Exact reconstruction of gene regulatory networks using compressive sensing

Background

We consider the problem of reconstructing a gene regulatory network structure from limited time series gene expression data, without any a priori knowledge of connectivity. We assume that the network is sparse, meaning the connectivity among genes is much less than full connectivity. We develop a method for network reconstruction based on compressive sensing, which takes advantage of the network’s sparseness.

Results

For the case in which all genes are accessible for measurement, and there is no measurement noise, we show that our method can be used to exactly reconstruct the network. For the more general problem, in which hidden genes exist and all measurements are contaminated by noise, we show that our method leads to reliable reconstruction. In both cases, coherence of the model is used to assess the ability to reconstruct the network and to design new experiments. We demonstrate that it is possible to use the coherence distribution to guide biological experiment design effectively. By collecting a more informative dataset, the proposed method helps reduce the cost of experiments. For each problem, a set of numerical examples is presented.

Conclusions

The method provides a guarantee on how well the inferred graph structure represents the underlying system, reveals deficiencies in the data and model, and suggests experimental directions to remedy the deficiencies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0400-4) contains supplementary material, which is available to authorized users.     

Sources of cell-to-cell variability in canonical nuclear factor-κB (NF-κB) signaling pathway inferred from single cell dynamic images

The canonical nuclear factor-κB (NF-κB) signaling pathway controls a gene network important in the cellular inflammatory response. Upon activation, NF-κB/RelA is released from cytoplasmic inhibitors, from where it translocates into the nucleus, subsequently activating negative feedback loops producing either monophasic or damped oscillatory nucleo-cytoplasmic dynamics. Although the population behavior of the NF-κB pathway has been extensively modeled, the sources of cell-to-cell variability are not well understood. We describe an integrated experimental-computational analysis of NF-κB/RelA translocation in a validated cell model exhibiting monophasic dynamics. Quantitative measures of cellular geometry and total cytoplasmic concentration and translocated RelA amounts were used as priors in Bayesian inference to estimate biophysically realistic parameter values based on dynamic live cell imaging studies of enhanced GFP-tagged RelA in stable transfectants. Bayesian inference was performed on multiple cells simultaneously, assuming identical reaction rate parameters, whereas cellular geometry and initial and total NF-κB concentration-related parameters were cell-specific. A subpopulation of cells exhibiting distinct kinetic profiles was identified that corresponded to differences in the IκBα translation rate. We conclude that cellular geometry, initial and total NF-κB concentration, IκBα translation, and IκBα degradation rates account for distinct cell-to-cell differences in canonical NF-κB translocation dynamics.     

Molecular systematics and biogeography of Nicrophorus in part--the investigator species group (Coleoptera: Silphidae) using mixture model MCMC

Burying beetles (Silphidae: Nicrophorus) are well-known for their biparental care and monopolization of small vertebrate carcasses in subterranean crypts. They have been the focus of intense behavioral ecological research since the 1980s yet no thorough phylogenetic estimate for the group exists. The relationships among the species, and the validity of some species, are poorly understood. Here, we infer the relationships and examine species boundaries among 50 individuals representing 15 species, primarily of the investigator species group, using a mixture-model Bayesian analysis. Two mitochondrial genes, COI and COII, were used, providing 2129 aligned nucleotides (567 parsimony-informative). The Akaike Information Criterion and Bayes Factors were used to select the best fitting model, in addition to Reversible Jump MCMC, which accommodated model uncertainty. A 21 parameter, three-partition GTR + G was the final model chosen. Despite a presumed Old World origin for the genus itself, the basal lineages and immediate outgroups of the investigator species group are New World species. Bayesian methods reconstruct the common ancestor of the investigator species group as New World and imply one later transition to the Old World with two return transitions to the New World. Prior hypotheses concerning the questionable validity of four species names, Nicrophorus praedator, Nicrophorus confusus, Nicrophorus encaustus and Nicrophorus mexicanus were tested. No evidence was found for the validity of the Nicrophorus investigator synonym N. praedator. We found evidence rejecting the species status of N. confusus (NEW SYNONYM of Nicrophorus sepultor). Weak evidence was found for the species status of N. encaustus and N. mexicanus, which are tentatively retained as valid. Our results strongly reject a recently published hypothesis that Nicrophorus interruptus (NEW STATUS as valid species) is a subspecies of N. investigator.     

Robust parameter estimation techniques for stochastic within-host macroparasite models

We present a stochastic model of the within-host population dynamics of lymphatic filariasis, and use a simulated goodness-of-fit (GOF) method to estimate immunological parameters and their confidence intervals from experimental data. A variety of deterministic moment closure approximations to the stochastic system are explored and compared with simulation results. For the maximum GOF parameter estimates, none of the methods of closure accurately reproduce the behaviour of the stochastic model. However, direct analysis of the stochastic model demonstrates that the high levels of variation observed in the data can be reproduced without requiring parameters to vary between hosts. This indicates that the observed aggregation of parasite load may be dynamically generated by random variation in the development of an effective immune response against parasite larvae.     

Sharp simultaneous confidence intervals for the means of selected populations with application to microarray data analysis

Summary Simultaneous inference for a large number, N, of parameters is a challenge. In some situations, such as microarray experiments, researchers are only interested in making inference for the K parameters corresponding to the K most extreme estimates. Hence it seems important to construct simultaneous confidence intervals for these K parameters. The naïve simultaneous confidence intervals for the K means (applied directly without taking into account the selection) have low coverage probabilities. We take an empirical Bayes approach (or an approach based on the random effect model) to construct simultaneous confidence intervals with good coverage probabilities. For N= 10,000 and K= 100, typical for microarray data, our confidence intervals could be 77% shorter than the naïve K‐dimensional simultaneous intervals.     

Drop-the-losers design: normal case

Drop-the-losers designs are statistical designs which have two stages of a trial separated by a data based decision. In the first stage k experimental treatments and a control are administered. During a transition period, the empirically best experimental treatment is selected for continuation into the second phase, along with the control. At the study's end, inference focuses on the comparison of the selected treatment with the control using both stages' data. Traditional methods used to make inferences based on both stages' data can yield tests with higher than advertised levels of significance and confidence intervals with lower than advertised confidence. For normally distributed data, methods are provided to correct these deficiencies, providing confidence intervals with accurate levels of confidence. Drop-the-losers designs are particularly applicable to biopharmaceutical clinical trials where they can allow Phase II and Phase III clinical trials to be conducted under a single protocol with the use of all available data.