74 | | For few trios, increase coverage (potentially only in parents, or even one parent); this will decrease the chance that we miss a heterozygote. We did calculations of what coverage should be so we get chance of het missing becoming comparable to the mutation rate; e.g. we aim chance het missing = 1e-8 or so (see Box below for computations). It appears that at ~32x only half of the situations described above will be attributable to inadequate coverage, while other half will be true ‘de novo’ mutations. |
75 | | |
76 | | Assume the heterozygote call is made when at least two reads show the variant. Let us also assume for the moment that coverage is always Nx. Denote reference sequence as “R” and alternative as “A”, so in fact the person is R/A. Let us compute the probability that we miss this heterozygote (i.e. will call it A/A or R/R): |
77 | | |
78 | | P(call R/A as R/R or A/A) = P(all N read R) + P([N-1] reads are R, and 1 read is A) + P(all N read A) + P([N-1] reads are A, and 1 read is R) |
| 74 | For few trios, increase coverage (potentially only in parents, or even one parent); this will decrease the chance that we miss a heterozygote. We did calculations of what coverage should be so we get chance of het missing becoming comparable to the mutation rate; e.g. we aim chance het missing = 1e-8 or so (see Box 1 below for computations). It appears that at ~32x only half of the situations described above will be attributable to inadequate coverage, while other half will be true ‘de novo’ mutations. |
| 75 | |
| 76 | |
| 77 | {{{ |
| 78 | Box 1 |
| 79 | |
| 80 | Assume the heterozygote call is made when at least two reads show the variant. |
| 81 | Let us also assume for the moment that coverage is always Nx. Denote reference |
| 82 | sequence as “R” and alternative as “A”, so in fact the person is R/A. Let us compute |
| 83 | the probability that we miss this heterozygote (i.e. will call it A/A or R/R): |
| 84 | |
| 85 | P(call R/A as R/R or A/A) = P(all N read R) + P([N-1] reads are R, and 1 read is A) |
| 86 | + P(all N read A) + P([N-1] reads are A, and 1 read is R) |
153 | | Reads in offspring |
154 | | |
155 | | {{{ |
156 | | |
157 | | rrCrrArrrr |
158 | | |
159 | | rrCrrArrrr |
160 | | |
161 | | rrCrrArrrr |
162 | | |
163 | | rrCrrArrrr |
164 | | |
165 | | rrCrrArrrr |
166 | | |
167 | | rrCrrArrrr |
168 | | |
169 | | rrrrrrrrrr |
170 | | |
171 | | rrrrrrrrrr |
172 | | |
173 | | rrrrrrrrrr |
174 | | |
175 | | rrrrrrrrrr |
176 | | |
177 | | rrrrrrrrrr |
178 | | |
179 | | rrrrrrrrrr |
180 | | |
181 | | }}} |
182 | | |
183 | | To address whether this is realistic scenario under which we can detect de novo mutations, we need to answer the question about probability that, given ‘de novo’ mutation occurs, what is the chance we will see that mutation in at least four reads (it is clear that for ‘de novo’ we must use more stringent calling criteria) and that in at least two of these 4 reads we will also see a heterozygote coming from a parent. Computations estimating this chance are provided below in the Box. |
184 | | |
185 | | From these computations, it appears that the chance to see ‘de novo’ in 4 or more reads, and see an existing (transmitted from a parent) variant in at least two of these reads is about 0.09. Thus, using outlined strategy we will be able to detect several de novo mutations per trio offspring, translating to hundreds (or thousands) de novo described from the whole data set. Note that in above we ignored the paired-end nature of our sequencing data, which, when properly accounted for, would probably double the numbers of detectable de novo mutations. |
186 | | |
187 | | The probability that we see a ‘de novo’ in at least 4 reads out of 12 is 0.93. The chance that an existing heterozygous site is covered in the same read can be computed assuming the read length of 100, uniform distribution of the read-start position across the genome, and heterozygote probability of 1/300 per site (Kai). Assume the ‘worst’ scenario of exactly 4 reads with ‘de novo’, what is the chance that in at least two of them we will see an existing heterozygote? |
