A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits.

The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the exact Gillespie algorithm using smooth functions, allowing for the calculation of gradients using backpropagation. The DGA can be used to quickly and accurately learn kinetic parameters using gradient descent and design biochemical networks with desired properties. As an illustration, we apply the DGA to study stochastic models of gene promoters. We show that the DGA can be used to: (i) successfully learn kinetic parameters from experimental measurements of mRNA expression levels from two distinct E. coli promoters and (ii) design nonequilibrium promoter architectures with desired input-output relationships. These examples illustrate the utility of the DGA for analyzing stochastic chemical kinetics, including a wide variety of problems of interest to synthetic and systems biology.

Phase Transition to Chaos in Complex Ecosystems with Nonreciprocal Species-Resource Interactions.

Nonreciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of nonreciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of nonreciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how nonreciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.

Generation of human alveolar epithelial type I cells from pluripotent stem cells.

Alveolar epithelial type I cells (AT1s) line the gas exchange barrier of the distal lung and have been historically challenging to isolate or maintain in cell culture. Here, we engineer a human in vitro AT1 model system via directed differentiation of induced pluripotent stem cells (iPSCs). We use primary adult AT1 global transcriptomes to suggest benchmarks and pathways, such as Hippo-LATS-YAP/TAZ signaling, enriched in these cells. Next, we generate iPSC-derived alveolar epithelial type II cells (AT2s) and find that nuclear YAP signaling is sufficient to promote a broad transcriptomic shift from AT2 to AT1 gene programs. The resulting cells express a molecular, morphologic, and functional phenotype reminiscent of human AT1 cells, including the capacity to form a flat epithelial barrier producing characteristic extracellular matrix molecules and secreted ligands. Our results provide an in vitro model of human alveolar epithelial differentiation and a potential source of human AT1s.

A universal niche geometry governs the response of ecosystems to environmental perturbations.

How ecosystems respond to environmental perturbations is a fundamental question in ecology, made especially challenging due to the strong coupling between species and their environment. Here, we introduce a theoretical framework for calculating the linear response of ecosystems to environmental perturbations in generalized consumer-resource models. Our construction is applicable to a wide class of systems, including models with non-reciprocal interactions, cross-feeding, and non-linear growth/consumption rates. Within our framework, all ecological variables are embedded into four distinct vector spaces and ecological interactions are represented by geometric transformations between these spaces. We show that near a steady state, such geometric transformations directly map environmental perturbations - in resource availability and mortality rates - to shifts in niche structure. We illustrate these ideas in a variety of settings including a minimal model for pH-induced toxicity in bacterial denitrification.

Les Houches Lectures on Community Ecology: From Niche Theory to Statistical Mechanics.

Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and statistical physics. We start by introducing the two classes of mathematical models that have served as the workhorses of community ecology: Consumer Resource Models (CRM) and the generalized Lotka-Volterra models (GLV). We place a special emphasis on graphical methods and general principles. We then review recent works showing a deep and surprising connection between ecological dynamics and constrained optimization. We then shift our focus by analyzing these same models in "high-dimensions" (i.e. in the limit where the number of species and resources in the ecosystem becomes large) and discuss how such complex ecosystems can be analyzed using methods from the statistical physics of disordered systems such as the cavity method and Random Matrix Theory.

Emergent competition shapes top-down versus bottom-up control in multi-trophic ecosystems.

Ecosystems are commonly organized into trophic levels-organisms that occupy the same level in a food chain (e.g., plants, herbivores, carnivores). A fundamental question in theoretical ecology is how the interplay between trophic structure, diversity, and competition shapes the properties of ecosystems. To address this problem, we analyze a generalized Consumer Resource Model with three trophic levels using the zero-temperature cavity method and numerical simulations. We derive the corresponding mean-field cavity equations and show that intra-trophic diversity gives rise to an effective "emergent competition" term between species within a trophic level due to feedbacks mediated by other trophic levels. This emergent competition gives rise to a crossover from a regime of top-down control (populations are limited by predators) to a regime of bottom-up control (populations are limited by primary producers) and is captured by a simple order parameter related to the ratio of surviving species in different trophic levels. We show that our theoretical results agree with empirical observations, suggesting that the theoretical approach outlined here can be used to understand complex ecosystems with multiple trophic levels.

Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions.

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of non-reciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how non-reciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.

Posterior Lateral Arthrodesis as a Treatment Option for Lumbar Spinal Stenosis: Safety and Early Clinical Outcomes.

