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Faculty professional development is an important lever for change in supporting instructors to adopt research-based instructional strategies that engage students intellectually, foster learning-supportive attitudes and habits of mind, and strengthen their persistence in mathematics. Yet the literature contains few well-rationalized models for faculty development in higher education. We describe the rationale and design for a model for discipline-based faculty development to support instructional change, and we detail our implementation of this model as applied to intensive workshops on inquiry-based learning (IBL) in college mathematics. These workshops seek to foster post-secondary mathematics instructors' adoption of IBL, to help them adapt inquiry approaches for their classrooms, and ultimately to increase student learning and persistence in science and mathematics. Based on observed faculty needs, four strands of activity help instructors develop a mental model for an IBL classroom, adapt that model to their teaching context, develop facilitation and task-design skills, and plan an IBL mathematics course. Evaluation data from surveys and observations illustrate participant responses to the workshop and its components. The model has been robust across 15 years of workshops implemented by three generations of workshop leaders and its features make it adaptive, strategic, and practical for other faculty developers.

Tumor evolution is driven by the progressive acquisition of genetic and epigenetic alterations that enable uncontrolled growth and expansion to neighboring and distal tissues. The study of phylogenetic relationships between cancer cells provides key insights into these processes. Here, we introduced an evolving lineage-tracing system with a single-cell RNA-seq readout into a mouse model of Kras;Trp53(KP)-driven lung adenocarcinoma and tracked tumor evolution from single-transformed cells to metastatic tumors at unprecedented resolution. We found that the loss of the initial, stable alveolar-type2-like state was accompanied by a transient increase in plasticity. This was followed by the adoption of distinct transcriptional programs that enable rapid expansion and, ultimately, clonal sweep of stable subclones capable of metastasizing. Finally, tumors develop through stereotypical evolutionary trajectories, and perturbing additional tumor suppressors accelerates progression by creating novel trajectories. Our study elucidates the hierarchical nature of tumor evolution and, more broadly, enables in-depth studies of tumor progression.

Detailed phylogenies of tumor populations can recount the history and chronology of critical events during cancer progression, such as metastatic dissemination. We applied a Cas9-based, single-cell lineage tracer to study the rates, routes, and drivers of metastasis in a lung cancer xenograft mouse model. We report deeply resolved phylogenies for tens of thousands of cancer cells traced over months of growth and dissemination. This revealed stark heterogeneity in metastatic capacity, arising from preexisting and heritable differences in gene expression. We demonstrate that these identified genes can drive invasiveness and uncovered an unanticipated suppressive role for KRT17 We also show that metastases disseminated via multidirectional tissue routes and complex seeding topologies. Overall, we demonstrate the power of tracing cancer progression at subclonal resolution and vast scale.

The pairing of CRISPR/Cas9-based gene editing with massively parallel single-cell readouts now enables large-scale lineage tracing. However, the rapid growth in complexity of data from these assays has outpaced our ability to accurately infer phylogenetic relationships. First, we introduce Cassiopeia-a suite of scalable maximum parsimony approaches for tree reconstruction. Second, we provide a simulation framework for evaluating algorithms and exploring lineage tracer design principles. Finally, we generate the most complex experimental lineage tracing dataset to date, 34,557 human cells continuously traced over 15 generations, and use it for benchmarking phylogenetic inference approaches. We show that Cassiopeia outperforms traditional methods by several metrics and under a wide variety of parameter regimes, and provide insight into the principles for the design of improved Cas9-enabled recorders. Together, these should broadly enable large-scale mammalian lineage tracing efforts. Cassiopeia and its benchmarking resources are publicly available at www.github.com/YosefLab/Cassiopeia.

