Analysis of expression profile using fuzzy adaptive resonance theory

MOTIVATION: It is well understood that the successful clustering of expression profiles give beneficial ideas to understand the functions of uncharacterized genes. In order to realize such a successful clustering, we investigate a clustering method based on adaptive resonance theory (ART) in this report. RESULTS: We apply Fuzzy ART as a clustering method for analyzing the time series expression data during sporulation of Saccharomyces cerevisiae. The clustering result by Fuzzy ART was compared with those by other clustering methods such as hierarchical clustering, k-means algorithm and self-organizing maps (SOMs). In terms of the mathematical validations, Fuzzy ART achieved the most reasonable clustering. We also verified the robustness of Fuzzy ART using noised data. Furthermore, we defined the correctness ratio of clustering, which is based on genes whose temporal expressions are characterized biologically. Using this definition, it was proved that the clustering ability of Fuzzy ART was superior to other clustering methods such as hierarchical clustering, k-means algorithm and SOMs. Finally, we validate the clustering results by Fuzzy ART in terms of biological functions and evidence. AVAILABILITY: The software is available at http//www.nubio.nagoya-u.ac.jp/proc/index.html     

Novel clustering algorithm for microarray expression data in a truncated SVD space

MOTIVATION: This paper introduces the application of a novel clustering method to microarray expression data. Its first stage involves compression of dimensions that can be achieved by applying SVD to the gene-sample matrix in microarray problems. Thus the data (samples or genes) can be represented by vectors in a truncated space of low dimensionality, 4 and 5 in the examples studied here. We find it preferable to project all vectors onto the unit sphere before applying a clustering algorithm. The clustering algorithm used here is the quantum clustering method that has one free scale parameter. Although the method is not hierarchical, it can be modified to allow hierarchy in terms of this scale parameter. RESULTS: We apply our method to three data sets. The results are very promising. On cancer cell data we obtain a dendrogram that reflects correct groupings of cells. In an AML/ALL data set we obtain very good clustering of samples into four classes of the data. Finally, in clustering of genes in yeast cell cycle data we obtain four groups in a problem that is estimated to contain five families. AVAILABILITY: Software is available as Matlab programs at http://neuron.tau.ac.il/~horn/QC.htm.     

Determining functional specificity from protein sequences

MOTIVATION: Given a large family of homologous protein sequences, many methods can divide the family into smaller groups that correspond to the different functions carried out by proteins within the family. One important problem, however, has been the absence of a general method for selecting an appropriate level of granularity, or size of the groups. RESULTS: We propose a consistent way of choosing the granularity that is independent of the sequence similarity and sequence clustering method used. We study three large, well-investigated protein families: basic leucine zippers, nuclear receptors and proteins with three consecutive C2H2 zinc fingers. Our method is tested against known functional information, the experimentally determined binding specificities, using a simple scoring method. The significance of the groups is also measured by randomizing the data. Finally, we compare our algorithm against a popular method of grouping proteins, the TRIBE-MCL method. In the end, we determine that dividing the families at the proposed level of granularity creates very significant and useful groups of proteins that correspond to the different DNA-binding motifs. We expect that such groupings will be useful in studying not only DNA binding but also other protein interactions.     

Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis

MOTIVATION: Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approximating high-dimensional data in a lower dimensional space. RESULTS: In this article, we introduce a novel formulation of sparse NMF and show how the new formulation leads to a convergent sparse NMF algorithm via alternating non-negativity-constrained least squares. We apply our sparse NMF algorithm to cancer-class discovery and gene expression data analysis and offer biological analysis of the results obtained. Our experimental results illustrate that the proposed sparse NMF algorithm often achieves better clustering performance with shorter computing time compared to other existing NMF algorithms. AVAILABILITY: The software is available as supplementary material.     

