The feasibility of genome-scale biological network inference using Graphics Processing Units

Systems research spanning fields from biology to finance involves the identification of models to represent the underpinnings of complex systems. Formal approaches for data-driven identification of network interactions include statistical inference-based approaches and methods to identify dynamical systems models that are capable of fitting multivariate data. Availability of large data sets and so-called ‘big data’ applications in biology present great opportunities as well as major challenges for systems identification/reverse engineering applications. For example, both inverse identification and forward simulations of genome-scale gene regulatory network models pose compute-intensive problems. This issue is addressed here by combining the processing power of Graphics Processing Units (GPUs) and a parallel reverse engineering algorithm for inference of regulatory networks. It is shown that, given an appropriate data set, information on genome-scale networks (systems of 1000 or more state variables) can be inferred using a reverse-engineering algorithm in a matter of days on a small-scale modern GPU cluster.     

Fully automated protein complex prediction based on topological similarity and community structure

To understand the function of protein complexes and their association with biological processes, a lot of studies have been done towards analyzing the protein-protein interaction (PPI) networks. However, the advancement in high-throughput technology has resulted in a humongous amount of data for analysis. Moreover, high level of noise, sparseness, and skewness in degree distribution of PPI networks limits the performance of many clustering algorithms and further analysis of their interactions.In addressing and solving these problems we present a novel random walk based algorithm that converts the incomplete and binary PPI network into a protein-protein topological similarity matrix (PP-TS matrix). We believe that if two proteins share some high-order topological similarities they are likely to be interacting with each other. Using the obtained PP-TS matrix, we constructed and used weighted networks to further study and analyze the interaction among proteins. Specifically, we applied a fully automated community structure finding algorithm (Auto-HQcut) on the obtained weighted network to cluster protein complexes. We then analyzed the protein complexes for significance in biological processes. To help visualize and analyze these protein complexes we also developed an interface that displays the resulting complexes as well as the characteristics associated with each complex.Applying our approach to a yeast protein-protein interaction network, we found that the predicted protein-protein interaction pairs with high topological similarities have more significant biological relevance than the original protein-protein interactions pairs. When we compared our PPI network reconstruction algorithm with other existing algorithms using gene ontology and gene co-expression, our algorithm produced the highest similarity scores. Also, our predicted protein complexes showed higher accuracy measure compared to the other protein complex predictions.     

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.     

On an improved clustering algorithm based on node density for WSN routing protocol

To better collect data in context to balance energy consumption, wireless sensor networks (WSN) need to be divided into clusters. The division of clusters makes the network become a hierarchical organizational structure, which plays the role of balancing the network load and prolonging the life cycle of the system. In clustering routing algorithm, the pros and cons of clustering algorithm directly affect the result of cluster division. In this paper, an algorithm for selecting cluster heads based on node distribution density and allocating remaining nodes is proposed for the defects of cluster head random election and uneven clustering in the traditional LEACH protocol clustering algorithm in WSN. Experiments show that the algorithm can realize the rapid selection of cluster heads and division of clusters, which is effective for node clustering and is conducive to equalizing energy consumption.

     

Clustering expressed genes on the basis of their association with a quantitative phenotype

Cluster analyses of gene expression data are usually conducted based on their associations with the phenotype of a particular disease. Many disease traits have a clearly defined binary phenotype (presence or absence), so that genes can be clustered based on the differences of expression levels between the two contrasting phenotypic groups. For example, cluster analysis based on binary phenotype has been successfully used in tumour research. Some complex diseases have phenotypes that vary in a continuous manner and the method developed for a binary trait is not immediately applicable to a continuous trait. However, understanding the role of gene expression in these complex traits is of fundamental importance. Therefore, it is necessary to develop a new statistical method to cluster expressed genes based on their association with a quantitative trait phenotype. We developed a model-based clustering method to classify genes based on their association with a continuous phenotype. We used a linear model to describe the relationship between gene expression and the phenotypic value. The model effects of the linear model (linear regression coefficients) represent the strength of the association. We assumed that the model effects of each gene follow a mixture of several multivariate Gaussian distributions. Parameter estimation and cluster assignment were accomplished via an Expectation-Maximization (EM) algorithm. The method was verified by analysing two simulated datasets, and further demonstrated using real data generated in a microarray experiment for the study of gene expression associated with Alzheimer's disease.     

