RESUMEN
The precise genetic origins of the first Neolithic farming populations in Europe and Southwest Asia, as well as the processes and the timing of their differentiation, remain largely unknown. Demogenomic modeling of high-quality ancient genomes reveals that the early farmers of Anatolia and Europe emerged from a multiphase mixing of a Southwest Asian population with a strongly bottlenecked western hunter-gatherer population after the last glacial maximum. Moreover, the ancestors of the first farmers of Europe and Anatolia went through a period of extreme genetic drift during their westward range expansion, contributing highly to their genetic distinctiveness. This modeling elucidates the demographic processes at the root of the Neolithic transition and leads to a spatial interpretation of the population history of Southwest Asia and Europe during the late Pleistocene and early Holocene.
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Agricultores , Genoma , Agricultura , ADN Mitocondrial/genética , Europa (Continente) , Flujo Genético , Genómica , Historia Antigua , Migración Humana , HumanosRESUMEN
Inferring past demographic history of natural populations from genomic data is of central concern in many studies across research fields. Previously, our group had developed dadi, a widely used demographic history inference method based on the allele frequency spectrum (AFS) and maximum composite-likelihood optimization. However, dadi's optimization procedure can be computationally expensive. Here, we present donni (demography optimization via neural network inference), a new inference method based on dadi that is more efficient while maintaining comparable inference accuracy. For each dadi-supported demographic model, donni simulates the expected AFS for a range of model parameters then trains a set of Mean Variance Estimation neural networks using the simulated AFS. Trained networks can then be used to instantaneously infer the model parameters from future genomic data summarized by an AFS. We demonstrate that for many demographic models, donni can infer some parameters, such as population size changes, very well and other parameters, such as migration rates and times of demographic events, fairly well. Importantly, donni provides both parameter and confidence interval estimates from input AFS with accuracy comparable to parameters inferred by dadi's likelihood optimization while bypassing its long and computationally intensive evaluation process. donni's performance demonstrates that supervised machine learning algorithms may be a promising avenue for developing more sustainable and computationally efficient demographic history inference methods.
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Frecuencia de los Genes , Modelos Genéticos , Aprendizaje Automático Supervisado , Genética de Población/métodos , Redes Neurales de la Computación , HumanosRESUMEN
AbstractRecent experimental evidence demonstrates that shifts in mutational biases-for example, increases in transversion frequency-can change the distribution of fitness effects of mutations (DFE). In particular, reducing or reversing a prevailing bias can increase the probability that a de novo mutation is beneficial. It has also been shown that mutator bacteria are more likely to emerge if the beneficial mutations they generate have a larger effect size than observed in the wild type. Here, we connect these two results, demonstrating that mutator strains that reduce or reverse a prevailing bias have a positively shifted DFE, which in turn can dramatically increase their emergence probability. Since changes in mutation rate and bias are often coupled through the gain and loss of DNA repair enzymes, our results predict that the invasion of mutator strains will be facilitated by shifts in mutation bias that offer improved access to previously undersampled beneficial mutations.
Asunto(s)
Tasa de Mutación , MutaciónRESUMEN
dadi is a popular but computationally intensive program for inferring models of demographic history and natural selection from population genetic data. I show that running dadi on a Graphics Processing Unit can dramatically speed computation compared with the CPU implementation, with minimal user burden. Motivated by this speed increase, I also extended dadi to four- and five-population models. This functionality is available in dadi version 2.1.0, https://bitbucket.org/gutenkunstlab/dadi/.
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Metodologías Computacionales , Genética de Población/métodos , Modelos Genéticos , Selección Genética , Programas InformáticosRESUMEN
The effect of a mutation on fitness may differ between populations depending on environmental and genetic context, but little is known about the factors that underlie such differences. To quantify genome-wide correlations in mutation fitness effects, we developed a novel concept called a joint distribution of fitness effects (DFE) between populations. We then proposed a new statistic w to measure the DFE correlation between populations. Using simulation, we showed that inferring the DFE correlation from the joint allele frequency spectrum is statistically precise and robust. Using population genomic data, we inferred DFE correlations of populations in humans, Drosophila melanogaster, and wild tomatoes. In these species, we found that the overall correlation of the joint DFE was inversely related to genetic differentiation. In humans and D. melanogaster, deleterious mutations had a lower DFE correlation than tolerated mutations, indicating a complex joint DFE. Altogether, the DFE correlation can be reliably inferred, and it offers extensive insight into the genetics of population divergence.
