Andrzej Kudlicki

Logic of the Yeast Metabolic Cycle: Temporal Compartmentalization of Cellular Processes

Budding yeast grown under continuous, nutrient-limited conditions exhibit robust, highly periodic cycles in the form of respiratory bursts. Microarray studies reveal that over half of the yeast genome is expressed periodically during these metabolic cycles. Genes encoding proteins having a common function exhibit similar temporal expression patterns, and genes specifying functions associated with energy and metabolism tend to be expressed with exceptionally robust periodicity. Essential cellular and metabolic events occur in synchrony with the metabolic cycle, demonstrating that key processes in a simple eukaryotic cell are compartmentalized in time.

High-resolution timing of cell cycle-regulated gene expression

The eukaryotic cell division cycle depends on an intricate sequence of transcriptional events. Using an algorithm based on maximum-entropy deconvolution, and expression data from a highly synchronized yeast culture, we have timed the peaks of expression of transcriptionally regulated cell cycle genes to an accuracy of 2 min (≈1% of the cell cycle time). The set of 1,129 cell cycle-regulated genes was identified by a comprehensive analysis encompassing all available cell cycle yeast data sets. Our results reveal distinct subphases of the cell cycle undetectable by morphological observation, as well as the precise timeline of macromolecular complex assembly during key cell cycle events.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Non-linearity and stochasticity in the density-velocity relation

We present results of the investigations of the statistical properties of a joint density and velocity divergence probability distribution function (PDF) in the mildly non-linear regime. For that purpose we use both perturbation theory results, extended here for a top-hat filter, and numerical simulations. In particular, we derive the quantitative (complete as possible up to third-order terms) and qualitative predictions for constrained averages and constrained dispersions – which describe the non-linearities and the stochasticity properties beyond the linear regime – and compare them against numerical simulations. We find overall a good agreement for constrained averages; however, the agreement for constrained dispersions is only qualitative. Scaling relations for the Ω-dependence of these quantities are satisfactorily reproduced. Guided by our analytical and numerical results, we finally construct a robust phenomenological description of the joint PDF in a closed analytic form. The good agreement of our formula with results of N-body simulations for a number of cosmological parameters provides a sound validation of the presented approach. Our results provide a basis for a potentially powerful tool with which it is possible to analyse galaxy survey data in order to test the gravitational instability paradigm beyond the linear regime and to put useful constraints on cosmological parameters. In particular, we show how the non-linearity in the density–velocity relation can be used to break the so-called Ω-bias degeneracy in cosmic density–velocity comparisons.

Modulation of Gene Expression Regulated by the Transcription Factor NF-κB/RelA

Background: Interacting proteins modulate the activity of NF-κB/RelA transcription factor and expression of its targets. Results: By analyzing gene expression, protein binding, and DNA binding, we inferred and characterized 8349 such modulations. Conclusion: Different modulator groups affect separate pathways. Significance: We provide new insight into the activity of NF-κB/RelA. Our inference model can be applied to other processes and pathways. Modulators (Ms) are proteins that modify the activity of transcription factors (TFs) and influence expression of their target genes (TGs). To discover modulators of NF-κB/RelA, we first identified 365 NF-κB/RelA-binding proteins using liquid chromatography-tandem mass spectrometry (LC-MS/MS). We used a probabilistic model to infer 8349 (M, NF-κB/RelA, TG) triplets and their modes of modulatory action from our combined LC-MS/MS and ChIP-Seq (ChIP followed by next generation sequencing) data, published RelA modulators and TGs, and a compendium of gene expression profiles. Hierarchical clustering of the derived modulatory network revealed functional subnetworks and suggested new pathways modulating RelA transcriptional activity. The modulators with the highest number of TGs and most non-random distribution of action modes (measured by Shannon entropy) are consistent with published reports. Our results provide a repertoire of testable hypotheses for experimental validation. One of the NF-κB/RelA modulators we identified is STAT1. The inferred (STAT1, NF-κB/RelA, TG) triplets were validated by LC-selected reaction monitoring-MS and the results of STAT1 deletion in human fibrosarcoma cells. Overall, we have identified 562 NF-κB/RelA modulators, which are potential drug targets, and clarified mechanisms of achieving NF-κB/RelA multiple functions through modulators. Our approach can be readily applied to other TFs.

