A self-exciting point process to study multicellular spatial signaling patterns

Answering open questions in biology using spatial genomics and structured methods

Genomics methods have uncovered patterns in a range of biological systems, but obscure important aspects of cell behavior: the shapes, relative locations, movement, and interactions of cells in space. Spatial technologies that collect genomic or epigenomic data while preserving spatial information have begun to overcome these limitations. These new data promise a deeper understanding of the factors that affect cellular behavior, and in particular the ability to directly test existing theories about cell state and variation in the context of morphology, location, motility, and signaling that could not be tested before. Rapid advancements in resolution, ease-of-use, and scale of spatial genomics technologies to address these questions also require an updated toolkit of statistical methods with which to interrogate these data. We present a framework to respond to this new avenue of research: four open biological questions that can now be answered using spatial genomics data paired with methods for analysis. We outline spatial data modalities for each open question that may yield specific insights, discuss how conflicting theories may be tested by comparing the data to conceptual models of biological behavior, and highlight statistical and machine learning-based tools that may prove particularly helpful to recover biological understanding.

Trapping of single diffusing particles by a circular disk on a reflecting flat surface. Absorbing hemisphere approximation

Recent progress in biophysics (for example, in studies of chemical sensing and spatiotemporal cell-signaling) poses new challenges to statistical theory of trapping of single diffusing particles. Here we deal with one of them, namely, trapping kinetics of single particles diffusing in a half-space bounded by a reflecting flat surface containing an absorbing circular disk. This trapping problem is essentially two-dimensional and the question of the angular dependence of the kinetics on the particle starting point is highly nontrivial. We propose an approximate approach to the problem that replaces the absorbing disk by an absorbing hemisphere of a properly chosen radius. This replacement makes the problem angular-independent and essentially one-dimensional. After the replacement one can find an exact solution for the particle propagator (Green's function) that allows one to completely characterize the kinetics. Extensive testing of the theoretical predictions based on the absorbing hemisphere approximation against three-dimensional Brownian dynamics simulations shows excellent agreement between the analytical and simulation results when the particle starts sufficiently far away from the disk. Our approach fails and the angular dependence of the kinetics is important when the distance of the particle starting point from the disk center is comparable with the disk radius. However, even when the initial distance is only two disk radii, the maximum relative error of the theoretical predictions is about 10%. The relative error rapidly decreases as the initial distance increases.

Towards 'end-to-end' analysis and understanding of biological timecourse data

Petabytes of increasingly complex and multidimensional live cell and tissue imaging data are generated every year. These videos hold large promise for understanding biology at a deep and fundamental level, as they capture single-cell and multicellular events occurring over time and space. However, the current modalities for analysis and mining of these data are scattered and user-specific, preventing more unified analyses from being performed over different datasets and obscuring possible scientific insights. Here, we propose a unified pipeline for storage, segmentation, analysis, and statistical parametrization of live cell imaging datasets.

Learning the rules of collective cell migration using deep attention networks

Collective, coordinated cellular motions underpin key processes in all multicellular organisms, yet it has been difficult to simultaneously express the ‘rules’ behind these motions in clear, interpretable forms that effectively capture high-dimensional cell-cell interaction dynamics in a manner that is intuitive to the researcher. Here we apply deep attention networks to analyze several canonical living tissues systems and present the underlying collective migration rules for each tissue type using only cell migration trajectory data. We use these networks to learn the behaviors of key tissue types with distinct collective behaviors—epithelial, endothelial, and metastatic breast cancer cells—and show how the results complement traditional biophysical approaches. In particular, we present attention maps indicating the relative influence of neighboring cells to the learned turning decisions of a ‘focal cell’–the primary cell of interest in a collective setting. Colloquially, we refer to this learned relative influence as ‘attention’, as it serves as a proxy for the physical parameters modifying the focal cell’s future motion as a function of each neighbor cell. These attention networks reveal distinct patterns of influence and attention unique to each model tissue. Endothelial cells exhibit tightly focused attention on their immediate forward-most neighbors, while cells in more expansile epithelial tissues are more broadly influenced by neighbors in a relatively large forward sector. Attention maps of ensembles of more mesenchymal, metastatic cells reveal completely symmetric attention patterns, indicating the lack of any particular coordination or direction of interest. Moreover, we show how attention networks are capable of detecting and learning how these rules change based on biophysical context, such as location within the tissue and cellular crowding. That these results require only cellular trajectories and no modeling assumptions highlights the potential of attention networks for providing further biological insights into complex cellular systems.

Collective behaviors are crucial to the function of multicellular life, with large-scale, coordinated cell migration enabling processes spanning organ formation to coordinated skin healing. However, we lack effective tools to discover and cleanly express collective rules at the level of an individual cell. Here, we employ a carefully structured neural network to extract collective information directly from cell trajectory data. The network is trained on data from various systems, including canonical collective cell systems (HUVEC and MDCK cells) which display visually distinct forms of collective motion, and metastatic cancer cells (MDA-MB-231) which are highly uncoordinated. Using these trained networks, we can produce attention maps for each system, which indicate how a cell within a tissue takes in information from its surrounding neighbors, as a function of weights assigned to those neighbors. Thus for a cell type in which cells tend to follow the path of the cell in front, the attention maps will display high weights for cells spatially forward of the focal cell. We present results in terms of additional metrics, such as accuracy plots and number of interacting cells, and encourage future development of improved metrics.

Forecasting cellular states: from descriptive to predictive biology via single-cell multiomics

As the single cell field races to characterize each cell type, state, and behavior, the complexity of the computational analysis approaches the complexity of the biological systems. Single cell and imaging technologies now enable unprecedented measurements of state transitions in biological systems, providing high-throughput data that capture tens-of-thousands of measurements on hundreds-of-thousands of samples. Thus, the definition of cell type and state is evolving to encompass the broad range of biological questions now attainable. To answer these questions requires the development of computational tools for integrated multi-omics analysis. Merged with mathematical models, these algorithms will be able to forecast future states of biological systems, going from statistical inferences of phenotypes to time course predictions of the biological systems with dynamic maps analogous to weather systems. Thus, systems biology for forecasting biological system dynamics from multi-omic data represents the future of cell biology empowering a new generation of technology-driven predictive medicine.