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Drosophila melanogaster , Aptitud Genética , Animales , Drosophila melanogaster/genética , Frecuencia de los Genes , Genoma , Modelos Genéticos , MutaciónRESUMEN
Largely understudied, mesophotic coral ecosystems lie below shallow reefs (at >30 m depth) and comprise ecologically distinct communities. Brooding reproductive modes appear to predominate among mesophotic-specialist corals and may limit genetic connectivity among populations. Using reduced representation genomic sequencing, we assessed spatial population genetic structure at 50 m depth in an ecologically important mesophotic-specialist species Agaricia grahamae, among locations in the Southern Caribbean. We also tested for hybridisation with the closely related (but depth-generalist) species Agaricia lamarcki, within their sympatric depth zone (50 m). In contrast to our expectations, no spatial genetic structure was detected between the reefs of Curaçao and Bonaire (~40 km apart) within A. grahamae. However, cryptic taxa were discovered within both taxonomic species, with those in A. lamarcki (incompletely) partitioned by depth and those in A. grahamae occurring sympatrically (at the same depth). Hybrid analyses and demographic modelling identified contemporary and historical gene flow among cryptic taxa, both within and between A. grahamae and A. lamarcki. These results (1) indicate that spatial connectivity and subsequent replenishment may be possible between islands of moderate geographic distances for A. grahamae, an ecologically important mesophotic species, (2) that cryptic taxa occur in the mesophotic zone and environmental selection along shallow to mesophotic depth gradients may drive divergence in depth-generalists such as A. lamarcki, and (3) highlight that gene flow links taxa within this relativity diverse Caribbean genus.
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Antozoos , Animales , Antozoos/genética , Arrecifes de Coral , Ecosistema , Flujo Génico , ReproducciónRESUMEN
Demographic inference using the site frequency spectrum (SFS) is a common way to understand historical events affecting genetic variation. However, most methods for estimating demography from the SFS assume random mating within populations, precluding these types of analyses in inbred populations. To address this issue, we developed a model for the expected SFS that includes inbreeding by parameterizing individual genotypes using beta-binomial distributions. We then take the convolution of these genotype probabilities to calculate the expected frequency of biallelic variants in the population. Using simulations, we evaluated the model's ability to coestimate demography and inbreeding using one- and two-population models across a range of inbreeding levels. We also applied our method to two empirical examples, American pumas (Puma concolor) and domesticated cabbage (Brassica oleracea var. capitata), inferring models both with and without inbreeding to compare parameter estimates and model fit. Our simulations showed that we are able to accurately coestimate demographic parameters and inbreeding even for highly inbred populations (F = 0.9). In contrast, failing to include inbreeding generally resulted in inaccurate parameter estimates in simulated data and led to poor model fit in our empirical analyses. These results show that inbreeding can have a strong effect on demographic inference, a pattern that was especially noticeable for parameters involving changes in population size. Given the importance of these estimates for informing practices in conservation, agriculture, and elsewhere, our method provides an important advancement for accurately estimating the demographic histories of these species.