Reconstructing cosmic peculiar velocities from the mildly non-linear density field

We present a numerical study of the cosmic density vs. velocity divergence relation (DVDR) in the mildly non-linear regime. We approximate the dark matter as a nonrelativistic pressureless fluid, and solve its equations of motion on a grid fixed in comoving coordinates. Unlike N-body schemes, this method yields directly the volumeaveraged velocity field. The results of our simulations are compared with the predictions of the third-order perturbation theory (3PT) for the DVDR. We investigate both the mean ‘forward’ relation (density in terms of velocity divergence) and the mean ‘inverse’ relation (velocity divergence in terms of density), with emphasis on the latter. On scales larger than about 20 megaparsecs, our code recovers the predictions of 3PT remarkably well, significantly better than recent N-body simulations. On scales of a few megaparsecs, the DVDR predicted by 3PT differs slightly from the simulated one. In particular, approximating the inverse DVDR by a third-order polynomial turns out to be a poor fit. We propose a simple analytical description of the inverse relation, which works well for mildly non-linear scales.

Inferring Genome-Wide Functional Modulatory Network: A Case Study on NF-κB/RelA Transcription Factor

How different pathways lead to the activation of a specific transcription factor (TF) with specific effects is not fully understood. We model context-specific transcriptional regulation as a modulatory network: triplets composed of a TF, target gene, and modulator. Modulators usually affect the activity of a specific TF at the posttranscriptional level in a target gene-specific action mode. This action may be classified as enhancement, attenuation, or inversion of either activation or inhibition. As a case study, we inferred, from a large collection of expression profiles, all potential modulations of NF-κB/RelA. The predicted modulators include many proteins previously not reported as physically binding to RelA but with relevant functions, such as RNA processing, cell cycle, mitochondrion, ubiquitin-dependent proteolysis, and chromatin modification. Modulators from different processes exert specific prevalent action modes on distinct pathways. Modulators from noncoding RNA, RNA-binding proteins, TFs, and kinases modulate the NF-κB/RelA activity with specific action modes consistent with their molecular functions and modulation level. The modulatory networks of NF-κB/RelA in the context epithelial-mesenchymal transition (EMT) and burn injury have different modulators, including those involved in extracellular matrix (FBN1), cytoskeletal regulation (ACTN1), and metastasis-associated lung adenocarcinoma transcript 1 (MALAT1), a long intergenic nonprotein coding RNA, and tumor suppression (FOXP1) for EMT, and TXNIP, GAPDH, PKM2, IFIT5, LDHA, NID1, and TPP1 for burn injury.

Gaussianity of cosmic velocity fields and linearity of the velocity–gravity relation

ABSTRACT We present a numerical study of the relation between the cosmic peculiar velocity fieldand the gravitationalaccelerationfield. We show that on mildly non-linear scales (4–10h −1 Mpc Gaussian smoothing), the distribution of the Cartesian coordinates of eachof these fields is well approximated by a Gaussian. In particular, their kurtoses andnegentropies are small compared to those of the velocity divergence and density fields.We find that at these scales the relation between the velocity and gravity field followslinear theory to good accuracy. Specifically, the systematic errors in velocity–velocitycomparisons due to assuming the linear model do not exceed 6% in β. To correct forthem, we test various nonlinear estimators of velocity from density. We show that aslight modification of the α-formula proposed by Kudlicki et al. yields an estimatorwhich is essentially unbiased and has a small variance.Key words: cosmology: theory – cosmology: dark matter – large-scale structure ofthe Universe – methods: numerical

The crystallographic fast Fourier transform. I. p3 symmetry

An algorithm for computing the discrete Fourier transform of data with threefold symmetry axes is presented. This algorithm is straightforward and easily implemented. It reduces the computational complexity of such a Fourier transform by a factor of 3. There are no restrictive requirements imposed on the initial data. Explicit formulae and a scheme of computing the Fourier transform are given. The algorithm has been tested and benchmarked against FFT on the unit cell, revealing the expected increase in speed. This is a non-trivial example of a more general approach developed recently by the authors.

Coordinate transformations in modern crystallographic computing

A review of 4 x 4-matrix notation and of tensor formalism focused on crystallographic applications is presented. A discussion of examples shows how this notation simplifies tasks encountered in crystallographic computing.