Geometry of the Gene Expression Space of Individual Cells

Characterization of Alternative Splicing in High-Risk Wilms' Tumors

The significant heterogeneity of Wilms' tumors between different patients is thought to arise from genetic and epigenetic distortions that occur during various stages of fetal kidney development in a way that is poorly understood. To address this, we characterized the heterogeneity of alternative mRNA splicing in Wilms' tumors using a publicly available RNAseq dataset of high-risk Wilms' tumors and normal kidney samples. Through Pareto task inference and cell deconvolution, we found that the tumors and normal kidney samples are organized according to progressive stages of kidney development within a triangle-shaped region in latent space, whose vertices, or "archetypes", resemble the cap mesenchyme, the nephrogenic stroma, and epithelial tubular structures of the fetal kidney. We identified a set of genes that are alternatively spliced between tumors located in different regions of latent space and found that many of these genes are associated with the epithelial-to-mesenchymal transition (EMT) and muscle development. Using motif enrichment analysis, we identified putative splicing regulators, some of which are associated with kidney development. Our findings provide new insights into the etiology of Wilms' tumors and suggest that specific splicing mechanisms in early stages of development may contribute to tumor development in different patients.

Functional transcriptional signatures for tumor-type-agnostic phenotype prediction

Cancer transcriptional patterns exhibit both shared and unique features across diverse cancer types, but whether these patterns are sufficient to characterize the full breadth of tumor phenotype heterogeneity remains an open question. We hypothesized that cancer transcriptional diversity mirrors patterns in normal tissues optimized for distinct functional tasks. Starting with normal tissue transcriptomic profiles, we use non-negative matrix factorization to derive six distinct transcriptomic phenotypes, called archetypes, which combine to describe both normal tissue patterns and variations across a broad spectrum of malignancies. We show that differential enrichment of these signatures correlates with key tumor characteristics, including overall patient survival and drug sensitivity, independent of clinically actionable DNA alterations. Additionally, we show that in HR+/HER2- breast cancers, metastatic tumors adopt transcriptomic signatures consistent with the invaded tissue. Broadly, our findings suggest that cancer often arrogates normal tissue transcriptomic characteristics as a component of both malignant progression and drug response. This quantitative framework provides a strategy for connecting the diversity of cancer phenotypes and could potentially help manage individual patients.

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.

Tissue Biology: In Search of a New Paradigm

Animal tissues are made up of multiple cell types that are increasingly well-characterized, yet our understanding of the core principles that govern tissue organization is still incomplete. This is in part because many observable tissue characteristics, such as cellular composition and spatial patterns, are emergent properties, and as such, they cannot be explained through the knowledge of individual cells alone. Here we propose a complex systems theory perspective to address this fundamental gap in our understanding of tissue biology. We introduce the concept of cell categories, which is based on cell relations rather than cell identity. Based on these notions we then discuss common principles of tissue modularity, introducing compositional, structural, and functional tissue modules. Cell diversity and cell relations provide a basis for a new perspective on the underlying principles of tissue organization in health and disease.

Emergence of division of labor in tissues through cell interactions and spatial cues

Most cell types in multicellular organisms can perform multiple functions. However, not all functions can be optimally performed simultaneously by the same cells. Functions incompatible at the level of individual cells can be performed at the cell population level, where cells divide labor and specialize in different functions. Division of labor can arise due to instruction by tissue environment or through self-organization. Here, we develop a computational framework to investigate the contribution of these mechanisms to division of labor within a cell-type population. By optimizing collective cellular task performance under trade-offs, we find that distinguishable expression patterns can emerge from cell-cell interactions versus instructive signals. We propose a method to construct ligand-receptor networks between specialist cells and use it to infer division-of-labor mechanisms from single-cell RNA sequencing (RNA-seq) and spatial transcriptomics data of stromal, epithelial, and immune cells. Our framework can be used to characterize the complexity of cell interactions within tissues.

Sex-dependent control of pheromones on social organization within groups of wild house mice

Dominance hierarchy is a fundamental social phenomenon in a wide range of mammalian species, critically affecting fitness and health. Here, we investigate the role of pheromone signals in the control of social hierarchies and individual personalities within groups of wild mice. For this purpose, we combine high-throughput behavioral phenotyping with computational tools in freely interacting groups of wild house mice, males and females, in an automated, semi-natural system. We show that wild mice form dominance hierarchies in both sexes but use sex-specific strategies, displaying distinct male-typical and female-typical behavioral personalities that were also associated with social ranking. Genetic disabling of VNO-mediated pheromone detection generated opposite behavioral effects within groups, enhancing social interactions in males and reducing them in females. Behavioral personalities in the mutated mice displayed mixtures of male-typical and female-typical behaviors, thus blurring sex differences. In addition, rank-associated personalities were abolished despite the fact that both sexes of mutant mice formed stable hierarchies. These findings suggest that group organization is governed by pheromone-mediated sex-specific neural circuits and pave the way to investigate the mechanisms underlying sexual dimorphism in dominance hierarchies under naturalistic settings.

