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Interpreting short tandem repeat variations in humans using mutational constraint


Identifying regions of the genome that are depleted of mutations can distinguish potentially deleterious variants. Short tandem repeats (STRs), also known as microsatellites, are among the largest contributors of de novo mutations in humans. However, per-locus studies of STR mutations have been limited to highly ascertained panels of several dozen loci. Here we harnessed bioinformatics tools and a novel analytical framework to estimate mutation parameters for each STR in the human genome by correlating STR genotypes with local sequence heterozygosity. We applied our method to obtain robust estimates of the impact of local sequence features on mutation parameters and used these estimates to create a framework for measuring constraint at STRs by comparing observed versus expected mutation rates. Constraint scores identified known pathogenic variants with early-onset effects. Our metric will provide a valuable tool for prioritizing pathogenic STRs in medical genetics studies.

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Figure 1: Estimating STR mutation parameters from diploid data.
Figure 2: Accurate estimation of STR mutation parameters from simulated data.
Figure 3: A framework for measuring STR constraint.
Figure 4: Constraint scores can be used for STR prioritization.


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We thank N. Patterson, M. Daly, Y. Wan, and A. Goren for helpful discussions. D.R. was supported by NIH grants GM100233 and HG006399 and is a Howard Hughes Medical Institute investigator. M.G. was supported by NIH/NIMH grant 1U01MH105669-01. Y.E. holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund. This study was supported in part by National Institute of Justice grant 2014-DN-BX-K089 (Y.E., T.W., M.G.) and by a generous gift from Paul and Andria Heafy (Y.E.).

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Authors and Affiliations



M.G., D.R., and Y.E. conceived the study. M.G. prepared the initial manuscript and performed analyses. T.W. developed the likelihood-maximization procedure and helped design analyses. All authors contributed to the development of the mutation model and mutation rate estimation technique.

Corresponding author

Correspondence to Melissa Gymrek.

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Competing interests

Y.E. is the Chief Science Officer of and consults for companies that operate in the DNA forensics domain.

Integrated supplementary information

Supplementary Figure 1 Modeling the STR mutation process.

(a) A mean-centered random walk imposes a length constraint on allele size. The leftmost diagram represents two copies of an AC repeat descended from a common ancestor. The upper right plot shows the number of repeats at each leaf node versus the number of generations passed for 100 simulations of a stepwise model (gray) and two example haplotypes (black; denoted as m and n). The lower right plot shows the same simulations using a mean-centered model. (b) Allelic variance saturates at large TMRCAs. The solid and dashed lines represent the relationship between mean squared allele difference and TMRCA under the stepwise model and mean-centered model, respectively. The mean-centered scenario recapitulates the saturation in the STR molecular clock observed in population data. (c) Example step-size distributions for a mean-centered model. Histograms give probability distributions for step sizes assuming current alleles of –2 (left), 0 (center), or +2 (right) repeats from the optimal allele.

Supplementary Figure 2 Previously reported step-size distributions.

(a,b) Step-size distributions for dinucleotides (a) and tetranucleotides (b). Lines give the geometric distribution with parameter p, where p is the probability of a step of a single unit obtained from each study (Supplementary Table 1).

Supplementary Figure 3 Calibrating standard errors.

(a) Multiplier versus truth coverage on simulated data. For each mutation rate estimate, the standard error was multiplied by a constant (x axis). Truth coverage is calculated as the percentage of loci for which the true mutation rate falls within the maximum-likelihood estimate ± 1.96 × standard error × multiplier. Colors represent a range of simulated mutation rates. (b) Scaled multiplier (γ) versus truth coverage. The x axis represents the multiplier from a scaled by the absolute value of the log of the maximum-likelihood mutation rate estimate. The inset shows data aggregated across mutation rates for simulations with (red) and without (black) stutter noise. (c) Calibrating γ against MUTEA Y-STR estimates. (d) Calibrating γ against Ballantyne Y-STR estimates. (e) Calibrating γ for autosomal STRs.

Supplementary Figure 4 Per-locus simulation results.

(ad) Plots are shown for the log10 (mutation rate) (a), step-size parameter σ2 = (2 – p)/p2 (b), length constraint (c), and effective length constraint, defined as β/σ2.

Supplementary Figure 5 Modeling genotyping errors.

(a) Adjusting genotypes for stutter errors reduces bias. Solid black lines show simulated values of mutation rate and effective length constraint. Red dots give values estimated from genotypes with simulated stutter errors. Black dots give estimates after inferring stutter parameters and adjusting genotype likelihoods. Dashed gray lines give boundaries enforced during numerical likelihood maximization. (b) Stutter parameters are accurately recovered from simulated data. Black points represent estimated stutter parameters for reads with no simulated stutter errors (d = 0, υ = 0). Red points represent estimated stutter parameters for reads simulated at 5× coverage with stutter parameters υ = 0.1, d = 0.05, and p = 0.9.

Supplementary Figure 6 Validating mutation parameters at Y-STRs.

(a,b) Mutation parameter estimates for mutation rate (a) and effective length constraint (b) are highly concordant across data sets (n = 48). (c) Y-STR mutation rate estimates are concordant with de novo studies. Each point represents a single Y-STR. Gray dashed lines denote the diagonal (n = 41). (d) Pairwise Pearson correlation between Y-STR estimates from each study.

Supplementary Figure 7 CODIS mutation rate estimates are concordant with de novo studies.

Each dot represents an individual CODIS locus. The gray dashed line denotes the diagonal (n = 11).

Supplementary Figure 8 Comparison of autosomal mutation parameters with de novo studies.

(a,b) Shown are estimated length constraints (a) and step-size parameters (b) for 1,634 STRs also analyzed by Sun et al. Dashed lines give the median estimate across loci. Solid lines give the empirical mutation rate from trio data analyzed by Sun et al. A comparison of mutation rates is shown in Figure 2d.

Supplementary Figure 9 Per-locus stutter parameter estimates by repeat motif length.

(a) Probability of stutter deleting repeat units. (b) Probability of stutter inserting repeat units. (c) Parameter describing the geometric distribution of step sizes. Each plot shows the cumulative distribution across all autosomal loci.

Supplementary Figure 10 Comparison of per-locus mutation rate estimates versus rates predicted by MUTEA.

Each point represents a locus. The red line represents the diagonal (n = 480,623).

Supplementary Figure 11 Per-locus estimates of mutation parameters.

(ac) Plots give the cumulative distributions of the per-locus estimates of mutation rate (a), length constraint (b), and step-size parameter (c). Dashed lines indicate the 50th percentile.

Supplementary Figure 12 Relationship between mutation rate and local sequence features.

Each dot represents the mean mutation rate for each category. The dashed line gives the mean mutation rate across all loci for each motif length.

Supplementary Figure 13 Constraint score distribution.

Distribution of constraint scores for loci with mutation rates not at the lower optimization boundary (gray) and for loci with high or undefined standard errors with mutation rates likely below our mutation rate detection threshold (cyan). The black line denotes a standard normal distribution.

Supplementary Figure 14 Enrichment of constrained STRs in highly expressed genes.

Red denotes brain tissues. The gray line gives P = 0.05. Constraint score distributions were compared in the top 20% versus the bottom 80% of expressed genes in each tissue. The x axis gives unadjusted P values.

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Supplementary Figures 1–14, Supplementary Tables 1–5 and Supplementary Note (PDF 3106 kb)

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Gymrek, M., Willems, T., Reich, D. et al. Interpreting short tandem repeat variations in humans using mutational constraint. Nat Genet 49, 1495–1501 (2017).

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