Department of Mathematics, UCI

A new mathematical theory is proposed to explain the population size oscillations described in the paper by P. Turchin. The model is based on Turchin's demographic-structural theory and includes the "inertia of war" phenomenon together with the tendency for retribution in military conflicts.

Rosacea is a chronic inflammatory skin disorder, whose underlying cellular and molecular mechanisms remain obscure. Here, we generate a single-cell atlas of facial skin from female rosacea patients and healthy individuals. Among keratinocytes, a subpopulation characterized by IFNγ-mediated barrier function damage is found to be unique to rosacea lesions. Blocking IFNγ signaling alleviates rosacea-like phenotypes and skin barrier damage in mice. The papulopustular rosacea is featured by expansion of pro-inflammatory fibroblasts, Schwann, endothelial and macrophage/dendritic cells. The frequencies of type 1/17 and skin-resident memory T cells are increased, and vascular mural cells are characterized by activation of inflammatory pathways and impaired muscle contraction function in rosacea. Most importantly, fibroblasts are identified as the leading cell type producing pro-inflammatory and vasodilative signals in rosacea. Depletion of fibroblasts or knockdown of PTGDS, a gene specifically upregulated in fibroblasts, blocks rosacea development in mice. Our study provides a comprehensive understanding of the aberrant alterations of skin-resident cell populations and identifies fibroblasts as a key determinant in rosacea development.

From single-cell RNA-sequencing (scRNA-seq) and spatial transcriptomics (ST), one can extract high-dimensional gene expression patterns that can be described by intercellular communication networks or decoupled gene modules. These two descriptions of information flow are often assumed to occur independently. However, intercellular communication drives directed flows of information that are mediated by intracellular gene modules, in turn triggering outflows of other signals. Methodologies to describe such intercellular flows are lacking. We present FlowSig, a method that infers communication-driven intercellular flows from scRNA-seq or ST data using graphical causal modeling and conditional independence. We benchmark FlowSig using newly generated experimental cortical organoid data and synthetic data generated from mathematical modeling. We demonstrate FlowSig's utility by applying it to various studies, showing that FlowSig can capture stimulation-induced changes to paracrine signaling in pancreatic islets, demonstrate shifts in intercellular flows due to increasing COVID-19 severity and reconstruct morphogen-driven activator-inhibitor patterns in mouse embryogenesis.

Understanding cell fate decision-making during complex biological processes is an open challenge that is now aided by high-resolution single-cell sequencing technologies. Specifically, it remains challenging to identify and characterize transition states corresponding to "tipping points" whereby cells commit to new cell states. Here, we present a computational method that takes advantage of single-cell transcriptomics data to infer the stability and gene regulatory networks (GRNs) along cell lineages. Our method uses the unspliced and spliced counts from single-cell RNA sequencing data and cell ordering along lineage trajectories to train an RNA splicing multivariate model, from which cell-state stability along the lineage is inferred based on spectral analysis of the model's Jacobian matrix. Moreover, the model infers the RNA cross-species interactions resulting in GRNs and their variation along the cell lineage. When applied to epithelial-mesenchymal transition in ovarian and lung cancer-derived cell lines, our model predicts a saddle-node transition between the epithelial and mesenchymal states passing through an unstable, intermediate cell state. Furthermore, we show that the underlying GRN controlling epithelial-mesenchymal transition rearranges during the transition, resulting in denser and less modular networks in the intermediate state. Overall, our method represents a flexible tool to study cell lineages with a combination of theory-driven modeling and single-cell transcriptomics data.

The self-organization of cells relies on the profound complexity of protein-protein interactions. Challenges in directly observing these events have hindered progress toward understanding their diverse behaviors. One notable example is the interaction between molecular motors and cytoskeletal systems that combine to perform a variety of cellular functions. In this work, we leverage theory and experiments to identify and quantify the rate-limiting mechanism of the initial association between a cargo-bound kinesin motor and a microtubule track. Recent advances in optical tweezers provide binding times for several lengths of kinesin motors trapped at varying distances from a microtubule, empowering the investigation of competing models. We first explore a diffusion-limited model of binding. Through Brownian dynamics simulations and simulation-based inference, we find this simple diffusion model fails to explain the experimental binding times, but an extended model that accounts for the ADP state of the molecular motor agrees closely with the data, even under the scrutiny of penalizing for additional model complexity. We provide quantification of both kinetic rates and biophysical parameters underlying the proposed binding process. Our model suggests that a typical binding event is limited by ADP state rather than physical search. Lastly, we predict how these association rates can be modulated in distinct ways through variation of environmental concentrations and physical properties.

