ARTICLE Parent of Origin, Mosaicism, and Recurrence Risk: Probabilistic Modeling Explains the Broken Symmetry of Transmission Genetics Ian M. Campbell, 1 Jonathan R. Stewart, 2 Regis A. James, 3 James R. Lupski, 1,4,5,6 Pawe1 Stankiewicz, 1,7 Peter Olofsson, 8 and Chad A. Shaw 1,2,9, * Most new mutations are observed to arise in fathers, and increasing paternal age positively correlates with the risk of new variants. Inter- estingly, 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 muta- tions. 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 trans- mitted 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 dramat- ically increases the expected risk of recurrence in another pregnancy. Parental somatic mosaicism considerably elevates risk for both par- ents. 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 un- derlying parameters that influence recurrence risk and could be useful for analyzing risk in diverse family structures. Introduction New mutations are the sole source of disease risk for ge- netic disorders that eliminate reproductive fitness and for lethal alleles that can only exist in a mosaic state. Likewise, new mutations account for approximately one-third of dis- ease risk in severe X-linked recessive conditions that diminish reproduction. In some instances, these new mu- tations are mitotic in origin (they arise during embryologic development of a parent) and are present in a low-level mosaic state. Such mutations can include single-nucleo- tide variations (SNVs), indels, nonrecurrent copy-number variations (CNVs), and other nonrecurrent copy-number- neutral structural variations. 1 Importantly, these muta- tions can be present in the germline of parents and can be potentially recurrently transmitted to future offspring. 2–4 Unexpected recurrences can occur, as evi- denced by multiple affected children harboring the same apparently de novo variation. The birth of a single child with a severe genetic disease presents considerable psycho- logical, social, and economic challenges; consequently, recurrence of the same disorder in a second child is a situ- ation many couples prefer to avoid. 5 Families who have had children affected by apparently de novo mutations can therefore benefit from well-informed risk counseling to make reproductive choices and plan prenatal care for additional pregnancies. These recurrence-risk estimates are an important aspect of the health care provided to such couples, particularly in severe and highly penetrant genetic disorders for which medical therapy remains limited. Geneticists commonly use the value of <1% to estimate the risk of recurrence for simplex de novo mutations 6 to be transmitted to additional pregnancies. However, consider- ation of the literature shows that this risk assessment is often inconsistent with empirical risk for some specific dis- orders, 7 particularly those caused by mutations in genes located on the X chromosome. 8,9 These examples provide insight into understanding exceptions to rarity of recur- rence of apparently de novo mutations: males affected by X-linked recessive conditions necessarily harbor mutations on the chromosome inherited from their mothers. This maternal bias stands in contrast to the observations that most new mutations arise in the paternal lineage and that the risk of de novo mutation increases with paternal age. 10,11 This paternal bias is broadly consistent with the mitotic origin of many de novo mutations and the addi- tional mitoses experienced by germ cells as fathers age. We hypothesized that sexual dimorphism in gametogen- esis might underlie the juxtaposition of these contrasting biases in higher recurrence risk for X-linked disease and the increased paternal origin of most de novo transmitted 1 Department of Molecular and Human Genetics, Baylor College of Medicine, Houston, TX 77030, USA; 2 Department of Statistics, Rice University, Houston, TX 77005, USA; 3 Department of Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, TX 77030, USA; 4 Texas Children’s Hospital, Houston, TX 77030, USA; 5 Department of Pediatrics, Baylor College of Medicine, Houston, TX 77030, USA; 6 Human Genome Sequencing Center, Baylor College of Medicine, Houston, TX 77030, USA; 7 Institute of Mother and Child, Warsaw 01-211, Poland; 8 Mathematics Depart- ment, Trinity University, San Antonio, TX 78212, USA; 9 Department of Structural and Computational Biology and Molecular Biophysics, Baylor College of Medicine, Houston, TX 77030, USA *Correspondence: cashaw@bcm.edu http://dx.doi.org/10.1016/j.ajhg.2014.08.010. Ó2014 by The American Society of Human Genetics. All rights reserved. The American Journal of Human Genetics 95, 1–15, October 02, 2014 1 Please cite this article in press as: Campbell et al., Parent of Origin, Mosaicism, and Recurrence Risk: Probabilistic Modeling Explains the Broken Symmetry of..., The American Journal of Human Genetics (2014), http://dx.doi.org/10.1016/j.ajhg.2014.08.010