Protein conformations are shaped by cellular environments, but how environmental changes alter the conformational landscapes of specific proteins in vivo remains largely uncharacterized, in part due to the challenge of probing protein structures in living cells. Here, we use deep mutational scanning to investigate how a toxic conformation of α-synuclein, a dynamic protein linked to Parkinson's disease, responds to perturbations of cellular proteostasis. In the context of a course for graduate students in the UCSF Integrative Program in Quantitative Biology, we screened a comprehensive library of α-synuclein missense mutants in yeast cells treated with a variety of small molecules that perturb cellular processes linked to α-synuclein biology and pathobiology. We found that the conformation of α-synuclein previously shown to drive yeast toxicity-an extended, membrane-bound helix-is largely unaffected by these chemical perturbations, underscoring the importance of this conformational state as a driver of cellular toxicity. On the other hand, the chemical perturbations have a significant effect on the ability of mutations to suppress α-synuclein toxicity. Moreover, we find that sequence determinants of α-synuclein toxicity are well described by a simple structural model of the membrane-bound helix. This model predicts that α-synuclein penetrates the membrane to constant depth across its length but that membrane affinity decreases toward the C terminus, which is consistent with orthogonal biophysical measurements. Finally, we discuss how parallelized chemical genetics experiments can provide a robust framework for inquiry-based graduate coursework.

We present Vision, a tool for annotating the sources of variation in single cell RNA-seq data in an automated and scalable manner. Vision operates directly on the manifold of cell-cell similarity and employs a flexible annotation approach that can operate either with or without preconceived stratification of the cells into groups or along a continuum. We demonstrate the utility of Vision in several case studies and show that it can derive important sources of cellular variation and link them to experimental meta-data even with relatively homogeneous sets of cells. Vision produces an interactive, low latency and feature rich web-based report that can be easily shared among researchers, thus facilitating data dissemination and collaboration.

Ontogeny describes the emergence of complex multicellular organisms from single totipotent cells. This field is particularly challenging in mammals, owing to the indeterminate relationship between self-renewal and differentiation, variation in progenitor field sizes, and internal gestation in these animals. Here we present a flexible, high-information, multi-channel molecular recorder with a single-cell readout and apply it as an evolving lineage tracer to assemble mouse cell-fate maps from fertilization through gastrulation. By combining lineage information with single-cell RNA sequencing profiles, we recapitulate canonical developmental relationships between different tissue types and reveal the nearly complete transcriptional convergence of endodermal cells of extra-embryonic and embryonic origins. Finally, we apply our cell-fate maps to estimate the number of embryonic progenitor cells and their degree of asymmetric partitioning during specification. Our approach enables massively parallel, high-resolution recording of lineage and other information in mammalian systems, which will facilitate the construction of a quantitative framework for understanding developmental processes.

Nationwide, many students fail to complete the key mathematics courses that are required for most STEM majors, including Precalculus. This paper describes the rationale, implementation, and impact of the redesign of Precalculus at one regional west coast institution. Prior to the redesign, pass rates in Precalculus were modest (75.8% of all students, calendar years 2009-2014). The redesigned course emphasizes active learning including group work based on conceptual questions and utilizes standards-based grading with a supporting emphasis on growth mindset. In the first three semesters of implementation, 88% of students passed the redesigned course. While the authors focus on the redesign of a Precalculus course, it is our hope that instructors of other core mathematics courses for STEM majors may find information of value in this work.

A significant issue mathematics instructors face is how to cover all the material. Mathematics teachers of all levels have some external and internal pressures to "get through" all the required material. The authors define "the coverage issue" to be the set of difficulties that arise in attempting to cover a lengthy list of topics. Principal among these is that material must be presented quickly, to ensure a course covers all the topics in the syllabus. The authors address coverage versus depth as a false dichotomy, and reframe the issue in terms of critical questions for instructors to consider regarding student learning. They also review some key reasons to favor inquiry-based learning as an approach to undergraduate instruction.

In this article, we describe the development of a lesson plan template and its basis in research. In particular, we summarize research supporting the need for mathematics instructors to build students' conceptual understanding and to engage students throughout instruction. We explain how these elements were incorporated into the lesson plan and include excerpts from sample plans. Then, we describe how this lesson plan template was used as the basis for professional development for local adjunct mathematics instructors, and the participants' evaluation of the experience. Finally, we describe what the authors learned from the evaluation and the participants' lessons.

