Case Studies in Spatial Point Process Modeling: 185 (Lecture Notes in Statistics)

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At day 80, MUC6 is farthest to Group 1 among 17 genes, but is the fifth closest to Group 1 at day This suggests that MUC6 might play a particularly dynamic role in islet development. To characterize the spatial distribution of the expression level among different genes, we carried out the analysis based on a statistical model.

Advances in Applied Probability

Here we use the multitype Strauss process model 26 , The statistical model is evaluated on two simulated datasets and shown to successfully capture the gene-gene spatial correlations. We compared our multitype Strauss model with two other methods— a baseline model with preliminary statistics and a pairwise Strauss process model. The multitype model significantly outperformed the other models in its ability to distinguish between spatial correlation and spatial co-occurrence.

In the experiment, to increase the resolution of our analysis we applied this model within each cluster of endocrine cells to test for clustering or inhibition effects among these cells. One plausible explanation for the observed lack of correlation is that the selected genes are distinctive of different cell types.


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Within the forming pancreatic islets at this developmental stage, there seem to be no evident clustering effect between distinct cells types bringing them physically close to each other. The positive spatial correlation observed between MUC6 and stem cell markers is certainly interesting because it may indicate a potential role of MUC6 in the differentiation of precursor cells into endocrine cells. Most in situ transcriptomic studies have so far focused on identification and localization of specific cell types in different organs, mapping data obtained by single-cell RNA sequencing back to tissue sections.

Fewer studies have focused at identifying the relations in gene expression between cell types or to other structural and morphological features of the tissue 12 , 28 , We describe a general analysis tool for spatial correlations of gene expression and carry out temporal study of in situ sequencing data on human fetal pancreas at three developmental ages. We increase the efficiency of the method by probing multiple sites on each transcript and adopting a combinatorial hybridization readout.

A density profile-based method is proposed to study the distribution of transcripts in relation to tissue structures and a statistical model is built to study the spatial correlation between transcripts. The difference between the profiles of each transcript allows us to identify two groups of genes. Notably, we are able to analyze the profiles at different time points and observe how clusters of genes markedly separate from each other. Analyzing samples at three time points, we are able to capture the temporal distribution of single genes within the clusters.

We show that MUC6 distribution profile becomes more similar to the group of genes containing endocrine markers and this may indicate a previously unknown role of this gene in the development of pancreatic endocrine cells. The role of mucins genes in the fetal development of several human organs is already known Also, MUC6 expression has been identified as an early event in certain pancreatic cancers 31 , Our spatial analysis shows that MUC6 distribution positively correlates with other stemness genes and its gene expression clusters with forming endocrine islets following a temporal trend.

Altogether these observations identify MUC6 as a candidate marker gene of endocrine differentiation. Notably, other genes of the mucins gene family are present in our panel, but none show strong spatial correlation with endocrine cell or stemness markers. This might be due to low expression of these genes at the analyzed timepoints combined with the limited detection efficiency of our method.

Our novel computational tool could be used in combination with such molecular methods increasing the resolution and the sensitivity of our gene spatial correlation analysis.

Implementations of methods

Our density profile-based method is a powerful tool to identify genes of interest at a whole-tissue level. We show that we can increase the resolution of the spatial analysis by applying our statistical model to genes expressed within clusters of endocrine cells. We find that most gene expressions within identified clusters of endocrine cells are not correlated with each other at the examined time points. In this work, we applied our statistical tool to the analysis of human fetal pancreas. Understanding the molecular components which contribute to pancreas development will have direct implication for the clinical treatment of diabetes.

Recently, a novel model of pancreas development has been proposed which contradicts the most recent description of how precursor endocrine cells differentiate and form adult islets 33 and highlights the necessity of refining our knowledge on how human tissues develop. Emerging molecular technologies such as single-cell RNA sequencing and 3D imaging of whole-mount organs are pivotal in advancing such knowledge and the tool we described in this work can contribute to such understanding by analyzing spatiotemporal gene interactions and identifying genes involved in a specific developmental process.

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In conclusion, we present a novel method to analyze spatially-resolved transcriptomic dataset which is widely applicable to different technologies and applications. We describe a novel way to explore gene expression data which can be now produced in high throughput by a number of imaged-based techniques. For instance, we demonstrate our method on in situ sequencing data, but the same analysis is applicable to other FISH-based assays.

Developmental biology is an ideal application for spatially and temporal-resolved transcriptomic analysis and we demonstrate that our tool can be used to explore and identify potentially novel gene expression patterns and temporal changes. Moreover, our method can be applied to investigate other biological questions as well.

The Human Cell Atlas initiative aims to profile the gene expression of all the cells composing the human body Our method could be used to measure spatial relationships of specific genes in normal tissues and compare them to diseased ones, identifying candidate target genes for diagnostics and treatment.

Most figures in this paper can be reproduced with the codes and datasets in the GitHub repository. Janiszewska, M. In situ single-cell analysis identifies heterogeneity for pik3ca mutation and her2 amplification in her2-positive breast cancer. Nature genetics 47 , Grundberg, I. In situ mutation detection and visualization of intratumor heterogeneity for cancer research and diagnostics.

Oncotarget 4 , Huang, S. Non-genetic heterogeneity of cells in development: more than just noise.

Noel Cressie: Research Publications

Development , — OHuallachain, M. Extensive genetic variation in somatic human tissues. Proceedings of the National Academy of Sciences , — Ke, R. In situ sequencing for rna analysis in preserved tissue and cells. Nature methods 10 , Lee, J. Highly multiplexed subcellular rna sequencing in situ.

Science , — Chen, K. Spatially resolved, highly multiplexed rna profiling in single cells. Science , aaa Shah, S. In situ transcription profiling of single cells reveals spatial organization of cells in the mouse hippocampus. Neuron 92 , — Lein, E. The promise of spatial transcriptomics for neuroscience in the era of molecular cell typing. Science , 64—69 La Manno, G. Molecular diversity of midbrain development in mouse, human, and stem cells.

Cell , — Mignardi, M. Bridging histology and bioinformaticscomputational analysis of spatially resolved transcriptomics.

Poisson process 1 - Probability and Statistics - Khan Academy

Proceedings of the IEEE , — Svensson, V. Spatialde: identification of spatially variable genes. Nature methods 15 , Crosetto, N. Spatially resolved transcriptomics and beyond. Nature Reviews Genetics 16 , 57 Valm, A.

7. Spatial Point Pattern Analysis

Systems-level analysis of microbial community organization through combinatorial labeling and spectral imaging. Lubeck, E. Single-cell systems biology by super-resolution imaging and combinatorial labeling. Nature methods 9 , Darmanis, S. Single-cell rna-seq analysis of infiltrating neoplastic cells at the migrating front of human glioblastoma.


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  • Cell reports 21 , — Hellman, B. Actual distribution of the number and volume of the islets of langerhans in different size classes in non-diabetic humans of varying ages. Nature , Bosco, D.