Colorectal Cancer Cells Enter a Diapause-like DTP State to Survive Chemotherapy.

Cancer cells enter a reversible drug-tolerant persister (DTP) state to evade death from chemotherapy and targeted agents. It is increasingly appreciated that DTPs are important drivers of therapy failure and tumor relapse. We combined cellular barcoding and mathematical modeling in patient-derived colorectal cancer models to identify and characterize DTPs in response to chemotherapy. Barcode analysis revealed no loss of clonal complexity of tumors that entered the DTP state and recurred following treatment cessation. Our data fit a mathematical model where all cancer cells, and not a small subpopulation, possess an equipotent capacity to become DTPs. Mechanistically, we determined that DTPs display remarkable transcriptional and functional similarities to diapause, a reversible state of suspended embryonic development triggered by unfavorable environmental conditions. Our study provides insight into how cancer cells use a developmentally conserved mechanism to drive the DTP state, pointing to novel therapeutic opportunities to target DTPs.

A dynamical systems treatment of transcriptomic trajectories in hematopoiesis.

Inspired by Waddington's illustration of an epigenetic landscape, cell-fate transitions have been envisioned as bifurcating dynamical systems, wherein exogenous signaling dynamics couple to the enormously complex signaling and transcriptional machinery of a cell to elicit qualitative transitions in its collective state. Single-cell RNA sequencing (scRNA-seq), which measures the distributions of possible transcriptional states in large populations of differentiating cells, provides an alternate view, in which development is marked by the variations of a myriad of genes. Here, we present a mathematical formalism for rigorously evaluating, from a dynamical systems perspective, whether scRNA-seq trajectories display statistical signatures consistent with bifurcations and, as a case study, pinpoint regions of multistability along the neutrophil branch of hematopoeitic differentiation. Additionally, we leverage the geometric features of linear instability to identify the low-dimensional phase plane in gene expression space within which the multistability unfolds, highlighting novel genetic players that are crucial for neutrophil differentiation. Broadly, we show that a dynamical systems treatment of scRNA-seq data provides mechanistic insights into the high-dimensional processes of cellular differentiation, taking a step toward systematic construction of mathematical models for transcriptomic dynamics.

Phenomenology and dynamics of competitive ecosystems beyond the niche-neutral regimes.

Structure, composition, and stability of ecological populations are shaped by the inter- and intraspecies interactions within their communities. It remains to be fully understood how the interplay of these interactions with other factors, such as immigration, controls the structure, the diversity, and the long-term stability of ecological systems in the presence of noise and fluctuations. We address this problem using a minimal model of interacting multispecies ecological communities that incorporates competition, immigration, and demographic noise. We find that a complete phase diagram exhibits rich behavior with multiple regimes that go beyond the classical "niche" and "neutral" regimes, extending and modifying the "rare biosphere" or "niche-like" dichotomy. In particular, we observe regimes that cannot be characterized as either niche or neutral where a multimodal species abundance distribution is observed. We characterize the transitions between the different regimes and show how these arise from the underlying kinetics of the species turnover, extinction, and invasion. Our model serves as a minimal null model of noisy competitive ecological systems, against which more complex models that include factors such as mutations and environmental noise can be compared.

petiteFinder: an automated computer vision tool to compute Petite colony frequencies in baker's yeast.

BACKGROUND: Mitochondrial respiration is central to cellular and organismal health in eukaryotes. In baker's yeast, however, respiration is dispensable under fermentation conditions. Because yeast are tolerant of this mitochondrial dysfunction, yeast are widely used by biologists as a model organism to ask a variety of questions about the integrity of mitochondrial respiration. Fortunately, baker's yeast also display a visually identifiable Petite colony phenotype that indicates when cells are incapable of respiration. Petite colonies are smaller than their Grande (wild-type) counterparts, and their frequency can be used to infer the integrity of mitochondrial respiration in populations of cells. Unfortunately, the computation of Petite colony frequencies currently relies on laborious manual colony counting methods which limit both experimental throughput and reproducibility. RESULTS: To address these problems, we introduce a deep learning enabled tool, petiteFinder, that increases the throughput of the Petite frequency assay. This automated computer vision tool detects Grande and Petite colonies and computes Petite colony frequencies from scanned images of Petri dishes. It achieves accuracy comparable to human annotation but at up to 100 times the speed and outperforms semi-supervised Grande/Petite colony classification approaches. Combined with the detailed experimental protocols we provide, we believe this study can serve as a foundation to standardize this assay. Finally, we comment on how Petite colony detection as a computer vision problem highlights ongoing difficulties with small object detection in existing object detection architectures. CONCLUSION: Colony detection with petiteFinder results in high accuracy Petite and Grande detection in images in a completely automated fashion. It addresses issues in scalability and reproducibility of the Petite colony assay which currently relies on manual colony counting. By constructing this tool and providing details of experimental conditions, we hope this study will enable larger-scale experiments that rely on Petite colony frequencies to infer mitochondrial function in yeast.