The author responds to the recent work of Kaminski, Sloutsky, and Heckler (2008) and advances two major concerns about their research and its applicability to learning mathematics: a confounding variable that arises from the mathematical differences between the generic examples and concrete examples poses a threat to the construct validity of the experiments, and the overgeneralization of the success of the treatment, given that the measure of success is a prompted near-transfer task. (Contains 1 table and 1 figure.)

Teaching is often an isolated activity, with experience and intuition the only sources to spur improvement. One way to move teaching from trial-and-error to a systematic effort to apply research-based strategies is by reading pedagogical literature. Pedagogical literature comes in two varieties: general and discipline-specific. As college faculty identify strongly with their disciplines, those who read the literature on effective teaching often rely on discipline-specific sources. This article aims to illustrate the lessons that can be learned from reading the general literature and reviews a sample of the available books on effective teaching.

Significance: Our study harnesses a CRISPR-based method to examine ecDNA biogenesis, uncovering efficient circularization between double-strand breaks. ecDNAs and their corresponding chromosomal scars can form via nonhomologous end joining or microhomology-mediated end joining, but the ecDNA and scar formation processes are distinct. Based on our findings, we establish a mechanistic model of excisional ecDNA formation., (©2024 The Authors; Published by the American Association for Cancer Research.)

Oncogene amplification on extrachromosomal DNA (ecDNA) is strongly associated with treatment resistance and shorter survival for patients with cancer, including patients with glioblastoma. The non-chromosomal inheritance of ecDNA during cell division is a major contributor to intratumoral genetic heterogeneity. At present, the spatial dynamics of ecDNA, and the impact on tumor evolutionary trajectories, are not well understood. Here, we investigate the spatial-temporal evolution of ecDNA and its clinical impact by analyzing tumor samples from 94 treatment-naive human IDH -wildtype glioblastoma patients. We developed a spatial-temporal computational model of ecDNA positive tumors ('SPECIES') that integrates whole-genome sequencing, multi-region DNA FISH, and nascent RNAscope, to provide unique insight into the spatial dynamics of ecDNA evolution. Random segregation in combination with positive selection of ecDNAs induce large, predictable spatial patterns of cell-to-cell ecDNA copy number variation that are highly dependent on the oncogene encoded on the circular DNA. EGFR ecDNAs often reach high mean copy number (mean of 50 copies per tumor cell), are under strong positive selection (mean selection coefficient, s > 2) and do not co-amplify other oncogenes on the same ecDNA particles. In contrast, PDGFRA ecDNAs have lower mean copy number (mean of 15 copies per cell), are under weaker positive selection and frequently co-amplify other oncogenes on the same ecDNA. Evolutionary modeling suggests that EGFR ecDNAs often accumulate prior to clonal expansion. EGFR structural variants, including vIII and c-terminal deletions are under strong positive selection, are found exclusively on ecDNA, and are intermixed with wild-type EGFR ecDNAs. Simulations show EGFRvIII ecDNA likely arises after ecDNA formation in a cell with high wild-type EGFR copy number (> 10) before the onset of the most recent clonal expansion. This remains true even in cases of co-selection and co-amplification of multiple oncogenic ecDNA species in a subset of patients. Overall, our results suggest a potential time window in which early ecDNA detection may provide an opportunity for more effective intervention., Highlights: ecDNA is the most common mechanism of focal oncogene amplification in IDH wt glioblastoma. EGFR and its variants on ecDNA are particularly potent, likely arising early in tumor development, providing a strong oncogenic stimulus to drive tumorigenesis. Wild-type and variant EGFR ecDNA heteroplasmy (co-occurrence) is common with EGFR vIII or c-terminal deletions being derived from EGFR wild-type ecDNA prior to the most recent clonal expansion. Tumors with ecDNA amplified EGFR versus PDGFRA exhibit different evolutionary trajectories. SPECIES model can infer spatial evolutionary dynamics of ecDNA in cancer.A delay between ecDNA accumulation and subsequent oncogenic mutation may give a therapeutic window for early intervention.

