Department of Mathematics, UCI

As the circadian clock regulates fundamental biological processes, disrupted clocks are often observed in patients and diseased tissues. Determining the circadian time of the patient or the tissue of focus is essential in circadian medicine and research. Here we present tauFisher, a computational pipeline that accurately predicts circadian time from a single transcriptomic sample by finding correlations between rhythmic genes within the sample. We demonstrate tauFishers performance in adding timestamps to both bulk and single-cell transcriptomic samples collected from multiple tissue types and experimental settings. Application of tauFisher at a cell-type level in a single-cell RNAseq dataset collected from mouse dermal skin implies that greater circadian phase heterogeneity may explain the dampened rhythm of collective core clock gene expression in dermal immune cells compared to dermal fibroblasts. Given its robustness and generalizability across assay platforms, experimental setups, and tissue types, as well as its potential application in single-cell RNAseq data analysis, tauFisher is a promising tool that facilitates circadian medicine and research.

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.

Angiogenesis is a morphogenic process resulting in the formation of new blood vessels from pre-existing ones, usually in hypoxic micro-environments. The initial steps of angiogenesis depend on robust differentiation of oligopotent endothelial cells into the Tip and Stalk phenotypic cell fates, controlled by NOTCH-dependent cell-cell communication. The dynamics of spatial patterning of this cell fate specification are only partially understood. Here, by combining a controlled experimental angiogenesis model with mathematical and computational analyses, we find that the regular spatial Tip-Stalk cell patterning can undergo an order-disorder transition at a relatively high input level of a pro-angiogenic factor VEGF. The resulting differentiation is robust but temporally unstable for most cells, with only a subset of presumptive Tip cells leading sprout extensions. We further find that sprouts form in a manner maximizing their mutual distance, consistent with a Turing-like model that may depend on local enrichment and depletion of fibronectin. Together, our data suggest that NOTCH signaling mediates a robust way of cell differentiation enabling but not instructing subsequent steps in angiogenic morphogenesis, which may require additional cues and self-organization mechanisms. This analysis can assist in further understanding of cell plasticity underlying angiogenesis and other complex morphogenic processes.

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.

Time-series single-cell RNA sequencing (scRNA-seq) datasets provide unprecedented opportunities to learn dynamic processes of cellular systems. Due to the destructive nature of sequencing, it remains challenging to link the scRNA-seq snapshots sampled at different time points. Here we present TIGON, a dynamic, unbalanced optimal transport algorithm that reconstructs dynamic trajectories and population growth simultaneously as well as the underlying gene regulatory network from multiple snapshots. To tackle the high-dimensional optimal transport problem, we introduce a deep learning method using a dimensionless formulation based on the Wasserstein-Fisher-Rao (WFR) distance. TIGON is evaluated on simulated data and compared with existing methods for its robustness and accuracy in predicting cell state transition and cell population growth. Using three scRNA-seq datasets, we show the importance of growth in the temporal inference, TIGONs capability in reconstructing gene expression at unmeasured time points and its applications to temporal gene regulatory networks and cell-cell communication inference.

Animal pigment patterns are excellent models to elucidate mechanisms of biological organization. Although theoretical simulations, such as Turing reaction-diffusion systems, recapitulate many animal patterns, they are insufficient to account for those showing a high degree of spatial organization and reproducibility. Here, we study the coat of the African striped mouse (Rhabdomys pumilio) to uncover how periodic stripes form. Combining transcriptomics, mathematical modelling and mouse transgenics, we show that the Wnt modulator Sfrp2 regulates the distribution of hair follicles and establishes an embryonic prepattern that foreshadows pigment stripes. Moreover, by developing in vivo gene editing in striped mice, we find that Sfrp2 knockout is sufficient to alter the stripe pattern. Strikingly, mutants exhibited changes in pigmentation, revealing that Sfrp2 also regulates hair colour. Lastly, through evolutionary analyses, we find that striped mice have evolved lineage-specific changes in regulatory elements surrounding Sfrp2, many of which may be implicated in modulating the expression of this gene. Altogether, our results show that a single factor controls coat pattern formation by acting both as an orienting signalling mechanism and a modulator of pigmentation. More broadly, our work provides insights into how spatial patterns are established in developing embryos and the mechanisms by which phenotypic novelty originates.

The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to perform maximum a posteriori estimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra.

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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.