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Endogamia , Modelos Genéticos , Animales , Brassica/genética , Simulación por Computador , Polimorfismo de Nucleótido Simple , Dinámica Poblacional , Puma/genéticaRESUMEN
African Pygmies practicing a mobile hunter-gatherer lifestyle are phenotypically and genetically diverged from other anatomically modern humans, and they likely experienced strong selective pressures due to their unique lifestyle in the Central African rainforest. To identify genomic targets of adaptation, we sequenced the genomes of four Biaka Pygmies from the Central African Republic and jointly analyzed these data with the genome sequences of three Baka Pygmies from Cameroon and nine Yoruba famers. To account for the complex demographic history of these populations that includes both isolation and gene flow, we fit models using the joint allele frequency spectrum and validated them using independent approaches. Our two best-fit models both suggest ancient divergence between the ancestors of the farmers and Pygmies, 90,000 or 150,000 yr ago. We also find that bidirectional asymmetric gene flow is statistically better supported than a single pulse of unidirectional gene flow from farmers to Pygmies, as previously suggested. We then applied complementary statistics to scan the genome for evidence of selective sweeps and polygenic selection. We found that conventional statistical outlier approaches were biased toward identifying candidates in regions of high mutation or low recombination rate. To avoid this bias, we assigned P-values for candidates using whole-genome simulations incorporating demography and variation in both recombination and mutation rates. We found that genes and gene sets involved in muscle development, bone synthesis, immunity, reproduction, cell signaling and development, and energy metabolism are likely to be targets of positive natural selection in Western African Pygmies or their recent ancestors.
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Población Negra/genética , Genética de Población , Genoma , Genómica , Pan paniscus/genética , Selección Genética , Adaptación Biológica , Animales , Biología Computacional , Simulación por Computador , Flujo Génico , Variación Genética , Secuenciación de Nucleótidos de Alto Rendimiento , Humanos , Desequilibrio de Ligamiento , Modelos Genéticos , Modelos Estadísticos , Reproducibilidad de los ResultadosRESUMEN
Comparisons of whole-genome sequences from ancient and contemporary samples have pointed to several instances of archaic admixture through interbreeding between the ancestors of modern non-Africans and now extinct hominids such as Neanderthals and Denisovans. One implication of these findings is that some adaptive features in contemporary humans may have entered the population via gene flow with archaic forms in Eurasia. Within Africa, fossil evidence suggests that anatomically modern humans (AMH) and various archaic forms coexisted for much of the last 200,000 yr; however, the absence of ancient DNA in Africa has limited our ability to make a direct comparison between archaic and modern human genomes. Here, we use statistical inference based on high coverage whole-genome data (greater than 60×) from contemporary African Pygmy hunter-gatherers as an alternative means to study the evolutionary history of the genus Homo. Using whole-genome simulations that consider demographic histories that include both isolation and gene flow with neighboring farming populations, our inference method rejects the hypothesis that the ancestors of AMH were genetically isolated in Africa, thus providing the first whole genome-level evidence of African archaic admixture. Our inferences also suggest a complex human evolutionary history in Africa, which involves at least a single admixture event from an unknown archaic population into the ancestors of AMH, likely within the last 30,000 yr.
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Población Negra/genética , Evolución Molecular , Genética de Población , Genoma Humano , Genoma , Genómica , Pan paniscus/genética , Animales , Flujo Génico , Frecuencia de los Genes , Sitios Genéticos , Haplotipos , Humanos , Desequilibrio de Ligamiento , Polimorfismo de Nucleótido SimpleRESUMEN
Motivation: Tumor genome sequencing offers great promise for guiding research and therapy, but spurious variant calls can arise from multiple sources. Mouse contamination can generate many spurious calls when sequencing patient-derived xenografts. Paralogous genome sequences can also generate spurious calls when sequencing any tumor. We developed a BLAST-based algorithm, Mouse And Paralog EXterminator (MAPEX), to identify and filter out spurious calls from both these sources. Results: When calling variants from xenografts, MAPEX has similar sensitivity and specificity to more complex algorithms. When applied to any tumor, MAPEX also automatically flags calls that potentially arise from paralogous sequences. Our implementation, mapexr, runs quickly and easily on a desktop computer. MAPEX is thus a useful addition to almost any pipeline for calling genetic variants in tumors. Availability and implementation: The mapexr package for R is available at https://github.com/bmannakee/mapexr under the MIT license. Contact: mannakee@email.arizona.edu or rgutenk@email.arizona.edu or eknudsen@email.arizona.edu. Supplementary information: Supplementary data are available at Bioinformatics online.