Characterization of Continuous Transcriptional Heterogeneity in High-Risk Blastemal-Type Wilms' Tumors Using Unsupervised Machine Learning

Wilms' tumors are pediatric malignancies that are thought to arise from faulty kidney development. They contain a wide range of poorly differentiated cell states resembling various distorted developmental stages of the fetal kidney, and as a result, differ between patients in a continuous manner that is not well understood. Here, we used three computational approaches to characterize this continuous heterogeneity in high-risk blastemal-type Wilms' tumors. Using Pareto task inference, we show that the tumors form a triangle-shaped continuum in latent space that is bounded by three tumor archetypes with "stromal", "blastemal", and "epithelial" characteristics, which resemble the un-induced mesenchyme, the cap mesenchyme, and early epithelial structures of the fetal kidney. By fitting a generative probabilistic "grade of membership" model, we show that each tumor can be represented as a unique mixture of three hidden "topics" with blastemal, stromal, and epithelial characteristics. Likewise, cellular deconvolution allows us to represent each tumor in the continuum as a unique combination of fetal kidney-like cell states. These results highlight the relationship between Wilms' tumors and kidney development, and we anticipate that they will pave the way for more quantitative strategies for tumor stratification and classification.

Archetype tasks link intratumoral heterogeneity to plasticity and cancer hallmarks in small cell lung cancer

Small cell lung cancer (SCLC) tumors comprise heterogeneous mixtures of cell states, categorized into neuroendocrine (NE) and non-neuroendocrine (non-NE) transcriptional subtypes. NE to non-NE state transitions, fueled by plasticity, likely underlie adaptability to treatment and dismal survival rates. Here, we apply an archetypal analysis to model plasticity by recasting SCLC phenotypic heterogeneity through multi-task evolutionary theory. Cell line and tumor transcriptomics data fit well in a five-dimensional convex polytope whose vertices optimize tasks reminiscent of pulmonary NE cells, the SCLC normal counterparts. These tasks, supported by knowledge and experimental data, include proliferation, slithering, metabolism, secretion, and injury repair, reflecting cancer hallmarks. SCLC subtypes, either at the population or single-cell level, can be positioned in archetypal space by bulk or single-cell transcriptomics, respectively, and characterized as task specialists or multi-task generalists by the distance from archetype vertex signatures. In the archetype space, modeling single-cell plasticity as a Markovian process along an underlying state manifold indicates that task trade-offs, in response to microenvironmental perturbations or treatment, may drive cell plasticity. Stifling phenotypic transitions and plasticity may provide new targets for much-needed translational advances in SCLC. A record of this paper's Transparent Peer Review process is included in the supplemental information.

Mapping Phenotypic Plasticity upon the Cancer Cell State Landscape Using Manifold Learning

ABSTRACT

Phenotypic plasticity describes the ability of cancer cells to undergo dynamic, nongenetic cell state changes that amplify cancer heterogeneity to promote metastasis and therapy evasion. Thus, cancer cells occupy a continuous spectrum of phenotypic states connected by trajectories defining dynamic transitions upon a cancer cell state landscape. With technologies proliferating to systematically record molecular mechanisms at single-cell resolution, we illuminate manifold learning techniques as emerging computational tools to effectively model cell state dynamics in a way that mimics our understanding of the cell state landscape. We anticipate that "state-gating" therapies targeting phenotypic plasticity will limit cancer heterogeneity, metastasis, and therapy resistance.

SIGNIFICANCE

Nongenetic mechanisms underlying phenotypic plasticity have emerged as significant drivers of tumor heterogeneity, metastasis, and therapy resistance. Herein, we discuss new experimental and computational techniques to define phenotypic plasticity as a scaffold to guide accelerated progress in uncovering new vulnerabilities for therapeutic exploitation.

Archetypal Analysis of Injury in Kidney Transplant Biopsies Identifies Two Classes of Early AKI

