One major challenge in analyzing spatial transcriptomic datasets is to simultaneously incorporate the cell transcriptome similarity and their spatial locations. Here, we introduce SpaceFlow, which generates spatially-consistent low-dimensional embeddings by incorporating both expression similarity and spatial information using spatially regularized deep graph networks. Based on the embedding, we introduce a pseudo-Spatiotemporal Map that integrates the pseudotime concept with spatial locations of the cells to unravel spatiotemporal patterns of cells. By comparing with multiple existing methods on several spatial transcriptomic datasets at both spot and single-cell resolutions, SpaceFlow is shown to produce a robust domain segmentation and identify biologically meaningful spatiotemporal patterns. Applications of SpaceFlow reveal evolving lineage in heart developmental data and tumor-immune interactions in human breast cancer data. Our study provides a flexible deep learning framework to incorporate spatiotemporal information in analyzing spatial transcriptomic data.

The rapid development of spatial transcriptomics (ST) techniques has allowed the measurement of transcriptional levels across many genes together with the spatial positions of cells. This has led to an explosion of interest in computational methods and techniques for harnessing both spatial and transcriptional information in analysis of ST datasets. The wide diversity of approaches in aim, methodology and technology for ST provides great challenges in dissecting cellular functions in spatial contexts. Here, we synthesize and review the key problems in analysis of ST data and methods that are currently applied, while also expanding on open questions and areas of future development.

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5 kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through “flexible” clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, “rigid” clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions.

Our understanding of how chromosomes structurally organize and dynamically interact has been revolutionized through the lens of long-chain polymer physics. Major protein contributors to chromosome structure and dynamics are condensin and cohesin that stochastically generate loops within and between chains, and entrap proximal strands of sister chromatids. In this paper, we explore the ability of transient, protein-mediated, gene-gene crosslinks to induce clusters of genes, thereby dynamic architecture, within the highly repeated ribosomal DNA that comprises the nucleolus of budding yeast. We implement three approaches: live cell microscopy; computational modeling of the full genome during G1 in budding yeast, exploring four decades of timescales for transient crosslinks between 5kbp domains (genes) in the nucleolus on Chromosome XII; and, temporal network models with automated community (cluster) detection algorithms applied to the full range of 4D modeling datasets. The data analysis tools detect and track gene clusters, their size, number, persistence time, and their plasticity (deformation). Of biological significance, our analysis reveals an optimal mean crosslink lifetime that promotes pairwise and cluster gene interactions through "flexible" clustering. In this state, large gene clusters self-assemble yet frequently interact (merge and separate), marked by gene exchanges between clusters, which in turn maximizes global gene interactions in the nucleolus. This regime stands between two limiting cases each with far less global gene interactions: with shorter crosslink lifetimes, "rigid" clustering emerges with clusters that interact infrequently; with longer crosslink lifetimes, there is a dissolution of clusters. These observations are compared with imaging experiments on a normal yeast strain and two condensin-modified mutant cell strains. We apply the same image analysis pipeline to the experimental and simulated datasets, providing support for the modeling predictions. Author SummaryThe spatiotemporal organization of the genome plays an important role in cellular processes involving DNA, but remains poorly understood, especially in the nucleolus, May 21, 2019 1/25 which does not facilitate conventional techniques. Polymer chain models have shown ability in recent years to make accurate predictions of the dynamics of the genome. We consider a polymer bead-chain model of the full yeast genome during the interphase portion of the cell cycle, featuring special dynamic crosslinking to model the effects of structural maintenance proteins in the nucleolus, and investigate how the kinetic timescale on which the crosslinks bind and unbind affects the resulting dynamics inside the nucleolus. It was previously known that when this timescale is sufficiently short, large, stable clusters appear, but when it is long, there is no resulting structure. We find that there additionally exists a range of timescales for which flexible clusters appear, in which beads frequently enter and leave clusters. Furthermore, we demonst...

The rise of machine learning and deep learning technologies have allowed researchers to automate image classification. We describe a method that incorporates automated image classification and principal component analysis to evaluate computational models of biological structures. We use a computational model of the kinetochore to demonstrate our artificial-intelligence (AI)-assisted modeling method. The kinetochore is a large protein complex that connects chromosomes to the mitotic spindle to facilitate proper cell division. The kinetochore can be divided into two regions: the inner kinetochore, including proteins that interact with DNA; and the outer kinetochore, comprised of microtubule-binding proteins. These two kinetochore regions have been shown to have different distributions during metaphase in live budding yeast and therefore act as a test case for our forward modeling technique. We find that a simple convolutional neural net (CNN) can correctly classify fluorescent images of inner and outer kinetochore proteins and show a CNN trained on simulated, fluorescent images can detect difference in experimental images. A polymer model of the ribosomal DNA locus serves as a second test for the method. The nucleolus surrounds the ribosomal DNA locus and appears amorphous in live-cell, fluorescent microscopy experiments in budding yeast, making detection of morphological changes challenging. We show a simple CNN can detect subtle differences in simulated images of the ribosomal DNA locus, demonstrating our CNN-based classification technique can be used on a variety of biological structures.

Understanding information processing in the brain requires the ability to determine the functional connectivity between the different regions of the brain. We present a method using transfer entropy to extract this flow of information between brain regions from spike-train data commonly obtained in neurological experiments. Transfer entropy is a statistical measure based in information theory that attempts to quantify the information flow from one process to another, and has been applied to find connectivity in simulated spike-train data. Due to statistical error in the estimator, inferring functional connectivity requires a method for determining significance in the transfer entropy values. We discuss the issues with numerical estimation of transfer entropy and resulting challenges in determining significance before presenting the trial-shuffle method as a viable option. The trial-shuffle method, for spike-train data that is split into multiple trials, determines significant transfer entropy values independently for each individual pair of neurons by comparing to a created baseline distribution using a rigorous statistical test. This is in contrast to either globally comparing all neuron transfer entropy values or comparing pairwise values to a single baseline value. In establishing the viability of this method by comparison to several alternative approaches in the literature, we find evidence that preserving the inter-spike-interval timing is important. We then use the trial-shuffle method to investigate information flow within a model network as we vary model parameters. This includes investigating the global flow of information within a connectivity network divided into two well-connected subnetworks, going beyond local transfer of information between pairs of neurons.

Modularity-based community detection encompasses a number of widely used, efficient heuristics for identification of structure in networks. Recently, a belief propagation approach to modularity optimization provided a useful guide for identifying nontrivial structure in single-layer networks in a way that other optimization heuristics have not. In this paper, we extend modularity belief propagation to multilayer networks. As part of this development, we also directly incorporate a resolution parameter. We show that adjusting the resolution parameter affects the convergence properties of the algorithm and yields different community structures than the baseline. We compare our approach with a widely used community detection tool, GenLouvain, across a range of synthetic, multilayer benchmark networks, demonstrating that our method performs comparably to the state of the art. Finally, we demonstrate the practical advantages of the additional information provided by our tool by way of two real-world network examples. We show how the convergence properties of the algorithm can be used in selecting the appropriate resolution and coupling parameters and how the node-level marginals provide an interpretation for the strength of attachment to the identified communities. We have released our tool as a Python package for convenient use.

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