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Variación Genética , Neoplasias/genética , Algoritmos , Animales , Xenoinjertos , Secuenciación de Nucleótidos de Alto Rendimiento , Humanos , Ratones , Programas InformáticosRESUMEN
The past decade has seen major investment in genome-wide association studies (GWAS). Among the many goals of GWAS, a major one is to identify and motivate research on novel genes involved in complex human disease. To assess whether this goal is being met, we quantified the effect of GWAS on the overall distribution of biomedical research publications and on the subsequent publication history of genes newly associated with complex disease. We found that the historical skew of publications toward genes involved in Mendelian disease has not changed since the advent of GWAS. Genes newly implicated by GWAS in complex disease do experience additional publications compared to control genes, and they are more likely to become exceptionally studied. But the magnitude of both effects has declined over the past decade. Our results suggest that reforms to encourage follow-up studies may be needed for GWAS to most successfully guide biomedical research toward the molecular mechanisms underlying complex human disease.
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Investigación Biomédica , Enfermedades Genéticas Congénitas/genética , Estudio de Asociación del Genoma Completo , Regulación de la Expresión Génica/genética , Humanos , Polimorfismo de Nucleótido Simple , PublicacionesRESUMEN
The long-held principle that functionally important proteins evolve slowly has recently been challenged by studies in mice and yeast showing that the severity of a protein knockout only weakly predicts that protein's rate of evolution. However, the relevance of these studies to evolutionary changes within proteins is unknown, because amino acid substitutions, unlike knockouts, often only slightly perturb protein activity. To quantify the phenotypic effect of small biochemical perturbations, we developed an approach to use computational systems biology models to measure the influence of individual reaction rate constants on network dynamics. We show that this dynamical influence is predictive of protein domain evolutionary rate within networks in vertebrates and yeast, even after controlling for expression level and breadth, network topology, and knockout effect. Thus, our results not only demonstrate the importance of protein domain function in determining evolutionary rate, but also the power of systems biology modeling to uncover unanticipated evolutionary forces.
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Evolución Molecular , Dominios Proteicos/genética , Selección Genética/genética , Biología de Sistemas , Sustitución de Aminoácidos/genética , Animales , Biología Computacional , Humanos , Ratones , Levaduras/genéticaRESUMEN
Siberia is one of the coldest environments on Earth and has great seasonal temperature variation. Long-term settlement in northern Siberia undoubtedly required biological adaptation to severe cold stress, dramatic variation in photoperiod, and limited food resources. In addition, recent archeological studies show that humans first occupied Siberia at least 45,000 years ago; yet our understanding of the demographic history of modern indigenous Siberians remains incomplete. In this study, we use whole-exome sequencing data from the Nganasans and Yakuts to infer the evolutionary history of these two indigenous Siberian populations. Recognizing the complexity of the adaptive process, we designed a model-based test to systematically search for signatures of polygenic selection. Our approach accounts for stochasticity in the demographic process and the hitchhiking effect of classic selective sweeps, as well as potential biases resulting from recombination rate and mutation rate heterogeneity. Our demographic inference shows that the Nganasans and Yakuts diverged â¼12,000-13,000 years ago from East-Asian ancestors in a process involving continuous gene flow. Our polygenic selection scan identifies seven candidate gene sets with Siberian-specific signals. Three of these gene sets are related to diet, especially to fat metabolism, consistent with the hypothesis of adaptation to a fat-rich animal diet. Additional testing rejects the effect of hitchhiking and favors a model in which selection yields small allele frequency changes at multiple unlinked genes.
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Aclimatación/genética , Adaptación Biológica/genética , Alelos , Pueblo Asiatico/genética , Evolución Biológica , ADN Mitocondrial/genética , Demografía/métodos , Dieta , Grasas de la Dieta , Etnicidad/genética , Exoma/genética , Flujo Génico/genética , Frecuencia de los Genes/genética , Variación Genética/genética , Genética de Población/métodos , Humanos , Herencia Multifactorial/genética , Filogenia , Siberia , Secuenciación del Exoma/métodosRESUMEN
Many population genetics tools employ composite likelihoods, because fully modeling genomic linkage is challenging. But traditional approaches to estimating parameter uncertainties and performing model selection require full likelihoods, so these tools have relied on computationally expensive maximum-likelihood estimation (MLE) on bootstrapped data. Here, we demonstrate that statistical theory can be applied to adjust composite likelihoods and perform robust computationally efficient statistical inference in two demographic inference tools: ∂a∂i and TRACTS. On both simulated and real data, the adjustments perform comparably to MLE bootstrapping while using orders of magnitude less computational time.
