Generative modeling of single-cell time series with PRESCIENT enables prediction of cell trajectories with interventions

Uncovering underlying physical principles and driving forces of cell differentiation and reprogramming from single-cell transcriptomics

Recent advances in single-cell sequencing technology have revolutionized our ability to acquire whole transcriptome data. However, uncovering the underlying transcriptional drivers and nonequilibrium driving forces of cell function directly from these data remains challenging. We address this by learning cell state vector fields from discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium driving forces as landscape and flux. From single-cell data, we quantified the Waddington landscape, showing that optimal paths for differentiation and reprogramming deviate from the naively expected landscape gradient paths and may not pass through landscape saddles at finite fluctuations, challenging conventional transition state estimation of kinetic rate for cell fate decisions due to the presence of the flux. A key insight from our study is that stem/progenitor cells necessitate greater energy dissipation for rapid cell cycles and self-renewal, maintaining pluripotency. We predict optimal developmental pathways and elucidate the nucleation mechanism of cell fate decisions, with transition states as nucleation sites and pioneer genes as nucleation seeds. The concept of loop flux quantifies the contributions of each cycle flux to cell state transitions, facilitating the understanding of cell dynamics and thermodynamic cost, and providing insights into optimizing biological functions. We also infer cell-cell interactions and cell-type-specific gene regulatory networks, encompassing feedback mechanisms and interaction intensities, predicting genetic perturbation effects on cell fate decisions from single-cell omics data. Essentially, our methodology validates the landscape and flux theory, along with its associated quantifications, offering a framework for exploring the physical principles underlying cellular differentiation and reprogramming and broader biological processes through high-throughput single-cell sequencing experiments.

Cellular proliferation biases clonal lineage tracing and trajectory inference

MOTIVATION

Lineage tracing and trajectory inference from single-cell RNA-sequencing data hold tremendous potential for uncovering the genetic programs driving development and disease. Single cell datasets are thought to provide an unbiased view on the diverse cellular architecture of tissues. Sampling bias, however, can skew single cell datasets away from the cellular composition they are meant to represent.

RESULTS

We demonstrate a novel form of sampling bias, caused by a statistical phenomenon related to repeated sampling from a growing, heterogeneous population. Relative growth rates of cells influence the probability that they will be sampled in clones observed across multiple time points. We support our probabilistic derivations with a simulation study and an analysis of a real time-course of T-cell development. We find that this bias can impact fate probability predictions, and we explore how to develop trajectory inference methods which are robust to this bias.

AVAILABILITY AND IMPLEMENTATION

Source code for the simulated datasets and to create the figures in this manuscript is freely available in python at https://github.com/rbonhamcarter/simulate-clones. A python implementation of the extension of the LineageOT method is freely available at https://github.com/rbonhamcarter/LineageOT/tree/multi-time-clones.

Refining the optimal CAF cluster marker for predicting TME-dependent survival expectancy and treatment benefits in NSCLC patients

The tumor microenvironment (TME) plays a pivotal role in the onset, progression, and treatment response of cancer. Among the various components of the TME, cancer-associated fibroblasts (CAFs) are key regulators of both immune and non-immune cellular functions. Leveraging single-cell RNA sequencing (scRNA) data, we have uncovered previously hidden and promising roles within this specific CAF subgroup, paving the way for its clinical application. However, several critical questions persist, primarily stemming from the heterogeneous nature of CAFs and the use of different fibroblast markers in various sample analyses, causing confusion and hindrance in their clinical implementation. In this groundbreaking study, we have systematically screened multiple databases to identify the most robust marker for distinguishing CAFs in lung cancer, with a particular focus on their potential use in early diagnosis, staging, and treatment response evaluation. Our investigation revealed that COL1A1, COL1A2, FAP, and PDGFRA are effective markers for characterizing CAF subgroups in most lung adenocarcinoma datasets. Through comprehensive analysis of treatment responses, we determined that COL1A1 stands out as the most effective indicator among all CAF markers. COL1A1 not only deciphers the TME signatures related to CAFs but also demonstrates a highly sensitive and specific correlation with treatment responses and multiple survival outcomes. For the first time, we have unveiled the distinct roles played by clusters of CAF markers in differentiating various TME groups. Our findings confirm the sensitive and unique contributions of CAFs to the responses of multiple lung cancer therapies. These insights significantly enhance our understanding of TME functions and drive the translational application of extensive scRNA sequence results. COL1A1 emerges as the most sensitive and specific marker for defining CAF subgroups in scRNA analysis. The CAF ratios represented by COL1A1 can potentially serve as a reliable predictor of treatment responses in clinical practice, thus providing valuable insights into the influential roles of TME components. This research marks a crucial step forward in revolutionizing our approach to cancer diagnosis and treatment.