All transplanted kidneys are subjected to some degree of injury as a result of the donation-implantation process and various post-transplant stresses such as rejection. Because transplants are frequently biopsied, they present an opportunity to explore the full spectrum of kidney response-to-wounding from all causes. Defining parenchymal damage in transplanted organs is important for clinical management because it determines function and survival. In this study, we classified the scenarios associated with parenchymal injury in genome-wide microarray results from 1,526 kidney transplant indication biopsies collected during the INTERCOMEX study. We defined injury groups by using archetypal analysis (AA) of scores for gene sets and classifiers previously identified in various injury states. Six groups and their characteristics were defined in this population: No injury, minor injury, two classes of acute kidney injury ("AKI," AKI1, and AKI2), chronic kidney disease (CKD), and CKD combined with AKI. We compared the two classes of AKI, namely, AKI1 and AKI2. AKI1 had a poor function and increased parenchymal dedifferentiation but minimal response-to-injury and inflammation, instead having increased expression of PARD3, a gene previously characterized as being related to epithelial polarity and adherens junctions. In contrast, AKI2 had a poor function and increased response-to-injury, significant inflammation, and increased macrophage activity. In random forest analysis, the most important predictors of function (estimated glomerular filtration rate) and graft loss were injury-based molecular scores, not rejection scores. AKI1 and AKI2 differed in 3-year graft survival, with better survival in the AKI2 group. Thus, injury archetype analysis of injury-induced gene expression shows new heterogeneity in kidney response-to-wounding, revealing AKI1, a class of early transplants with a poor function but minimal inflammation or response to injury, a deviant response characterized as PC3, and an increased risk of failure. Given the relationship between parenchymal injury and kidney survival, further characterization of the injury phenotypes in kidney transplants will be important for an improved understanding that could have implications for understanding native kidney diseases (ClinicalTrials.gov #NCT01299168).

Pinpointing Cancer Sub-Type Specific Metabolic Tasks Facilitates Identification of Anti-cancer Targets

Metabolic reprogramming is one of the hallmarks of tumorigenesis. Understanding the metabolic changes in cancer cells may provide attractive therapeutic targets and new strategies for cancer therapy. The metabolic states are not the same in different cancer types or subtypes, even within the same sample of solid tumors. In order to understand the heterogeneity of cancer cells, we used the Pareto tasks inference method to analyze the metabolic tasks of different cancers, including breast cancer, lung cancer, digestive organ cancer, digestive tract cancer, and reproductive cancer. We found that cancer subtypes haves different propensities toward metabolic tasks, and the biological significance of these metabolic tasks also varies greatly. Normal cells treat metabolic tasks uniformly, while different cancer cells focus on different pathways. We then integrated the metabolic tasks into the multi-objective genome-scale metabolic network model, which shows higher accuracy in the in silico prediction of cell states after gene knockout than the conventional biomass maximization model. The predicted potential single drug targets could potentially turn into biomarkers or drug design targets. We further implemented the multi-objective genome-scale metabolic network model to predict synthetic lethal target pairs of the Basal and Luminal B subtypes of breast cancer. By analyzing the predicted synthetic lethal targets, we found that mitochondrial enzymes are potential targets for drug combinations. Our study quantitatively analyzes the metabolic tasks of cancer and establishes cancer type-specific metabolic models, which opens a new window for the development of specific anti-cancer drugs and provides promising treatment plans for specific cancer subtypes.

Rampant False Detection of Adaptive Phenotypic Optimization by ParTI-Based Pareto Front Inference

Organisms face tradeoffs in performing multiple tasks. Identifying the optimal phenotypes maximizing the organismal fitness (or Pareto front) and inferring the relevant tasks allow testing phenotypic adaptations and help delineate evolutionary constraints, tradeoffs, and critical fitness components, so are of broad interest. It has been proposed that Pareto fronts can be identified from high-dimensional phenotypic data, including molecular phenotypes such as gene expression levels, by fitting polytopes (lines, triangles, tetrahedrons, and so on), and a program named ParTI was recently introduced for this purpose. ParTI has identified Pareto fronts and inferred phenotypes best for individual tasks (or archetypes) from numerous data sets such as the beak morphologies of Darwin’s finches and mRNA concentrations in human tumors, implying evolutionary optimizations of the involved traits. Nevertheless, the reliabilities of these findings are unknown. Using real and simulated data that lack evolutionary optimization, we here report extremely high false-positive rates of ParTI. The errors arise from phylogenetic relationships or population structures of the organisms analyzed and the flexibility of data analysis in ParTI that is equivalent to p-hacking. Because these problems are virtually universal, our findings cast doubt on almost all ParTI-based results and suggest that reliably identifying Pareto fronts and archetypes from high-dimensional phenotypic data are currently generally difficult.

The geometry of clinical labs and wellness states from deeply phenotyped humans

Longitudinal multi-omics measurements are highly valuable in studying heterogeneity in health and disease phenotypes. For thousands of people, we have collected longitudinal multi-omics data. To analyze, interpret and visualize this extremely high-dimensional data, we use the Pareto Task Inference (ParTI) method. We find that the clinical labs data fall within a tetrahedron. We then use all other data types to characterize the four archetypes. We find that the tetrahedron comprises three wellness states, defining a wellness triangular plane, and one aberrant health state that captures aspects of commonality in movement away from wellness. We reveal the tradeoffs that shape the data and their hierarchy, and use longitudinal data to observe individual trajectories. We then demonstrate how the movement on the tetrahedron can be used for detecting unexpected trajectories, which might indicate transitions from health to disease and reveal abnormal conditions, even when all individual blood measurements are in the norm.