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Biología Computacional/métodos , Demografía , Genética de Población/métodos , Funciones de Verosimilitud , Modelos Genéticos , HumanosRESUMEN
Demographic modelling is often used with population genomic data to infer the relationships and ages among populations. However, relatively few analyses are able to validate these inferences with independent data. Here, we leverage written records that describe distinct Brassica rapa crops to corroborate demographic models of domestication. Brassica rapa crops are renowned for their outstanding morphological diversity, but the relationships and order of domestication remain unclear. We generated genomewide SNPs from 126 accessions collected globally using high-throughput transcriptome data. Analyses of more than 31,000 SNPs across the B. rapa genome revealed evidence for five distinct genetic groups and supported a European-Central Asian origin of B. rapa crops. Our results supported the traditionally recognized South Asian and East Asian B. rapa groups with evidence that pak choi, Chinese cabbage and yellow sarson are likely monophyletic groups. In contrast, the oil-type B. rapa subsp. oleifera and brown sarson were polyphyletic. We also found no evidence to support the contention that rapini is the wild type or the earliest domesticated subspecies of B. rapa. Demographic analyses suggested that B. rapa was introduced to Asia 2,400-4,100 years ago, and that Chinese cabbage originated 1,200-2,100 years ago via admixture of pak choi and European-Central Asian B. rapa. We also inferred significantly different levels of founder effect among the B. rapa subspecies. Written records from antiquity that document these crops are consistent with these inferences. The concordance between our age estimates of domestication events with historical records provides unique support for our demographic inferences.
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Brassica rapa/genética , Domesticación , Fitomejoramiento , Asia , Documentación , Efecto Fundador , Polimorfismo de Nucleótido Simple , TranscriptomaRESUMEN
Protein tyrosine phosphorylation is a key regulatory modification in metazoans, and the corresponding kinase enzymes have diversified dramatically. This diversification is correlated with a genome-wide reduction in protein tyrosine content, and it was recently suggested that this reduction was driven by selection to avoid promiscuous phosphorylation that might be deleterious. We tested three predictions of this intriguing hypothesis. 1) Selection should be stronger on residues that are more likely to be phosphorylated due to local solvent accessibility or structural disorder. 2) Selection should be stronger on proteins that are more likely to be promiscuously phosphorylated because they are abundant. We tested these predictions by comparing distributions of tyrosine within and among human and yeast orthologous proteins. 3) Selection should be stronger against mutations that create tyrosine versus remove tyrosine. We tested this prediction using human population genomic variation data. We found that all three predicted effects are modest for tyrosine when compared with the other amino acids, suggesting that selection against deleterious phosphorylation was not dominant in driving metazoan tyrosine loss.
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Evolución Molecular , Proteínas Quinasas/metabolismo , Proteínas/química , Proteínas/genética , Tirosina/genética , Tirosina/metabolismo , Levaduras/metabolismo , Animales , Proteínas Fúngicas/química , Proteínas Fúngicas/genética , Proteínas Fúngicas/metabolismo , Frecuencia de los Genes , Genoma Fúngico , Genoma Humano , Humanos , Mutación , Fosforilación , Selección Genética , Levaduras/genéticaRESUMEN
BACKGROUND: Selection on proteins is typically measured with the assumption that each protein acts independently. However, selection more likely acts at higher levels of biological organization, requiring an integrative view of protein function. Here, we built a kinetic model for de novo pyrimidine biosynthesis in the yeast Saccharomyces cerevisiae to relate pathway function to selective pressures on individual protein-encoding genes. RESULTS: Gene families across yeast were constructed for each member of the pathway and the ratio of nonsynonymous to synonymous nucleotide substitution rates (dN/dS) was estimated for each enzyme from S. cerevisiae and closely related species. We found a positive relationship between the influence that each enzyme has on pathway function and its selective constraint. CONCLUSIONS: We expect this trend to be locally present for enzymes that have pathway control, but over longer evolutionary timescales we expect that mutation-selection balance may change the enzymes that have pathway control.