Towards a Treatment for Leukodystrophy Using Cell-Based Interception and Precision Medicine

Cell-based interception and precision medicine is a novel approach aimed at improving healthcare through the early detection and treatment of diseased cells. Here, we describe our recent progress towards developing cell-based interception and precision medicine to detect, understand, and advance the development of novel therapeutic approaches through a single-cell omics and drug screening platform, as part of a multi-laboratory collaborative effort, for a group of neurodegenerative disorders named leukodystrophies. Our strategy aims at the identification of diseased cells as early as possible to intercept progression of the disease prior to severe clinical impairment and irreversible tissue damage.

Cell State Transition Models Stratify Breast Cancer Cell Phenotypes and Reveal New Therapeutic Targets

Understanding signaling patterns of transformation and controlling cell phenotypes is a challenge of current biology. Here we applied a cell State Transition Assessment and Regulation (cSTAR) approach to a perturbation dataset of single cell phosphoproteomic patterns of multiple breast cancer (BC) and normal breast tissue-derived cell lines. Following a separation of luminal, basal, and normal cell states, we identified signaling nodes within core control networks, delineated causal connections, and determined the primary drivers underlying oncogenic transformation and transitions across distinct BC subtypes. Whereas cell lines within the same BC subtype have different mutational and expression profiles, the architecture of the core network was similar for all luminal BC cells, and mTOR was a main oncogenic driver. In contrast, core networks of basal BC were heterogeneous and segregated into roughly four major subclasses with distinct oncogenic and BC subtype drivers. Likewise, normal breast tissue cells were separated into two different subclasses. Based on the data and quantified network topologies, we derived mechanistic cSTAR models that serve as digital cell twins and allow the deliberate control of cell movements within a Waddington landscape across different cell states. These cSTAR models suggested strategies of normalizing phosphorylation networks of BC cell lines using small molecule inhibitors.

OneSC: A computational platform for recapitulating cell state transitions

Computational modelling of cell state transitions has been a great interest of many in the field of developmental biology, cancer biology and cell fate engineering because it enables performing perturbation experiments in silico more rapidly and cheaply than could be achieved in a wet lab. Recent advancements in single-cell RNA sequencing (scRNA-seq) allow the capture of high-resolution snapshots of cell states as they transition along temporal trajectories. Using these high-throughput datasets, we can train computational models to generate in silico 'synthetic' cells that faithfully mimic the temporal trajectories. Here we present OneSC, a platform that can simulate synthetic cells across developmental trajectories using systems of stochastic differential equations govern by a core transcription factors (TFs) regulatory network. Different from the current network inference methods, OneSC prioritizes on generating Boolean network that produces faithful cell state transitions and steady cell states that mimic real biological systems. Applying OneSC to real data, we inferred a core TF network using a mouse myeloid progenitor scRNA-seq dataset and showed that the dynamical simulations of that network generate synthetic single-cell expression profiles that faithfully recapitulate the four myeloid differentiation trajectories going into differentiated cell states (erythrocytes, megakaryocytes, granulocytes and monocytes). Finally, through the in-silico perturbations of the mouse myeloid progenitor core network, we showed that OneSC can accurately predict cell fate decision biases of TF perturbations that closely match with previous experimental observations.

Deep generative models in single-cell omics

Deep Generative Models (DGMs) are becoming instrumental for inferring probability distributions inherent to complex processes, such as most questions in biomedical research. For many years, there was a lack of mathematical methods that would allow this inference in the scarce data scenario of biomedical research. The advent of single-cell omics has finally made square the so-called "skinny matrix", allowing to apply mathematical methods already extensively used in other areas. Moreover, it is now possible to integrate data at different molecular levels in thousands or even millions of samples, thanks to the number of single-cell atlases being collaboratively generated. Additionally, DGMs have proven useful in other frequent tasks in single-cell analysis pipelines, from dimensionality reduction, cell type annotation to RNA velocity inference. In spite of its promise, DGMs need to be used with caution in biomedical research, paying special attention to its use to answer the right questions and the definition of appropriate error metrics and validation check points that confirm not only its correct use but also its relevance. All in all, DGMs provide an exciting tool that opens a bright future for the integrative analysis of single-cell -omics to understand health and disease.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

BACKGROUND

Gene regulatory network (GRN) models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such gene regulatory ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the underlying GRN governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impede either scalability, explainability, or both.

