Dataset Information

USE OF MULTIPLE SINGULAR VALUE DECOMPOSITIONS TO ANALYZE COMPLEX INTRACELLULAR CALCIUM ION SIGNALS.

ABSTRACT: We compare calcium ion signaling (Ca(2+)) between two exposures; the data are present as movies, or, more prosaically, time series of images. This paper describes novel uses of singular value decompositions (SVD) and weighted versions of them (WSVD) to extract the signals from such movies, in a way that is semi-automatic and tuned closely to the actual data and their many complexities. These complexities include the following. First, the images themselves are of no interest: all interest focuses on the behavior of individual cells across time, and thus, the cells need to be segmented in an automated manner. Second, the cells themselves have 100+ pixels, so that they form 100+ curves measured over time, so that data compression is required to extract the features of these curves. Third, some of the pixels in some of the cells are subject to image saturation due to bit depth limits, and this saturation needs to be accounted for if one is to normalize the images in a reasonably un-biased manner. Finally, the Ca(2+) signals have oscillations or waves that vary with time and these signals need to be extracted. Thus, our aim is to show how to use multiple weighted and standard singular value decompositions to detect, extract and clarify the Ca(2+) signals. Our signal extraction methods then lead to simple although finely focused statistical methods to compare Ca(2+) signals across experimental conditions.

SUBMITTER: Martinez JG

PROVIDER: S-EPMC2859732 | biostudies-literature | 2009

REPOSITORIES: biostudies-literature

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USE OF MULTIPLE SINGULAR VALUE DECOMPOSITIONS TO ANALYZE COMPLEX INTRACELLULAR CALCIUM ION SIGNALS.

Martinez Josue G JG Huang Jianhua Z JZ Burghardt Robert C RC Barhoumi Rola R Carroll Raymond J RJ

The annals of applied statistics 20090101 4

We compare calcium ion signaling (Ca(2+)) between two exposures; the data are present as movies, or, more prosaically, time series of images. This paper describes novel uses of singular value decompositions (SVD) and weighted versions of them (WSVD) to extract the signals from such movies, in a way that is semi-automatic and tuned closely to the actual data and their many complexities. These complexities include the following. First, the images themselves are of no interest: all interest focuses ...[more]

PMID: 20428493

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Project description:Dynamic processes, such as intracellular calcium signaling, are hallmark of cellular biology. As real-time imaging modalities become widespread, a need for analytical tools to reliably characterize time-series data without prior knowledge of the nature of the recordings becomes more pressing. The goal of this study is to develop a signal-processing algorithm for MATLAB that autonomously computes the parameters characterizing prominent single transient responses (TR) and/or multi-peaks responses (MPR). The algorithm corrects for signal contamination and decomposes experimental recordings into contributions from drift, TRs, and MPRs. It subsequently provides numerical estimates for the following parameters: time of onset after stimulus application, activation time (time for signal to increase from 10 to 90% of peak), and amplitude of response. It also provides characterization of the (i) TRs by quantifying their area under the curve (AUC), response duration (time between 1/2 amplitude on ascent and descent of the transient), and decay constant of the exponential decay region of the deactivation phase of the response, and (ii) MPRs by quantifying the number of peaks, mean peak magnitude, mean periodicity, standard deviation of periodicity, oscillatory persistence (time between first and last discernable peak), and duty cycle (fraction of period during which system is active) for all the peaks in the signal, as well as coherent oscillations (i.e., deterministic spikes). We demonstrate that the signal detection performance of this algorithm is in agreement with user-mediated detection and that parameter estimates obtained manually and algorithmically are correlated. We then apply this algorithm to study how metabolic acidosis affects purinergic (P2) receptor-mediated calcium signaling in osteoclast precursor cells. Our results reveal that acidosis significantly attenuates the amplitude and AUC calcium responses at high ATP concentrations. Collectively, our data validated this algorithm as a general framework for comprehensively analyzing dynamic time-series.

Project description:The number of high-dimensional datasets recording multiple aspects of a single phenomenon is increasing in many areas of science, accompanied by a need for mathematical frameworks that can compare multiple large-scale matrices with different row dimensions. The only such framework to date, the generalized singular value decomposition (GSVD), is limited to two matrices. We mathematically define a higher-order GSVD (HO GSVD) for N≥2 matrices D(i)∈R(m(i) × n), each with full column rank. Each matrix is exactly factored as D(i)=U(i)Σ(i)V(T), where V, identical in all factorizations, is obtained from the eigensystem SV=VΛ of the arithmetic mean S of all pairwise quotients A(i)A(j)(-1) of the matrices A(i)=D(i)(T)D(i), i≠j. We prove that this decomposition extends to higher orders almost all of the mathematical properties of the GSVD. The matrix S is nondefective with V and Λ real. Its eigenvalues satisfy λ(k)≥1. Equality holds if and only if the corresponding eigenvector v(k) is a right basis vector of equal significance in all matrices D(i) and D(j), that is σ(i,k)/σ(j,k)=1 for all i and j, and the corresponding left basis vector u(i,k) is orthogonal to all other vectors in U(i) for all i. The eigenvalues λ(k)=1, therefore, define the "common HO GSVD subspace." We illustrate the HO GSVD with a comparison of genome-scale cell-cycle mRNA expression from S. pombe, S. cerevisiae and human. Unlike existing algorithms, a mapping among the genes of these disparate organisms is not required. We find that the approximately common HO GSVD subspace represents the cell-cycle mRNA expression oscillations, which are similar among the datasets. Simultaneous reconstruction in the common subspace, therefore, removes the experimental artifacts, which are dissimilar, from the datasets. In the simultaneous sequence-independent classification of the genes of the three organisms in this common subspace, genes of highly conserved sequences but significantly different cell-cycle peak times are correctly classified.

Project description:BackgroundBoth microarrays and quantitative real-time PCR are convenient tools for studying the transcriptional levels of genes. The former is preferable for large scale studies while the latter is a more targeted technique. Because of platform-dependent systematic effects, simple comparisons or merging of datasets obtained by these technologies are difficult, even though they may often be desirable. These difficulties are exacerbated if there is only partial overlap between the experimental conditions and genes probed in the two datasets.ResultsWe show here that the generalized singular value decomposition provides a practical tool for merging a small, targeted dataset obtained by quantitative real-time PCR of specific genes with a much larger microarray dataset. The technique permits, for the first time, the identification of genes present in only one dataset co-expressed with a target gene present exclusively in the other dataset, even when experimental conditions for the two datasets are not identical. With the rapidly increasing number of publically available large scale microarray datasets the latter is frequently the case. The method enables us to discover putative candidate genes involved in the biosynthesis of the (1,3;1,4)-beta-D-glucan polysaccharide found in plant cell walls.ConclusionWe show that the generalized singular value decomposition provides a viable tool for a combined analysis of two gene expression datasets with only partial overlap of both gene sets and experimental conditions. We illustrate how the decomposition can be optimized self-consistently by using a judicious choice of genes to define it. The ability of the technique to seamlessly define a concept of "co-expression" across both datasets provides an avenue for meaningful data integration. We believe that it will prove to be particularly useful for exploiting large, publicly available, microarray datasets for species with unsequenced genomes by complementing them with more limited in-house expression measurements.

Dataset Information

USE OF MULTIPLE SINGULAR VALUE DECOMPOSITIONS TO ANALYZE COMPLEX INTRACELLULAR CALCIUM ION SIGNALS.

Publications

USE OF MULTIPLE SINGULAR VALUE DECOMPOSITIONS TO ANALYZE COMPLEX INTRACELLULAR CALCIUM ION SIGNALS.

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