Department of Mathematics, UCI

The literature about mutant invasion and fixation typically assumes populations to exist in isolation from their ecosystem. Yet, populations are part of ecological communities, and enemy-victim (e.g. predator-prey or pathogen-host) interactions are particularly common. We use spatially explicit, computational pathogen-host models (with wild-type and mutant hosts) to re-visit the established theory about mutant fixation, where the pathogen equally attacks both wild-type and mutant individuals. Mutant fitness is assumed to be unrelated to infection. We find that pathogen presence substantially weakens selection, increasing the fixation probability of disadvantageous mutants and decreasing it for advantageous mutants. The magnitude of the effect rises with the infection rate. This occurs because infection induces spatial structures, where mutant and wild-type individuals are mostly spatially separated. Thus, instead of mutant and wild-type individuals competing with each other, it is mutant and wild-type patches that compete, resulting in smaller fitness differences and weakened selection. This implies that the deleterious mutant burden in natural populations might be higher than expected from traditional theory.

Spatial gene expression in tissue is characterized by regions in which particular genes are enriched or depleted. Frequently, these regions contain nested inside them subregions with distinct expression patterns. Segmentation methods in spatial transcriptomic (ST) data extract disjoint regions maximizing similarity over the greatest number of genes, typically on a particular spatial scale, thus lacking the ability to find region-within-region structure. We present NeST, which extracts spatial structure through coexpression hotspots-regions exhibiting localized spatial coexpression of some set of genes. Coexpression hotspots identify structure on any spatial scale, over any possible subset of genes, and are highly explainable. NeST also performs spatial analysis of cell-cell interactions via ligand-receptor, identifying active areas de novo without restriction of cell type or other groupings, in both two and three dimensions. Through application on ST datasets of varying type and resolution, we demonstrate the ability of NeST to reveal a new level of biological structure.

Cell-cell interactions instruct cell fate and function. These interactions are hijacked to promote cancer development. Single-cell transcriptomics and spatial transcriptomics have become powerful new tools for researchers to profile the transcriptional landscape of cancer at unparalleled genetic depth. In this review, we discuss the rapidly growing array of computational tools to infer cell-cell interactions from non-spatial single-cell RNA-sequencing and the limited but growing number of methods for spatial transcriptomics data. Downstream analyses of these computational tools and applications to cancer studies are highlighted. We finish by suggesting several directions for further extensions that anticipate the increasing availability of multi-omics cancer data.

Macrophages are essential for skeletal muscle homeostasis, but how their dysregulation contributes to the development of fibrosis in muscle disease remains unclear. Here, we used single-cell transcriptomics to determine the molecular attributes of dystrophic and healthy muscle macrophages. We identified six clusters and unexpectedly found that none corresponded to traditional definitions of M1 or M2 macrophages. Rather, the predominant macrophage signature in dystrophic muscle was characterized by high expression of fibrotic factors, galectin-3 (gal-3) and osteopontin (Spp1). Spatial transcriptomics, computational inferences of intercellular communication, and in vitro assays indicated that macrophage-derived Spp1 regulates stromal progenitor differentiation. Gal-3⁺ macrophages were chronically activated in dystrophic muscle, and adoptive transfer assays showed that the gal-3⁺ phenotype was the dominant molecular program induced within the dystrophic milieu. Gal-3⁺ macrophages were also elevated in multiple human myopathies. These studies advance our understanding of macrophages in muscular dystrophy by defining their transcriptional programs and reveal Spp1 as a major regulator of macrophage and stromal progenitor interactions.