The research of constructing dynamic cognition model based on brain network

Estimating the functional interactions and connections between brain regions to corresponding process in cognitive, behavioral and psychiatric domains is a central pursuit for understanding the human connectome. Few studies have examined the effects of dynamic evolution on cognitive processing and brain activation using brain network model in scalp electroencephalography (EEG) data. Aim of this study was to investigate the brain functional connectivity and construct dynamic programing model from EEG data and to evaluate a possible correlation between topological characteristics of the brain connectivity and cognitive evolution processing. Here, functional connectivity between brain regions is defined as the statistical dependence between EEG signals in different brain areas and is typically determined by calculating the relationship between regional time series using wavelet coherence. We present an accelerated dynamic programing algorithm to construct dynamic cognitive model that we found that spatially distributed regions coherence connection difference, the topologic characteristics with which they can transfer information, producing temporary network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time after variation audio stimulation, dynamic programing model gives the dynamic evolution processing at different time and frequency. In this paper, by applying a new construct approach to understand whole brain network dynamics, firstly, brain network is constructed by wavelet coherence, secondly, different time active brain regions are selected by network topological characteristics and minimum spanning tree. Finally, dynamic evolution model is constructed to understand cognitive process by dynamic programing algorithm, this model is applied to the auditory experiment, results showed that, quantitatively, more correlation was observed after variation audio stimulation, the EEG function connection dynamic evolution model on cognitive processing is feasible with wavelet coherence EEG recording.     

Clustering microarray gene expression data using weighted Chinese restaurant process

MOTIVATION: Clustering microarray gene expression data is a powerful tool for elucidating co-regulatory relationships among genes. Many different clustering techniques have been successfully applied and the results are promising. However, substantial fluctuation contained in microarray data, lack of knowledge on the number of clusters and complex regulatory mechanisms underlying biological systems make the clustering problems tremendously challenging. RESULTS: We devised an improved model-based Bayesian approach to cluster microarray gene expression data. Cluster assignment is carried out by an iterative weighted Chinese restaurant seating scheme such that the optimal number of clusters can be determined simultaneously with cluster assignment. The predictive updating technique was applied to improve the efficiency of the Gibbs sampler. An additional step is added during reassignment to allow genes that display complex correlation relationships such as time-shifted and/or inverted to be clustered together. Analysis done on a real dataset showed that as much as 30% of significant genes clustered in the same group display complex relationships with the consensus pattern of the cluster. Other notable features including automatic handling of missing data, quantitative measures of cluster strength and assignment confidence. Synthetic and real microarray gene expression datasets were analyzed to demonstrate its performance. AVAILABILITY: A computer program named Chinese restaurant cluster (CRC) has been developed based on this algorithm. The program can be downloaded at http://www.sph.umich.edu/csg/qin/CRC/.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

MORE: Mixed Optimization for Reverse Engineering-An Application to Modeling Biological Networks Response via Sparse Systems of Nonlinear Differential Equations

Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.     

Clustering of resting state networks

Background

The goal of the study was to demonstrate a hierarchical structure of resting state activity in the healthy brain using a data-driven clustering algorithm.

Methodology/Principal Findings

The fuzzy-c-means clustering algorithm was applied to resting state fMRI data in cortical and subcortical gray matter from two groups acquired separately, one of 17 healthy individuals and the second of 21 healthy individuals. Different numbers of clusters and different starting conditions were used. A cluster dispersion measure determined the optimal numbers of clusters. An inner product metric provided a measure of similarity between different clusters. The two cluster result found the task-negative and task-positive systems. The cluster dispersion measure was minimized with seven and eleven clusters. Each of the clusters in the seven and eleven cluster result was associated with either the task-negative or task-positive system. Applying the algorithm to find seven clusters recovered previously described resting state networks, including the default mode network, frontoparietal control network, ventral and dorsal attention networks, somatomotor, visual, and language networks. The language and ventral attention networks had significant subcortical involvement. This parcellation was consistently found in a large majority of algorithm runs under different conditions and was robust to different methods of initialization.

Conclusions/Significance

The clustering of resting state activity using different optimal numbers of clusters identified resting state networks comparable to previously obtained results. This work reinforces the observation that resting state networks are hierarchically organized.     

Gossip-Style Failure Detection and Distributed Consensus for Scalable Heterogeneous Clusters

Gossip protocols provide a means by which failures can be detected in large, distributed systems in an asynchronous manner without the limits associated with reliable multicasting for group communications. However, in order to be effective with application recovery and reconfiguration, these protocols require mechanisms by which failures can be detected with system-wide consensus in a scalable fashion. This paper presents three new gossip-style protocols supported by a novel algorithm to achieve consensus in scalable, heterogeneous clusters. The round-robin protocol improves on basic randomized gossiping by distributing gossip messages in a deterministic order that optimizes bandwidth consumption. Redundant gossiping is completely eliminated in the binary round-robin protocol, and the round-robin with sequence check protocol is a useful extension that yields efficient detection times without the need for system-specific optimization. The distributed consensus algorithm works with these gossip protocols to achieve agreement among the operable nodes in the cluster on the state of the system featuring either a flat or a layered design. The various protocols are simulated and evaluated in terms of consensus time and scalability using a high-fidelity, fault-injection model for distributed systems comprised of clusters of workstations connected by high-performance networks.     

Biomarker discovery in microarray gene expression data with Gaussian processes

MOTIVATION: In clinical practice, pathological phenotypes are often labelled with ordinal scales rather than binary, e.g. the Gleason grading system for tumour cell differentiation. However, in the literature of microarray analysis, these ordinal labels have been rarely treated in a principled way. This paper describes a gene selection algorithm based on Gaussian processes to discover consistent gene expression patterns associated with ordinal clinical phenotypes. The technique of automatic relevance determination is applied to represent the significance level of the genes in a Bayesian inference framework. RESULTS: The usefulness of the proposed algorithm for ordinal labels is demonstrated by the gene expression signature associated with the Gleason score for prostate cancer data. Our results demonstrate how multi-gene markers that may be initially developed with a diagnostic or prognostic application in mind are also useful as an investigative tool to reveal associations between specific molecular and cellular events and features of tumour physiology. Our algorithm can also be applied to microarray data with binary labels with results comparable to other methods in the literature.     

Evaluating functional network inference using simulations of complex biological systems

MOTIVATION: Although many network inference algorithms have been presented in the bioinformatics literature, no suitable approach has been formulated for evaluating their effectiveness at recovering models of complex biological systems from limited data. To overcome this limitation, we propose an approach to evaluate network inference algorithms according to their ability to recover a complex functional network from biologically reasonable simulated data. RESULTS: We designed a simulator to generate data representing a complex biological system at multiple levels of organization: behaviour, neural anatomy, brain electrophysiology, and gene expression of songbirds. About 90% of the simulated variables are unregulated by other variables in the system and are included simply as distracters. We sampled the simulated data at intervals as one would sample from a biological system in practice, and then used the sampled data to evaluate the effectiveness of an algorithm we developed for functional network inference. We found that our algorithm is highly effective at recovering the functional network structure of the simulated system-including the irrelevance of unregulated variables-from sampled data alone. To assess the reproducibility of these results, we tested our inference algorithm on 50 separately simulated sets of data and it consistently recovered almost perfectly the complex functional network structure underlying the simulated data. To our knowledge, this is the first approach for evaluating the effectiveness of functional network inference algorithms at recovering models from limited data. Our simulation approach also enables researchers a priori to design experiments and data-collection protocols that are amenable to functional network inference.     