RESULTS

We developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that overcomes limitations of other methods by flexibly incorporating prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of GRN ODEs. We tested the accuracy of PHOENIX in a series of in silico experiments, benchmarking it against several currently used tools. We demonstrated PHOENIX's flexibility by modeling regulation of oscillating expression profiles obtained from synchronized yeast cells. We also assessed the scalability of PHOENIX by modeling genome-scale GRNs for breast cancer samples ordered in pseudotime and for B cells treated with Rituximab.

CONCLUSIONS

PHOENIX uses a combination of user-defined prior knowledge and functional forms from systems biology to encode biological "first principles" as soft constraints on the GRN allowing us to predict subsequent gene expression patterns in a biologically explainable manner.

Data- and theory-driven approaches for understanding paths of epithelial-mesenchymal transition

Reversible transitions between epithelial and mesenchymal cell states are a crucial form of epithelial plasticity for development and disease progression. Recent experimental data and mechanistic models showed multiple intermediate epithelial-mesenchymal transition (EMT) states as well as trajectories of EMT underpinned by complex gene regulatory networks. In this review, we summarize recent progress in quantifying EMT and characterizing EMT paths with computational methods and quantitative experiments including omics-level measurements. We provide perspectives on how these studies can help relating fundamental cell biology to physiological and pathological outcomes of EMT.

Detecting abnormal cell behaviors from dry mass time series

The prediction of pathological changes on single cell behaviour is a challenging task for deep learning models. Indeed, in self-supervised learning methods, no prior labels are used for the training and all of the information for event predictions are extracted from the data themselves. We present here a novel self-supervised learning model for the detection of anomalies in a given cell population, StArDusTS. Cells are monitored over time, and analysed to extract time-series of dry mass values. We assessed its performances on different cell lines, showing a precision of 96% in the automatic detection of anomalies. Additionally, anomaly detection was also associated with cell measurement errors inherent to the acquisition or analysis pipelines, leading to an improvement of the upstream methods for feature extraction. Our results pave the way to novel architectures for the continuous monitoring of cell cultures in applied research or bioproduction applications, and for the prediction of pathological cellular changes.

Resource allocation in mammalian systems

Cells execute biological functions to support phenotypes such as growth, migration, and secretion. Complementarily, each function of a cell has resource costs that constrain phenotype. Resource allocation by a cell allows it to manage these costs and optimize their phenotypes. In fact, the management of resource constraints (e.g., nutrient availability, bioenergetic capacity, and macromolecular machinery production) shape activity and ultimately impact phenotype. In mammalian systems, quantification of resource allocation provides important insights into higher-order multicellular functions; it shapes intercellular interactions and relays environmental cues for tissues to coordinate individual cells to overcome resource constraints and achieve population-level behavior. Furthermore, these constraints, objectives, and phenotypes are context-dependent, with cells adapting their behavior according to their microenvironment, resulting in distinct steady-states. This review will highlight the biological insights gained from probing resource allocation in mammalian cells and tissues.

A time- and single-cell-resolved model of murine bone marrow hematopoiesis

The paradigmatic hematopoietic tree model is increasingly recognized to be limited, as it is based on heterogeneous populations largely defined by non-homeostatic assays testing cell fate potentials. Here, we combine persistent labeling with time-series single-cell RNA sequencing to build a real-time, quantitative model of in vivo tissue dynamics for murine bone marrow hematopoiesis. We couple cascading single-cell expression patterns with dynamic changes in differentiation and growth speeds. The resulting explicit linkage between molecular states and cellular behavior reveals widely varying self-renewal and differentiation properties across distinct lineages. Transplanted stem cells show strong acceleration of differentiation at specific stages of erythroid and neutrophil production, illustrating how the model can quantify the impact of perturbations. Our reconstruction of dynamic behavior from snapshot measurements is akin to how a kinetoscope allows sequential images to merge into a movie. We posit that this approach is generally applicable to understanding tissue-scale dynamics at high resolution.

