Clone Size Distribution Research Articles

Clonal dynamics of surface-driven growing tissues.

The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted therapies for aberrant growth, such as in cancer. Inferring the mode of tissue growth, whether it is driven by cells on the surface or by cells in the bulk, is possible in cell culture experiments but difficult in most tissues in living organisms (in vivo). Genetic tracing experiments, where a subset of cells is labeled with inheritable markers, have become important experimental tools to study cell fate in vivo. Here we show that the mode of tissue growth is reflected in the size distribution of the progeny of marked cells. To this end, we derive the clone size distributions using analytical calculations in the limit of negligible cell migration and cell death, and we test our predictions with an agent-based stochastic sampling technique. We show that for surface-driven growth the clone size distribution takes a characteristic power-law form with an exponent determined by fluctuations of the tissue surface. Our results propose a possible way of determining the mode of tissue growth from genetic tracing experiments.

Minimizing cell number fluctuations in self-renewing tissues with a stem-cell niche.

Self-renewing tissues require that a constant number of proliferating cells is maintained over time. This maintenance can be ensured at the single-cell level or the population level. Maintenance at the population level leads to fluctuations in the number of proliferating cells over time. Often, it is assumed that those fluctuations can be reduced by increasing the number of asymmetric divisions, i.e., divisions where only one of the daughter cells remains proliferative. Here, we study a model of cell proliferation that incorporates a stem-cell niche of fixed size, and explicitly model the cells inside and outside the niche. We find that in this model, fluctuations are minimized when the difference in growth rate between the niche and the rest of the tissue is maximized and all divisions are symmetric divisions, producing either two proliferating or two nonproliferating daughters. We show that this optimal state leaves visible signatures in clone size distributions and could thus be detected experimentally.

Aplastic Anemia Patients Have Diverse T Cell Repertoires and Flexible T Cell Responses Similar to Healthy Individuals

Acquired aplastic anemia (AA) is a bone marrow failure disease caused by T cell-mediated autoimmune attack on hematopoietic stem and progenitor cells (HSPCs). Identifying autoreactive T cells in AA has been challenging. Advances in T cell receptor (TCR) sequencing and the discovery of Human Leukocyte Antigen Class I (HLA-I) risk alleles linked to autoantigen presentation in AA have rekindled interest in exploring T cell repertoires in AA. We hypothesized that autoreactive CD8 + T cells in AA may have convergent TCR structures allowing them to recognize AA autoantigens presented by specific HLA-I risk alleles. To test our hypothesis, we analyzed TCR repertoires and HLA-restricted CD8 + T cell reactivity in AA patients. Using TCR Vβ (TRB) sequencing, we analyzed 83 patient samples obtained at AA diagnosis or relapse. High-risk alleles HLA-B*14:02 and B*40:02 were present in 26% and 10% of patients, respectively. HLA-DR*15 was present in 24%. Patient samples were largely sorted bone marrow (BM) CD8 + T lymphocytes. Patient TRB repertoires were compared to those in 709 control samples, largely of unsorted peripheral blood (PB). To account for sampling differences, we downsampled sequences to the minimum number of clones in the matching tissue. Normalized clone size distributions were visualized on rank plots (Fig 1). TRB repertoires in both patients and controls were diverse. Highly expanded clones (>5%) were rare in either group. Patients had 1,415,069 unique CDR3 amino acid sequences (CDR3AA), of which 106,446 (7.5%) were shared by ≥2 patients. Among the 106,446 shared CDR3AA, 95.4% were found in controls, and 4.3% TCRs had reported specificity to exogenous (mostly viral) or endogenous antigens in VDJdb. 4,920 (4.6%) of the shared CDR3AA were detected only in patients (median 2 patients (2-25)). Of these, 190 exhibited TCR convergence in ≥1 patient, such that the same CDR3AA was encoded by ≥2 distinct nucleotide sequences. Clustering 4,920 patient-associated CDR3AA using GLIPH (Grouping of lymphocyte interactions by paratope hotspots) identified 43 TCR antigen convergence groups. CDR3AA in each cluster were not significantly expanded in the majority of patients and were not enriched for the high-risk alleles HLA-B*14:02 or B*40:02. Our data suggest that most CDR3AA in AA are private (unique to individual patients). Shared autoreactive CDR3AA may exist in patients but are likely to also be present in healthy individuals. As the next step towards identifying autoreactive T cells, we focused on AA patients with known HLA-I risk alleles. We tested their CD8 + T cells for reactivity with endogenously expressed antigens by stimulating T cells with hematopoietic cell lines engineered to express single HLA-I alleles matching those of the patients (Fig 2). TRB sequencing showed increased clonality and significant expansion of a subset of clonotypes after T cell stimulation. Interferon γ enzyme-linked immunospot assays confirmed the expanded T cells' responsiveness to antigens presented by HLA alleles used for T cell stimulation. Additionally, these expanded T cells demonstrated variable reactivity to cells expressing other HLA alleles from the same patient. Among the 1% of CDR3AA clonotypes most highly expanded with single HLA-I alleles (63-3000-fold), we identified several that were expanded in an HLA-restricted manner. However, several highly expanded CDR3AA were highly expanded with multiple HLA alleles. Potential reasons for expansion of some CDR3AA after stimulation with cells expressing different HLA alleles include 1) binding of the same CDR3AA to different antigens presented by distinct HLA alleles, 2) expansion in response to the same antigens presented by distinct HLA alleles, or 3) expansion in response to non-HLA antigens. In conclusion, our data show diverse and mostly private TRB repertoires in AA patients. Our in vitro findings suggest that much like T cell responses in non-AA individuals, T cell responses in AA are diverse and exhibit flexibility with respect to activation in response to various endogenous antigens in the context of different self HLA-I alleles. Given the diversity of TCR responses observed in AA patients, the tissue specificity of autoimmune attack and established association with risk HLA-I alleles in AA remain a mystery and likely require HSPC-specific autoantigen expression and efficient autoantigen presentation by individual patients' HLA-I alleles.

