Stochastic dynamic modeling of short gene expression time-series data

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the expectation maximization (EM) algorithm is applied for modeling the gene regulatory network from gene time-series data. The gene regulatory network is viewed as a stochastic dynamic model, which consists of the noisy gene measurement from microarray and the gene regulation first-order autoregressive (AR) stochastic dynamic process. By using the EM algorithm, both the model parameters and the actual values of the gene expression levels can be identified simultaneously. Moreover, the algorithm can deal with the sparse parameter identification and the noisy data in an efficient way. It is also shown that the EM algorithm can handle the microarray gene expression data with large number of variables but a small number of observations. The gene expression stochastic dynamic models for four real-world gene expression data sets are constructed to demonstrate the advantages of the introduced algorithm. Several indices are proposed to evaluate the models of inferred gene regulatory networks, and the relevant biological properties are discussed

Networks from gene expression time series: characterization of correlation patterns

This paper describes characteristic features of networks reconstructed from gene expression time series data. Several null models are considered in order to discriminate between informations embedded in the network that are related to real data, and features that are due to the method used for network reconstruction (time correlation).Comment: 10 pages, 3 BMP figures, 1 Table. To appear in Int. J. Bif. Chaos, July 2007, Volume 17, Issue

Probabilities of spurious connections in gene networks: Application to expression time series

Motivation: The reconstruction of gene networks from gene expression microarrays is gaining popularity as methods improve and as more data become available. The reliability of such networks could be judged by the probability that a connection between genes is spurious, resulting from chance fluctuations rather than from a true biological relationship. Results: Unlike the false discovery rate and positive false discovery rate, the decisive false discovery rate (dFDR) is exactly equal to a conditional probability without assuming independence or the randomness of hypothesis truth values. This property is useful not only in the common application to the detection of differential gene expression, but also in determining the probability of a spurious connection in a reconstructed gene network. Estimators of the dFDR can estimate each of three probabilities: 1. The probability that two genes that appear to be associated with each other lack such association. 2. The probability that a time ordering observed for two associated genes is misleading. 3. The probability that a time ordering observed for two genes is misleading, either because they are not associated or because they are associated without a lag in time. The first probability applies to both static and dynamic gene networks, and the other two only apply to dynamic gene networks. Availability: Cross-platform software for network reconstruction, probability estimation, and plotting is free from http://www.davidbickel.com as R functions and a Java application.Comment: Like q-bio.GN/0404032, this was rejected in March 2004 because it was submitted to the math archive. The only modification is a corrected reference to q-bio.GN/0404032, which was not modified at al

Estimating the time evolution of NMR systems via quantum speed limit-like expression

Finding the solutions of the equations that describe the dynamics of a given physical system is crucial in order to obtain important information about its evolution. However, by using estimation theory, it is possible to obtain, under certain limitations, some information on its dynamics. The quantum-speed-limit (QSL) theory was originally used to estimate the shortest time in which a Hamiltonian drives an initial state to a final one for a given fidelity. Using the QSL theory in a slightly different way, we are able to estimate the running time of a given quantum process. For that purpose, we impose the saturation of the Anandan-Aharonov bound in a rotating frame of reference where the state of the system travels slower than in the original frame (laboratory frame). Through this procedure it is possible to estimate the actual evolution time in the laboratory frame of reference with good accuracy when compared to previous methods. Our method is tested successfully to predict the time spent in the evolution of nuclear spins 1/2 and 3/2 in NMR systems. We find that the estimated time according to our method is better than previous approaches by up to four orders of magnitude. One disadvantage of our method is that we need to solve a number of transcendental equations, which increases with the system dimension and parameter discretization used to solve such equations numerically.Comment: 14 pages, 10 figures, title changed, one appendix added, partially rewritten, similar to the version published in PR

Variation in the flowering time orthologs BrFLC and BrSOC1 in a natural population of Brassica rapa.

Understanding the genetic basis of natural phenotypic variation is of great importance, particularly since selection can act on this variation to cause evolution. We examined expression and allelic variation in candidate flowering time loci in Brassica rapa plants derived from a natural population and showing a broad range in the timing of first flowering. The loci of interest were orthologs of the Arabidopsis genes FLC and SOC1 (BrFLC and BrSOC1, respectively), which in Arabidopsis play a central role in the flowering time regulatory network, with FLC repressing and SOC1 promoting flowering. In B. rapa, there are four copies of FLC and three of SOC1. Plants were grown in controlled conditions in the lab. Comparisons were made between plants that flowered the earliest and latest, with the difference in average flowering time between these groups ∼30 days. As expected, we found that total expression of BrSOC1 paralogs was significantly greater in early than in late flowering plants. Paralog-specific primers showed that expression was greater in early flowering plants in the BrSOC1 paralogs Br004928, Br00393 and Br009324, although the difference was not significant in Br009324. Thus expression of at least 2 of the 3 BrSOC1 orthologs is consistent with their predicted role in flowering time in this natural population. Sequences of the promoter regions of the BrSOC1 orthologs were variable, but there was no association between allelic variation at these loci and flowering time variation. For the BrFLC orthologs, expression varied over time, but did not differ between the early and late flowering plants. The coding regions, promoter regions and introns of these genes were generally invariant. Thus the BrFLC orthologs do not appear to influence flowering time in this population. Overall, the results suggest that even for a trait like flowering time that is controlled by a very well described genetic regulatory network, understanding the underlying genetic basis of natural variation in such a quantitative trait is challenging

Expression profile of genes involved in hydrogen sulphide liberation by _Saccharomyces cerevisiae_ grown under different nitrogen concentrations

The present work aims to elucidate molecular mechanisms underlying hydrogen sulphide production in _S. cerevisiae_ associated to nitrogen deficiency. To assess, at a genome-wide level, how the yeast strain adapted to the progressive nitrogen depletion and to nitrogen re-feeding, gene expression profiles were evaluated during fermentation at different nitrogen concentrations, using the DNA array technology. The results showed that most MET genes displayed higher expression values at the beginning of both control and N-limiting fermentation, just before the time at which the release of sulphide was observed. MET genes were downregulated when yeast stopped growing which could associate MET gene expression levels with cell growth. The over expression of MET genes after nitrogen addition was confirmed by a new release of H2S during the new set of fermentation experiments. In addition, to confirm gene expression profiles observed from macroarray results, real time RT-PCR was performed on 6 genes using additional sets of biological replicates. These genes were selected based on the assumption that differences in sulphide production observed among strains are due to genetic variations of the expression of genes involved in the Sulphate Reduction Pathway. An integration of expression data of genes involved in sulphur assimilation and sulphur amino acid biosynthesis with hydrogen sulphide production is presented