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The continued scaling of genetic perturbation technologies combined with high-dimensional assays (microscopy and RNA-sequencing) has enabled genome-scale reverse-genetics experiments that go beyond single-endpoint measurements of growth or lethality. Datasets emerging from these experiments can be combined to construct “maps of biology”, in which perturbation readouts are placed in unified, relatable embedding spaces to capture known biological relationships and discover new ones. Construction of maps involves many technical choices in both experimental and computational protocols, motivating the design of benchmark procedures by which to evaluate map quality in a systematic, unbiased manner.In this work, we propose a framework for the steps involved in map building and demonstrate key classes of benchmarks to assess the quality of a map. We describe univariate benchmarks assessing perturbation quality and multivariate benchmarks assessing recovery of known biological relationships from large-scale public data sources. We demonstrate the application and interpretation of these benchmarks through example maps of scRNA-seq and phenomic imaging data.

Charting an organs’ biological atlas requires us to spatially resolve the entire single-cell transcriptome, and to relate such cellular features to the anatomical scale. Single-cell and single-nucleus RNA-seq (sc/snRNA-seq) can profile cells comprehensively, but lose spatial information. Spatial transcriptomics allows for spatial measurements, but at lower resolution and with limited sensitivity. Targeted in situ technologies solve both issues, but are limited in gene throughput. To overcome these limitations we present Tangram, a method that aligns sc/snRNA-seq data to various forms of spatial data collected from the same region, including MERFISH, STARmap, smFISH, Spatial Transcriptomics (Visium) and histological images. Tangram can map any type of sc/snRNA-seq data, including multimodal data such as those from SHARE-seq, which we used to reveal spatial patterns of chromatin accessibility. We demonstrate Tangram on healthy mouse brain tissue, by reconstructing a genome-wide anatomically integrated spatial map at single-cell resolution of the visual and somatomotor areas.

Establishing causal relationships between genetic alterations of human cancers and specific phenotypes of malignancy remains a challenge. We sequentially introduced mutations into healthy human melanocytes in up to five genes spanning six commonly disrupted melanoma pathways, forming nine genetically distinct cellular models of melanoma. We connected mutant melanocyte genotypes to malignant cell expression programs in vitro and in vivo, replicative immortality, malignancy, rapid tumor growth, pigmentation, metastasis, and histopathology. Mutations in malignant cells also affected tumor microenvironment composition and cell states. Our melanoma models shared genotype-associated expression programs with patient melanomas, and a deep learning model showed that these models partially recapitulated genotype-associated histopathological features as well. Thus, a progressive series of genome-edited human cancer models can causally connect genotypes carrying multiple mutations to phenotype.

With the advent of multiplex fluorescence in situ hybridization (FISH) and in situ RNA sequencing technologies, spatial transcriptomics analysis is advancing rapidly. Spatial transcriptomics provides spatial location and pattern information about cells in tissue sections at single cell resolution. Cell type classification of spatially-resolved cells can also be inferred by matching the spatial transcriptomics data to reference single cell RNA-sequencing (scRNA-seq) data with cell types determined by their gene expression profiles. However, robust cell type matching of the spatial cells is challenging due to the intrinsic differences in resolution between the spatial and scRNA-seq data. In this study, we systematically evaluated six computational algorithms for cell type matching across four spatial transcriptomics experimental protocols (MERFISH, smFISH, BaristaSeq, and ExSeq) conducted on the same mouse primary visual cortex (VISp) brain region. We find that while matching results of individual algorithms vary to some degree, they also show agreement to some extent. We present two ensembl meta-analysis strategies to combine the individual matching results and share the consensus matching results in the Cytosplore Viewer (https://viewer.cytosplore.org) for interactive visualization and data exploration. The consensus matching can also guide spot-based spatial data analysis using SSAM, allowing segmentation-free cell type assignment.