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Vías Biosintéticas , Evolución Molecular , Pirimidinas/biosíntesis , Proteínas de Saccharomyces cerevisiae/genética , Saccharomyces cerevisiae/enzimología , Saccharomyces cerevisiae/genética , Mutación , Filogenia , Saccharomyces cerevisiae/metabolismoRESUMEN
Partially recessive variants under positive selection are expected to go to fixation more quickly on the X chromosome as a result of hemizygosity, an effect known as faster-X. Conversely, purifying selection is expected to reduce substitution rates more effectively on the X chromosome. Previous work in humans contrasted divergence on the autosomes and X chromosome, with results tending to support the faster-X effect. However, no study has yet incorporated both divergence and polymorphism to quantify the effects of both purifying and positive selection, which are opposing forces with respect to divergence. In this study, we develop a framework that integrates previously developed theory addressing differential rates of X and autosomal evolution with methods that jointly estimate the level of purifying and positive selection via modeling of the distribution of fitness effects (DFE). We then utilize this framework to estimate the proportion of nonsynonymous substitutions fixed by positive selection (α) using exome sequence data from a West African population. We find that varying the female to male breeding ratio (ß) has minimal impact on the DFE for the X chromosome, especially when compared with the effect of varying the dominance coefficient of deleterious alleles (h). Estimates of α range from 46% to 51% and from 4% to 24% for the X chromosome and autosomes, respectively. While dependent on h, the magnitude of the difference between α values estimated for these two systems is highly statistically significant over a range of biologically realistic parameter values, suggesting faster-X has been operating in humans.
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Población Negra/genética , Cromosomas Humanos X/genética , Cromosomas Humanos/genética , Biología Computacional/métodos , África Occidental , Sustitución de Aminoácidos , Islas de CpG , Evolución Molecular , Exoma , Femenino , Frecuencia de los Genes , Aptitud Genética , Humanos , Masculino , Modelos Genéticos , Selección Genética , Análisis de Secuencia de ADNRESUMEN
Secondary bacterial infections are a leading cause of illness and death during epidemic and pandemic influenza. Experimental studies suggest a lethal synergism between influenza and certain bacteria, particularly Streptococcus pneumoniae, but the precise processes involved are unclear. To address the mechanisms and determine the influences of pathogen dose and strain on disease, we infected groups of mice with either the H1N1 subtype influenza A virus A/Puerto Rico/8/34 (PR8) or a version expressing the 1918 PB1-F2 protein (PR8-PB1-F2(1918)), followed seven days later with one of two S. pneumoniae strains, type 2 D39 or type 3 A66.1. We determined that, following bacterial infection, viral titers initially rebound and then decline slowly. Bacterial titers rapidly rise to high levels and remain elevated. We used a kinetic model to explore the coupled interactions and study the dominant controlling mechanisms. We hypothesize that viral titers rebound in the presence of bacteria due to enhanced viral release from infected cells, and that bacterial titers increase due to alveolar macrophage impairment. Dynamics are affected by initial bacterial dose but not by the expression of the influenza 1918 PB1-F2 protein. Our model provides a framework to investigate pathogen interaction during coinfections and to uncover dynamical differences based on inoculum size and strain.
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Coinfección , Subtipo H1N1 del Virus de la Influenza A/inmunología , Infecciones por Orthomyxoviridae/complicaciones , Infecciones Neumocócicas/complicaciones , Streptococcus pneumoniae/inmunología , Animales , Coinfección/microbiología , Coinfección/fisiopatología , Coinfección/virología , Femenino , Subtipo H1N1 del Virus de la Influenza A/patogenicidad , Cinética , Pulmón/virología , Ratones , Ratones Endogámicos BALB C , Modelos Teóricos , Infecciones por Orthomyxoviridae/inmunología , Infecciones Neumocócicas/inmunología , Streptococcus pneumoniae/patogenicidad , Factores de TiempoRESUMEN
Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated long-lived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis.