Hidden Common Causes

Inferring the gene regulatory network (GRN) is crucial to understanding the working of the cell. Many computational methods attempt to infer the GRN from time series expression data, instead of through expensive and time-consuming experiments. However, existing methods make the convenient but unrealistic assumption of causal sufficiency, i.e. all the relevant factors in the causal network have been observed and there are no unobserved common cause. In principle, in the real world, it is impossible to be certain that all relevant factors or common causes have been observed, because some factors may not have been conceived of, and therefore are impossible to measure. In view of this, we have developed a novel algorithm named HCC-CLINDE to infer an GRN from time series data allowing the presence of hidden common cause(s). We assume there is a sparse causal graph (possibly with cycles) of interest, where the variables are continuous and each causal link has a delay (possibly more than one time step). A small but unknown number of variables are not observed. Each unobserved variable has only observed variables as children and parents, with at least two children, and the children are not linked to each other. Since it is difficult to obtain very long time series, our algorithm is also capable of utilizing multiple short time series, which is more realistic. To our knowledge, our algorithm is far less restrictive than previous works. We have performed extensive experiments using synthetic data on GRNs of size up to 100, with up to 10 hidden nodes. The results show that our algorithm can adequately recover the true causal GRN and is robust to slight deviation from Gaussian distribution in the error terms. We have also demonstrated the potential of our algorithm on small YEASTRACT subnetworks using limited real data.

Inferring Time-Delayed Causal Gene Network Using Time-Series Expression Data

Inferring gene regulatory network (GRN) from the microarray expression data is an important problem in Bioinformatics, because knowing the GRN is an essential first step in understanding the inner workings of the cell and the related diseases. Time delays exist in the regulatory effects from one gene to another due to the time needed for transcription, translation, and to accumulate a sufficient number of needed proteins. Also, it is known that the delays are important for oscillatory phenomenon. Therefore, it is crucial to develop a causal gene network model, preferably as a function of time. In this paper, we propose an algorithm CLINDE to infer causal directed links in GRN with time delays and regulatory effects in the links from time-series microarray gene expression data. It is one of the most comprehensive in terms of features compared to the state-of-the-art discrete gene network models. We have tested CLINDE on synthetic data, the in vivo IRMA (On and Off) datasets and the [1] yeast expression data validated using KEGG pathways. Results show that CLINDE can effectively recover the links, the time delays and the regulatory effects in the synthetic data, and outperforms other algorithms in the IRMA in vivo datasets.

Minimum network constraint on reverse engineering to develop biological regulatory networks

Reconstructing the topological structure of biological regulatory networks from microarray expression data or data of protein expression profiles is one of major tasks in systems biology. In recent years, various mathematical methods have been developed to meet this task. Here, based on our previously reported reverse engineering method, we propose a new constraint, i.e., the minimum network constraint, to facilitate the reconstruction of biological networks. Three well studied regulatory networks (the budding yeast cell cycle network, the fission yeast cell cycle network, and the SOS network of Escherichia coli) were used as the test sets to verify the performance of this method. Numerical results show that the biological networks prefer to use the minimal networks to fulfill their functional tasks, making it possible to apply minimal network criteria in the network reconstruction process. Two scenarios were considered in the reconstruction process: generating data using different initial conditions; and generating data from knock out and over-expression experiments. In both cases, network structures are revealed faithfully in a few steps using our approach.

Decision tree-based method for integrating gene expression, demographic, and clinical data to determine disease endotypes

Background

Complex diseases are often difficult to diagnose, treat and study due to the multi-factorial nature of the underlying etiology. Large data sets are now widely available that can be used to define novel, mechanistically distinct disease subtypes (endotypes) in a completely data-driven manner. However, significant challenges exist with regard to how to segregate individuals into suitable subtypes of the disease and understand the distinct biological mechanisms of each when the goal is to maximize the discovery potential of these data sets.

Results

A multi-step decision tree-based method is described for defining endotypes based on gene expression, clinical covariates, and disease indicators using childhood asthma as a case study. We attempted to use alternative approaches such as the Student’s t-test, single data domain clustering and the Modk-prototypes algorithm, which incorporates multiple data domains into a single analysis and none performed as well as the novel multi-step decision tree method. This new method gave the best segregation of asthmatics and non-asthmatics, and it provides easy access to all genes and clinical covariates that distinguish the groups.

Conclusions

The multi-step decision tree method described here will lead to better understanding of complex disease in general by allowing purely data-driven disease endotypes to facilitate the discovery of new mechanisms underlying these diseases. This application should be considered a complement to ongoing efforts to better define and diagnose known endotypes. When coupled with existing methods developed to determine the genetics of gene expression, these methods provide a mechanism for linking genetics and exposomics data and thereby accounting for both major determinants of disease.

Recent development and biomedical applications of probabilistic Boolean networks

Probabilistic Boolean network (PBN) modelling is a semi-quantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rule-based representation and probability makes PBN appealing for large-scale modelling of biological networks where degrees of uncertainty need to be considered.A considerable expansion of our knowledge in the field of theoretical research on PBN can be observed over the past few years, with a focus on network inference, network intervention and control. With respect to areas of applications, PBN is mainly used for the study of gene regulatory networks though with an increasing emergence in signal transduction, metabolic, and also physiological networks. At the same time, a number of computational tools, facilitating the modelling and analysis of PBNs, are continuously developed.A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on PBN versus similar models with respect to concepts and biomedical applications. Due to their many advantages, we consider PBN to stand as a suitable modelling framework for the description and analysis of complex biological systems, ranging from molecular to physiological levels.