Single cell RNA-Seq (scRNA-seq) and other profiling assays have opened new windows into understanding the properties, regulation, dynamics, and function of cells at unprecedented resolution and scale. However, these assays are inherently destructive, precluding us from tracking the temporal dynamics of live cells, in cell culture or whole organisms. Raman microscopy offers a unique opportunity to comprehensively report on the vibrational energy levels of molecules in a label-free and non-destructive manner at a subcellular spatial resolution, but it lacks in genetic and molecular interpretability. Here, we developed Raman2RNA (R2R), an experimental and computational framework to infer single-cell expression profiles in live cells through label-free hyperspectral Raman microscopy images and multi-modal data integration and domain translation. We used spatially resolved single-molecule RNA-FISH (smFISH) data as anchors to link scRNA-seq profiles to the paired spatial hyperspectral Raman images, and trained machine learning models to infer expression profiles from Raman spectra at the single-cell level. In reprogramming of mouse fibroblasts into induced pluripotent stem cells (iPSCs), R2R accurately (r>0.96) inferred from Raman images the expression profiles of various cell states and fates, including iPSCs, mesenchymal-epithelial transition (MET) cells, stromal cells, epithelial cells, and fibroblasts. R2R outperformed inference from brightfield images, showing the importance of spectroscopic content afforded by Raman microscopy. Raman2RNA lays a foundation for future investigations into exploring single-cell genome-wide molecular dynamics through imaging data, in vitro and in vivo.

Single-cell RNA sequencing has revealed extensive transcriptional cell state diversity in cancer, often observed independently of genetic heterogeneity, raising the central question of how malignant cell states are encoded epigenetically. To address this, here we performed multiomics single-cell profiling-integrating DNA methylation, transcriptome and genotype within the same cells-of diffuse gliomas, tumors characterized by defined transcriptional cell state diversity. Direct comparison of the epigenetic profiles of distinct cell states revealed key switches for state transitions recapitulating neurodevelopmental trajectories and highlighted dysregulated epigenetic mechanisms underlying gliomagenesis. We further developed a quantitative framework to directly measure cell state heritability and transition dynamics based on high-resolution lineage trees in human samples. We demonstrated heritability of malignant cell states, with key differences in hierarchal and plastic cell state architectures in IDH-mutant glioma versus IDH-wild-type glioblastoma, respectively. This work provides a framework anchoring transcriptional cancer cell states in their epigenetic encoding, inheritance and transition dynamics.

Transformative technologies are enabling the construction of three-dimensional maps of tissues with unprecedented spatial and molecular resolution. Over the next seven years, the NIH Common Fund Human Biomolecular Atlas Program (HuBMAP) intends to develop a widely accessible framework for comprehensively mapping the human body at single-cell resolution by supporting technology development, data acquisition, and detailed spatial mapping. HuBMAP will integrate its efforts with other funding agencies, programs, consortia, and the biomedical research community at large towards the shared vision of a comprehensive, accessible three-dimensional molecular and cellular atlas of the human body, in health and under various disease conditions., HuBMAP supports technology development, data acquisition, and spatial analyses to generate comprehensive molecular and cellular three-dimensional tissue maps.

Charting a biological atlas of an organ, such as the brain, requires us to spatially-resolve whole transcriptomes of single cells, and to relate such cellular features to the histological and anatomical scales. Single-cell and single-nucleus RNA-Seq (sc/snRNA-seq) can map cells comprehensively5,6, but relating those to their histological and anatomical positions in the context of an organ’s common coordinate framework remains a major challenge and barrier to the construction of a cell atlas7–10. Conversely, Spatial Transcriptomics allows forin-situmeasurements11–13at the histological level, but at lower spatial resolution and with limited sensitivity. Targetedin situtechnologies1–3solve both issues, but are limited in gene throughput which impedes profiling of the entire transcriptome. Finally, as samples are collected for profiling, their registration to anatomical atlases often require human supervision, which is a major obstacle to build pipelines at scale. Here, we demonstrate spatial mapping of cells, histology, and anatomy in the somatomotor area and the visual area of the healthy adult mouse brain. We devise Tangram, a method that aligns snRNA-seq data to various forms of spatial data collected from the same brain region, including MERFISH1, STARmap2, smFISH3, and Spatial Transcriptomics4(Visium), as well as histological images and public atlases. Tangram can map any type of sc/snRNA-seq data, including multi-modal data such as SHARE-seq data5, which we used to reveal spatial patterns of chromatin accessibility. We equipped Tangram with a deep learning computer vision pipeline, which allows for automatic identification of anatomical annotations on histological images of mouse brain. By doing so, Tangram reconstructs a genome-wide, anatomically-integrated, spatial map of the visual and somatomotor area with ∼30,000 genes at single-cell resolution, revealing spatial gene expression and chromatin accessibility patterning beyond current limitation ofin-situtechnologies.