Cells make decisions through their communication with other cells and receiving signals from their environment. Using single-cell transcriptomics, computational tools have been developed to infer cell-cell communication through ligands and receptors. However, the existing methods only deal with signals sent by the measured cells in the data, the received signals from the external system are missing in the inference. Here, we present exFINDER, a method that identifies such external signals received by the cells in the single-cell transcriptomics datasets by utilizing the prior knowledge of signaling pathways. In particular, exFINDER can uncover external signals that activate the given target genes, infer the external signal-target signaling network (exSigNet), and perform quantitative analysis on exSigNets. The applications of exFINDER to scRNA-seq datasets from different species demonstrate the accuracy and robustness of identifying external signals, revealing critical transition-related signaling activities, inferring critical external signals and targets, clustering signal-target paths, and evaluating relevant biological events. Overall, exFINDER can be applied to scRNA-seq data to reveal the external signal-associated activities and maybe novel cells that send such signals.

We consider an in-network optimal resource allocation problem in which a group of agents interacting over a connected graph want to meet a demand while minimizing their collective cost. The contribution of this paper is to design a distributed continuous-time algorithm for this problem inspired by a recently developed first-order transformed primal-dual method. The solution applies to cluster-based setting where each agent may have a set of subagents, and its local cost is the sum of the cost of these subagents. The proposed algorithm guarantees an exponential convergence for strongly convex costs and asymptotic convergence for convex costs. Exponential convergence when the local cost functions are strongly convex is achieved even when the local gradients are only locally Lipschitz. For convex local cost functions, our algorithm guarantees asymptotic convergence to a point in the minimizer set. Through numerical examples, we show that our proposed algorithm delivers a faster convergence compared to existing distributed resource allocation algorithms.

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

Niche signals maintain stem cells in a prolonged quiescence or transiently activate them for proper regeneration¹. Altering balanced niche signalling can lead to regenerative disorders. Melanocytic skin nevi in human often display excessive hair growth, suggesting hair stem cell hyperactivity. Here, using genetic mouse models of nevi^2,3, we show that dermal clusters of senescent melanocytes drive epithelial hair stem cells to exit quiescence and change their transcriptome and composition, potently enhancing hair renewal. Nevus melanocytes activate a distinct secretome, enriched for signalling factors. Osteopontin, the leading nevus signalling factor, is both necessary and sufficient to induce hair growth. Injection of osteopontin or its genetic overexpression is sufficient to induce robust hair growth in mice, whereas germline and conditional deletions of either osteopontin or CD44, its cognate receptor on epithelial hair cells, rescue enhanced hair growth induced by dermal nevus melanocytes. Osteopontin is overexpressed in human hairy nevi, and it stimulates new growth of human hair follicles. Although broad accumulation of senescent cells, such as upon ageing or genotoxic stress, is detrimental for the regenerative capacity of tissue⁴, we show that signalling by senescent cell clusters can potently enhance the activity of adjacent intact stem cells and stimulate tissue renewal. This finding identifies senescent cells and their secretome as an attractive therapeutic target in regenerative disorders.

The monocytic/macrophage system is essential for skeletal muscle homeostasis, but its dysregulation contributes to the pathogenesis of muscle degenerative disorders. Despite our increasing knowledge of the role of macrophages in degenerative disease, it still remains unclear how macrophages contribute to muscle fibrosis. Here, we used single-cell transcriptomics to determine the molecular attributes of dystrophic and healthy muscle macrophages. We identified six novel clusters. Unexpectedly, none corresponded to traditional definitions of M1 or M2 macrophage activation. Rather, the predominant macrophage signature in dystrophic muscle was characterized by high expression of fibrotic factors, galectin-3 and spp1. Spatial transcriptomics and computational inferences of intercellular communication indicated that spp1 regulates stromal progenitor and macrophage interactions during muscular dystrophy. Galectin-3 + macrophages were chronically activated in dystrophic muscle and adoptive transfer assays showed that the galectin-3 + phenotype was the dominant molecular program induced within the dystrophic milieu. Histological examination of human muscle biopsies revealed that galectin-3 + macrophages were also elevated in multiple myopathies. These studies advance our understanding of macrophages in muscular dystrophy by defining the transcriptional programs induced in muscle macrophages, and reveal spp1 as a major regulator of macrophage and stromal progenitor interactions.