Inference of differentiation trajectories by transfer learning across biological processes

Stem cells differentiate into distinct fates by transitioning through a series of transcriptional states. Current computational approaches allow reconstruction of differentiation trajectories from single-cell transcriptomics data, but it remains unknown to what degree differentiation can be predicted across biological processes. Here, we use transfer learning to infer differentiation processes and quantify predictability in early embryonic development and adult hematopoiesis. Overall, we find that non-linear methods outperform linear approaches, and we achieved the best predictions with a custom variational autoencoder that explicitly models changes in transcriptional variance. We observed a high accuracy of predictions in embryonic development, but we found somewhat lower agreement with the real data in adult hematopoiesis. We demonstrate that this discrepancy can be explained by a higher degree of concordant transcriptional processes along embryonic differentiation compared with adult homeostasis. In summary, we establish a framework for quantifying and exploiting predictability of cellular differentiation trajectories.

Reconstructing growth and dynamic trajectories from single-cell transcriptomics data

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, TIGON's capability in reconstructing gene expression at unmeasured time points and its applications to temporal gene regulatory networks and cell-cell communication inference.

cSTAR analysis identifies endothelial cell cycle as a key regulator of flow-dependent artery remodeling

Fluid shear stress (FSS) from blood flow is sensed by vascular endothelial cells (ECs) to determine vessel stability, remodeling and susceptibility to atherosclerosis and other inflammatory diseases but the regulatory networks that govern these behaviors are only partially understood. We used cSTAR, a powerful new computational method, to define EC transcriptomic states under low shear stress (LSS) that triggers vessel inward remodeling, physiological shear stress (PSS) that stabilizes vessels, high shear stress (HSS) that triggers outward remodeling, and oscillatory shear stress (OSS) that confers disease susceptibility, all in comparison to cells under static conditions (STAT). We combined these results with the LINCS database where EC transcriptomic responses to drug treatments to define a preliminary regulatory network in which the cyclin-dependent kinases CDK1/2 play a central role in promoting vessel stability. Experimental analysis showed that PSS induced a strong late G1 cell cycle arrest in which CDK2 was activated. EC deletion of CDK2 in mice resulted in inward artery remodeling and both pulmonary and systemic hypertension. These results validate use of cSTAR to determine EC state and in vivo vessel behavior, reveal unexpected features of EC phenotype under different FSS conditions, and identify CDK2 as a key element within the EC regulatory network that governs artery remodeling.

Generative modeling of single-cell gene expression for dose-dependent chemical perturbations

Single-cell sequencing reveals the heterogeneity of cellular response to chemical perturbations. However, testing all relevant combinations of cell types, chemicals, and doses is a daunting task. A deep generative learning formalism called variational autoencoders (VAEs) has been effective in predicting single-cell gene expression perturbations for single doses. Here, we introduce single-cell variational inference of dose-response (scVIDR), a VAE-based model that predicts both single-dose and multiple-dose cellular responses better than existing models. We show that scVIDR can predict dose-dependent gene expression across mouse hepatocytes, human blood cells, and cancer cell lines. We biologically interpret the latent space of scVIDR using a regression model and use scVIDR to order individual cells based on their sensitivity to chemical perturbation by assigning each cell a "pseudo-dose" value. We envision that scVIDR can help reduce the need for repeated animal testing across tissues, chemicals, and doses.

A systematic comparison of computational methods for expression forecasting

Due to the abundance of single cell RNA-seq data, a number of methods for predicting expression after perturbation have recently been published. Expression prediction methods are enticing because they promise to answer pressing questions in fields ranging from developmental genetics to cell fate engineering and because they are faster, cheaper, and higher-throughput than their experimental counterparts. However, the absolute and relative accuracy of these methods is poorly characterized, limiting their informed use, their improvement, and the interpretation of their predictions. To address these issues, we created a benchmarking platform that combines a panel of large-scale perturbation datasets with an expression forecasting software engine that encompasses or interfaces to current methods. We used our platform to systematically assess methods, parameters, and sources of auxiliary data. We found that uninformed baseline predictions, which were not always included in prior evaluations, yielded the same or better mean absolute error than benchmarked methods in all test cases. These results cast doubt on the ability of current expression forecasting methods to provide mechanistic insights or to rank hypotheses for experimental follow-up. However, given the rapid pace of innovation in the field, new approaches may yield more accurate expression predictions. Our platform will serve as a neutral benchmark to improve methods and to identify contexts in which expression prediction can succeed.