Bridging scales: From cell biology to physiology using in situ single-cell technologies

Biological organization crosses multiple spatial scales: from molecular, cellular, to tissues and organs. The proliferation of molecular profiling technologies enables increasingly detailed cataloging of the components at each scale. However, the scarcity of spatial profiling has made it challenging to bridge across these scales. Emerging technologies based on highly multiplexed in situ profiling are paving the way to study the spatial organization of cells and tissues in greater detail. These new technologies provide the data needed to cross the scale from cell biology to physiology and identify the fundamental principles that govern tissue organization. Here, we provide an overview of these key technologies and discuss the current and future insights these powerful techniques enable.

Gene expression rearrangements denoting changes in the biological state

In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may be the result of a selective pressure, as in the Long Term Evolution Experiment with E. Coli populations, or the progression to Alzheimer disease in aged brains, or the progression from a normal tissue to the cancer state. The first two cases seem to belong to a class of transitions, where the initial and final states are relatively close to each other, and the distribution function for the differential expressions is short ranged, with a tail of only a few dozens of strongly varying genes. In the latter case, cancer, the initial and final states are far apart and separated by a low-fitness barrier. The distribution function shows a very heavy tail, with thousands of silenced and over-expressed genes. We characterize the biological states by means of their principal component representations, and the expression distribution functions by their maximal and minimal differential expression values and the exponents of the Pareto laws describing the tails.

Joint probabilistic modeling of single-cell multi-omic data with totalVI

The paired measurement of RNA and surface proteins in single cells with cellular indexing of transcriptomes and epitopes by sequencing (CITE-seq) is a promising approach to connect transcriptional variation with cell phenotypes and functions. However, combining these paired views into a unified representation of cell state is made challenging by the unique technical characteristics of each measurement. Here we present Total Variational Inference (totalVI; https://scvi-tools.org ), a framework for end-to-end joint analysis of CITE-seq data that probabilistically represents the data as a composite of biological and technical factors, including protein background and batch effects. To evaluate totalVI's performance, we profiled immune cells from murine spleen and lymph nodes with CITE-seq, measuring over 100 surface proteins. We demonstrate that totalVI provides a cohesive solution for common analysis tasks such as dimensionality reduction, the integration of datasets with different measured proteins, estimation of correlations between molecules and differential expression testing.

Interpretable factor models of single-cell RNA-seq via variational autoencoders

Motivation

Single-cell RNA-seq makes possible the investigation of variability in gene expression among cells, and dependence of variation on cell type. Statistical inference methods for such analyses must be scalable, and ideally interpretable.

Results

We present an approach based on a modification of a recently published highly scalable variational autoencoder framework that provides interpretability without sacrificing much accuracy. We demonstrate that our approach enables identification of gene programs in massive datasets. Our strategy, namely the learning of factor models with the auto-encoding variational Bayes framework, is not domain specific and may be useful for other applications.

Availability and implementation

The factor model is available in the scVI package hosted at https://github.com/YosefLab/scVI/.

Contact

v@nxn.se

Supplementary information

Supplementary data are available at Bioinformatics online.

High accuracy gene expression profiling of sorted cell subpopulations from breast cancer PDX model tissue

Intratumor Heterogeneity (ITH) is a functionally important property of tumor tissue and may be involved in drug resistance mechanisms. Although descriptions of ITH can be traced back to very early reports about cancer tissue, mechanistic investigations are still limited by the precision of analysis methods and access to relevant tissue sources. PDX models have provided a reproducible source of tissue with at least a partial representation of naturally occurring ITH. We investigated the properties of phenotypically distinct cell populations by Fluorescence activated cell sorting (FACS) tissue derived cells from multiple tumors from a triple negative breast cancer patient derived xenograft (PDX) model. We subsequently subjected each population to in depth gene expression analysis. Our findings suggest that process related gene expression changes (caused by tissue dissociation and FACS sorting) are restricted to Immediate Early Genes (IEGs). This allowed us to discover highly reproducible gene expression profiles of distinct cellular compartments identifiable by cell surface markers in this particular tumor model. Within the context of data from a previously published model our work suggests that gene expression profiles associated with hypoxia, stemness and drug resistance may reside in tumor subpopulations predictably growing in PDX models. This approach provides a novel opportunity for prospective mechanistic studies of ITH.

Cancer-associated fibroblast compositions change with breast cancer progression linking the ratio of S100A4+ and PDPN+ CAFs to clinical outcome

Tumors are supported by cancer-associated fibroblasts (CAFs). CAFs are heterogeneous and carry out distinct cancer-associated functions. Understanding the full repertoire of CAFs and their dynamic changes as tumors evolve could improve the precision of cancer treatment. Here we comprehensively analyze CAFs using index and transcriptional single-cell sorting at several time points along breast tumor progression in mice, uncovering distinct subpopulations. Notably, the transcriptional programs of these subpopulations change over time and in metastases, transitioning from an immunoregulatory program to wound-healing and antigen-presentation programs, indicating that CAFs and their functions are dynamic. Two main CAF subpopulations are also found in human breast tumors, where their ratio is associated with disease outcome across subtypes and is particularly correlated with BRCA mutations in triple-negative breast cancer. These findings indicate that the repertoire of CAF changes over time in breast cancer progression, with direct clinical implications.

Tumour heterogeneity and the evolutionary trade-offs of cancer

Tumours vary in gene expression programmes and genetic alterations. Understanding this diversity and its biological meaning requires a theoretical framework, which could in turn guide the development of more accurate prognosis and therapy. Here, we review the theory of multi-task evolution of cancer, which is based upon the premise that tumours evolve in the host and face selection trade-offs between multiple biological functions. This theory can help identify the major biological tasks that cancer cells perform and the trade-offs between these tasks. It introduces the concept of specialist tumours, which focus on one task, and generalist tumours, which perform several tasks. Specialist tumours are suggested to be sensitive to therapy targeting their main task. Driver mutations tune gene expression towards specific tasks in a tissue-dependent manner and thus help to determine whether a tumour is specialist or generalist. We discuss potential applications of the theory of multi-task evolution to interpret the spatial organization of tumours and intratumour heterogeneity.

Principles of Cell Circuits for Tissue Repair and Fibrosis

Tissue repair is a protective response after injury, but repetitive or prolonged injury can lead to fibrosis, a pathological state of excessive scarring. To pinpoint the dynamic mechanisms underlying fibrosis, it is important to understand the principles of the cell circuits that carry out tissue repair. In this study, we establish a cell-circuit framework for the myofibroblast-macrophage circuit in wound healing, including the accumulation of scar-forming extracellular matrix. We find that fibrosis results from multistability between three outcomes, which we term "hot fibrosis" characterized by many macrophages, "cold fibrosis" lacking macrophages, and normal wound healing. This framework clarifies several unexplained phenomena including the paradoxical effect of macrophage depletion, the limited time-window in which removing inflammation leads to healing, and why scar maturation takes months. We define key parameters that control the transition from healing to fibrosis, which may serve as potential targets for therapeutic reduction of fibrosis.

A data-driven classification of 3D foot types by archetypal shapes based on landmarks

The taxonomy of foot shapes or other parts of the body is important, especially for design purposes. We propose a methodology based on archetypoid analysis (ADA) that overcomes the weaknesses of previous methodologies used to establish typologies. ADA is an objective, data-driven methodology that seeks extreme patterns, the archetypal profiles in the data. ADA also explains the data as percentages of the archetypal patterns, which makes this technique understandable and accessible even for non-experts. Clustering techniques are usually considered for establishing taxonomies, but we will show that finding the purest or most extreme patterns is more appropriate than using the central points returned by clustering techniques. We apply the methodology to an anthropometric database of 775 3D right foot scans representing the Spanish adult female and male population for footwear design. Each foot is described by a 5626 × 3 configuration matrix of landmarks. No multivariate features are used for establishing the taxonomy, but all the information gathered from the 3D scanning is employed. We use ADA for shapes described by landmarks. Women’s and men’s feet are analyzed separately. We have analyzed 3 archetypal feet for both men and women. These archetypal feet could not have been recovered using multivariate techniques.

Tumor diversity and the trade-off between universal cancer tasks

Recent advances have enabled powerful methods to sort tumors into prognosis and treatment groups. We are still missing, however, a general theoretical framework to understand the vast diversity of tumor gene expression and mutations. Here we present a framework based on multi-task evolution theory, using the fact that tumors need to perform multiple tasks that contribute to their fitness. We find that trade-offs between tasks constrain tumor gene-expression to a continuum bounded by a polyhedron whose vertices are gene-expression profiles, each specializing in one task. We find five universal cancer tasks across tissue-types: cell-division, biomass and energy, lipogenesis, immune-interaction and invasion and tissue-remodeling. Tumors that specialize in a task are sensitive to drugs that interfere with this task. Driver, but not passenger, mutations tune gene-expression towards specialization in specific tasks. This approach can integrate additional types of molecular data into a framework of tumor diversity grounded in evolutionary theory.