188 | | |
189 | | Denoting the ‘de novo’ position in the read as 0, the ‘coverable’ position of a heterozygote may vary from -99 to +99. The chance that a heterozygote at +99 is included in the read is 0.01; if heterozygote is at +1, the chance is 0.99. Thus, for a heterozygote at position ‘j’ (j in -99 to -1 and 1 to 99) the chance to be included in the read is (1-abs(j/100)). We assume that a chance to have a ‘linked’ alternative variant at a position is ½ * 1/300 = 1/600. Thus the probability to detect a ‘linked’ variant in at least two reads out of 4 is: |
| 192 | To address whether this is realistic scenario under which we can detect de novo mutations, we need to answer the question about probability that, given ‘de novo’ mutation occurs, what is the chance we will see that mutation in at least four reads (it is clear that for ‘de novo’ we must use more stringent calling criteria) and that in at least two of these 4 reads we will also see a heterozygote coming from a parent. Computations estimating this chance are provided below in the Box 2. |
| 193 | |
| 194 | From these computations, it appears that the chance to see ‘de novo’ in 4 or more reads, and see an existing (transmitted from a parent) variant in at least two of these reads is about 0.09. Thus, using outlined strategy we will be able to detect several de novo mutations per trio offspring, translating to hundreds (or thousands) de novo described from the whole data set. Note that in above we ignored the paired-end nature of our sequencing data, which, when properly accounted for, would probably double the numbers of detectable de novo mutations. Next, if cross-reads phasing works accurately and at longer distances this will allow to bring this proportion even higher. |
| 195 | |
| 196 | {{{ |
| 197 | Box 2 |
| 198 | |
| 199 | The probability that we see a ‘de novo’ in at least 4 reads out of 12 is 0.93. |
| 200 | The chance that an existing heterozygous site is covered in the same read |
| 201 | can be computed assuming the read length of 100, uniform distribution of |
| 202 | the read-start position across the genome, and heterozygote probability of |
| 203 | 1/300 per site (Kai). Assume the ‘worst’ scenario of exactly 4 reads with |
| 204 | ‘de novo’, what is the chance that in at least two of them we will see an |
| 205 | existing heterozygote? |
| 206 | |
| 207 | Denoting the ‘de novo’ position in the read as 0, the ‘coverable’ position |
| 208 | of a heterozygote may vary from -99 to +99. The chance that a heterozygote |
| 209 | at +99 is included in the read is 0.01; if heterozygote is at +1, the chance is |
| 210 | 0.99. Thus, for a heterozygote at position ‘j’ (j in -99 to -1 and 1 to 99) the |
| 211 | chance to be included in the read is (1-abs(j/100)). We assume that a chance |
| 212 | to have a ‘linked’ alternative variant at a position is ½ * 1/300 = 1/600. Thus |
| 213 | the probability to detect a ‘linked’ variant in at least two reads out of 4 is: |
193 | | = P(variant is at -99) * P(see variant in >=2 reads | variant is at -99) + P(variant is at -98) * P(see variant in >=2 reads | variant is at -98) + … + P(variant is at +99) * P(see variant in >=2 reads | variant is at +99) |
194 | | |
195 | | = 1/600 (P(see variant in >=2 reads | variant is at -99) + … P(see variant in >=2 reads | variant is at +99)) |
196 | | |
197 | | = 1/600 [ 2 * SUM,,j=(1,99),, SUM,,k=2,4,, (1-j/100)^k^ * (j/100)^(4-k)^ ] |
| 217 | = P(variant is at -99) * P(see variant in >=2 reads | variant is at -99) |
| 218 | + P(variant is at -98) * P(see variant in >=2 reads | variant is at -98) + |
| 219 | … + P(variant is at +99) * P(see variant in >=2 reads | variant is at +99) |
| 220 | |
| 221 | = 1/600 (P(see variant in >=2 reads | variant is at -99) |
| 222 | + … P(see variant in >=2 reads | variant is at +99)) |
| 223 | |
| 224 | = 1/600 [ 2 * SUM_{j=(1,99)} SUM_{k=2,4} (1-j/100)^k * (j/100)^(4-k) ] |