Peter Olofsson

Parental Somatic Mosaicism Is Underrecognized and Influences Recurrence Risk of Genomic Disorders

New human mutations are thought to originate in germ cells, thus making a recurrence of the same mutation in a sibling exceedingly rare. However, increasing sensitivity of genomic technologies has anecdotally revealed mosaicism for mutations in somatic tissues of apparently healthy parents. Such somatically mosaic parents might also have germline mosaicism that can potentially cause unexpected intergenerational recurrences. Here, we show that somatic mosaicism for transmitted mutations among parents of children with simplex genetic disease is more common than currently appreciated. Using the sensitivity of individual-specific breakpoint PCR, we prospectively screened 100 families with children affected by genomic disorders due to rare deletion copy-number variants (CNVs) determined to be de novo by clinical analysis of parental DNA. Surprisingly, we identified four cases of low-level somatic mosaicism for the transmitted CNV in DNA isolated from parental blood. Integrated probabilistic modeling of gametogenesis developed in response to our observations predicts that mutations in parental blood increase recurrence risk substantially more than parental mutations confined to the germline. Moreover, despite the fact that maternally transmitted mutations are the minority of alleles, our model suggests that sexual dimorphisms in gametogenesis result in a greater proportion of somatically mosaic transmitting mothers who are thus at increased risk of recurrence. Therefore, somatic mosaicism together with sexual differences in gametogenesis might explain a considerable fraction of unexpected recurrences of X-linked recessive disease. Overall, our results underscore an important role for somatic mosaicism and mitotic replicative mutational mechanisms in transmission genetics.

Stochastic models of telomere shortening

Shortening of chromosome ends, known as telomeres, is one of the supposed mechanisms of cellular aging and death. We provide a probabilistic analysis of the process of loss of telomere ends. The first work concerned with that issue is the paper by Levy et al. [J. Molec. Biol. 225 (1992) 951-960]. Their deterministic model reproduced the observed frequencies of viable cells in the in vitro experiments. Arino et al. [J. Theor. Biol. 177 (1995) 45-57] reformulated the model of Levy et al. (1992) in the terms of branching processes with denumerable type space. In the present paper, the mathematical results of Arino et al. (1995) are extended to the case in which cell death is present, in cells with telomeres above and below the critical threshold of length, generally with differing probabilities. Both exact and asymptotic results are provided, as well as a discussion of biological relevance of the results.

Parent of Origin, Mosaicism, and Recurrence Risk: Probabilistic Modeling Explains the Broken Symmetry of Transmission Genetics

Most new mutations are observed to arise in fathers, and increasing paternal age positively correlates with the risk of new variants. Interestingly, new mutations in X-linked recessive disease show elevated familial recurrence rates. In male offspring, these mutations must be inherited from mothers. We previously developed a simulation model to consider parental mosaicism as a source of transmitted mutations. In this paper, we extend and formalize the model to provide analytical results and flexible formulas. The results implicate parent of origin and parental mosaicism as central variables in recurrence risk. Consistent with empirical data, our model predicts that more transmitted mutations arise in fathers and that this tendency increases as fathers age. Notably, the lack of expansion later in the male germline determines relatively lower variance in the proportion of mutants, which decreases with paternal age. Subsequently, observation of a transmitted mutation has less impact on the expected risk for future offspring. Conversely, for the female germline, which arrests after clonal expansion in early development, variance in the mutant proportion is higher, and observation of a transmitted mutation dramatically increases the expected risk of recurrence in another pregnancy. Parental somatic mosaicism considerably elevates risk for both parents. These findings have important implications for genetic counseling and for understanding patterns of recurrence in transmission genetics. We provide a convenient online tool and source code implementing our analytical results. These tools permit varying the underlying parameters that influence recurrence risk and could be useful for analyzing risk in diverse family structures.

Branching processes with local dependencies

This paper is an overview of results for branching processes with dependencies that are local in the family tree. We illustrate principal problems by giving some simple examples of Galton-Watson processes with sibling dependencies. Results for general (Crump-Mode-Jagers) processes are stated and discussed without proofs.

Exact sampling formulas for multi-type Galton-Watson processes

Abstract. Exact formulas for the mean and variance of the proportion of different types in a fixed generation of a multi-type Galton-Watson process are derived. The formulas are given in terms of iterates of the probability generating function of the offspring distribution. It is also shown that the sequence of types backwards from a randomly sampled particle in a fixed generation is a non-homogeneous Markov chain where the transition probabilities can be given explicitly, again in terms of probability generating functions. Two biological applications are considered: mutations in mitochondrial DNA and the polymerase chain reaction.

A branching process model of telomere shortening

A branching process model of a certain cell population is considered. The population is divided into types according to the number of remaining chromosome end units. This leads to a reducible multi-type Bellman-Harris branching process which turns out to exhibit polynomial growth dynamics: let be the expected number of j-type cells of age less than a at time t starting from a k-type ancestor cell. Then, as where the constant C depends on a,j and k. and can be given explicitely. The proof is fairly short and simple, using elementary results from renewal theory and a Tauberian theorem for Laplace-Stieltjes transforms

General branching processes with immigration

A general multi-type branching process where new individuals immigrate according to some point process is considered. An intrinsic submartingale is defined and a convergence result for processes counted with random characteristics is obtained. Some examples are given.

A stochastic model for the development of Bateson–Dobzhansky–Muller incompatibilities that incorporates protein interaction networks

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. Intrinsic post-zygotic barriers of the type envisioned by Bateson, Dobzhansky, and Muller are deleterious epistatic interactions among loci that reduce hybrid fitness, leading to reproductive isolation. The first formal population genetic model of the development of these barriers was published by Orr in 1995, and here we develop a more general model of this process by incorporating finite protein-protein interaction networks, which reduce the probability of deleterious interactions in vivo. Our model shows that the development of deleterious interactions is limited by the density of the protein-protein interaction network. We have confirmed our analytical predictions of the number of possible interactions given the number of allele substitutions by using simulations on the Saccharomyces cerevisiae protein-protein interaction network. These results allow us to define the rate at which deleterious interactions are expected to form, and hence the speciation rate, for any protein-protein interaction network.

Size-biased branching population measures and the multi-type x log x condition

We investigate the xlog x condition for a general (Crump–Mode– Jagers) multi-type branching process with a general type space by constructing a size-biased population measure that relates to the ordinary population measure via an intrinsic martingale Wt. Sufficiency of the xlog x condition for a non-degenerate limit of Wt is proved and conditions for necessity are investigated. GENERAL BRANCHING PROCESS; XLOGX CONDITION; IMMIGRATION; SIZE-BIASED MEASURE

Modeling and estimating bacterial lag phase

A branching process model of a bacterial population with initial lag phase is developed. Approximations are established in order to facilitate parameter estimation. The validity of approximations and estimation procedures is tested with simulated data.