Impact of crowding on the diversity of expanding populations

Crowding effects critically impact the self-organization of densely packed cellular assemblies, such as biofilms, solid tumors, and developing tissues. When cells grow and divide, they push each other apart, remodeling the structure and extent of the population's range. Recent work has shown that crowding has a strong impact on the strength of natural selection. However, the impact of crowding on neutral processes, which controls the fate of new variants as long as they are rare, remains unclear. Here, we quantify the genetic diversity of expanding microbial colonies and uncover signatures of crowding in the site frequency spectrum. By combining Luria-Delbrück fluctuation tests, lineage tracing in a novel microfluidic incubator, cell-based simulations, and theoretical modeling, we find that the majority of mutations arise behind the expanding frontier, giving rise to clones that are mechanically "pushed out" of the growing region by the proliferating cells in front. These excluded-volume interactions result in a clone-size distribution that solely depends on where the mutation first arose relative to the front and is characterized by a simple power law for low-frequency clones. Our model predicts that the distribution depends on a single parameter-the characteristic growth layer thickness-and hence allows estimation of the mutation rate in a variety of crowded cellular populations. Combined with previous studies on high-frequency mutations, our finding provides a unified picture of the genetic diversity in expanding populations over the whole frequency range and suggests a practical method to assess growth dynamics by sequencing populations across spatial scales.

Inferring the T cell repertoire dynamics of healthy individuals

The adaptive immune system is a diverse ecosystem that responds to pathogens by selecting cells with specific receptors. While clonal expansion in response to particular immune challenges has been extensively studied, we do not know the neutral dynamics that drive the immune system in the absence of strong stimuli. Here, we learn the parameters that underlie the clonal dynamics of the T cell repertoire in healthy individuals of different ages, by applying Bayesian inference to longitudinal immune repertoire sequencing (RepSeq) data. Quantifying the experimental noise accurately for a given RepSeq technique allows us to disentangle real changes in clonal frequencies from noise. We find that the data are consistent with clone sizes following a geometric Brownian motion and show that its predicted steady state is in quantitative agreement with the observed power-law behavior of the clone-size distribution. The inferred turnover time scale of the repertoire increases with patient age and depends on the clone size in some individuals.

Stem cell homeostasis regulated by hierarchy and neutral competition

Tissue stem cells maintain themselves through self-renewal while constantly supplying differentiating cells. Two distinct models have been proposed as mechanisms of stem cell homeostasis. According to the classical model, there is hierarchy among stem cells, and master stem cells produce stem cells by asymmetric division; whereas, according to the recent model, stem cells are equipotent and neutrally compete. However, the mechanism remains controversial in several tissues and species. Here, we developed a mathematical model linking the two models, named the hierarchical neutral competition (hNC) model. Our theoretical analysis showed that the combination of the hierarchy and neutral competition exhibited bursts in clonal expansion, which was consistent with experimental data of rhesus macaque hematopoiesis. Furthermore, the scaling law in clone size distribution, considered a unique characteristic of the recent model, was satisfied even in the hNC model. Based on the findings above, we proposed the criterion for distinguishing the three models based on experiments.