Negative Co-stimulation Constrains T Cell Differentiation by Imposing Boundaries on Possible Cell States

Co-stimulation regulates T cell activation, but it remains unclear whether co-stimulatory pathways also control T cell differentiation. We used mass cytometry to profile T cells generated in the genetic absence of the negative co-stimulatory molecules CTLA-4 and PD-1. Our data indicate that negative co-stimulation constrains the possible cell states that peripheral T cells can acquire. CTLA-4 imposes major boundaries on CD4⁺ T cell phenotypes, whereas PD-1 subtly limits CD8⁺ T cell phenotypes. By computationally reconstructing T cell differentiation paths, we identified protein expression changes that underlied the abnormal phenotypic expansion and pinpointed when lineage choice events occurred during differentiation. Similar alterations in T cell phenotypes were observed after anti-CTLA-4 and anti-PD-1 antibody blockade. These findings implicate negative co-stimulation as a key regulator and determinant of T cell differentiation and suggest that checkpoint blockade might work in part by altering the limits of T cell phenotypes.

Evolutionary trade-offs and the structure of polymorphisms

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species.This article is part of the theme issue 'Self-organization in cell biology'.

A brief review of single-cell transcriptomic technologies

In recent years, there has been an effort to develop new technologies for measuring gene expression and sequence information from thousands of individual cells. Large data sets that were obtained using these 'single cell' technologies have allowed scientists to address fundamental questions in biomedicine ranging from stems cells and development to cancer and immunology. Here, we provide a brief review of recent developments in single-cell technology. Our intention is to provide a quick background for newcomers to the field as well as a deeper description of some of the leading technologies to date.

Central dogma rates and the trade-off between precision and economy in gene expression

Steady-state protein abundance is set by four rates: transcription, translation, mRNA decay and protein decay. A given protein abundance can be obtained from infinitely many combinations of these rates. This raises the question of whether the natural rates for each gene result from historical accidents, or are there rules that give certain combinations a selective advantage? We address this question using high-throughput measurements in rapidly growing cells from diverse organisms to find that about half of the rate combinations do not exist: genes that combine high transcription with low translation are strongly depleted. This depletion is due to a trade-off between precision and economy: high transcription decreases stochastic fluctuations but increases transcription costs. Our theory quantitatively explains which rate combinations are missing, and predicts the curvature of the fitness function for each gene. It may guide the design of gene circuits with desired expression levels and noise.

Archetypes of human cognition defined by time preference for reward and their brain correlates: An evolutionary trade-off approach

Biological systems carry out multiple tasks in their lifetime, which, in the course of evolution, may lead to trade-offs. In fact phenotypes (different species, individuals within a species, circuits, bacteria, proteins, etc.) cannot be optimal at all tasks, and, according to Pareto optimality theory, lay into a well-defined geometrical distribution (polygons and/or polyhedrons) in the space of traits. The vertices of this distribution contain archetypes, namely phenotypes that are specialists at one of the tasks, whereas phenotypes toward the center of the geometrical distribution show average performance across tasks. We applied this theory to the variability of cognitive and behavioral scores measured in 1206 individuals from the Human Connectome Project. Among all possible combinations of pairs of traits, we found the best fit to Pareto optimality when individuals were plotted in the trait-space of time preferences for reward, evaluated with the Delay Discounting Task (DDT). The DDT measures subjects' preference in choosing either immediate smaller rewards or delayed larger rewards. Time preference for reward was described by a triangular distribution in which each of the three vertices included individuals who used a particular strategy to discount reward. These archetypes accounted for variability on many cognitive, personality, and socioeconomic status variables, as well as differences in brain structure and functional connectivity, with only a weak influence of genetics. In summary, time preference for reward reflects a core variable that biases human phenotypes via natural and cultural selection.

Geometry of Gene Expression Space of Wilms' Tumors From Human Patients

Wilms' tumor is a pediatric malignancy that is thought to originate from faulty kidney development during the embryonic stage. However, there is a large variation between tumors from different patients in both histology and gene expression that is not well characterized. Here we use a meta-analysis of published microarray datasets to show that Favorable Histology Wilms' Tumors (FHWT's) fill a triangle-shaped continuum in gene expression space of which the vertices represent three idealized “archetypes”. We show that these archetypes have predominantly renal blastemal, stromal, and epithelial characteristics and that they correlate well with the three major lineages of the developing embryonic kidney. Moreover, we show that advanced stage tumors shift towards the renal blastemal archetype. These results illustrate the potential of this methodology for characterizing the cellular composition of Wilms' tumors and for assessing disease progression.