The size of the immune repertoire of bacteria.

Some bacteria and archaea possess an immune system, based on the CRISPR-Cas mechanism, that confers adaptive immunity against viruses. In such species, individual prokaryotes maintain cassettes of viral DNA elements called spacers as a memory of past infections. Typically, the cassettes contain several dozen expressed spacers. Given that bacteria can have very large genomes and since having more spacers should confer a better memory, it is puzzling that so little genetic space would be devoted by prokaryotes to their adaptive immune systems. Here, assuming that CRISPR functions as a long-term memory-based defense against a diverse landscape of viral species, we identify a fundamental tradeoff between the amount of immune memory and effectiveness of response to a given threat. This tradeoff implies an optimal size for the prokaryotic immune repertoire in the observational range.

How adaptive immunity constrains the composition and fate of large bacterial populations.

Features of the CRISPR-Cas system, in which bacteria integrate small segments of phage genome (spacers) into their DNA to neutralize future attacks, suggest that its effect is not limited to individual bacteria but may control the fate and structure of whole populations. Emphasizing the population-level impact of the CRISPR-Cas system, recent experiments show that some bacteria regulate CRISPR-associated genes via the quorum sensing (QS) pathway. Here we present a model that shows that from the highly stochastic dynamics of individual spacers under QS control emerges a rank-abundance distribution of spacers that is time invariant, a surprising prediction that we test with dynamic spacer-tracking data from literature. This distribution depends on the state of the competing phage-bacteria population, which due to QS-based regulation may coexist in multiple stable states that vary significantly in their phage-to-bacterium ratio, a widely used ecological measure to characterize microbial systems.

Single-Cell RNA Sequencing: A New Window into Cell Scale Dynamics.

Single-cell genomics has recently emerged as a powerful tool for observing multicellular systems at a much higher level of resolution and depth than previously possible. High-throughput single-cell RNA sequencing techniques are able to simultaneously quantify expression levels of several thousands of genes within individual cells for tens of thousands of cells within a complex tissue. This has led to development of novel computational methods to analyze this high-dimensional data, investigating longstanding and fundamental questions regarding the granularity of cell types, the definition of cell states, and transitions from one cell type to another along developmental trajectories. In this perspective, we outline this emerging field starting from the "input data" (e.g., quantifying transcription levels in single cells), which are analyzed to define "identities" (e.g., cell types, states, and key genes) and to build "interactions" using models that can infer relations and transitions between cells.

Collective polarization model for gradient sensing via Dachsous-Fat intercellular signaling.

Dachsous-Fat signaling via the Hippo pathway influences proliferation during Drosophila development, and some of its mammalian homologs are tumor suppressors, highlighting its role as a universal growth regulator. The Fat/Hippo pathway responds to morphogen gradients and influences the in-plane polarization of cells and orientation of divisions, linking growth with tissue patterning. Remarkably, the Fat pathway transduces a growth signal through the polarization of transmembrane complexes that responds to both morphogen level and gradient. Dissection of these complex phenotypes requires a quantitative model that provides a systematic characterization of the pathway. In the absence of detailed knowledge of molecular interactions, we take a phenomenological approach that considers a broad class of simple models, which are sufficiently constrained by observations to enable insight into possible mechanisms. We predict two modes of local/cooperative interactions among Fat-Dachsous complexes, which are necessary for the collective polarization of tissues and enhanced sensitivity to weak gradients. Collective polarization convolves level and gradient of input signals, reproducing known phenotypes while generating falsifiable predictions. Our construction of a simplified signal transduction map allows a generalization of the positional value model and emphasizes the important role intercellular interactions play in growth and patterning of tissues.

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques.

BACKGROUND: How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10(11) mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages. RESULTS: While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs. CONCLUSIONS: Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Dynamics of immune memory and learning in bacterial communities.

From bacteria to humans, adaptive immune systems provide learned memories of past infections. Despite their vast biological differences, adaptive immunity shares features from microbes to vertebrates such as emergent immune diversity, long-term coexistence of hosts and pathogens, and fitness pressures from evolving pathogens and adapting hosts, yet there is no conceptual model that addresses all of these together. To this end, we propose and solve a simple phenomenological model of CRISPR-based adaptive immunity in microbes. We show that in coexisting phage and bacteria populations, immune diversity in both populations is coupled and emerges spontaneously, that bacteria track phage evolution with a context-dependent lag, and that high levels of diversity are paradoxically linked to low overall CRISPR immunity. We define average immunity, an important summary parameter predicted by our model, and use it to perform synthetic time-shift analyses on available experimental data to reveal different modalities of coevolution. Finally, immune cross-reactivity in our model leads to qualitatively different states of evolutionary dynamics, including an influenza-like traveling wave regime that resembles a similar state in models of vertebrate adaptive immunity. Our results show that CRISPR immunity provides a tractable model, both theoretically and experimentally, to understand general features of adaptive immunity.