Introduction: Lumbar spinal stenosis (LSS) is a common condition caused by degenerative changes in the lumbar spine with age. LSS is caused by a variety of factors, including degenerative spondylosis and spondylolisthesis. People suffering with LSS experience neurogenic claudication, which causes severe physical limitations, discomfort, and a decrease in quality of life. Less invasive procedures are now being researched to improve the prognosis, success rate, and safety of LSS treatments. Posterior lateral spinal arthrodesis (PLSA) is a new surgical treatment for LSS. This study looks at the procedural and patient safety of PLSA. Materials and methods: This study is a multicenter retrospective analysis of the safety of PLSA who met the clinical indications for PLSA and underwent the procedure at eight interventional spine practices. Data was collected on demographical information, pre-procedural numeric rating scale score (NRS), post-procedural NRS, and complication reporting. Patients who were included had LSS with or without spondylolisthesis and had failed conservative treatments. A descriptive statistical analysis was performed to report the outcomes. Results were reported as mean and standard deviations for continuous outcomes, and frequency (%) for categorical outcomes. Results: This retrospective analysis involved 191 patients and 202 PLSA implants. The majority of patients were male Caucasians with a mean age of 69.2 years and a BMI of 31.1. A large majority of implants were placed at the L4-5 level, and the average pre-procedural NRS was 6.3 while the average post-procedural NRS was 3.1, indicating a 50.8% reduction in pain (p < 0.0001). Two patients reported complications, but they were unrelated to the device or surgical procedure; no infections, device malfunctions, or migrations were reported in the patient cohort. Conclusion: Preliminary results with PLSA implants indicate that it is a safe treatment option for patients with moderate LSS who do not respond to conservative management.

Comparison of Contrast-Enhanced 3D Imaging with 2D Imaging in the Evaluation of Perianal Fistula at 3T: A Prospective Observational Study.

Introduction Perianal fistula and its recurrence is a challenging entity for surgeons. It is a well-establi1shed fact that magnetic resonance imaging (MRI) findings influence surgical procedures and reduce the rate of recurrence. In this study, we assessed the contrast-enhanced (CE) three dimensional T1 sequences [sampling perfection with application optimized contrast using different flip angle evolution (SPACE) and volumetric interpolated breath-hold examination (VIBE)] in a 3T MRI system to evaluate perianal fistulas and compared them with two-dimensional (2D) sequences. Materials and Methods Forty-four patients (mean age, 38.8 ± 15.3 [standard deviation]; 32 males, 12 females) with perianal fistula were included in this prospective study. The patients underwent conventional noncontrast, 2D sequences, diffusion-weighted imaging, followed by postcontrast, 2D T1 images in both axial and coronal planes, and 3D sequences at 3T. Acquisition times were recorded for each sequence. Each postcontrast sequence was evaluated in terms of image quality, presence of artifacts, fistula type, presence of an abscess, visibility, and number of internal orifices. The surgical findings were considered the gold standard. The imaging findings were compared with the surgical findings. Results In all three sequences, the fistula type and abscess were identified correctly in all patients. The sensitivity value for identification of ramifications utilizing CE 3D T1 VIBE sequence, CE 3D T1 SPACE, and CE 2D T1 images was 100, 86, and 36%, respectively. The number of internal orifices was identified by the CE 3D T1 VIBE and CE 3D T1 SPACE sequences in 100 and 92% of patients, respectively. CE 2D T1 images correctly identified internal orifices in 80% of patients. The overall scan time for each 3D sequence was shorter than for the combined postcontrast 2D sequences. Conclusion CE 3D T1 SPACE and CE 3D T1 VIBE sequences outperformed conventional CE 2D sequences in the evaluation of perianal fistulas in terms of visibility and the number of internal orifices with a shorter scanning time. Among the 3D sequences, CE 3D T1 VIBE is slightly superior to CE 3D T1 SPACE sequence.

Metabolic similarity and the predictability of microbial community assembly.

When microbial communities form, their composition is shaped by selective pressures imposed by the environment. Can we predict which communities will assemble under different environmental conditions? Here, we hypothesize that quantitative similarities in metabolic traits across metabolically similar environments lead to predictable similarities in community composition. To that end, we measured the growth rate and by-product profile of a library of proteobacterial strains in a large number of single nutrient environments. We found that growth rates and secretion profiles were positively correlated across environments when the supplied substrate was metabolically similar. By analyzing hundreds of in-vitro communities experimentally assembled in an array of different synthetic environments, we then show that metabolically similar substrates select for taxonomically similar communities. These findings lead us to propose and then validate a comparative approach for quantitatively predicting the effects of novel substrates on the composition of complex microbial consortia.

Geometry of ecological coexistence and niche differentiation.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's R^{*} and species coexistence cones. Here, we extend these arguments by constructing a geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.

scTOP: physics-inspired order parameters for cellular identification and visualization.

Advances in single-cell RNA sequencing provide an unprecedented window into cellular identity. The abundance of data requires new theoretical and computational frameworks to analyze the dynamics of differentiation and integrate knowledge from cell atlases. We present 'single-cell Type Order Parameters' (scTOP): a statistical, physics-inspired approach for quantifying cell identity given a reference basis of cell types. scTOP can accurately classify cells, visualize developmental trajectories and assess the fidelity of engineered cells. Importantly, scTOP does this without feature selection, statistical fitting or dimensional reduction (e.g. uniform manifold approximation and projection, principle components analysis, etc.). We illustrate the power of scTOP using human and mouse datasets. By reanalyzing mouse lung data, we characterize a transient hybrid alveolar type 1/alveolar type 2 cell population. Visualizations of lineage tracing hematopoiesis data using scTOP confirm that a single clone can give rise to multiple mature cell types. We assess the transcriptional similarity between endogenous and donor-derived cells in the context of murine pulmonary cell transplantation. Our results suggest that physics-inspired order parameters can be an important tool for understanding differentiation and characterizing engineered cells. scTOP is available as an easy-to-use Python package.