Regulation of stem cell dynamics through volume exclusion

The maintenance and regeneration of adult tissues rely on the self-renewal of stem cells. Regeneration without over-proliferation requires precise regulation of the stem cell proliferation and differentiation rates. The nature of such regulatory mechanisms in different tissues, and how to incorporate them in models of stem cell population dynamics, is incompletely understood. The critical birth-death (CBD) process is widely used to model stem cell populations, capturing key phenomena, such as scaling laws in clone size distributions. However, the CBD process neglects regulatory mechanisms. Here, we propose the birth-death process with volume exclusion (vBD), a variation of the birth-death process that considers crowding effects, such as may arise due to limited space in a stem cell niche. While the deterministic rate equations predict a single non-trivial attracting steady state, the master equation predicts extinction and transient distributions of stem cell numbers with three possible behaviours: long-lived quasi-steady state (QSS), and short-lived bimodal or unimodal distributions. In all cases, we approximate solutions to the vBD master equation using a renormalized system-size expansion, QSS approximation and the Wentzel–Kramers–Brillouin method. Our study suggests that the size distribution of a stem cell population bears signatures that are useful to detect negative feedback mediated via volume exclusion.

Branching structure of genealogies in spatially growing populations and its implications for population genetics inference

Spatial models where growth is limited to the population edge have been instrumental to understanding the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.

Lineage tracing in human tissues.

The dynamical process of cell division that underpins homeostasis in the human body cannot be directly observed in vivo, but instead is measurable from the pattern of somatic genetic or epigenetic mutations that accrue in tissues over an individual's lifetime. Because somatic mutations are heritable, they serve as natural lineage tracing markers that delineate clonal expansions. Mathematical analysis of the distribution of somatic clone sizes gives a quantitative readout of the rates of cell birth, death, and replacement. In this review we explore the broad range of somatic mutation types that have been used for lineage tracing in human tissues, introduce the mathematical concepts used to infer dynamical information from these clone size data, and discuss the insights of this lineage tracing approach for our understanding of homeostasis and cancer development. We use the human colon as a particularly instructive exemplar tissue. There is a rich history of human somatic cell dynamics surreptitiously written into the cell genomes that is being uncovered by advances in sequencing and careful mathematical analysis lineage of tracing data. © 2022 The Authors. The Journal of Pathology published by John Wiley & Sons Ltd on behalf of The Pathological Society of Great Britain and Ireland.

Clonal Architecture and Evolutionary Dynamics in Acute Myeloid Leukemias.

Simple SummaryAcute myeloid leukemias (AML) results from the accumulation of genetic and epigenetic alterations, often in the context of an aging hematopoietic environment. The development of high-throughput sequencing—and more recently, of single-cell technologies—has shed light on the intratumoral diversity of leukemic cells. Taking AML as a model disease, we review the multiple sources of heterogeneity of leukemic cells and discuss the definition of a leukemic clone. After introducing the two dimensions contributing to clonal diversity, namely, richness (number of leukemic clones) and evenness (distribution of clone sizes), we discuss the mechanisms at the origin of clonal emergence and the causes of clonal dynamics including neutral drift, and cell-intrinsic and -extrinsic influences on clonal fitness. After reviewing the prognostic role of leukemic diversity on patients’ outcome, we discuss how a better understanding of AML as an evolutionary process could lead to the design of novel therapeutic strategies for this disease. Acute myeloid leukemias (AML) results from the accumulation of genetic and epigenetic alterations, often in the context of an aging hematopoietic environment. The development of high-throughput sequencing—and more recently, of single-cell technologies—has shed light on the intratumoral diversity of leukemic cells. Taking AML as a model disease, we review the multiple sources of genetic, epigenetic, and functional heterogeneity of leukemic cells and discuss the definition of a leukemic clone extending its definition beyond genetics. After introducing the two dimensions contributing to clonal diversity, namely, richness (number of leukemic clones) and evenness (distribution of clone sizes), we discuss the mechanisms at the origin of clonal emergence (mutation rate, number of generations, and effective size of the leukemic population) and the causes of clonal dynamics. We discuss the possible role of neutral drift, but also of cell-intrinsic and -extrinsic influences on clonal fitness. After reviewing available data on the prognostic role of genetic and epigenetic diversity of leukemic cells on patients’ outcome, we discuss how a better understanding of AML as an evolutionary process could lead to the design of novel therapeutic strategies in this disease.

