In the analysis of gene expression data, network approaches take a system perspective and have played an irreplaceably important role. Gaussian graphical models (GGMs) have been popular in the network analysis of gene expression data. They investigate the conditional dependence between genes and “transform” the problem of estimating network structures into a sparse estimation of precision matrices. When there is a moderate to large number of genes, the number of parameters to be estimated may overwhelm the limited sample size, leading to unreliable estimation and selection. In this article, we propose incorporating information from previous studies (for example, those deposited at PubMed) to assist estimating the network structure in the present data. It is recognized that such information can be partial, biased, or even wrong. A penalization‐based estimation approach is developed, shown to have consistency properties, and realized using an effective computational algorithm. Simulation demonstrates its competitive performance under various information accuracy scenarios. The analysis of TCGA lung cancer prognostic genes leads to network structures different from the alternatives.
In this article, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model converges to one. When there are multiple groups of data available, instead of estimating the networks independently for each group, joint estimation of the networks may utilize the shared information among groups and lead to improved estimation for each individual network. Our method is extended to jointly estimate GGMs in multiple groups of data with complex structures, including spatial data, temporal data, and data with both spatial and temporal structures. Markov random field (MRF) models are used to efficiently incorporate the complex data structures. We develop and implement an efficient algorithm for statistical inference that enables parallel computing. Simulation studies suggest that our approach achieves better accuracy in network estimation compared with methods not incorporating spatial and temporal dependencies when there are shared structures among the networks, and that it performs comparably well otherwise. Finally, we illustrate our method using the human brain gene expression microarray dataset, where the expression levels of genes are measured in different brain regions across multiple time periods.
more » « less- NSF-PAR ID:
- 10486001
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 73
- Issue:
- 3
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 769-779
- Size(s):
- ["p. 769-779"]
- Sponsoring Org:
- National Science Foundation
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Abstract Probabilistic graphical models have become an important unsupervised learning tool for detecting network structures for a variety of problems, including the estimation of functional neuronal connectivity from two‐photon calcium imaging data. However, in the context of calcium imaging, technological limitations only allow for partially overlapping layers of neurons in a brain region of interest to be jointly recorded. In this case, graph estimation for the full data requires inference for edge selection when many pairs of neurons have no simultaneous observations. This leads to the graph quilting problem, which seeks to estimate a graph in the presence of block‐missingness in the empirical covariance matrix. Solutions for the graph quilting problem have previously been studied for Gaussian graphical models; however, neural activity data from calcium imaging are often non‐Gaussian, thereby requiring a more flexible modelling approach. Thus, in our work, we study two approaches for nonparanormal graph quilting based on the Gaussian copula graphical model, namely, a maximum likelihood procedure and a low rank‐based framework. We provide theoretical guarantees on edge recovery for the former approach under similar conditions to those previously developed for the Gaussian setting, and we investigate the empirical performance of both methods using simulations as well as real data calcium imaging data. Our approaches yield more scientifically meaningful functional connectivity estimates compared to existing Gaussian graph quilting methods for this calcium imaging data set.
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INTRODUCTION Neurons are by far the most diverse of all cell types in animals, to the extent that “cell types” in mammalian brains are still mostly heterogeneous groups, and there is no consensus definition of the term. The Drosophila optic lobes, with approximately 200 well-defined cell types, provides a tractable system with which to address the genetic basis of neuronal type diversity. We previously characterized the distinct developmental gene expression program of each of these types using single-cell RNA sequencing (scRNA-seq), with one-to-one correspondence to the known morphological types. RATIONALE The identity of fly neurons is determined by temporal and spatial patterning mechanisms in stem cell progenitors, but it remained unclear how these cell fate decisions are implemented and maintained in postmitotic neurons. It was proposed in Caenorhabditis elegans that unique combinations of terminal selector transcription factors (TFs) that are continuously expressed in each neuron control nearly all of its type-specific gene expression. This model implies that it should be possible to engineer predictable and complete switches of identity between different neurons just by modifying these sustained TFs. We aimed to test this prediction in the Drosophila visual system. RESULTS Here, we used our developmental scRNA-seq atlases to identify the potential terminal selector genes in all optic lobe neurons. We found unique combinations of, on average, 10 differentially expressed and stably maintained (across all stages of development) TFs in each neuron. Through genetic gain- and loss-of-function experiments in postmitotic neurons, we showed that modifications of these selector codes are sufficient to induce predictable switches of identity between various cell types. Combinations of terminal selectors jointly control both developmental (e.g., morphology) and functional (e.g., neurotransmitters and their receptors) features of neurons. The closely related Transmedullary 1 (Tm1), Tm2, Tm4, and Tm6 neurons (see the figure) share a similar code of terminal selectors, but can be distinguished from each other by three TFs that are continuously and specifically expressed in one of these cell types: Drgx in Tm1, Pdm3 in Tm2, and SoxN in Tm6. We showed that the removal of each of these selectors in these cell types reprograms them to the default Tm4 fate. We validated these conversions using both morphological features and molecular markers. In addition, we performed scRNA-seq to show that ectopic expression of pdm3 in Tm4 and Tm6 neurons converts them to neurons with transcriptomes that are nearly indistinguishable from that of wild-type Tm2 neurons. We also show that Drgx expression in Tm1 neurons is regulated by Klumpfuss, a TF expressed in stem cells that instructs this fate in progenitors, establishing a link between the regulatory programs that specify neuronal fates and those that implement them. We identified an intronic enhancer in the Drgx locus whose chromatin is specifically accessible in Tm1 neurons and in which Klu motifs are enriched. Genomic deletion of this region knocked down Drgx expression specifically in Tm1 neurons, leaving it intact in the other cell types that normally express it. We further validated this concept by demonstrating that ectopic expression of Vsx (visual system homeobox) genes in Mi15 neurons not only converts them morphologically to Dm2 neurons, but also leads to the loss of their aminergic identity. Our results suggest that selector combinations can be further sculpted by receptor tyrosine kinase signaling after neurogenesis, providing a potential mechanism for postmitotic plasticity of neuronal fates. Finally, we combined our transcriptomic datasets with previously generated chromatin accessibility datasets to understand the mechanisms that control brain wiring downstream of terminal selectors. We built predictive computational models of gene regulatory networks using the Inferelator framework. Experimental validations of these networks revealed how selectors interact with ecdysone-responsive TFs to activate a large and specific repertoire of cell surface proteins and other effectors in each neuron at the onset of synapse formation. We showed that these network models can be used to identify downstream effectors that mediate specific cellular decisions during circuit formation. For instance, reduced levels of cut expression in Tm2 neurons, because of its negative regulation by pdm3 , controls the synaptic layer targeting of their axons. Knockdown of cut in Tm1 neurons is sufficient to redirect their axons to the Tm2 layer in the lobula neuropil without affecting other morphological features. CONCLUSION Our results support a model in which neuronal type identity is primarily determined by a relatively simple code of continuously expressed terminal selector TFs in each cell type throughout development. Our results provide a unified framework of how specific fates are initiated and maintained in postmitotic neurons and open new avenues to understanding synaptic specificity through gene regulatory networks. The conservation of this regulatory logic in both C. elegans and Drosophila makes it likely that the terminal selector concept will also be useful in understanding and manipulating the neuronal diversity of mammalian brains. 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