Hierarchical Dirichlet process model for gene expression clustering

Clustering is an important data processing tool for interpreting microarray data and genomic network inference. In this article, we propose a clustering algorithm based on the hierarchical Dirichlet processes (HDP). The HDP clustering introduces a hierarchical structure in the statistical model which captures the hierarchical features prevalent in biological data such as the gene express data. We develop a Gibbs sampling algorithm based on the Chinese restaurant metaphor for the HDP clustering. We apply the proposed HDP algorithm to both regulatory network segmentation and gene expression clustering. The HDP algorithm is shown to outperform several popular clustering algorithms by revealing the underlying hierarchical structure of the data. For the yeast cell cycle data, we compare the HDP result to the standard result and show that the HDP algorithm provides more information and reduces the unnecessary clustering fragments.     

A seriation approach for visualization-driven discovery of co-expression patterns in Serial Analysis of Gene Expression (SAGE) data

Background

Serial Analysis of Gene Expression (SAGE) is a DNA sequencing-based method for large-scale gene expression profiling that provides an alternative to microarray analysis. Most analyses of SAGE data aimed at identifying co-expressed genes have been accomplished using various versions of clustering approaches that often result in a number of false positives.

Principal Findings

Here we explore the use of seriation, a statistical approach for ordering sets of objects based on their similarity, for large-scale expression pattern discovery in SAGE data. For this specific task we implement a seriation heuristic we term ‘progressive construction of contigs’ that constructs local chains of related elements by sequentially rearranging margins of the correlation matrix. We apply the heuristic to the analysis of simulated and experimental SAGE data and compare our results to those obtained with a clustering algorithm developed specifically for SAGE data. We show using simulations that the performance of seriation compares favorably to that of the clustering algorithm on noisy SAGE data.

Conclusions

We explore the use of a seriation approach for visualization-based pattern discovery in SAGE data. Using both simulations and experimental data, we demonstrate that seriation is able to identify groups of co-expressed genes more accurately than a clustering algorithm developed specifically for SAGE data. Our results suggest that seriation is a useful method for the analysis of gene expression data whose applicability should be further pursued.     

Geometry preserving projections algorithm for predicting membrane protein types

Given a new uncharacterized protein sequence, a biologist may want to know whether it is a membrane protein or not? If it is, which membrane protein type it belongs to? Knowing the type of an uncharacterized membrane protein often provides useful clues for finding the biological function of the query protein, developing the computational methods to address these questions can be really helpful. In this study, a sequence encoding scheme based on combing pseudo position-specific score matrix (PsePSSM) and dipeptide composition (DC) is introduced to represent protein samples. However, this sequence encoding scheme would correspond to a very high dimensional feature vector. A dimensionality reduction algorithm, the so-called geometry preserving projections (GPP) is introduced to extract the key features from the high-dimensional space and reduce the original high-dimensional vector to a lower-dimensional one. Finally, the K-nearest neighbor (K-NN) and support vector machine (SVM) classifiers are employed to identify the types of membrane proteins based on their reduced low-dimensional features. Our jackknife and independent dataset test results thus obtained are quite encouraging, which indicate that the above methods are used effectively to deal with this complicated problem of predicting the membrane protein type.     

A unified representation of multiprotein complex data for modeling interaction networks

The protein interaction network presents one perspective for understanding cellular processes. Recent experiments employing high-throughput mass spectrometric characterizations have resulted in large data sets of physiologically relevant multiprotein complexes. We present a unified representation of such data sets based on an underlying bipartite graph model that is an advance over existing models of the network. Our unified representation allows for weighting of connections between proteins shared in more than one complex, as well as addressing the higher level organization that occurs when the network is viewed as consisting of protein complexes that share components. This representation also allows for the application of the rigorous MinMaxCut graph clustering algorithm for the determination of relevant protein modules in the networks. Statistically significant annotations of clusters in the protein-protein and complex-complex networks using terms from the Gene Ontology indicate that this method will be useful for posing hypotheses about uncharacterized components of protein complexes or uncharacterized relationships between protein complexes.     

Defining the boundaries and characterizing the landscape of functional genome expression in vascular tissues of Populus using shotgun proteomics

Current state-of-the-art experimental and computational proteomic approaches were integrated to obtain a comprehensive protein profile of Populus vascular tissue. This featured: (1) a large sample set consisting of two genotypes grown under normal and tension stress conditions, (2) bioinformatics clustering to effectively handle gene duplication, and (3) an informatics approach to track and identify single amino acid polymorphisms (SAAPs). By applying a clustering algorithm to the Populus database, the number of protein entries decreased from 64,689 proteins to a total of 43,069 protein groups, thereby reducing 7505 identified proteins to a total of 4226 protein groups, in which 2016 were singletons. This reduction implies that ～50% of the measured proteins shared extensive sequence homology. Using conservative search criteria, we were able to identify 1354 peptides containing a SAAP and 201 peptides that become tryptic due to a K or R substitution. These newly identified peptides correspond to 502 proteins, including 97 previously unidentified proteins. In total, the integration of deep proteome measurements on an extensive sample set with protein clustering and peptide sequence variants provided an exceptional level of proteome characterization for Populus, allowing us to spatially resolve the vascular tissue proteome.     

Microarray data clustering based on temporal variation: FCV with TSD preclustering

The aim of this paper is to present a new clustering algorithm for short time-series gene expression data that is able to characterise temporal relations in the clustering environment (ie data-space), which is not achieved by other conventional clustering algorithms such as k -means or hierarchical clustering. The algorithm called fuzzy c -varieties clustering with transitional state discrimination preclustering (FCV-TSD) is a two-step approach which identifies groups of points ordered in a line configuration in particular locations and orientations of the data-space that correspond to similar expressions in the time domain. We present the validation of the algorithm with both artificial and real experimental datasets, where k -means and random clustering are used for comparison. The performance was evaluated with a measure for internal cluster correlation and the geometrical properties of the clusters, showing that the FCV-TSD algorithm had better performance than the k -means algorithm on both datasets.     

Visualization methods for statistical analysis of microarray clusters

Background  

The most common method of identifying groups of functionally related genes in microarray data is to apply a clustering algorithm. However, it is impossible to determine which clustering algorithm is most appropriate to apply, and it is difficult to verify the results of any algorithm due to the lack of a gold-standard. Appropriate data visualization tools can aid this analysis process, but existing visualization methods do not specifically address this issue.     

Integrated analysis of multiple data sources reveals modular structure of biological networks

It has been a challenging task to integrate high-throughput data into investigations of the systematic and dynamic organization of biological networks. Here, we presented a simple hierarchical clustering algorithm that goes a long way to achieve this aim. Our method effectively reveals the modular structure of the yeast protein-protein interaction network and distinguishes protein complexes from functional modules by integrating high-throughput protein-protein interaction data with the added subcellular localization and expression profile data. Furthermore, we take advantage of the detected modules to provide a reliably functional context for the uncharacterized components within modules. On the other hand, the integration of various protein-protein association information makes our method robust to false-positives, especially for derived protein complexes. More importantly, this simple method can be extended naturally to other types of data fusion and provides a framework for the study of more comprehensive properties of the biological network and other forms of complex networks.     

Statistical discovery of site inter-dependencies in sub-molecular hierarchical protein structuring

Background

Much progress has been made in understanding the 3D structure of proteins using methods such as NMR and X-ray crystallography. The resulting 3D structures are extremely informative, but do not always reveal which sites and residues within the structure are of special importance. Recently, there are indications that multiple-residue, sub-domain structural relationships within the larger 3D consensus structure of a protein can be inferred from the analysis of the multiple sequence alignment data of a protein family. These intra-dependent clusters of associated sites are used to indicate hierarchical inter-residue relationships within the 3D structure. To reveal the patterns of associations among individual amino acids or sub-domain components within the structure, we apply a k-modes attribute (aligned site) clustering algorithm to the ubiquitin and transthyretin families in order to discover associations among groups of sites within the multiple sequence alignment. We then observe what these associations imply within the 3D structure of these two protein families.

Results

The k-modes site clustering algorithm we developed maximizes the intra-group interdependencies based on a normalized mutual information measure. The clusters formed correspond to sub-structural components or binding and interface locations. Applying this data-directed method to the ubiquitin and transthyretin protein family multiple sequence alignments as a test bed, we located numerous interesting associations of interdependent sites. These clusters were then arranged into cluster tree diagrams which revealed four structural sub-domains within the single domain structure of ubiquitin and a single large sub-domain within transthyretin associated with the interface among transthyretin monomers. In addition, several clusters of mutually interdependent sites were discovered for each protein family, each of which appear to play an important role in the molecular structure and/or function.

Conclusions

Our results demonstrate that the method we present here using a k- modes site clustering algorithm based on interdependency evaluation among sites obtained from a sequence alignment of homologous proteins can provide significant insights into the complex, hierarchical inter-residue structural relationships within the 3D structure of a protein family.

     

More reliable protein NMR peak assignment via improved 2-interval scheduling.

Protein NMR peak assignment refers to the process of assigning a group of "spin systems" obtained experimentally to a protein sequence of amino acids. The automation of this process is still an unsolved and challenging problem in NMR protein structure determination. Recently, protein NMR peak assignment has been formulated as an interval scheduling problem (ISP), where a protein sequence P of amino acids is viewed as a discrete time interval I (the amino acids on P one-to-one correspond to the time units of I), each subset S of spin systems that are known to originate from consecutive amino acids from P is viewed as a "job" j(s), the preference of assigning S to a subsequence P of consecutive amino acids on P is viewed as the profit of executing job j(s) in the subinterval of I corresponding to P, and the goal is to maximize the total profit of executing the jobs (on a single machine) during I. The interval scheduling problem is max SNP-hard in general; but in the real practice of protein NMR peak assignment, each job j(s) usually requires at most 10 consecutive time units, and typically the jobs that require one or two consecutive time units are the most difficult to assign/schedule. In order to solve these most difficult assignments, we present an efficient 13/7-approximation algorithm for the special case of the interval scheduling problem where each job takes one or two consecutive time units. Combining this algorithm with a greedy filtering strategy for handling long jobs (i.e., jobs that need more than two consecutive time units), we obtain a new efficient heuristic for protein NMR peak assignment. Our experimental study shows that the new heuristic produces the best peak assignment in most of the cases, compared with the NMR peak assignment algorithms in the recent literature. The above algorithm is also the first approximation algorithm for a nontrivial case of the well-known interval scheduling problem that breaks the ratio 2 barrier.     

High-throughput inference of protein-protein interfaces from unassigned NMR data

SUMMARY: We cast the problem of identifying protein-protein interfaces, using only unassigned NMR spectra, into a geometric clustering problem. Identifying protein-protein interfaces is critical to understanding inter- and intra-cellular communication, and NMR allows the study of protein interaction in solution. However it is often the case that NMR studies of a protein complex are very time-consuming, mainly due to the bottleneck in assigning the chemical shifts, even if the apo structures of the constituent proteins are known. We study whether it is possible, in a high-throughput manner, to identify the interface region of a protein complex using only unassigned chemical shifts and residual dipolar coupling (RDC) data. We introduce a geometric optimization problem where we must cluster the cells in an arrangement on the boundary of a 3-manifold, where the arrangement is induced by a spherical quadratic form [corrected] The arrangement is induced by a spherical quadratic form, which in turn is parameterized by a SO(3)xR2. We show that this formalism derives directly from the physics of RDCs. We present an optimal algorithm for this problem that runs in O(n3 log n) time for an n-residue protein. We then use this clustering algorithm as a subroutine in a practical algorithm for identifying the interface region of a protein complex from unassigned NMR data. We present the results of our algorithm on NMR data for seven proteins from five protein complexes, and show that our approach is useful for high-throughput applications in which we seek to rapidly identify the interface region of a protein complex. AVAILABILITY: Contact authors for source code.     