Single-cell transcriptomics can provide quantitative molecular signatures for large, unbiased samples of the diverse cell types in the brain1–3. With the proliferation of multi-omics datasets, a major challenge is to validate and integrate results into a biological understanding of cell-type organization. Here we generated transcriptomes and epigenomes from more than 500,000 individual cells in the mouse primary motor cortex, a structure that has an evolutionarily conserved role in locomotion. We developed computational and statistical methods to integrate multimodal data and quantitatively validate cell-type reproducibility. The resulting reference atlas—containing over 56 neuronal cell types that are highly replicable across analysis methods, sequencing technologies and modalities—is a comprehensive molecular and genomic account of the diverse neuronal and non-neuronal cell types in the mouse primary motor cortex. The atlas includes a population of excitatory neurons that resemble pyramidal cells in layer 4 in other cortical regions4. We further discovered thousands of concordant marker genes and gene regulatory elements for these cell types. Our results highlight the complex molecular regulation of cell types in the brain and will directly enable the design of reagents to target specific cell types in the mouse primary motor cortex for functional analysis., The authors describe an integrated atlas of the diverse cell types in the mouse primary motor cortex.

Single cell transcriptomics has transformed the characterization of brain cell identity by providing quantitative molecular signatures for large, unbiased samples of brain cell populations. With the proliferation of taxonomies based on individual datasets, a major challenge is to integrate and validate results toward defining biologically meaningful cell types. We used a battery of single-cell transcriptome and epigenome measurements generated by the BRAIN Initiative Cell Census Network (BICCN) to comprehensively assess the molecular signatures of cell types in the mouse primary motor cortex (MOp). We further developed computational and statistical methods to integrate these multimodal data and quantitatively validate the reproducibility of the cell types. The reference atlas, based on more than 600,000 high quality single-cell or -nucleus samples assayed by six molecular modalities, is a comprehensive molecular account of the diverse neuronal and non-neuronal cell types in MOp. Collectively, our study indicates that the mouse primary motor cortex contains over 55 neuronal cell types that are highly replicable across analysis methods, sequencing technologies, and modalities. We find many concordant multimodal markers for each cell type, as well as thousands of genes and gene regulatory elements with discrepant transcriptomic and epigenomic signatures. These data highlight the complex molecular regulation of brain cell types and will directly enable design of reagents to target specific MOp cell types for functional analysis.

We consider a stochastic version of the Wilson–Cowan model which accommodates for discrete populations of excitatory and inhibitory neurons. The model assumes a finite carrying capacity with the two populations being constant in size. The master equation that governs the dynamics of the stochastic model is analyzed by an expansion in powers of the inverse population size, yielding a coupled pair of non-linear Langevin equations with multiplicative noise. Gillespie simulations show the validity of the obtained approximation, for the parameter region where the system exhibits dynamical bistability. We report analytical progress by silencing the retroaction of excitatory neurons on inhibitory neurons, while still assigning the parameters so to fall in the region of deterministic bistability for the excitatory species. The proposed approach forms the basis of a perturbative generalization which applies to the case where a modest degree of coupling is restored.