Phase transition to chaos in complex ecosystems with non-reciprocal species-resource interactions.

Non-reciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. Here, we investigate the effects of non-reciprocity in the context of theoretical ecology by analyzing a generalization of MacArthur's consumer-resource model with asymmetric interactions between species and resources. Using a mixture of analytic cavity calculations and numerical simulations, we show that such ecosystems generically undergo a phase transition to chaotic dynamics as the amount of non-reciprocity is increased. We analytically construct the phase diagram for this model and show that the emergence of chaos is controlled by a single quantity: the ratio of surviving species to surviving resources. We also numerically calculate the Lyapunov exponents in the chaotic phase and carefully analyze finite-size effects. Our findings show how non-reciprocal interactions can give rise to complex and unpredictable dynamical behaviors even in the simplest ecological consumer-resource models.

Engineering synthetic phosphorylation signaling networks in human cells.

Protein phosphorylation signaling networks play a central role in how cells sense and respond to their environment. Here, we describe the engineering of artificial phosphorylation networks in which "push-pull" motifs-reversible enzymatic phosphorylation cycles consisting of opposing kinase and phosphatase activities-are assembled from modular protein domain parts and then wired together to create synthetic phosphorylation circuits in human cells. We demonstrate that the composability of our design scheme enables model-guided tuning of circuit function and the ability to make diverse network connections; synthetic phosphorylation circuits can be coupled to upstream cell surface receptors to enable fast-timescale sensing of extracellular ligands, while downstream connections can regulate gene expression. We leverage these capabilities to engineer cell-based cytokine controllers that dynamically sense and suppress activated T cells. Our work introduces a generalizable approach for designing and building phosphorylation signaling circuits that enable user-defined sense-and-respond function for diverse biosensing and therapeutic applications.

Durable alveolar engraftment of PSC-derived lung epithelial cells into immunocompetent mice.

Durable reconstitution of the distal lung epithelium with pluripotent stem cell (PSC) derivatives, if realized, would represent a promising therapy for diseases that result from alveolar damage. Here, we differentiate murine PSCs into self-renewing lung epithelial progenitors able to engraft into the injured distal lung epithelium of immunocompetent, syngeneic mouse recipients. After transplantation, these progenitors mature in the distal lung, assuming the molecular phenotypes of alveolar type 2 (AT2) and type 1 (AT1) cells. After months in vivo, donor-derived cells retain their mature phenotypes, as characterized by single-cell RNA sequencing (scRNA-seq), histologic profiling, and functional assessment that demonstrates continued capacity of the engrafted cells to proliferate and differentiate. These results indicate durable reconstitution of the distal lung's facultative progenitor and differentiated epithelial cell compartments with PSC-derived cells, thus establishing a novel model for pulmonary cell therapy that can be utilized to better understand the mechanisms and utility of engraftment.

Catastrophic Antiphospholipid Syndrome: A Case Series.

Catastrophic antiphospholipid syndrome (CAPS) is the rare but most severe form of antiphospholipid syndrome with multiple organ ischemia developing over a short period of time. CAPS should be considered when imaging suggests an acute and concurrent multiorgan ischemia, associated with positive antiphospholipid antibodies. As CAPS can have fulminant irreversible complications, its early recognition is important to initiate the treatment promptly. We present three patients of CAPS who were managed at our institution.

Multipotent Embryonic Lung Progenitors: Foundational Units of In Vitro and In Vivo Lung Organogenesis.

Transient, tissue-specific, embryonic progenitors are important cell populations in vertebrate development. In the course of respiratory system development, multipotent mesenchymal and epithelial progenitors drive the diversification of fates that results to the plethora of cell types that compose the airways and alveolar space of the adult lungs. Use of mouse genetic models, including lineage tracing and loss-of-function studies, has elucidated signaling pathways that guide proliferation and differentiation of embryonic lung progenitors as well as transcription factors that underlie lung progenitor identity. Furthermore, pluripotent stem cell-derived and ex vivo expanded respiratory progenitors offer novel, tractable, high-fidelity systems that allow for mechanistic studies of cell fate decisions and developmental processes. As our understanding of embryonic progenitor biology deepens, we move closer to the goal of in vitro lung organogenesis and resulting applications in developmental biology and medicine.

Geometry of ecological coexistence and niche differentiation.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze Consumer Resource Models (CRMs) using geometric arguments. This has led to broadly applicable principles such as Tilman's R* and species coexistence cones. Here, we extend these arguments by constructing a novel geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species coexistence and enumerate ecologically-stable steady states and transitions between them. Collectively, these results constitute a qualitatively new way of understanding the role of species traits in shaping ecosystems within niche theory.

Geometry of ecological coexistence and niche differentiation.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's R* and species coexistence cones. Here, we extend these arguments by constructing a novel geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically-stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.