Tumor progression is driven by dynamic interactions between cancer cells and their surrounding microenvironment. Investigating the spatiotemporal evolution of tumors can provide crucial insights into how intrinsic changes within cancer cells and extrinsic alterations in the microenvironment cooperate to drive different stages of tumor progression. Here, we integrate high-resolution spatial transcriptomics and evolving lineage tracing technologies to elucidate how tumor expansion, plasticity, and metastasis co-evolve with microenvironmental remodeling in a Kras;p53 -driven mouse model of lung adenocarcinoma. We find that rapid tumor expansion contributes to a hypoxic, immunosuppressive, and fibrotic microenvironment that is associated with the emergence of pro-metastatic cancer cell states. Furthermore, metastases arise from spatially-confined subclones of primary tumors and remodel the distant metastatic niche into a fibrotic, collagen-rich microenvironment. Together, we present a comprehensive dataset integrating spatial assays and lineage tracing to elucidate how sequential changes in cancer cell state and microenvironmental structures cooperate to promote tumor progression., Competing Interests: DECLARATION OF INTERESTS M.G.J. consults for and has equity in Vevo Therapeutics. K.E.Y. is a consultant for Cartography Biosciences. T.J. is a member of the Board of Directors of Amgen and Thermo Fisher Scientific, and a co-Founder of Dragonfly Therapeutics and T2 Biosystems. T.J. serves on the Scientific Advisory Board of Dragonfly Therapeutics, SQZ Biotech, and Skyhawk Therapeutics. T.J. is the President of Break Through Cancer. None of these affiliations represent a conflict of interest with respect to the design or execution of this study or interpretation of data presented in this manuscript. J.S.W. declares outside interest in 5 AM Venture, Amgen, Chroma Medicine, KSQ Therapeutics, Maze Therapeutics, Tenaya Therapeutics, Tessera Therapeutics, Ziada Therapeutics, DEM Biopharma, and Third Rock Ventures. D.Y. declares outside interest in DEM Biopharma.

Extrachromosomal DNA (ecDNA) is a central mechanism for focal oncogene amplification in cancer, occurring in ∼15% of early-stage cancers and ∼30% of late-stage cancers. ecDNAs drive tumor formation, evolution, and drug resistance by dynamically modulating oncogene copy number and rewiring gene-regulatory networks. Elucidating the genomic architecture of ecDNA amplifications is critical for understanding tumor pathology and developing more effective therapies. Paired-end short-read (Illumina) sequencing and mapping have been utilized to represent ecDNA amplifications using a breakpoint graph, in which the inferred architecture of ecDNA is encoded as a cycle in the graph. Traversals of breakpoint graphs have been used to successfully predict ecDNA presence in cancer samples. However, short-read technologies are intrinsically limited in the identification of breakpoints, phasing together complex rearrangements and internal duplications, and deconvolution of cell-to-cell heterogeneity of ecDNA structures. Long-read technologies, such as from Oxford Nanopore Technologies, have the potential to improve inference as the longer reads are better at mapping structural variants and are more likely to span rearranged or duplicated regions. Here, we propose Complete Reconstruction of Amplifications with Long reads (CoRAL) for reconstructing ecDNA architectures using long-read data. CoRAL reconstructs likely cyclic architectures using quadratic programming that simultaneously optimizes parsimony of reconstruction, explained copy number, and consistency of long-read mapping. CoRAL substantially improves reconstructions in extensive simulations and 10 data sets from previously characterized cell lines compared with previous short- and long-read-based tools. As long-read usage becomes widespread, we anticipate that CoRAL will be a valuable tool for profiling the landscape and evolution of focal amplifications in tumors., (© 2024 Zhu et al.; Published by Cold Spring Harbor Laboratory Press.)

