Clustering of change patterns using Fourier coefficients

Single-cell RNA-seq data augmentation using generative Fourier transformer

Single-cell RNA sequencing (scRNA-seq) provides a powerful tool for dissecting cellular complexity and heterogeneity. However, its full potential to achieve statistically reliable conclusions is often constrained by the limited number of cells profiled, particularly in studies of rare diseases, specialized tissues, and uncommon cell types. Deep learning-based generative models (GMs) designed to address data scarcity often face similar limitations due to their reliance on pre-training or fine-tuning, inadvertently perpetuating a cycle of data inadequacy. To overcome this obstacle, we introduce scGFT (single-cell Generative Fourier Transformer), a train-free, cell-centric GM adept at synthesizing single cells that exhibit natural gene expression profiles present within authentic datasets. Using both simulated and experimental data, we demonstrate the mathematical rigor of scGFT and validate its ability to synthesize cells that preserve the intrinsic characteristics delineated in scRNA-seq data. Moreover, comparisons of scGFT with leading neural network-based GMs highlight its superior performance, driven by its analytical mechanism. By streamlining single-cell data augmentation, scGFT offers a scalable solution to mitigate data scarcity in cell-targeted research.

Partitioning of functional gene expression data using principal points

Background

DNA microarrays offer motivation and hope for the simultaneous study of variations in multiple genes. Gene expression is a temporal process that allows variations in expression levels with a characterized gene function over a period of time. Temporal gene expression curves can be treated as functional data since they are considered as independent realizations of a stochastic process. This process requires appropriate models to identify patterns of gene functions. The partitioning of the functional data can find homogeneous subgroups of entities for the massive genes within the inherent biological networks. Therefor it can be a useful technique for the analysis of time-course gene expression data. We propose a new self-consistent partitioning method of functional coefficients for individual expression profiles based on the orthonormal basis system.

Results

A principal points based functional partitioning method is proposed for time-course gene expression data. The method explores the relationship between genes using Legendre coefficients as principal points to extract the features of gene functions. Our proposed method provides high connectivity in connectedness after clustering for simulated data and finds a significant subsets of genes with the increased connectivity. Our approach has comparative advantages that fewer coefficients are used from the functional data and self-consistency of principal points for partitioning. As real data applications, we are able to find partitioned genes through the gene expressions found in budding yeast data and Escherichia coli data.

Conclusions

The proposed method benefitted from the use of principal points, dimension reduction, and choice of orthogonal basis system as well as provides appropriately connected genes in the resulting subsets. We illustrate our method by applying with each set of cell-cycle-regulated time-course yeast genes and E. coli genes. The proposed method is able to identify highly connected genes and to explore the complex dynamics of biological systems in functional genomics.

A method to identify differential expression profiles of time-course gene data with Fourier transformation

BACKGROUND

Time course gene expression experiments are an increasingly popular method for exploring biological processes. Temporal gene expression profiles provide an important characterization of gene function, as biological systems are both developmental and dynamic. With such data it is possible to study gene expression changes over time and thereby to detect differential genes. Much of the early work on analyzing time series expression data relied on methods developed originally for static data and thus there is a need for improved methodology. Since time series expression is a temporal process, its unique features such as autocorrelation between successive points should be incorporated into the analysis.

RESULTS

This work aims to identify genes that show different gene expression profiles across time. We propose a statistical procedure to discover gene groups with similar profiles using a nonparametric representation that accounts for the autocorrelation in the data. In particular, we first represent each profile in terms of a Fourier basis, and then we screen out genes that are not differentially expressed based on the Fourier coefficients. Finally, we cluster the remaining gene profiles using a model-based approach in the Fourier domain. We evaluate the screening results in terms of sensitivity, specificity, FDR and FNR, compare with the Gaussian process regression screening in a simulation study and illustrate the results by application to yeast cell-cycle microarray expression data with alpha-factor synchronization.The key elements of the proposed methodology: (i) representation of gene profiles in the Fourier domain; (ii) automatic screening of genes based on the Fourier coefficients and taking into account autocorrelation in the data, while controlling the false discovery rate (FDR); (iii) model-based clustering of the remaining gene profiles.

