Network module detection: Affinity search technique with the multi-node topological overlap measure

<p>Abstract</p> <p>Background</p> <p>Many clustering procedures only allow the user to input a <it>pairwise </it>dissimilarity or distance measure between objects. We propose a clustering method that can input a multi-point dissimilarity measure d(i1, i2, ..., iP) where the number of points P can be larger than 2. The work is motivated by gene network analysis where clusters correspond to modules of highly interconnected nodes. Here, we define modules as clusters of network nodes with high <it>multi-node </it>topological overlap. The topological overlap measure is a robust measure of interconnectedness which is based on shared network neighbors. In previous work, we have shown that the multi-node topological overlap measure yields biologically meaningful results when used as input of network neighborhood analysis.</p> <p>Findings</p> <p>We adapt network neighborhood analysis for the use of module detection. We propose the Module Affinity Search Technique (MAST), which is a generalized version of the Cluster Affinity Search Technique (CAST). MAST can accommodate a multi-node dissimilarity measure. Clusters grow around user-defined or automatically chosen seeds (e.g. hub nodes). We propose both local and global cluster growth stopping rules. We use several simulations and a gene co-expression network application to argue that the MAST approach leads to biologically meaningful results. We compare MAST with hierarchical clustering and partitioning around medoid clustering.</p> <p>Conclusion</p> <p>Our flexible module detection method is implemented in the MTOM software which can be downloaded from the following webpage: <url>http://www.genetics.ucla.edu/labs/horvath/MTOM/</url></p

PTOMSM: A modified version of Topological Overlap Measure used for predicting Protein-Protein Interaction Network

A variety of methods are developed to integrating diverse biological data to predict novel interaction relationship between proteins. However, traditional integration can only generate protein interaction pairs within existing relationships. Therefore, we propose a modified version of Topological Overlap Measure to identify not only extant direct PPIs links, but also novel protein interactions that can be indirectly inferred from various relationships between proteins. Our method is more powerful than a na&#xef;ve Bayesian-network-based integration in PPI prediction, and could generate more reliable candidate PPIs. Furthermore, we examined the influence of the sizes of training and test datasets on prediction, and further demonstrated the effectiveness of PTOMSM in predicting PPI. More importantly, this method can be extended naturally to predict other types of biological networks, and may be combined with Bayesian method to further improve the prediction

Revealing Dynamic Mechanisms of Cell Fate Decisions From Single-Cell Transcriptomic Data.

Cell fate decisions play a pivotal role in development, but technologies for dissecting them are limited. We developed a multifunction new method, Topographer, to construct a "quantitative" Waddington's landscape of single-cell transcriptomic data. This method is able to identify complex cell-state transition trajectories and to estimate complex cell-type dynamics characterized by fate and transition probabilities. It also infers both marker gene networks and their dynamic changes as well as dynamic characteristics of transcriptional bursting along the cell-state transition trajectories. Applying this method to single-cell RNA-seq data on the differentiation of primary human myoblasts, we not only identified three known cell types, but also estimated both their fate probabilities and transition probabilities among them. We found that the percent of genes expressed in a bursty manner is significantly higher at (or near) the branch point (~97%) than before or after branch (below 80%), and that both gene-gene and cell-cell correlation degrees are apparently lower near the branch point than away from the branching. Topographer allows revealing of cell fate mechanisms in a coherent way at three scales: cell lineage (macroscopic), gene network (mesoscopic), and gene expression (microscopic)

Retaining positive definiteness in thresholded matrices

Positive definite (p.d.) matrices arise naturally in many areas within mathematics and also feature extensively in scientific applications. In modern high-dimensional applications, a common approach to finding sparse positive definite matrices is to threshold their small off-diagonal elements. This thresholding, sometimes referred to as hard-thresholding, sets small elements to zero. Thresholding has the attractive property that the resulting matrices are sparse, and are thus easier to interpret and work with. In many applications, it is often required, and thus implicitly assumed, that thresholded matrices retain positive definiteness. In this paper we formally investigate the algebraic properties of p.d. matrices which are thresholded. We demonstrate that for positive definiteness to be preserved, the pattern of elements to be set to zero has to necessarily correspond to a graph which is a union of disconnected complete components. This result rigorously demonstrates that, except in special cases, positive definiteness can be easily lost. We then proceed to demonstrate that the class of diagonally dominant matrices is not maximal in terms of retaining positive definiteness when thresholded. Consequently, we derive characterizations of matrices which retain positive definiteness when thresholded with respect to important classes of graphs. In particular, we demonstrate that retaining positive definiteness upon thresholding is governed by complex algebraic conditions