Biologically informed NeuralODEs for genome-wide regulatory dynamics

Models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the causal gene-regulatory network (GRN) governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impedes scalability and/or explainability. To overcome these limitations, we developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that can flexibly incorporate prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of ODEs. We test accuracy of PHOENIX in a series of in silico experiments benchmarking it against several currently used tools for ODE estimation. We also demonstrate PHOENIX's flexibility by studying oscillating expression data from synchronized yeast cells and assess its scalability by modelling genome-scale breast cancer expression for samples ordered in pseudotime. Finally, we show how the combination of user-defined prior knowledge and functional forms from systems biology allows PHOENIX to encode key properties of the underlying GRN, and subsequently predict expression patterns in a biologically explainable way.

Discovery of drug-omics associations in type 2 diabetes with generative deep-learning models

The application of multiple omics technologies in biomedical cohorts has the potential to reveal patient-level disease characteristics and individualized response to treatment. However, the scale and heterogeneous nature of multi-modal data makes integration and inference a non-trivial task. We developed a deep-learning-based framework, multi-omics variational autoencoders (MOVE), to integrate such data and applied it to a cohort of 789 people with newly diagnosed type 2 diabetes with deep multi-omics phenotyping from the DIRECT consortium. Using in silico perturbations, we identified drug-omics associations across the multi-modal datasets for the 20 most prevalent drugs given to people with type 2 diabetes with substantially higher sensitivity than univariate statistical tests. From these, we among others, identified novel associations between metformin and the gut microbiota as well as opposite molecular responses for the two statins, simvastatin and atorvastatin. We used the associations to quantify drug-drug similarities, assess the degree of polypharmacy and conclude that drug effects are distributed across the multi-omics modalities.

Deep learning models will shape the future of stem cell research

Our ability to understand and control stem cell biology is being augmented by developments on two fronts, our ability to collect more data describing cell state and our capability to comprehend these data using deep learning models. Here we consider the impact deep learning will have in the future of stem cell research. We explore the importance of generating data suitable for these methods, the requirement for close collaboration between experimental and computational researchers, and the challenges we face to do this fairly and effectively. Achieving this will ensure that the resulting deep learning models are biologically meaningful and computationally tractable.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Reconstructing data-driven governing equations for cell phenotypic transitions: integration of data science and systems biology

Cells with the same genome can exist in different phenotypes and can change between distinct phenotypes when subject to specific stimuli and microenvironments. Some examples include cell differentiation during development, reprogramming for induced pluripotent stem cells and transdifferentiation, cancer metastasis and fibrosis progression. The regulation and dynamics of cell phenotypic conversion is a fundamental problem in biology, and has a long history of being studied within the formalism of dynamical systems. A main challenge for mechanism-driven modeling studies is acquiring sufficient amount of quantitative information for constraining model parameters. Advances in quantitative experimental approaches, especially high throughput single-cell techniques, have accelerated the emergence of a new direction for reconstructing the governing dynamical equations of a cellular system from quantitative single-cell data, beyond the dominant statistical approaches. Here I review a selected number of recent studies using live- and fixed-cell data and provide my perspective on future development.

Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.

Single-Cell RNA Sequencing of Human Corpus Cavernosum Reveals Cellular Heterogeneity Landscapes in Erectile Dysfunction

PURPOSE

To assess the diverse cell populations of human corpus cavernosum in patients with severe erectile dysfunction (ED) at the single-cell level.

METHODS

Penile tissues collected from three patients were subjected to single-cell RNA sequencing using the BD Rhapsody™ platform. Common bioinformatics tools were used to analyze cellular heterogeneity and gene expression profiles from generated raw data, including the packages Seurat, Monocle, and CellPhoneDB.