Extrachromosomal DNA (ecDNA) is a hallmark of aggressive cancer, contributing to both oncogene amplification and tumor heterogeneity. Here, we used Hi-C, super-resolution imaging, and long-read sequencing to explore the nuclear architecture of MYC -amplified ecDNA in colorectal cancer cells. Intriguingly, we observed frequent spatial proximity between ecDNA and 68 repetitive elements which we called ecDNA-interacting elements or EIEs. To characterize a potential regulatory role of EIEs, we focused on a fragment of the L1M4a1#LINE/L1 which we found to be co-amplified with MYC on ecDNA, gaining enhancer-associated chromatin marks in contrast to its normally silenced state. This EIE, in particular, existed as a naturally occurring structural variant upstream of MYC , gaining oncogenic potential in the transcriptionally permissive ecDNA environment. This EIE sequence is sufficient to enhance MYC expression and is required for cancer cell fitness. These findings suggest that silent repetitive genomic elements can be reactivated on ecDNA, leading to functional cooption and amplification. Repeat element activation on ecDNA represents a mechanism of accelerated evolution and tumor heterogeneity and may have diagnostic and therapeutic potential.

Oncogene amplification on extrachromosomal DNA (ecDNA) is a pervasive driver event in cancer, yet our understanding of how ecDNA forms is limited. Here, we couple a CRISPR-based method for induction of ecDNA with extensive characterization of newly formed ecDNA to examine ecDNA biogenesis. We find that DNA circularization is efficient, irrespective of 3D genome context, with formation of a 1 Mb and 1.8 Mb ecDNA both reaching 15%. We show non-homologous end joining and microhomology mediated end joining both contribute to ecDNA formation, while inhibition of DNA-PKcs and ATM have opposing impacts on ecDNA formation. EcDNA and the corresponding chromosomal excision scar form at significantly different rates and respond differently to DNA-PKcs and ATM inhibition. Taken together, our results support a model of ecDNA formation in which double strand break ends dissociate from their legitimate ligation partners prior to joining of illegitimate ends to form the ecDNA and excision scar., Competing Interests: DISCLOSURE H.Y.C. is a co-founder of Accent Therapeutics, Boundless Bio, Cartography Biosciences, Orbital Therapeutics, and an advisor of 10x Genomics, Arsenal Biosciences, Chroma Medicine, and Spring Discovery. P.S.M. is a co-founder and advisor of Boundless Bio. The remaining authors declare no competing interests.

The chromosomal theory of inheritance has dominated human genetics, including cancer genetics. Genes on the same chromosome segregate together while genes on different chromosomes assort independently, providing a fundamental tenet of Mendelian inheritance. Extrachromosomal DNA (ecDNA) is a frequent event in cancer that drives oncogene amplification, dysregulated gene expression and intratumoral heterogeneity, including through random segregation during cell division. Distinct ecDNA sequences, herein termed ecDNA species, can co-exist to facilitate intermolecular cooperation in cancer cells. However, how multiple ecDNA species within a tumor cell are assorted and maintained across somatic cell generations to drive cancer cell evolution is not known. Here we show that cooperative ecDNA species can be coordinately inherited through mitotic co-segregation. Imaging and single-cell analyses show that multiple ecDNAs encoding distinct oncogenes co-occur and are correlated in copy number in human cancer cells. EcDNA species are coordinately segregated asymmetrically during mitosis, resulting in daughter cells with simultaneous copy number gains in multiple ecDNA species prior to any selection. Computational modeling reveals the quantitative principles of ecDNA co-segregation and co-selection, predicting their observed distributions in cancer cells. Finally, we show that coordinated inheritance of ecDNAs enables co-amplification of specialized ecDNAs containing only enhancer elements and guides therapeutic strategies to jointly deplete cooperating ecDNA oncogenes. Coordinated inheritance of ecDNAs confers stability to oncogene cooperation and novel gene regulatory circuits, allowing winning combinations of epigenetic states to be transmitted across cell generations., Competing Interests: Competing Interests H.Y.C. is a co-founder of Accent Therapeutics, Boundless Bio, Cartography Biosciences, Orbital Therapeutics, and an advisor of 10x Genomics, Arsenal Biosciences, Chroma Medicine, and Spring Discovery. V.B. is a co-founder, paid consultant, SAB member and has equity interest in Boundless Bio, inc. and Abterra, Inc. The terms of this arrangement have been reviewed and approved by the University of California, San Diego in accordance with its conflict-of-interest policies. M.G.J. consults for and holds equity in Vevo Therapeutics. P.S.M. is a co-founder and advisor of Boundless Bio. The remaining authors declare no competing interests.