Mutation, drift and selection in single-driver hematologic malignancy: Example of secondary myelodysplastic syndrome following treatment of inherited neutropenia.

Cancer development is driven by series of events involving mutations, which may become fixed in a tumor via genetic drift and selection. This process usually includes a limited number of driver (advantageous) mutations and a greater number of passenger (neutral or mildly deleterious) mutations. We focus on a real-world leukemia model evolving on the background of a germline mutation. Severe congenital neutropenia (SCN) evolves to secondary myelodysplastic syndrome (sMDS) and/or secondary acute myeloid leukemia (sAML) in 30-40%. The majority of SCN cases are due to a germline ELANE mutation. Acquired mutations in CSF3R occur in >70% sMDS/sAML associated with SCN. Hypotheses underlying our model are: an ELANE mutation causes SCN; CSF3R mutations occur spontaneously at a low rate; in fetal life, hematopoietic stem and progenitor cells expands quickly, resulting in a high probability of several tens to several hundreds of cells with CSF3R truncation mutations; therapeutic granulocyte colony-stimulating factor (G-CSF) administration early in life exerts a strong selective pressure, providing mutants with a growth advantage. Applying population genetics theory, we propose a novel two-phase model of disease development from SCN to sMDS. In Phase 1, hematopoietic tissues expand and produce tens to hundreds of stem cells with the CSF3R truncation mutation. Phase 2 occurs postnatally through adult stages with bone marrow production of granulocyte precursors and positive selection of mutants due to chronic G-CSF therapy to reverse the severe neutropenia. We predict the existence of the pool of cells with the mutated truncated receptor before G-CSF treatment begins. The model does not require increase in mutation rate under G-CSF treatment and agrees with age distribution of sMDS onset and clinical sequencing data.

Genetic demographic networks: Mathematical model and applications.

Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise distributions of alleles, in the case of haploid non-recombining loci such as mitochondrial and Y-chromosome loci in humans.

Time to the MRCA of a sample in a Wright-Fisher model with variable population size.

Determining the expected distribution of the time to the most recent common ancestor of a sample of individuals may deliver important information about the genetic markers and evolution of the population. In this paper, we introduce a new recursive algorithm to calculate the distribution of the time to the most recent common ancestor of the sample from a population evolved by any conditional multinomial sampling model. The most important advantage of our method is that it can be applied to a sample of any size drawn from a population regardless of its size growth pattern. We also present a very efficient method to implement and store the genealogy tree of the population evolved by the Galton-Watson process. In the final section we present results applied to a simulated population with a single bottleneck event and to real populations of known size histories.

Asymptotic behavior of a Moran model with mutations, drift and recombination among multiple loci.

In this paper, we extend the theoretical treatment of the Moran model of genetic drift with recombination and mutation, which was previously introduced by us for the case of two loci, to the case of n loci. Recombination, when considered in the Wright-Fisher model, makes it considerably less tractable. In the works of Griffiths, Hudson and Kaplan and their colleagues important properties were established using the coalescent approach. Other more recent approaches form a body of work to which we would like to contribute. The specific framework used in our paper allows finding close-form relationships, which however are limited to a set of distributions, which jointly characterize allelic states at a number of loci at the same or different chromosome(s) but which do not jointly characterize allelic states at a single locus on two or more chromosomes. However, the system is sufficiently rich to allow computing, albeit in general numerically, all possible multipoint linkage disequilibria under recombination, mutation and drift. We explore the algorithms enabling construction of the transition probability matrices of the Markov chain describing the process. We find that asymptotically the effects of recombination become indistinguishable, at least as characterized by the set of distributions we consider, from the effects of mutation and drift. Mathematically, the results are based on the foundations of the theory of semi-groups of operators. This approach allows generalization to any Markov-type mutation model. Based on these fundamental results, we explore the rates of convergence to the limit distribution, using Dobrushin's coefficient and spectral gap.