Parent of origin, mosaicism, and recurrence risk: probabilistic modeling explains the broken symmetry of transmission genetics

Abstract

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.

Figure 1

Stochastic-Process Model of Sexual Dimorphisms during Gametogenesis Phase 1: both males and females experience a stochastic exponential cell-expansion phase modeling embryogenesis and germ cell proliferation. Mutations can arise in any cell division, and if they persist in the clonal lineage, they could ultimately be available to be transmitted to the next generation. Phase 2: in males, expansion is followed by a stochastic but nonexpanding self-renewal process modeling spermatogenesis. Phase 3: a single sperm and egg are randomly sampled after meiosis to fertilize an offspring. Adapted from Campbell et al. with permission.

Figure 2

Analysis of the Mean and Variance of the Unconditional Proportion of Mutant Gametes (A) Unconditional on the observation of an affected offspring, the mean proportion of mutant sperm and the expected risk of a first affected offspring (the sum of sperm and egg) are presented over various possible paternal ages according to our model. Mutation risk increases with paternal age. (B) Coefficient of variation of the proportion of mutant sperm as a function of paternal age. Notably, the curve sharply decreases, indicating that although the proportion of mutant gametes increases, the variability among fathers of a given age decreases in relation to the mean. For these analyses, we set λ₁ = λ₂ = 1 × 10⁻¹⁰, p = q = 0.9, α = 0.05, β = 0.05, γ = 0.05, and ξ = 0.05 (see Material and Methods). An interactive version of this analysis is available online.

Figure 3

Analysis of Recurrence Risk as a Function of Parent of Origin and Paternal Age Because oogenesis completes during embryogenesis, recurrence risk of maternally transmitted mutations is not expected to vary with maternal age. According to our model, recurrence risk of paternally transmitted mutations steadily decreases with age, despite an increasing risk of a first affected offspring. When the parent of origin is unknown, the overall recurrence risk is the probability-weighted sum of the recurrence risks for both parents. An interactive version of this analysis is available online.