Properties of Boolean networks and methods for their tests

Transcriptional regulation networks are often modeled as Boolean networks. We discuss certain properties of Boolean functions (BFs), which are considered as important in such networks, namely, membership to the classes of unate or canalizing functions. Of further interest is the average sensitivity (AS) of functions. In this article, we discuss several algorithms to test the properties of interest. To test canalizing properties of functions, we apply spectral techniques, which can also be used to characterize the AS of functions as well as the influences of variables in unate BFs. Further, we provide and review upper and lower bounds on the AS of unate BFs based on the spectral representation. Finally, we apply these methods to a transcriptional regulation network of Escherichia coli, which controls central parts of the E. coli metabolism. We find that all functions are unate. Also the analysis of the AS of the network reveals an exceptional robustness against transient fluctuations of the binary variables.^a

Growing seed genes from time series data and thresholded Boolean networks with perturbation

Models of gene regulatory networks (GRN) have been proposed along with algorithms for inferring their structure. By structure, we mean the relationships among the genes of the biological system under study. Despite the large number of genes found in the genome of an organism, it is believed that a small set of genes is responsible for maintaining a specific core regulatory mechanism (small subnetworks). We propose an algorithm for inference of subnetworks of genes from a small initial set of genes called seed and time series gene expression data. The algorithm has two main steps: First, it grows the seed of genes by adding genes to it, and second, it searches for subnetworks that can be biologically meaningful. The seed growing step is treated as a feature selection problem and we used a thresholded Boolean network with a perturbation model to design the criterion function that is used to select the features (genes). Given that the reverse engineering of GRN is a problem that does not necessarily have one unique solution, the proposed algorithm has as output a set of networks instead of one single network. The algorithm also analyzes the dynamics of the networks which can be time-consuming. Nevertheless, the algorithm is suitable when the number of genes is small. The results showed that the algorithm is capable of recovering an acceptable rate of gene interactions and to generate regulatory hypotheses that can be explored in the wet lab.

Reverse engineering Boolean networks: from Bernoulli mixture models to rule based systems

A Boolean network is a graphical model for representing and analyzing the behavior of gene regulatory networks (GRN). In this context, the accurate and efficient reconstruction of a Boolean network is essential for understanding the gene regulation mechanism and the complex relations that exist therein. In this paper we introduce an elegant and efficient algorithm for the reverse engineering of Boolean networks from a time series of multivariate binary data corresponding to gene expression data. We call our method ReBMM, i.e., reverse engineering based on Bernoulli mixture models. The time complexity of most of the existing reverse engineering techniques is quite high and depends upon the indegree of a node in the network. Due to the high complexity of these methods, they can only be applied to sparsely connected networks of small sizes. ReBMM has a time complexity factor, which is independent of the indegree of a node and is quadratic in the number of nodes in the network, a big improvement over other techniques and yet there is little or no compromise in accuracy. We have tested ReBMM on a number of artificial datasets along with simulated data derived from a plant signaling network. We also used this method to reconstruct a network from real experimental observations of microarray data of the yeast cell cycle. Our method provides a natural framework for generating rules from a probabilistic model. It is simple, intuitive and illustrates excellent empirical results.

A boolean model of the cardiac gene regulatory network determining first and second heart field identity

Two types of distinct cardiac progenitor cell populations can be identified during early heart development: the first heart field (FHF) and second heart field (SHF) lineage that later form the mature heart. They can be characterized by differential expression of transcription and signaling factors. These regulatory factors influence each other forming a gene regulatory network. Here, we present a core gene regulatory network for early cardiac development based on published temporal and spatial expression data of genes and their interactions. This gene regulatory network was implemented in a Boolean computational model. Simulations reveal stable states within the network model, which correspond to the regulatory states of the FHF and the SHF lineages. Furthermore, we are able to reproduce the expected temporal expression patterns of early cardiac factors mimicking developmental progression. Additionally, simulations of knock-down experiments within our model resemble published phenotypes of mutant mice. Consequently, this gene regulatory network retraces the early steps and requirements of cardiogenic mesoderm determination in a way appropriate to enhance the understanding of heart development.

Utilização da biofotogrametria para a avaliação da flexibilidade de tronco

INTRODUÇÃO: a ginástica rítmica (GR) é uma modalidade de ginástica que requer alto grau de flexibilidade, em virtude dos movimentos complexos que são requeridos. OBJETIVO: esta pesquisa objetivou comparar o teste de sentar e alcançar (TSA) e a técnica de biofotogrametria como indicadores de flexibilidade de tronco, em praticantes iniciantes de GR. METODOLOGIA: a amostra contou com 60 meninas (de cinco a 11 anos de idade) de um universo de 110, todas matriculadas em um centro de iniciação esportiva no estado do Paraná. A coleta de dados foi realizada no mês de novembro do ano de 2009. Para a comparação TSA com a biofotogrametria, foram traçados os ângulos de flexão da pelve (WP), flexão da coluna lombar (WC) e flexão do total do tronco (WT). RESULTADOS: o resultado médio atingido pelas participantes na escala do TSA foi de 27,75cm. Encontrou-se forte correlação do ângulo WT com o TSA. Por ser uma composição de WC e WP, o WT possibilita uma visualização global da distância do tronco até os membros inferiores quando ocorre a flexão durante o teste. Por isso, as correlações entre os ângulos são boas e significativas. CONCLUSÃO: uma vez que o TSA apresenta alguns fatores intervenientes que podem mascarar o seu resultado, a biofotogrametria é discutida como um teste que permite observar, através de imagens fotográficas e cálculos angulares, dados fidedignos para a mensuração de flexibilidade e compensações musculares não identificadas normalmente.