DifferentialEquations.jl is a package for solving differential equations in Julia. It covers discrete equations (function maps, discrete stochastic (Gillespie/Markov) simulations), ordinary differential equations, stochastic differential equations, algebraic differential equations, delay differential equations, hybrid differential equations, jump diffusions, and (stochastic) partial differential equations. Through extensive use of multiple dispatch, metaprogramming, plot recipes, foreign function interfaces (FFI), and call-overloading, DifferentialEquations.jl offers a unified user interface to solve and analyze various forms of differential equations while not sacrificing features or performance. Many modern features are integrated into the solvers, such as allowing arbitrary user-defined number systems for high-precision and arithmetic with physical units, built-in multithreading and parallelism, and symbolic calculation of Jacobians. Integrated into the package is an algorithm testing and benchmarking suite to both ensure accuracy and serve as an easy way for researchers to develop and distribute their own methods. Together, these features build a highly extendable suite which is feature-rich and highly performant.

We study solid tumor ( carcinoma) growth in the nonlinear regime using boundary-integral simulations. The tumor core is nonnecrotic and no inhibitor chemical species are present. A new formulation of the classical models [18,24,8,3] is developed and it is demonstrated that tumor evolution is described by a reduced set of two dimensionless parameters and is qualitatively unaffected by the number of spatial dimensions. One parameter describes the relative rate of mitosis to the relaxation mechanisms (cell mobility and cell-to-cell adhesion). The other describes the balance between apoptosis (programmed cell-death) and mitosis. Both parameters also include the effect of vascularization. Our analysis and nonlinear simulations reveal that the two new dimensionless groups uniquely subdivide tumor growth into three regimes associated with increasing degrees of vascularization: low (diffusion dominated, e.g., in vitro), moderate and high vascularization, that correspond to the regimes observed in vivo. We demonstrate that critical conditions exist for which the tumor evolves to nontrivial dormant states or grows self-similarly (i.e., shape invariant) in the first two regimes. This leads to the possibility of shape control and of controlling the release of tumor angiogenic factors by restricting the tumor volume-to-surface-area ratio. Away from these critical conditions, evolution may be unstable leading to invasive fingering into the external tissues and to topological transitions such as tumor breakup and reconnection. Interestingly we find that for highly vascularized tumors, while they grow unbounded, their shape always stays compact and invasive fingering does not occur. This is in agreement with recent experimental observations [30] of in vivo tumor growth, and suggests that the invasive growth of highly-vascularized tumors is associated to vascular and elastic anisotropies, which are not included in the model studied here.

Many patterns of cell and tissue organization are specified during development by gradients of morphogens, substances that assign different cell fates at different concentrations. Gradients form by morphogen transport from a localized site, but whether this occurs by simple diffusion or by more elaborate mechanisms is unclear. We attempt to resolve this controversy by analyzing recent data in ways that appropriately capture the complexity of systems in which transport, receptor interaction, endo- and exocytosis, and degradation occur together. We find that diffusive mechanisms of morphogen transport are much more plausible-and nondiffusive mechanisms much less plausible-than has generally been argued. Moreover, we show that a class of experiments, endocytic blockade, thought to effectively distinguish between diffusive and nondiffusive transport models actually fails to draw useful distinctions.

It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors (“chalones”) may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives—what, precisely, is being controlled, and to what degree—and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE—the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue—fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules—such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator—may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.