Multi-way clustering of microarray data using probabilistic sparse matrix factorization

MOTIVATION: We address the problem of multi-way clustering of microarray data using a generative model. Our algorithm, probabilistic sparse matrix factorization (PSMF), is a probabilistic extension of a previous hard-decision algorithm for this problem. PSMF allows for varying levels of sensor noise in the data, uncertainty in the hidden prototypes used to explain the data and uncertainty as to the prototypes selected to explain each data vector. RESULTS: We present experimental results demonstrating that our method can better recover functionally-relevant clusterings in mRNA expression data than standard clustering techniques, including hierarchical agglomerative clustering, and we show that by computing probabilities instead of point estimates, our method avoids converging to poor solutions.     

The predictive power of the CluSTr database

SUMMARY: The CluSTr database employs a fully automatic single-linkage hierarchical clustering method based on a similarity matrix. In order to compute the matrix, first all-against-all pair-wise comparisons between protein sequences are computed using the Smith-Waterman algorithm. The statistical significance of the similarity scores is then assessed using a Monte Carlo analysis, yielding Z-values, which are used to populate the matrix. This paper describes automated annotation experiments that quantify the predictive power and hence the biological relevance of the CluSTr data. The experiments utilized the UniProt data-mining framework to derive annotation predictions using combinations of InterPro and CluSTr. We show that this combination of data sources greatly increases the precision of predictions made by the data-mining framework, compared with the use of InterPro data alone. We conclude that the CluSTr approach to clustering proteins makes a valuable contribution to traditional protein classifications. AVAILABILITY: http://www.ebi.ac.uk/clustr/.     

Analysis of temporal gene expression profiles: clustering by simulated annealing and determining the optimal number of clusters

MOTIVATION: Cluster analysis of genome-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and samples. In the present paper, we focus on several important issues related to clustering algorithms that have not yet been fully studied. RESULTS: We describe a simple and robust algorithm for the clustering of temporal gene expression profiles that is based on the simulated annealing procedure. In general, this algorithm guarantees to eventually find the globally optimal distribution of genes over clusters. We introduce an iterative scheme that serves to evaluate quantitatively the optimal number of clusters for each specific data set. The scheme is based on standard approaches used in regular statistical tests. The basic idea is to organize the search of the optimal number of clusters simultaneously with the optimization of the distribution of genes over clusters. The efficiency of the proposed algorithm has been evaluated by means of a reverse engineering experiment, that is, a situation in which the correct distribution of genes over clusters is known a priori. The employment of this statistically rigorous test has shown that our algorithm places greater than 90% genes into correct clusters. Finally, the algorithm has been tested on real gene expression data (expression changes during yeast cell cycle) for which the fundamental patterns of gene expression and the assignment of genes to clusters are well understood from numerous previous studies.     

Graph-based clustering for finding distant relationships in a large set of protein sequences

MOTIVATION: Clustering of protein sequences is widely used for the functional characterization of proteins. However, it is still not easy to cluster distantly-related proteins, which have only regional similarity among their sequences. It is therefore necessary to develop an algorithm for clustering such distantly-related proteins. RESULTS: We have developed a time and space efficient clustering algorithm. It uses a graph representation where its vertices and edges denote proteins and their sequence similarities above a certain cutoff score, respectively. It repeatedly partitions the graph by removing edges that have small weights, which correspond to low sequence similarities. To find the appropriate partitions, we introduce a score combining the normalized cut and a locally minimal cut capacities. Our method is applied to the entire 40,703 human proteins in SWISS-PROT and TrEMBL. The resulting clusters shows a 76% recall (20,529 proteins) of the 26,917 classified by InterPro. It also finds relationships not found by other clustering methods. AVAILABILITY: The complete result of our algorithm for all the human proteins in SWISS-PROT and TrEMBL, and other supplementary information are available at http://motif.ics.es.osaka-u.ac.jp/Ncut-KL/