Modeling Cell Dynamics in Colon and Intestinal Crypts: The Significance of Central Stem Cells in Tumorigenesis

Colon and intestinal crypts have been widely chosen to study cell dynamics because of their fairly simple structures. In the colon and intestinal crypts, stem cells (SCs) are located at very bottom of the crypt, fully differentiated cells (FDs) are located in the top of the crypt, and transit-amplifying cells (TAs) are in the middle of the crypt between FDs and SCs. Recently, it has been discovered that there are two types of stem cells in the intestinal crypts: central stem cells (CeSCs) and border stem cells. To investigate dynamics of mutants in colon and intestinal crypts, we develop a four-compartmental stochastic model, which includes two SC compartments, and TAs and FDs compartments. We calculate the probability of the progeny of marked or mutant cells located at each of these compartments taking over the entire crypt or being washed out from the crypt. We found that the progeny of CeSCs will take over the entire crypt with a probability close to one. Interestingly, the progeny of advantageous mutant TAs and FDs will be washed out faster than disadvantageous mutants. Saliently, the model predicts that the time that the progeny of wild-type central stem cells will take over the mouse intestinal crypt is around 60 days, which is in perfect agreement with an experimental observation.

Recovering Gene Interactions from Single-Cell Data Using Data Diffusion

Single-cell RNA sequencing technologies suffer from many sources of technical noise, including under-sampling of mRNA molecules, often termed "dropout," which can severely obscure important gene-gene relationships. To address this, we developed MAGIC (Markov affinity-based graph imputation of cells), a method that shares information across similar cells, via data diffusion, to denoise the cell count matrix and fill in missing transcripts. We validate MAGIC on several biological systems and find it effective at recovering gene-gene relationships and additional structures. Applied to the epithilial to mesenchymal transition, MAGIC reveals a phenotypic continuum, with the majority of cells residing in intermediate states that display stem-like signatures, and infers known and previously uncharacterized regulatory interactions, demonstrating that our approach can successfully uncover regulatory relations without perturbations.

Signature of Pareto optimization in the Escherichia coli proteome

Proteins have coevolved with cellular environments to improve or preserve their functions, maintaining at the same time the degree of hydrophobicity necessary to fold correctly and enough solubility to perform their biological roles. Here, we study the Escherichia coli proteome using a Pareto front analysis in the solubility-hydrophobicity space. The results indicate the existence of a Pareto optimal front, a triangle whose vertices correspond to archetypal proteins specialized in distinct tasks, such as regulatory processes, membrane transport, outer-membrane pore formation, catalysis, and binding. The vertices are further enriched with proteins that occupy different subcellular compartments, namely, cytoplasmic, inner membrane, outer membrane, and outer membrane bounded periplasmic space. The combination of various enriching features offers an interpretation of how bacteria use the physico-chemical properties of proteins, both to drive them into their final destination in the cell and to have their tasks accomplished.

A geometric approach to characterize the functional identity of single cells

Single-cell transcriptomic data has the potential to radically redefine our view of cell-type identity. Cells that were previously believed to be homogeneous are now clearly distinguishable in terms of their expression phenotype. Methods for automatically characterizing the functional identity of cells, and their associated properties, can be used to uncover processes involved in lineage differentiation as well as sub-typing cancer cells. They can also be used to suggest personalized therapies based on molecular signatures associated with pathology. We develop a new method, called ACTION, to infer the functional identity of cells from their transcriptional profile, classify them based on their dominant function, and reconstruct regulatory networks that are responsible for mediating their identity. Using ACTION, we identify novel Melanoma subtypes with differential survival rates and therapeutic responses, for which we provide biomarkers along with their underlying regulatory networks.

Unsupervised Trajectory Analysis of Single-Cell RNA-Seq and Imaging Data Reveals Alternative Tuft Cell Origins in the Gut

Modern single-cell technologies allow multiplexed sampling of cellular states within a tissue. However, computational tools that can infer developmental cell-state transitions reproducibly from such single-cell data are lacking. Here, we introduce p-Creode, an unsupervised algorithm that produces multi-branching graphs from single-cell data, compares graphs with differing topologies, and infers a statistically robust hierarchy of cell-state transitions that define developmental trajectories. We have applied p-Creode to mass cytometry, multiplex immunofluorescence, and single-cell RNA-seq data. As a test case, we validate cell-state-transition trajectories predicted by p-Creode for intestinal tuft cells, a rare, chemosensory cell type. We clarify that tuft cells are specified outside of the Atoh1-dependent secretory lineage in the small intestine. However, p-Creode also predicts, and we confirm, that tuft cells arise from an alternative, Atoh1-driven developmental program in the colon. These studies introduce p-Creode as a reliable method for analyzing large datasets that depict branching transition trajectories.

Phenotypic heterogeneity in modeling cancer evolution

The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and non-stem cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exactly calculated results for the fixation probability of a mutant arising in each of the subpopulations. The exactly calculated results are in almost perfect agreement with the numerical simulations. Moreover, a condition for evolutionary advantage of a mutant cell versus the wild type population is given in the present study. We also show that microenvironment-induced plasticity in invading mutants leads to more aggressive mutants with higher fixation probability. Our model predicts that decreasing polarity between stem and non-stem cells’ turnover would raise the survivability of non-plastic mutants; while it would suppress the development of malignancy for plastic mutants. The derived results are novel and general with potential applications in nature; we discuss our model in the context of colorectal/intestinal cancer (at the epithelium). However, the model clearly needs to be validated through appropriate experimental data. This novel mathematical framework can be applied more generally to a variety of problems concerning selection in heterogeneous populations, in other contexts such as population genetics, and ecology.