Virtually every interesting natural phenomenon, not least life itself, entails physical systems being forced to flow thermodynamically up-hill, away from equilibrium rather than towards it. This requires the action of a mechanism, acting as an “engine”, which lashes the up-hill process to a more powerful one proceeding in its spontaneous, down-hill direction; in this way converting one disequilibrium into another. All organized and dynamic elements of creation, from the galactic to the atomic, can be viewed as powered by, or being the result of, engines of disequilibria conversion; each a link in a great hierarchical cascade of conversions. There is, however, widespread misunderstanding about how disequilibria conversions happen–and indeed about what physically causes them to happen–especially regarding the role of energy and of the physical meaning of free energy. We attempt here to describe and justify what we assert is the correct alternative view of how phenomena are powered in nature, focusing especially on the molecular-level conversion processes (often called “energy conserving”) that power life and that must, then acting in an entirely abiotic context, have driven it first into being.

Understanding the genetic and molecular drivers of phenotypic heterogeneity across individuals is central to biology. As new technologies enable fine-grained and spatially resolved molecular profiling, we need new computational approaches to integrate data from the same organ across different individuals into a consistent reference and to construct maps of molecular and cellular organization at histological and anatomical scales. Here, we review previous efforts and discuss challenges involved in establishing such a common coordinate framework, the underlying map of tissues and organs. We focus on strategies to handle anatomical variation across individuals and highlight the need for new technologies and analytical methods spanning multiple hierarchical scales of spatial resolution., National Institutes of Health (U.S.). The Human BioMolecular Atlas Program (Grant NIH 1OT2OD026673- 01), National Institutes of Health (U.S.). New Innovator Award (1DP2HG009623- 01), Chan Zuckerberg Initiative (Grant HCA2-A-1708-02755)

Human diffuse gliomas are incurable malignancies, where cellular state diversity fuels tumor progression and resistance to therapy. Single-cell RNA-sequencing (scRNAseq) studies recently charted the cellular states of the two major categories of human gliomas, IDH-mutant gliomas (IDH-MUT) and IDH-wildtype glioblastoma (GBM), showing that malignant cells partly recapitulate neurodevelopmental trajectories. This raises the central questions of how cell states are encoded epigenetically and whether unidirectional hierarchies or more plastic state transitions govern glioma cellular architectures. To address these questions, we generated multi-omics single-cell profiling, integrating DNA methylation (DNAme), transcriptome and genotyping of 1,728 cells from 11 GBM and IDH-MUT primary patient samples. Direct comparison of the methylomes of distinct glioma cell states revealed Polycomb repressive complex 2 (PRC2) targets DNAme as a key switch in the differentiation of malignant GBM cells. In contrast, dissecting aberrant circuits of hyper-methylation and gene expression in IDH-MUT gliomas, we observed a decoupling of the promoter methylation-expression relationship, with disruption of CTCF insulation and enhancer vulnerability which increases with cellular differentiation. To define cell state transition dynamics directly in patient samples, we generated high-resolution lineage histories of glioma cells using heritable DNAme changes, and projected the scRNAseq-derived cell states onto the lineage trees. This analysis demonstrated that cell states are heritable across malignant gliomas and, while in IDH-MUT differentiation far outpaces de-differentiation, GBM harbors a higher degree of cell state plasticity allowing reversion of GBM cells from a differentiated to a stem-like state. Overall, our work provides detailed insights into gliomagenesis, dissecting the epigenetic encoding, regulatory programs, and dynamics of the cellular states that drive human gliomas. Importantly, it also carries significant translational implication, as the high degree of de-differentiation in GBM challenges the paradigm of therapeutically targeting glioma stem-like cells to deprive tumors of their ability to regenerate.