CONCLUSIONS

Using this method, we identified a set of cell-cycle-regulated time-course yeast genes. The proposed method is general and can be potentially used to identify genes which have the same patterns or biological processes, and help facing the present and forthcoming challenges of data analysis in functional genomics.

How cyanobacteria pose new problems to old methods: challenges in microarray time series analysis

Background

The transcriptomes of several cyanobacterial strains have been shown to exhibit diurnal oscillation patterns, reflecting the diurnal phototrophic lifestyle of the organisms. The analysis of such genome-wide transcriptional oscillations is often facilitated by the use of clustering algorithms in conjunction with a number of pre-processing steps. Biological interpretation is usually focussed on the time and phase of expression of the resulting groups of genes. However, the use of microarray technology in such studies requires the normalization of pre-processing data, with unclear impact on the qualitative and quantitative features of the derived information on the number of oscillating transcripts and their respective phases.

Results

A microarray based evaluation of diurnal expression in the cyanobacterium Synechocystis sp. PCC 6803 is presented. As expected, the temporal expression patterns reveal strong oscillations in transcript abundance. We compare the Fourier transformation-based expression phase before and after the application of quantile normalization, median polishing, cyclical LOESS, and least oscillating set (LOS) normalization. Whereas LOS normalization mostly preserves the phases of the raw data, the remaining methods introduce systematic biases. In particular, quantile-normalization is found to introduce a phase-shift of 180°, effectively changing night-expressed genes into day-expressed ones. Comparison of a large number of clustering results of differently normalized data shows that the normalization method determines the result. Subsequent steps, such as the choice of data transformation, similarity measure, and clustering algorithm, only play minor roles. We find that the standardization and the DTF transformation are favorable for the clustering of time series in contrast to the 12 m transformation. We use the cluster-wise functional enrichment of a clustering derived by LOS normalization, clustering using flowClust, and DFT transformation to derive the diurnal biological program of Synechocystis sp..

Conclusion

Application of quantile normalization, median polishing, and also cyclic LOESS normalization of the presented cyanobacterial dataset lead to increased numbers of oscillating genes and the systematic shift of the expression phase. The LOS normalization minimizes the observed detrimental effects. As previous analyses employed a variety of different normalization methods, a direct comparison of results must be treated with caution.

Hierarchical signature clustering for time series microarray data

Existing clustering techniques provide clusters from time series microarray data, but the distance metrics used lack interpretability for these types of data. While some previous methods are concerned with matching levels, of interest are genes that behave in the same manner but with varying levels. These are not clustered together using an Euclidean metric, and are indiscernible using a correlation metric, so we propose a more appropriate metric and modified hierarchical clustering method to highlight those genes of interest. Use of hashing and bucket sort allows for fast clustering and the hierarchical dendrogram allows for direct comparison with easily understood meaning of the distance. The method also extends well to use k-means clustering when a desired number of clusters are known.

Automated analysis of biological oscillator models using mode decomposition

MOTIVATION

Oscillating signals produced by biological systems have shapes, described by their Fourier spectra, that can potentially reveal the mechanisms that generate them. Extracting this information from measured signals is interesting for the validation of theoretical models, discovery and classification of interaction types, and for optimal experiment design.

RESULTS

An automated workflow is described for the analysis of oscillating signals. A software package is developed to match signal shapes to hundreds of a priori viable model structures defined by a class of first-order differential equations. The package computes parameter values for each model by exploiting the mode decomposition of oscillating signals and formulating the matching problem in terms of systems of simultaneous polynomial equations. On the basis of the computed parameter values, the software returns a list of models consistent with the data. In validation tests with synthetic datasets, it not only shortlists those model structures used to generate the data but also shows that excellent fits can sometimes be achieved with alternative equations. The listing of all consistent equations is indicative of how further invalidation might be achieved with additional information. When applied to data from a microarray experiment on mice, the procedure finds several candidate model structures to describe interactions related to the circadian rhythm. This shows that experimental data on oscillators is indeed rich in information about gene regulation mechanisms.