The determination of enzyme-substrate dissociation rates by dynamic isotope exchange enhancement experiments

A new method for the determination of dissociation rates of enzyme-substrate complexes has been developed. The rate of exchange of a labeled product back into the substrate is measured during catalysis of the forward reaction when the forward reaction is kept far from equilibrium by the enzymatic removal of the nonexchanging product. The ratio of the exchange rate and the net rate for product formation is then determined at various concentrations of the exchanging product. A plot of this ratio is a diagnostic indication of the kinetic mechanism and the relative rates of product dissociation from the binary and ternary enzyme complexes. This technique has been applied to the reaction catalyzed by bovine liver argininosuccinate lyase. The ratio for the rate of exchange of fumarate into argininosuccinate and the net rate for product formation was found to increase with the concentration of fumarate but to reach a limit of 3.3. The ratio of rates was half-maximal at 36 mM fumarate. The data have been interpreted to indicate the argininosuccinate lyase has a random kinetic mechanism. The calculated lower limit for the rate of release of arginine from the enzyme-fumarate-arginine complex is 0.35 times as fast as the Vmax in the reverse direction. The rate of release of arginine from the enzyme-arginine binary complex is 210 times faster than Vmax in the reverse direction.     

Predicting Positive and Negative Relationships in Large Social Networks

In a social network, users hold and express positive and negative attitudes (e.g. support/opposition) towards other users. Those attitudes exhibit some kind of binary relationships among the users, which play an important role in social network analysis. However, some of those binary relationships are likely to be latent as the scale of social network increases. The essence of predicting latent binary relationships have recently began to draw researchers'' attention. In this paper, we propose a machine learning algorithm for predicting positive and negative relationships in social networks inspired by structural balance theory and social status theory. More specifically, we show that when two users in the network have fewer common neighbors, the prediction accuracy of the relationship between them deteriorates. Accordingly, in the training phase, we propose a segment-based training framework to divide the training data into two subsets according to the number of common neighbors between users, and build a prediction model for each subset based on support vector machine (SVM). Moreover, to deal with large-scale social network data, we employ a sampling strategy that selects small amount of training data while maintaining high accuracy of prediction. We compare our algorithm with traditional algorithms and adaptive boosting of them. Experimental results of typical data sets show that our algorithm can deal with large social networks and consistently outperforms other methods.     

An EM algorithm for mapping binary disease loci: application to fibrosarcoma in a four-way cross mouse family

Many diseases show dichotomous phenotypic variation but do not follow a simple Mendelian pattern of inheritance. Variances of these binary diseases are presumably controlled by multiple loci and environmental variants. A least-squares method has been developed for mapping such complex disease loci by treating the binary phenotypes (0 and 1) as if they were continuous. However, the least-squares method is not recommended because of its ad hoc nature. Maximum Likelihood (ML) and Bayesian methods have also been developed for binary disease mapping by incorporating the discrete nature of the phenotypic distribution. In the ML analysis, the likelihood function is usually maximized using some complicated maximization algorithms (e.g. the Newton-Raphson or the simplex algorithm). Under the threshold model of binary disease, we develop an Expectation Maximization (EM) algorithm to solve for the maximum likelihood estimates (MLEs). The new EM algorithm is developed by treating both the unobserved genotype and the disease liability as missing values. As a result, the EM iteration equations have the same form as the normal equation system in linear regression. The EM algorithm is further modified to take into account sexual dimorphism in the linkage maps. Applying the EM-implemented ML method to a four-way-cross mouse family, we detected two regions on the fourth chromosome that have evidence of QTLs controlling the segregation of fibrosarcoma, a form of connective tissue cancer. The two QTLs explain 50-60% of the variance in the disease liability. We also applied a Bayesian method previously developed (modified to take into account sex-specific maps) to this data set and detected one additional QTL on chromosome 13 that explains another 26% of the variance of the disease liability. All the QTLs detected primarily show dominance effects.