Human diffuse gliomas are incurable brain tumors, where cellular state diversity fuels tumor progression and resistance to therapy. Single-cell RNA-sequencing (scRNAseq) studies recently charted the cellular states of the two major categories of human gliomas, IDH-mutant gliomas (IDH-MUT) and IDH-wildtype glioblastoma (GBM), showing that malignant cells partly recapitulate neurodevelopmental trajectories. This raises the central questions of how cell states are encoded epigenetically and whether unidirectional hierarchies or more plastic state transitions govern glioma cellular architectures. To address these questions, we generated multi-omics single-cell profiling, integrating DNA methylation (DNAme), transcriptome and genotyping of 1,728 cells from 11 GBM and IDH-MUT primary patient samples. The assessment of DNAme intra-tumoral heterogeneity of malignant cells revealed that single-cell DNAme profiles within tumors span multiple bulk subtypes, are associated with important biological features of malignant cells, and may be confounded by the tumor micro-environment. Such sources of intra-tumoral heterogeneity in bulk profiles are important to recognize, as DNAme profiling is increasingly being utilized for bulk clinical brain tumor classification. The direct comparison of the methylomes of distinct glioma cellular states revealed Polycomb repressive complex 2 (PRC2) targets DNAme as a key switch in the differentiation of malignant GBM cells. In contrast, dissecting aberrant circuits of hypermethylation and gene expression in IDH-MUT gliomas, we observed a decoupling of the promoter methylation-expression relationship, with disruption of CTCF insulation and enhancer vulnerability which increases with cellular differentiation. To define cell state transition dynamics directly in patient samples, we generated high-resolution lineage histories of glioma cells using heritable DNAme changes, and projected the scRNAseq-derived cell states onto the lineage trees. This analysis demonstrated that cell states are heritable across malignant gliomas and, while in IDH-MUT differentiation far outpaces de-differentiation, GBM harbors a higher degree of cellular state plasticity allowing reversion of GBM cells from a differentiated to a stem-like state. Overall, our work provides detailed insights into gliomagenesis, dissecting the epigenetic encoding, regulatory programs, and dynamics of the cellular states that drive human gliomas. Importantly, it also carries significant translational implication, as the high degree of de-differentiation in GBM challenges the paradigm of therapeutically targeting glioma stem-like cells to deprive tumors of their ability to regenerate. Citation Format: Federico Gaiti, Ronan Chaligne, Dana Silverbush, Joshua S. Schiffman, Hannah R. Weisman, Lloyd Kluegel, Simon Gritsch, Sunil D. Deochand, Alyssa R. Richman, Johanna Klughammer, Tommaso Biancalani, Christoph Muus, Caroline Sheridan, Alicia Alonso, Franco Izzo, Orit Rozenblatt-Rosen, Aviv Regev, Mario L. Suvà, Dan A. Landau. Deciphering differentiation hierarchies, heritability and plasticity in human gliomas via single-cell multi-omics [abstract]. In: Proceedings of the AACR Virtual Special Conference on Tumor Heterogeneity: From Single Cells to Clinical Impact; 2020 Sep 17-18. Philadelphia (PA): AACR; Cancer Res 2020;80(21 Suppl):Abstract nr PO-019.

Quantifying virulence remains a central problem in human health, pest control, disease ecology, and evolutionary biology. Bacterial virulence is typically quantified by theLT50(i.e.the time taken to kill 50% of infected hosts), however, such an indicator cannot account for the full complexity of the infection process, such as distinguishing between the pathogen’s ability to colonize vs. kill the hosts. Indeed, the pathogen needs to breach the primary defenses in order to colonize, find a suitable environment to replicate, and finally express the virulence factors that cause disease. Here, we show that two virulence attributes, namely pathogen lethality and invasiveness, can be disentangled from the survival curves of a laboratory population ofCaenorhabditis elegansnematodes exposed to three bacterial pathogens:Pseudomonas aeruginosa,Serratia marcescensandSalmonella enterica. We first show that the host population eventually experiences a constant mortality rate, which quantifies the lethality of the pathogen. We then show that the time necessary to reach this constant-mortality rate regime depends on the pathogen growth rate and colonization rate, and thus determines the pathogen invasiveness. Our framework reveals thatSerratia marcescensis particularly good at the initial colonization of the host, whereasSalmonella entericais a poor colonizer yet just as lethal once established.Pseudomonas aeruginosa, on the other hand, is both a good colonizer and highly lethal after becoming established. The ability to quantitatively characterize the ability of different pathogens to perform each of these steps has implications for treatment and prevention of disease and for the evolution and ecology of pathogens.

All known life on the Earth exhibits at least two non-trivial common features: the canonical genetic code and biological homochirality, both of which emerged prior to the Last Universal Common Ancestor state. This article describes recent efforts to provide a narrative of this epoch using tools from statistical mechanics. During the emergence of self-replicating life far from equilibrium in a period of chemical evolution, minimal models of autocatalysis show that homochirality would have necessarily co-evolved along with the efficiency of early-life self-replicators. Dynamical system models of the evolution of the genetic code must explain its universality and its highly refined error-minimization properties. These have both been accounted for in a scenario where life arose from a collective, networked phase where there was no notion of species and perhaps even individuality itself. We show how this phase ultimately terminated during an event sometimes known as the Darwinian transition, leading to the present epoch of tree-like vertical descent of organismal lineages. These examples illustrate concrete examples of universal biology: the quest for a fundamental understanding of the basic properties of living systems, independent of precise instantiation in chemistry or other media. This article is part of the themed issue ‘Reconceptualizing the origins of life’.

The origin of homochirality, the observed single-handedness of biological amino acids and sugars, has long been attributed to autocatalysis, a frequently assumed precursor for early life self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross-inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here we present a theory for a stochastic individual-level model of autocatalytic prebiotic self-replicators that are maintained out of thermal equilibrium. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states. Moreover, we show that this noise-induced bistability is robust with respect to diffusion of molecules of opposite chirality, and systems of diffusively coupled autocatalytic chemical reactions synchronize their final homochiral states when the self-replication is the dominant production mechanism for the chiral molecules. We conclude that nonequilibrium autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition.

Mutualisms between species play an important role in ecosystem function and stability. However, in some environments, the competitive aspects of an interaction may dominate the mutualistic aspects. Although these transitions could have far-reaching implications, it has been difficult to study the causes and consequences of this mutualistic–competitive transition in experimentally tractable systems. Here, we study a microbial cross-feeding mutualism in which each yeast strain supplies an essential amino acid for its partner strain. We find that, depending upon the amount of freely available amino acid in the environment, this pair of strains can exhibit an obligatory mutualism, facultative mutualism, competition, parasitism, competitive exclusion, or failed mutualism leading to extinction of the population. A simple model capturing the essential features of this interaction explains how resource availability modulates the interaction and predicts that changes in the dynamics of the mutualism in deteriorating environments can provide advance warning that collapse of the mutualism is imminent. We confirm this prediction experimentally by showing that, in the high nutrient competitive regime, the strains rapidly reach a common carrying capacity before slowly reaching the equilibrium ratio between the strains. However, in the low nutrient regime, before collapse of the obligate mutualism, we find that the ratio rapidly reaches its equilibrium and it is the total abundance that is slow to reach equilibrium. Our results provide a general framework for how mutualisms may transition between qualitatively different regimes of interaction in response to changes in nutrient availability in the environment., National Institutes of Health (U.S.) (New Innovator Award), Paul G. Allen Family Foundation (Distinguished Investigator Award), National Science Foundation (U.S.) (CAREER Award), National Science Foundation (U.S.). Graduate Research Fellowship Program

The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and nonorthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism shows that fluctuation-induced Turing patterns are observable, and are not strongly limited by the amplitude of demographic stochasticity nor by the value of the diffusion coefficients.

The observed single-handedness of biological amino acids and sugars has long been attributed to autocatalysis. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, we present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially-extended systems. We conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition., 8 pages, 4 figures

We present an analytical treatment of a genetic switch model consisting of two mutually inhibiting genes operating without cooperative binding of the corresponding transcription factors. Previous studies have numerically shown that these systems can exhibit bimodal dynamics without possessing two stable fixed points at the deterministic level. We analytically show that bimodality is induced by the noise and find the critical repression strength that controls a transition between the bimodal and non-bimodal regimes. We also identify characteristic polynomial scaling laws of the mean switching time between bimodal states. These results, independent of the model under study, reveal essential differences between these systems and systems with cooperative binding, where there is no critical threshold for bimodality and the mean switching time scales exponentially with the system size., Comment: 12 pages, 4 figures. To appear in Phys. Rev. Lett. (2015)

We develop a theoretical framework for analyzing ecological models with a multidimensional niche space. Our approach relies on the fact that ecological niches are described by sequences of symbols, which allows us to include multiple phenotypic traits. Ecological drivers, such as competitive exclusion, are modeled by introducing the Hamming distance between two sequences. We show that a suitable transform diagonalizes the community interaction matrix of these models, making it possible to predict the conditions for niche differentiation and, close to the instability onset, the asymptotically long time population distributions of niches. We exemplify our method using the Lotka-Volterra equations with an exponential competition kernel.

Mutualisms between species play an important role in ecosystem function and stability. However, in some environments, the competitive aspects of an interaction may dominate the mutualistic aspects. Although these transitions could have far-reaching implications, it has been difficult to study the causes and consequences of this mutualistic-competitive transition in experimentally tractable systems. Here, we study a microbial cross-feeding mutualism in which each yeast strain supplies an essential amino acid for its partner strain. We find that, depending upon the amount of freely available amino acid in the environment, this pair of strains can exhibit an obligatory mutualism, facultative mutualism, competition, parasitism, competitive exclusion, or failed mutualism leading to extinction of the population. A simple model capturing the essential features of this interaction explains how resource availability modulates the interaction and predicts that changes in the dynamics of the mutualism in deteriorating environments can provide advance warning that collapse of the mutualism is imminent. We confirm this prediction experimentally by showing that, in the high nutrient competitive regime, the strains rapidly reach a common carrying capacity before slowly reaching the equilibrium ratio between the strains. However, in the low nutrient regime, before collapse of the obligate mutualism, we find that the ratio rapidly reaches its equilibrium and it is the total abundance that is slow to reach equilibrium. Our results provide a general framework for how mutualisms may transition between qualitatively different regimes of interaction in response to changes in nutrient availability in the environment.

Bistability indicates the ability of a system to reside in either of two states. This is a fairly general paradigm that has found numerous applications in science, from liquid crystal displays to the lac operon in E. coli to the cell cycle oscillator in Xenopus laevis.

In order to study the phenomenon of noise-induced bistability we have expanded the master equation with respect to the cell volume, and obtained an approximated stochastic differential equation which was more amenable to analytical manipulations. As already remarked, the technique we have used made it possible to capture the multiplicative nature of noise which was essential to describe the dynamics. For the majority of systems, the factor that multiplies the noise is not necessary, and the stochastic dynamics can be understood within approximation schemes in which the noise acts as a linear perturbation. This occurs, for instance, for the type of stochastic dynamics we shall be interested in this section in which we investigate the role of the noise in pattern forming systems.

The investigation of the stochastic waves in the previous chapter, has involved an analysis of a spatially extended model in which space was represented as a regular lattice.

Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its deterministic limit. The role of stochastic fluctuations is investigated and shown to drive the emergence of stochastic waves beyond the region of the instability predicted from the deterministic theory. Simulations are performed to test the theoretical results and are analyzed via a generalized Fourier transform algorithm. This transform is defined using the eigenvectors of the discrete Laplacian defined on the network. A peak in the numerical power spectrum of the fluctuations is observed in quantitative agreement with the theoretical predictions., Comment: submitted to Phys. Rev. E