To investigate the evolutionary history of the recent outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in China, a total of 70 genomes of virus strains from China and elsewhere with sampling dates between 24 December 2019 and 3 February 2020 were analyzed. To explore the potential intermediate animal host of the SARS-CoV-2 virus, we reanalyzed virome data sets from pangolins and representative SARS-related coronaviruses isolates from bats, with particular attention paid to the spike glycoprotein gene. We performed phylogenetic, split network, transmission network, likelihood-mapping, and comparative analyses of the genomes. Based on Bayesian time-scaled phylogenetic analysis using the tip-dating method, we estimated the time to the most recent common ancestor and evolutionary rate of SARS-CoV-2, which ranged from 22 to 24 November 2019 and 1.19 to 1.31 × 10 −3 substitutions per site per year, respectively. Our results also revealed that the BetaCoV/bat/Yunnan/RaTG13/2013 virus was more similar to the SARS-CoV-2 virus than the coronavirus obtained from the two pangolin samples (SRR10168377 and SRR10168378). We also identified a unique peptide (PRRA) insertion in the human SARS-CoV-2 virus, which may be involved in the proteolytic cleavage of the spike protein by cellular proteases, and thus could impact host range and transmissibility. Interestingly, the coronavirus carried by pangolins did not have the RRAR motif. Therefore, we concluded that the human SARS-CoV-2 virus, which is responsible for the recent outbreak of COVID-19, did not come directly from pangolins. K E Y W O R D S COVID-19, cross-species transmission, evolutionary rate, potential intermediate animal host, SARS-CoV-2, TMRCA

Understanding global communications among cells requires accurate representation of cell-cell signaling links and effective systems-level analyses of those links. We constructed a database of interactions among ligands, receptors and their cofactors that accurately represents known heteromeric molecular complexes. Based on mass action models, we then developed CellChat, a tool that is able to quantitively infer and analyze intercellular communication networks from single-cell RNA-sequencing (scRNA-seq) data. CellChat predicts major signaling inputs and outputs for cells and how those cells and signals coordinate for functions using network analysis and pattern recognition approaches. Through manifold learning and quantitative contrasts, CellChat classifies signaling pathways and delineates conserved and context-specific pathways across different datasets. Applications of CellChat to several mouse skin scRNA-seq datasets for embryonic development and adult wound healing shows its ability to extract complex signaling patterns, both previously known as well as novel. Our versatile and easy-to-use toolkit CellChat and a web-based Explorer (http://www.cellchat.org/) will help discover novel intercellular communications and build a cell-cell communication atlas in diverse tissues.

During wound healing in adult mouse skin, hair follicles and then adipocytes regenerate. Adipocytes regenerate from myofibroblasts, a specialized contractile wound fibroblast. Here we study wound fibroblast diversity using single-cell RNA-sequencing. On analysis, wound fibroblasts group into twelve clusters. Pseudotime and RNA velocity analyses reveal that some clusters likely represent consecutive differentiation states toward a contractile phenotype, while others appear to represent distinct fibroblast lineages. One subset of fibroblasts expresses hematopoietic markers, suggesting their myeloid origin. We validate this finding using single-cell western blot and single-cell RNA-sequencing on genetically labeled myofibroblasts. Using bone marrow transplantation and Cre recombinase-based lineage tracing experiments, we rule out cell fusion events and confirm that hematopoietic lineage cells give rise to a subset of myofibroblasts and rare regenerated adipocytes. In conclusion, our study reveals that wounding induces a high degree of heterogeneity among fibroblasts and recruits highly plastic myeloid cells that contribute to adipocyte regeneration.

Reversible epithelial-to-mesenchymal transition (EMT) is central to tissue development, epithelial stemness, and cancer metastasis. While many regulatory elements have been identified to induce EMT, the complex process underlying such cellular plasticity remains poorly understood. Utilizing a systems biology approach integrating modeling and experiments, we found multiple intermediate states contributing to EMT and that the robustness of the transitions is modulated by transcriptional factor Ovol2. In particular, we obtained evidence for a mutual inhibition relationship between Ovol2 and EMT inducer Zeb1, and observed that adding this regulation generates a novel four-state system consisting of two distinct intermediate phenotypes that differ in differentiation propensities and are favored in different environmental conditions. We identified epithelial cells that naturally exist in an intermediate state with bidirectional differentiation potential, and found the balance between EMT-promoting and -inhibiting factors to be critical in achieving and selecting between intermediate states. Our analysis suggests a new design principle in controlling cellular plasticity through multiple intermediate cell fates and underscores the critical involvement of Ovol2 and its associated molecular regulations.