Phenotypic variation among species is a product of evolutionary changes to developmental programs1,2. However, how these changes generate novel morphological traits remains largely unclear. Here we studied the genomic and developmental basis of the mammalian gliding membrane, or patagium-an adaptative trait that has repeatedly evolved in different lineages, including in closely related marsupial species. Through comparative genomic analysis of 15 marsupial genomes, both from gliding and non-gliding species, we find that the Emx2 locus experienced lineage-specific patterns of accelerated cis-regulatory evolution in gliding species. By combining epigenomics, transcriptomics and in-pouch marsupial transgenics, we show that Emx2 is a critical upstream regulator of patagium development. Moreover, we identify different cis-regulatory elements that may be responsible for driving increased Emx2 expression levels in gliding species. Lastly, using mouse functional experiments, we find evidence that Emx2 expression patterns in gliders may have been modified from a pre-existing program found in all mammals. Together, our results suggest that patagia repeatedly originated through a process of convergent genomic evolution, whereby regulation of Emx2 was altered by distinct cis-regulatory elements in independently evolved species. Thus, different regulatory elements targeting the same key developmental gene may constitute an effective strategy by which natural selection has harnessed regulatory evolution in marsupial genomes to generate phenotypic novelty.

In pursuit of a noncommutative spectrum functor, we argue that the Heyneman-Sweedler finite dual coalgebra can be viewed as a quantization of the maximal spectrum of a commutative affine algebra, integrating prior perspectives of Takeuchi, Batchelor, Kontsevich-Soibelman, and Le Bruyn. We introduce fully residually finite-dimensional algebras A as those with enough finite-dimensional representations to let A∘ act as an appropriate depiction of the noncommutative maximal spectrum of A; importantly, this class includes affine noetherian PI algebras. In the case of prime affine algebras that are module-finite over their center, we describe how the Azumaya locus is represented in the finite dual. This is used to describe the finite dual of quantum planes at roots of unity as an endeavor to visualize the noncommutative space on which these algebras act as functions. Finally, we discuss how a similar analysis can be carried out for other maximal orders over surfaces.

Most online chemical reaction databases are not publicly accessible or are fully downloadable. These databases tend to contain reactions in noncanonicalized formats and often lack comprehensive information regarding reaction pathways, intermediates, and byproducts. Within the few publicly available databases, reactions are typically stored in the form of unbalanced, overall transformations with minimal interpretability of the underlying chemistry. These limitations present significant obstacles to data-driven applications including the development of machine learning models. As an effort to overcome these challenges, we introduce PMechDB, a publicly accessible platform designed to curate, aggregate, and share polar chemical reaction data in the form of elementary reaction steps. Our initial version of PMechDB consists of over 100,000 such steps. In the PMechDB, all reactions are stored as canonicalized and balanced elementary steps, featuring accurate atom mapping and arrow-pushing mechanisms. As an online interactive database, PMechDB provides multiple interfaces that enable users to search, download, and upload chemical reactions. We anticipate that the public availability of PMechDB and its standardized data representation will prove beneficial for chemoinformatics research and education and the development of data-driven, interpretable models for predicting reactions and pathways. PMechDB platform is accessible online at https://deeprxn.ics.uci.edu/pmechdb.

Cutaneous melanomas are clinically and histologically heterogeneous. Most display activating mutations in Braf or Nras and complete loss of function of one or more tumor suppressor genes. Mouse models that replicate such mutations produce fast-growing, pigmented tumors. However, mice that combine Braf activation with only heterozygous loss of Pten also produce tumors and, as we show here, in an Albino background this occurs even with Braf activation alone. Such tumors arise rarely, grow slowly, and express low levels of pigmentation genes. The timing of their appearance was consistent with a single step stochastic event, but no evidence could be found that it required de novo mutation, suggesting instead the involvement of an epigenetic transition. Single-cell transcriptomic analysis revealed such tumors to be heterogeneous, including a minor cell type we term LNM ( L ow-pigment, N eural- and extracellular M atrix-signature) that displays gene expression resembling "neural crest"-like cell subsets detected in the fast-growing tumors of more heavily-mutated mice, as well as in human biopsy and xenograft samples. We provide evidence that LNM cells pre-exist in normal skin, are expanded by Braf activation, can transition into malignant cells, and persist with malignant cells through multiple rounds of transplantation. We discuss the possibility that LNM cells not only serve as a pre-malignant state in the production of some melanomas, but also as an important intermediate in the development of drug resistance.