Assessing rejection-related disease in kidney transplant biopsies based on archetypal analysis of molecular phenotypes

Conventional histologic diagnosis of rejection in kidney transplants has limited repeatability due to its inherent requirement for subjective assessment of lesions, in a rule-based system that does not acknowledge diagnostic uncertainty. Molecular phenotyping affords opportunities for increased precision and improved disease classification to address the limitations of conventional histologic diagnostic systems and quantify levels of uncertainty. Microarray data from 1,208 kidney transplant biopsies were collected prospectively from 13 centers. Cross-validated classifier scores predicting the presence of antibody-mediated rejection (ABMR), T cell-mediated rejection (TCMR), and 5 related histologic lesions were generated using supervised machine learning methods. These scores were used as input for archetypal analysis, an unsupervised method similar to cluster analysis, to examine the distribution of molecular phenotypes related to rejection. Six archetypes were generated: no rejection, TCMR, 3 associated with ABMR (early-stage, fully developed, and late-stage), and mixed rejection (TCMR plus early-stage ABMR). Each biopsy was assigned 6 scores, one for each archetype, representing a probabilistic assessment of that biopsy based on its rejection-related molecular properties. Viewed as clusters, the archetypes were similar to existing histologic Banff categories, but there was 32% disagreement, much of it probably reflecting the "noise" in the current histologic assessment system. Graft survival was lowest for fully developed and late-stage ABMR, and it was better predicted by molecular archetype scores than histologic diagnoses. The results provide a system for precision molecular assessment of biopsies and a new standard for recalibrating conventional diagnostic systems.

Revealing the vectors of cellular identity with single-cell genomics

Single-cell genomics has now made it possible to create a comprehensive atlas of human cells. At the same time, it has reopened definitions of a cell's identity and of the ways in which identity is regulated by the cell's molecular circuitry. Emerging computational analysis methods, especially in single-cell RNA sequencing (scRNA-seq), have already begun to reveal, in a data-driven way, the diverse simultaneous facets of a cell's identity, from discrete cell types to continuous dynamic transitions and spatial locations. These developments will eventually allow a cell to be represented as a superposition of 'basis vectors', each determining a different (but possibly dependent) aspect of cellular organization and function. However, computational methods must also overcome considerable challenges-from handling technical noise and data scale to forming new abstractions of biology. As the scale of single-cell experiments continues to increase, new computational approaches will be essential for constructing and characterizing a reference map of cell identities.

A reduced-dimensionality approach to uncovering dyadic modes of body motion in conversations

Face-to-face conversations are central to human communication and a fascinating example of joint action. Beyond verbal content, one of the primary ways in which information is conveyed in conversations is body language. Body motion in natural conversations has been difficult to study precisely due to the large number of coordinates at play. There is need for fresh approaches to analyze and understand the data, in order to ask whether dyads show basic building blocks of coupled motion. Here we present a method for analyzing body motion during joint action using depth-sensing cameras, and use it to analyze a sample of scientific conversations. Our method consists of three steps: defining modes of body motion of individual participants, defining dyadic modes made of combinations of these individual modes, and lastly defining motion motifs as dyadic modes that occur significantly more often than expected given the single-person motion statistics. As a proof-of-concept, we analyze the motion of 12 dyads of scientists measured using two Microsoft Kinect cameras. In our sample, we find that out of many possible modes, only two were motion motifs: synchronized parallel torso motion in which the participants swayed from side to side in sync, and still segments where neither person moved. We find evidence of dyad individuality in the use of motion modes. For a randomly selected subset of 5 dyads, this individuality was maintained for at least 6 months. The present approach to simplify complex motion data and to define motion motifs may be used to understand other joint tasks and interactions. The analysis tools developed here and the motion dataset are publicly available.

Asymmetric latent semantic indexing for gene expression experiments visualization

We propose a new method to visualize gene expression experiments inspired by the latent semantic indexing technique originally proposed in the textual analysis context. By using the correspondence word-gene document-experiment, we define an asymmetric similarity measure of association for genes that accounts for potential hierarchies in the data, the key to obtain meaningful gene mappings. We use the polar decomposition to obtain the sources of asymmetry of the similarity matrix, which are later combined with previous knowledge. Genetic classes of genes are identified by means of a mixture model applied in the genes latent space. We describe the steps of the procedure and we show its utility in the Human Cancer dataset.

Mathematics in modern immunology

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space

When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes--phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.