AVAILABILITY

The software package is available at http://babylone.ulb.ac.be/autoosc/.

Clustering change patterns using Fourier transformation with time-course gene expression data

To understand the behavior of genes, it is important to explore how the patterns of gene expression change over a period of time because biologically related gene groups can share the same change patterns. In this study, the problem of finding similar change patterns is induced to clustering with the derivative Fourier coefficients. This work is aimed at discovering gene groups with similar change patterns which share similar biological properties. We developed a statistical model using derivative Fourier coefficients to identify similar change patterns of gene expression. We used a model-based method to cluster the Fourier series estimation of derivatives. We applied our model to cluster change patterns of yeast cell cycle microarray expression data with alpha-factor synchronization. It showed that, as the method clusters with the probability-neighboring data, the model-based clustering with our proposed model yielded biologically interpretable results. We expect that our proposed Fourier analysis with suitably chosen smoothing parameters could serve as a useful tool in classifying genes and interpreting possible biological change patterns.

Comparative analysis of missing value imputation methods to improve clustering and interpretation of microarray experiments

Background

Microarray technologies produced large amount of data. In a previous study, we have shown the interest of k-Nearest Neighbour approach for restoring the missing gene expression values, and its positive impact of the gene clustering by hierarchical algorithm. Since, numerous replacement methods have been proposed to impute missing values (MVs) for microarray data. In this study, we have evaluated twelve different usable methods, and their influence on the quality of gene clustering. Interestingly we have used several datasets, both kinetic and non kinetic experiments from yeast and human.

Results

We underline the excellent efficiency of approaches proposed and implemented by Bo and co-workers and especially one based on expected maximization (EM_array). These improvements have been observed also on the imputation of extreme values, the most difficult predictable values. We showed that the imputed MVs have still important effects on the stability of the gene clusters. The improvement on the clustering obtained by hierarchical clustering remains limited and, not sufficient to restore completely the correct gene associations. However, a common tendency can be found between the quality of the imputation method and the gene cluster stability. Even if the comparison between clustering algorithms is a complex task, we observed that k-means approach is more efficient to conserve gene associations.

Conclusions

More than 6.000.000 independent simulations have assessed the quality of 12 imputation methods on five very different biological datasets. Important improvements have so been done since our last study. The EM_array approach constitutes one efficient method for restoring the missing expression gene values, with a lower estimation error level. Nonetheless, the presence of MVs even at a low rate is a major factor of gene cluster instability. Our study highlights the need for a systematic assessment of imputation methods and so of dedicated benchmarks. A noticeable point is the specific influence of some biological dataset.

Maximization of negative correlations in time-course gene expression data for enhancing understanding of molecular pathways

Positive correlation can be diversely instantiated as shifting, scaling or geometric pattern, and it has been extensively explored for time-course gene expression data and pathway analysis. Recently, biological studies emerge a trend focusing on the notion of negative correlations such as opposite expression patterns, complementary patterns and self-negative regulation of transcription factors (TFs). These biological ideas and primitive observations motivate us to formulate and investigate the problem of maximizing negative correlations. The objective is to discover all maximal negative correlations of statistical and biological significance from time-course gene expression data for enhancing our understanding of molecular pathways. Given a gene expression matrix, a maximal negative correlation is defined as an activation–inhibition two-way expression pattern (AIE pattern). We propose a parameter-free algorithm to enumerate the complete set of AIE patterns from a data set. This algorithm can identify significant negative correlations that cannot be identified by the traditional clustering/biclustering methods. To demonstrate the biological usefulness of AIE patterns in the analysis of molecular pathways, we conducted deep case studies for AIE patterns identified from Yeast cell cycle data sets. In particular, in the analysis of the Lysine biosynthesis pathway, new regulation modules and pathway components were inferred according to a significant negative correlation which is likely caused by a co-regulation of the TFs at the higher layer of the biological network. We conjecture that maximal negative correlations between genes are actually a common characteristic in molecular pathways, which can provide insights into the cell stress response study, drug response evaluation, etc.