RESULTS

Disease-related heterogeneity of cell types was determined in the cavernous tissue such as endothelial cells (ECs), smooth muscle cells, fibroblasts, and immune cells. Reclustering analysis of ECs identified an arteriole ECs subcluster and another one with gene signatures of fibroblasts. The proportion of fibroblasts was higher than the other cell populations and had the most significant cellular heterogeneity, in which a distinct subcluster co-expressed endothelial markers. The transition trajectory of differentiation from smooth muscle cells into fibroblasts was depicted using the pseudotime analysis, suggesting that the expansion of corpus cavernosum is possibly compromised as a result of fibrosis. Cell-cell communications among ECs, smooth muscle cells, fibroblasts, and macrophages were robust, which indicated that inflammation may also have a crucial role in the development of ED.

CONCLUSIONS

Our study has demonstrated a comprehensive single-cell atlas of cellular components in human corpus cavernosum of ED, providing in-depth insights into the pathogenesis. Future research is warranted to explore disease-specific alterations for individualized treatment of ED.

Dynamic inference of cell developmental complex energy landscape from time series single-cell transcriptomic data

Time series single-cell RNA sequencing (scRNA-seq) data are emerging. However, dynamic inference of an evolving cell population from time series scRNA-seq data is challenging owing to the stochasticity and nonlinearity of the underlying biological processes. This calls for the development of mathematical models and methods capable of reconstructing cellular dynamic transition processes and uncovering the nonlinear cell-cell interactions. In this study, we present GraphFP, a nonlinear Fokker-Planck equation on graph based model and dynamic inference framework, with the aim of reconstructing the cell state-transition complex potential energy landscape from time series single-cell transcriptomic data. The free energy of our model explicitly takes into account of the cell-cell interactions in a nonlinear quadratic term. We then recast the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the adjoint method of optimal control. We evaluated GraphFP on the time series scRNA-seq data set of embryonic murine cerebral cortex development. We illustrated that it 1) reconstructs cell state potential energy, which is a measure of cellular differentiation potency, 2) faithfully charts the probability flows between paired cell states over the dynamic processes of cell differentiation, and 3) accurately quantifies the stochastic dynamics of cell type frequencies on probability simplex in continuous time. We also illustrated that GraphFP is robust in terms of cluster labelling with different resolutions, as well as parameter choices. Meanwhile, GraphFP provides a model-based approach to delineate the cell-cell interactions that drive cell differentiation. GraphFP software is available at https://github.com/QiJiang-QJ/GraphFP.

Dynamic inference of cell development processes from time series scRNA-seq data is a major challenge. Here, we present GraphFP, a coherent computational framework that simultaneously reconstructs the cell state-transition complex potential energy landscape and infers cell-cell interactions from time series single-cell transcriptomic data. Based on the mathematical framework of nonlinear Fokker-Planck equation on graph, GraphFP models the stochastic dynamics of the cell state/type frequencies on probability simplex in continuous time, where the free energy with a nonlinear quadratic interaction term is employed to characterize cell-cell interactions. We formulate the model inference problem in the form of a dynamic optimal transport framework and solve it efficiently with the celebrated adjoint method. GraphFP allows for 1) reconstructing cell state potential energy, which is a measure of cellular differentiation potency, 2) charting the probability flows between paired cell states over dynamic processes, 3) quantifying the stochastic dynamics of cell type frequencies on probability simplex in continuous time, and 4) delineating cell-cell interactions that drive cell differentiation. We show how GraphFP can be used to faithfully reveal and accurately quantify the cell development processes using the embryonic murine cerebral cortex development time series scRNA-seq dataset.

Artificial intelligence: A powerful paradigm for scientific research

Artificial intelligence (AI) coupled with promising machine learning (ML) techniques well known from computer science is broadly affecting many aspects of various fields including science and technology, industry, and even our day-to-day life. The ML techniques have been developed to analyze high-throughput data with a view to obtaining useful insights, categorizing, predicting, and making evidence-based decisions in novel ways, which will promote the growth of novel applications and fuel the sustainable booming of AI. This paper undertakes a comprehensive survey on the development and application of AI in different aspects of fundamental sciences, including information science, mathematics, medical science, materials science, geoscience, life science, physics, and chemistry. The challenges that each discipline of science meets, and the potentials of AI techniques to handle these challenges, are discussed in detail. Moreover, we shed light on new research trends entailing the integration of AI into each scientific discipline. The aim of this paper is to provide a broad research guideline on fundamental sciences with potential infusion of AI, to help motivate researchers to deeply understand the state-of-the-art applications of AI-based fundamental sciences, and thereby to help promote the continuous development of these fundamental sciences.