Matrix positivity preservers in fixed dimension. I

A classical theorem proved in 1942 by I.J. Schoenberg describes all real-valued functions that preserve positivity when applied entrywise to positive semidefinite matrices of arbitrary size; such functions are necessarily analytic with non-negative Taylor coefficients. Despite the great deal of interest generated by this theorem, a characterization of functions preserving positivity for matrices of fixed dimension is not known. In this paper, we provide a complete description of polynomials of degree $N$ that preserve positivity when applied entrywise to matrices of dimension $N$. This is the key step for us then to obtain negative lower bounds on the coefficients of analytic functions so that these functions preserve positivity in a prescribed dimension. The proof of the main technical inequality is representation theoretic, and employs the theory of Schur polynomials. Interpreted in the context of linear pencils of matrices, our main results provide a closed-form expression for the lowest critical value, revealing at the same time an unexpected spectral discontinuity phenomenon. Tight linear matrix inequalities for Hadamard powers of matrices and a sharp asymptotic bound for the matrix-cube problem involving Hadamard powers are obtained as applications. Positivity preservers are also naturally interpreted as solutions of a variational inequality involving generalized Rayleigh quotients. This optimization approach leads to a novel description of the simultaneous kernels of Hadamard powers, and a family of stratifications of the cone of positive semidefinite matrices.Comment: Changed notation for extreme critical value from $\mathfrak{C}$ to $\mathcal{C}$. Addressed referee remarks to improve exposition, including Remarks 1.2 and 3.3. Final version, 39 pages, to appear in Advances in Mathematic

Linking proteins to signaling pathways for experiment design and evaluation

Biomedical experimental work often focuses on altering the functions of selected proteins. These changes can hit signaling pathways, and can therefore unexpectedly and non-specifically affect cellular processes. We propose PathwayLinker, an online tool that can provide a first estimate of the possible signaling effects of such changes, e.g., drug or microRNA treatments. PathwayLinker minimizes the users' efforts by integrating protein-protein interaction and signaling pathway data from several sources with statistical significance tests and clear visualization. We demonstrate through three case studies that the developed tool can point out unexpected signaling bias in normal laboratory experiments and identify likely novel signaling proteins among the interactors of known drug targets. In our first case study we show that knockdown of the Caenorhabditis elegans gene cdc-25.1 (meant to avoid progeny) may globally affect the signaling system and unexpectedly bias experiments. In the second case study we evaluate the loss-of-function phenotypes of a less known C. elegans gene to predict its function. In the third case study we analyze GJA1, an anti-cancer drug target protein in human, and predict for this protein novel signaling pathway memberships, which may be sources of side effects. Compared to similar services, a major advantage of PathwayLinker is that it drastically reduces the necessary amount of manual literature searches and can be used without a computational background. PathwayLinker is available at http://PathwayLinker.org. Detailed documentation and source code are available at the website. © 2012 Farkas et al

Linking Proteins to Signaling Pathways for Experiment Design and Evaluation

Biomedical experimental work often focuses on altering the functions of selected proteins. These changes can hit signaling pathways, and can therefore unexpectedly and non-specifically affect cellular processes. We propose PathwayLinker, an online tool that can provide a first estimate of the possible signaling effects of such changes, e.g., drug or microRNA treatments. PathwayLinker minimizes the users' efforts by integrating protein-protein interaction and signaling pathway data from several sources with statistical significance tests and clear visualization. We demonstrate through three case studies that the developed tool can point out unexpected signaling bias in normal laboratory experiments and identify likely novel signaling proteins among the interactors of known drug targets. In our first case study we show that knockdown of the Caenorhabditis elegans gene cdc-25.1 (meant to avoid progeny) may globally affect the signaling system and unexpectedly bias experiments. In the second case study we evaluate the loss-of-function phenotypes of a less known C. elegans gene to predict its function. In the third case study we analyze GJA1, an anti-cancer drug target protein in human, and predict for this protein novel signaling pathway memberships, which may be sources of side effects. Compared to similar services, a major advantage of PathwayLinker is that it drastically reduces the necessary amount of manual literature searches and can be used without a computational background. PathwayLinker is available at http://PathwayLinker.org. Detailed documentation and source code are available at the website