Inferring single-cell transcriptomic dynamics with structured latent gene expression dynamics.

Gene expression dynamics provide directional information for trajectory inference from single-cell RNA sequencing data. Traditional approaches compute RNA velocity using strict modeling assumptions about transcription and splicing of RNA. This can fail in scenarios where multiple lineages have distinct gene dynamics or where rates of transcription and splicing are time dependent. We present "LatentVelo," an approach to compute a low-dimensional representation of gene dynamics with deep learning. LatentVelo embeds cells into a latent space with a variational autoencoder and models differentiation dynamics on this "dynamics-based" latent space with neural ordinary differential equations. LatentVelo infers a latent regulatory state that controls the dynamics of an individual cell to model multiple lineages. LatentVelo can predict latent trajectories, describing the inferred developmental path for individual cells rather than just local RNA velocity vectors. The dynamics-based embedding batch corrects cell states and velocities, outperforming comparable autoencoder batch correction methods that do not consider gene expression dynamics.

Contingency and selection in mitochondrial genome dynamics.

High frequencies of mutant mitochondrial DNA (mtDNA) in human cells lead to cellular defects that are associated with aging and disease. Yet much remains to be understood about the dynamics of the generation of mutant mtDNAs and their relative replicative fitness that informs their fate within cells and tissues. To address this, we utilize long-read single-molecule sequencing to track mutational trajectories of mtDNA in the model organism Saccharomyces cerevisiae. This model has numerous advantages over mammalian systems due to its much larger mtDNA and ease of artificially competing mutant and wild-type mtDNA copies in cells. We show a previously unseen pattern that constrains subsequent excision events in mtDNA fragmentation in yeast. We also provide evidence for the generation of rare and contentious non-periodic mtDNA structures that lead to persistent diversity within individual cells. Finally, we show that measurements of relative fitness of mtDNA fit a phenomenological model that highlights important biophysical parameters governing mtDNA fitness. Altogether, our study provides techniques and insights into the dynamics of large structural changes in genomes that we show are applicable to more complex organisms like humans.

Characterization of the minimal residual disease state reveals distinct evolutionary trajectories of human glioblastoma.

Recurrence of solid tumors renders patients vulnerable to advanced, treatment-refractory disease state with mutational and oncogenic landscape distinctive from initial diagnosis. Improving outcomes for recurrent cancers requires a better understanding of cell populations that expand from the post-therapy, minimal residual disease (MRD) state. We profile barcoded tumor stem cell populations through therapy at tumor initiation, MRD, and recurrence in our therapy-adapted, patient-derived xenograft models of glioblastoma (GBM). Tumors show distinct patterns of recurrence in which clonal populations exhibit either a pre-existing fitness advantage or an equipotency fitness acquired through therapy. Characterization of the MRD state by single-cell and bulk RNA sequencing reveals a tumor-intrinsic immunomodulatory signature with prognostic significance at the transcriptomic level and in proteomic analysis of cerebrospinal fluid (CSF) collected from patients with GBM. Our results provide insight into the innate and therapy-driven dynamics of human GBM and the prognostic value of interrogating the MRD state in solid cancers.

Achieving optimal growth through product feedback inhibition in metabolism.

Recent evidence suggests that the metabolism of some organisms, such as Escherichia coli, is remarkably efficient, producing close to the maximum amount of biomass per unit of nutrient consumed. This observation raises the question of what regulatory mechanisms enable such efficiency. Here, we propose that simple product-feedback inhibition by itself is capable of leading to such optimality. We analyze several representative metabolic modules--starting from a linear pathway and advancing to a bidirectional pathway and metabolic cycle, and finally to integration of two different nutrient inputs. In each case, our mathematical analysis shows that product-feedback inhibition is not only homeostatic but also, with appropriate feedback connections, can minimize futile cycling and optimize fluxes. However, the effectiveness of simple product-feedback inhibition comes at the cost of high levels of some metabolite pools, potentially associated with toxicity and osmotic imbalance. These large metabolite pool sizes can be restricted if feedback inhibition is ultrasensitive. Indeed, the multi-layer regulation of metabolism by control of enzyme expression, enzyme covalent modification, and allostery is expected to result in such ultrasensitive feedbacks. To experimentally test whether the qualitative predictions from our analysis of feedback inhibition apply to metabolic modules beyond linear pathways, we examine the case of nitrogen assimilation in E. coli, which involves both nutrient integration and a metabolic cycle. We find that the feedback regulation scheme suggested by our mathematical analysis closely aligns with the actual regulation of the network and is sufficient to explain much of the dynamical behavior of relevant metabolite pool sizes in nutrient-switching experiments.