Understanding adaptive immune system as reinforcement learning

The adaptive immune system of vertebrates can detect, respond to, and memorize diverse pathogens from past experience. While the clonal selection of T helper (Th) cells is the simple and established mechanism to better recognize new pathogens, the question that still remains unexplored is how the Th cells can acquire better ways to bias the responses of immune cells for eliminating pathogens more efficiently by translating the recognized antigen information into regulatory signals. In this work, we address this problem by associating the adaptive immune network organized by the Th cells with reinforcement learning (RL). By employing recent advancements of network-based RL, we show that the Th immune network can acquire the association between antigen patterns of and the effective responses to pathogens. Moreover, the clonal selection as well as other inter-cellular interactions are derived as a learning rule of the network. We also demonstrate that the stationary clone-size distribution after learning shares characteristic features with those observed experimentally. Our theoretical framework may contribute to revising and renewing our understanding of adaptive immunity as a learning system.

The naive T-cell receptor repertoire has an extremely broad distribution of clone sizes.

The clone size distribution of the human naive T-cell receptor (TCR) repertoire is an important determinant of adaptive immunity. We estimated the abundance of TCR sequences in samples of naive T cells from blood using an accurate quantitative sequencing protocol. We observe most TCR sequences only once, consistent with the enormous diversity of the repertoire. However, a substantial number of sequences were observed multiple times. We detect abundant TCR sequences even after exclusion of methodological confounders such as sort contamination, and multiple mRNA sampling from the same cell. By combining experimental data with predictions from models we describe two mechanisms contributing to TCR sequence abundance. TCRα abundant sequences can be primarily attributed to many identical recombination events in different cells, while abundant TCRβ sequences are primarily derived from large clones, which make up a small percentage of the naive repertoire, and could be established early in the development of the T-cell repertoire.

A marker-independent lineage-tracing system to quantify clonal dynamics and stem cell functionality in cancer tissue.

Lineage tracing is a powerful tool that can be used to uncover cell fates. Here, we describe a novel method for the quantitative analysis of clonal dynamics in grafted cancer tissues. The protocol involves the preparation and validation of cells for lineage tracing, establishment of grafts and label induction, analysis of clone-size distribution and fitting of the experimental data to a mathematical tumor growth model. In contrast to other lineage-tracing strategies, the method described here assesses stem cell functionality and infers tumor expansion dynamics independently of molecular markers such as putative cancer stem cell (CSC)-specific genes. The experimental system and analytical framework presented can be used to quantify clonal advantages that specific mutations provide, in both the absence and presence of (targeted) therapeutic agents. This protocol typically takes ~20 weeks to complete from cell line selection to inference of growth dynamics, depending on the grafted cancer growth rate.

Relating evolutionary selection and mutant clonal dynamics in normal epithelia.

Cancer develops from mutated cells in normal tissues. Whether somatic mutations alter normal cell dynamics is key to understanding cancer risk and guiding interventions to reduce it. An analysis of the first incomplete moment of size distributions of clones carrying cancer-associated mutations in normal human eyelid skin gives a good fit with neutral drift, arguing mutations do not affect cell fate. However, this suggestion conflicts with genetic evidence in the same dataset that argues for strong positive selection of a subset of mutations. This implies cells carrying these mutations have a competitive advantage over normal cells, leading to large clonal expansions within the tissue. In the normal epithelium, clone growth is constrained by the limited size of the proliferating compartment and competition with surrounding cells. We show that if these factors are taken into account, the first incomplete moment of the clone size distribution is unable to exclude non-neutral behaviour. Furthermore, experimental factors can make a non-neutral clone size distribution appear neutral. We validate these principles with a new experimental dataset showing that when experiments are appropriately designed, the first incomplete moment can be a useful indicator of non-neutral competition. Finally, we discuss the complex relationship between mutant clone sizes and genetic selection.

PowerTCR: A model-based approach to comparative analysis of the clone size distribution of the T cell receptor repertoire.

Sequencing of the T cell receptor (TCR) repertoire is a powerful tool for deeper study of immune response, but the unique structure of this type of data makes its meaningful quantification challenging. We introduce a new method, the Gamma-GPD spliced threshold model, to address this difficulty. This biologically interpretable model captures the distribution of the TCR repertoire, demonstrates stability across varying sequencing depths, and permits comparative analysis across any number of sampled individuals. We apply our method to several datasets and obtain insights regarding the differentiating features in the T cell receptor repertoire among sampled individuals across conditions. We have implemented our method in the open-source R package powerTCR.

Stem cell functionality is microenvironmentally defined during tumour expansion and therapy response in colon cancer.

Solid malignancies have been speculated to depend on cancer stem cells (CSCs) for expansion and relapse after therapy. Here we report on quantitative analyses of lineage tracing data from primary colon cancer xenograft tissue to assess CSC functionality in a human solid malignancy. The temporally obtained clone size distribution data support a model in which stem cell function in established cancers is not intrinsically but entirely spatiotemporally orchestrated. Functional stem cells that drive tumour expansion predominantly reside at the tumour edge, close to cancer-associated fibroblasts (CAFs). Hence, stem cell properties change in time depending on the cell location. Furthermore, although chemotherapy enriches for cells with a CSC phenotype, also in this context functional stem cell properties are fully defined by the microenvironment. To conclude, we identified osteopontin (OPN) as a key CAF-produced factor that drives in situ clonogenicity in colon cancer.

Predominant Asymmetrical Stem Cell Fate Outcome Limits the Rate of Niche Succession in Human Colonic Crypts

Stem cell (SC) dynamics within the human colorectal crypt SC niche remain poorly understood, with previous studies proposing divergent hypotheses on the predominant mode of SC self-renewal and the rate of SC replacement. Here we use age-related mitochondrial oxidative phosphorylation (OXPHOS) defects to trace clonal lineages within human colorectal crypts across the adult life-course. By resolving the frequency and size distribution of OXPHOS-deficient clones, quantitative analysis shows that, in common with mouse, long-term maintenance of the colonic epithelial crypt relies on stochastic SC loss and replacement mediated by competition for limited niche access. We find that the colonic crypt is maintained by ~5 effective SCs. However, with a SC loss/replacement rate estimated to be slower than once per year, our results indicate that the vast majority of individual SC divisions result in asymmetric fate outcome. These findings provide a quantitative platform to detect and study deviations from human colorectal crypt SC niche homeostasis during the process of colorectal carcinogenesis.

Spatial constraints govern competition of mutant clones in human epidermis

Deep sequencing can detect somatic DNA mutations in tissues permitting inference of clonal relationships. This has been applied to human epidermis, where sun exposure leads to the accumulation of mutations and an increased risk of skin cancer. However, previous studies have yielded conflicting conclusions about the relative importance of positive selection and neutral drift in clonal evolution. Here, we sequenced larger areas of skin than previously, focusing on cancer-prone skin spanning five decades of life. The mutant clones identified were too large to be accounted for solely by neutral drift. Rather, using mathematical modelling and computational lattice-based simulations, we show that observed clone size distributions can be explained by a combination of neutral drift and stochastic nucleation of mutations at the boundary of expanding mutant clones that have a competitive advantage. These findings demonstrate that spatial context and cell competition cooperate to determine the fate of a mutant stem cell.

Universal Asymptotic Clone Size Distribution for General Population Growth.

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed the Luria–Delbrück or Lea–Coulson model, is often assumed but seldom realistic. In this article, we generalise this model to different types of wild-type population growth, with mutants evolving as a birth–death branching process. Our focus is on the size distribution of clones—that is the number of progeny of a founder mutant—which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. Additionally, for a large class of population growth, we prove that the long-time limit of the clone size distribution has a general two-parameter form, whose tail decays as a power-law. Considering metastases in cancer as the mutant clones, upon analysing a data-set of their size distribution, we indeed find that a power-law tail is more likely than an exponential one.

The role of idiotypic interactions in the adaptive immune system: a belief-propagation approach

In this work we use belief-propagation techniques to study the equilibrium behaviour of a minimal model for the immune system comprising interacting T and B clones. We investigate the effect of the so-called idiotypic interactions among complementary B clones on the system’s activation. Our results show that B–B interactions increase the system’s resilience to noise, making clonal activation more stable, while increasing the cross-talk between different clones. We derive analytically the noise level at which a B clone gets activated, in the absence of cross-talk, and find that this increases with the strength of idiotypic interactions and with the number of T cells sending signals to the B clones. We also derive, analytically and numerically, via population dynamics, the critical line where clonal cross-talk arises. Our approach allows us to derive the B clone size distribution, which can be experimentally measured and gives important information about the adaptive immune system response to antigens and vaccination.