Case 3 - SMA carrier risk calculation - Results

Gamete square method

Go to downloadable spreadsheets, with rounded and unrounded allele frequency calculations.

Rounded allele frequencies

The approach illustrated here is to construct a gamete square, where all possible gametes are listed for both parents of II2 (I1 and I2) along with frequencies for their predicted occurrence. This is the only really tricky part of the calculation, and is obtained by examining the possible genotypes of the parents. Once these are fixed, the gamete square is completed by determining all possible zygotes, and their predicted frequencies are determined by multiplying the relevant parental gamete frequencies. The final carrier risk figure is determined by examining which zygotes have clinical status and SMN1 copy number compatible with MLPA results.

1. Initial assumptions. The possibility of new mutations is not considered. The possibility of alleles which are deleted for SMN1, but have multiple copies of SMN2 and mask clinical disease is not considered. In this illustration, for simplicity, the rare possibility of point mutations has been ignored and allele frequencies have been rounded to the nearest whole percentage. Thus: deletion allele (del; 1%); normal allele with 1 copy of SMN1 (n1; 95%); normal allele with 2 copies of SMN1 (n2; 4%). A calculation by the same method, not ignoring point mutations and using the frequencies exactly as quoted in the question is illustrated on a downloadable spreadsheet.

2. Prior knowledge of parental genotypes, and determining gamete frequencies.
a) Parent 1: We know from the MLPA result in II2 (2x dosage) that one parent (nominated ‘parent 1’) must be a heterozygous carrier of an SMN1 deletion. Because this parent is also clinically unaffected, the opposite allele must be ‘normal’, although it may have either 1 or 2 copies of SMN1. Therefore, parent 1 must have one of 2 genotypes: del/n1 or del/n2 (see figure 1). The relative likelihood of these genotypes is equal to the relative frequencies of n1 and n2 in the population. Half of gametes from parent 1 must therefore be ‘del’ alleles. The other half could be either ‘n1’ or ‘n2’ at frequencies ‘½ x 95/99’ or ‘½ x 4/99’ respectively (see figure 2).
b) Parent 2: We also know from II2’s MLPA result that at least one of the alleles in parent 2 must be ‘normal’ and with a single copy of SMN1 (n1). We know nothing about the other allele in parent 2 (if for the moment we ignore knowledge of clinical status in II3). Therefore, the genotype of parent 2 could be any of the following: n1/del, n1/n1 or n1/n2. The relative likelihood of these genotypes is equal to the relative frequencies of the 3 alleles in the population (1:95:4). Half of gametes from parent 2 must therefore be ‘n1’ alleles. The other half could be either ‘del’, ‘n1’ or ‘n2’ at frequencies ‘½ x 1/100’, ‘½ x 95/100’ or ‘½ x 4/100’.
 

Figure 1. Pedigree drawing, showing possible genotypes for parents of II2.

3. Completion of gamete square – zygote genotypes and frequencies. All possible zygote genotypes are determined by examining the gamete contributions from each parent. The zygote frequencies are determined by multiplying the gamete frequencies together. The clinical status and copy number of SMN1 is noted.

Figure 2. Gamete square construction for calculation of zygote frequencies which are compatible with MLPA results.

4. Final calculation stage. The zygotes in the gamete square and examined, and those compatible with MLPA analysis in II3 (2x dosage) are highlighted. Two of these are carriers (highlighted in yellow, figure 2) while one is a non-carrier (highlighted in green). Thus the carrier risk for II3 is equal to the frequency of this non-carrier zygote, divided by all unaffected zygotes compatible with 2x dosage. This is 0.02114 or around 1 in 47.

Spreadsheets for download with calculations

    Rounded allele frequencies - download spreadsheet

    Unrounded allele frequencies - download spreadsheet

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