Roles of phenotypic heterogeneity and microenvironment feedback in early tumor development.

The local microenvironment of a tumor plays an important and commonly observed role in cancer development and progression. Dynamic changes in the tissue microenvironment are thought to epigenetically disrupt healthy cellular phenotypes and drive cancer incidence. Despite the experimental work in this area there are no conceptual models to understand the interplay between the epigenetic dysregulation in the microenvironment of early tumors and the appearance of cancer driver mutations. Here, we develop a minimal model of the tissue microenvironment which considers three interacting subpopulations: healthy, phenotypically dysregulated, and mutated cancer cells. Healthy cells can epigenetically (reversibly) transition to the dysregulated phenotype, and from there to the cancer state. The epigenetic transition rates of noncancer cells can be influenced by the number of cancer cells in the microenvironment (termed microenvironment feedback). Our model delineates the regime in which microenvironment feedback accelerates the rate of cancer initiation. In addition, the model shows when and how microenvironment feedback may inhibit cancer progression. We discuss how our framework may provide resolution to some of the puzzling experimental observations of slow cancer progression.

An Automated Tabletop Continuous Culturing System with Multicolor Fluorescence Monitoring for Microbial Gene Expression and Long-Term Population Dynamics.

Real-time monitoring of gene expression dynamics and population levels in a multispecies microbial community could enable the study of the role of changing gene expression patterns on eco-evolutionary outcomes. Here we report the design and validation of a unique experimental platform with an in situ fluorescence measurement system that has high dynamic range and temporal resolution and is capable of monitoring multiple fluorophores for long-term gene expression and population dynamics experiments. We demonstrate the capability of our system to capture gene expression dynamics in response to external perturbations in two synthetic genetic systems: a simple inducible genetic circuit and a bistable toggle switch. Finally, in exploring the population dynamics of a two species microbial community, we show that our system can capture the switch between competitive exclusion and long-term coexistence in response to different nutrient conditions.

Information processing and signal integration in bacterial quorum sensing.

Bacteria communicate using secreted chemical signaling molecules called autoinducers in a process known as quorum sensing. The quorum-sensing network of the marine bacterium Vibrio harveyi uses three autoinducers, each known to encode distinct ecological information. Yet how cells integrate and interpret the information contained within these three autoinducer signals remains a mystery. Here, we develop a new framework for analyzing signal integration on the basis of information theory and use it to analyze quorum sensing in V. harveyi. We quantify how much the cells can learn about individual autoinducers and explain the experimentally observed input-output relation of the V. harveyi quorum-sensing circuit. Our results suggest that the need to limit interference between input signals places strong constraints on the architecture of bacterial signal-integration networks, and that bacteria probably have evolved active strategies for minimizing this interference. Here, we analyze two such strategies: manipulation of autoinducer production and feedback on receptor number ratios.

A quantitative comparison of sRNA-based and protein-based gene regulation.

Small non-coding RNAs (sRNAs) have important functions as genetic regulators in prokaryotes. sRNAs act post-transcriptionally through complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. Although the mean steady-state behavior of sRNA-regulated proteins exhibits a distinctive tunable threshold linear behavior, our analysis shows that transcriptional bursting leads to significantly higher intrinsic noise in sRNA-based regulation than in TF-based regulation in a large range of expression levels and limits the ability of sRNAs to perform quantitative signaling. Nonetheless, we find that sRNAs are better than TFs at filtering noise in input signals. Additionally, we find that sRNAs allow cells to respond rapidly to large changes in input signals. These features suggest a 'niche' for sRNAs in allowing cells to transition quickly yet reliably between distinct states. This functional niche is consistent with the widespread appearance of sRNAs in stress response and quasi-developmental networks in prokaryotes.

Cell competition during reprogramming gives rise to dominant clones.

The ability to generate induced pluripotent stem cells from differentiated cell types has enabled researchers to engineer cell states. Although studies have identified molecular networks that reprogram cells to pluripotency, the cellular dynamics of these processes remain poorly understood. Here, by combining cellular barcoding, mathematical modeling, and lineage tracing approaches, we demonstrate that reprogramming dynamics in heterogeneous populations are driven by dominant "elite" clones. Clones arise a priori from a population of poised mouse embryonic fibroblasts derived from Wnt1-expressing cells that may represent a neural crest-derived population. This work highlights the importance of cellular dynamics in fate programming outcomes and uncovers cell competition as a mechanism by which cells with eliteness emerge to occupy and dominate the reprogramming niche.