Transcript Deconvoluting Mixtures Using Proportional Allele Sharing What does it mean and how do you do it?

Deconvoluting Mixtures Using
Proportional Allele Sharing
What does it mean and how do you
do it?
What is a mixture?
• If you start with two single source profiles and
combine them, you have a mixture
Male Ref
Mixture
Female Ref
• Two sources combined and looks like a two
person mixture
Same references mixed differently
• Two sources combined that looks like a single
source profile
Dad
Ellie
Mom
• Her birthday is at Thanksgiving
What is deconvolution?
• Start with the mixture, and then go backwards
to the single source profiles.
Deconvolution
• Some loci are easy to deconvolute
• Major/minor contributors
Deconvolution
• Some loci are harder to deconvolute
Mixture - Victim
= Foreign
• But if you can assume a contributor…
• It can become easier
How do you deal with shared alleles?
• Common to find shared alleles in any mixture
of two people.
• How is the shared allele distributed between
the two contributors?
• Lots of papers published and various software
programs deal with this issue.
AB BC Sharing
• Donor 1 is AB (10,12)
• Donor 2 is BC (12,13)
• Mixture is ABC (10,12,13)
AB BC Sharing
• But how do you work backwards from this
• To this?
AB BC Sharing
• Validation studies give PHR expectations
– These expectations show up in protocols for
interpretation
– Used in setting stochastic thresholds
– Used in determining number of contributors
• At times you may have a major contributor
that helps
• At times you can assume a contributor
AB BC Sharing – Test 1
• Assume 50% PHR rule
for AB (10,12)
• Can you then assume
250 rfu from the 12
goes with the 10?
250
• So for 10,12 type:
250 ÷ 500 = 0.5 PHR
500
1500 790
250 + 500
= 0.27 P
500 + 1500 + 790 (proportion)
AB BC Sharing – Test 1
• So for 12,13 type:
1250
500
1500 790
790 ÷ 1250 = 0.63 PHR
1250 + 790
= 0.73 P
500 + 1500 + 790
AB BC Sharing – Test 2
• Or
• Assume 1000 rfu of the
12 goes with the 10
1000
• So for 10,12 type:
500 ÷ 1000 = 0.5 PHR
1000 + 500
500 + 1500 + 790 = 0.54 P
500
1500 790
• Note the PHR is the
same, but P is double
AB BC Sharing – Test 2
• 12,13 type is now:
500
500 ÷ 790 = 0.5 PHR
500 + 790
= 0.46 P
500 + 1500 + 790
• Note that PHR is the
same as Test 1
• Proportion is about 1/3
less than Test 1
500
1500 790
AB BC Sharing Summary
• Test 1
• Test 2
• AB PHR = 0.5
• AB PHR = 0.5
• AB portion = 0.27
• AB portion = 0.54
• BC PHR = 0.63
• BC PHR = 0.63
• BC portion = 0.73
• BC portion = 0.46
• 1:4 mixture
• 1:1 mixture
Time to Vote
1. Test 1 is correct
2. Test 2 is correct
3. The truth is
somewhere in
between
4. You cannot make a
determination at all
5. I just want lunch
20%
1
20%
20%
2
3
20%
4
20%
5
AA AB Sharing
• Donor 1 is AA (8,8)
• Donor 2 is AB (8,12)
• Mixture is AB (8,12)
AA AB Sharing
• How do you work backward from this
• To this
AA AB Sharing – Test 1
• Assume 50% PHR rule
for AB (8,12)
• Can you then assume
250 rfu from the 8 goes
with the 12?
• So for 8,12 type:
250 ÷ 500 = 0.5 PHR
250 + 500
= 0.42 P
1300 + 500
250
1300
500
AA AB Sharing – Test 1
• So for 8,8 type:
No PHR
1050
1300 + 500
1050
1300
500
= 0.58 P
AA AB Sharing – Test 2
• Or
• Assume 1000 rfu from
the 8 goes with the 12?
• So for 8,12 type:
1000
500 ÷ 1000 = 0.5 PHR
500 + 1000 = 0.83 P
1300 + 500
• Note PHR is the same,
but P doubles
1300
500
AA AB Sharing – Test 2
• So for 8,8 type:
No PHR
300
= 0.17 P
1300 + 500
• Note that P is smaller
by a factor of ~3 ½
300
1300
500
AA AB Sharing Summary
• Test 1
• Test 2
• AB PHR = 0.5
• AB PHR = 0.5
• AB portion = 0.42
• AB portion = 0.83
• AA portion = 0.58
• AA portion = 0.17
• ≈1:1 mixture
• ≈1:6 mixture
Time to Vote
1. Test 1 is correct
2. Test 2 is correct
3. The truth is out
there
4. Who cares, a 1:1
mixture looks like a
1:6 mixture anyway
5. I said I wanted lunch
20%
1
20%
20%
2
3
20%
4
20%
5
How do you deal with shared alleles?
• Don’t rely on a major or assumed contributor
– That inserts the analyst into the amp tube
– The enzyme certainly doesn’t care whose DNA it
amps
• Calculate the PHR and P without bias
– Use the same set of rules every time
– Calculate every possible combination, then see
what fits
Should we do this?
• Section 3.5 – SWGDAM
3.5. Interpretation of DNA Typing Results for Mixed Samples
An individual’s contribution to a mixed biological sample is generally
proportional to their quantitative representation within the DNA typing results.
Accordingly, depending on the relative contribution of the various contributors to
a mixture, the DNA typing results may potentially be further refined.
Should we do this?
• Section 3.5.2 – SWGDAM
3.5.2. The laboratory should define and document what, if any, assumptions are
used in a particular mixture deconvolution.
3.5.2.1. If no assumptions are made as to the number of contributors, at a
minimum, the laboratory should assign to a major contributor an allele (e.g.,
homozygous) or pair of alleles (e.g., heterozygous) of greater amplitude at
a given locus that do not meet peak height ratio expectations with any other
allelic peak(s).
3.5.2.2. If assumptions are made as to the number of contributors,
additional information such as the number of alleles at a given locus and
the relative peak heights can be used to distinguish major and minor
contributors.
Should we do this?
• Section 3.5.3 – SWGDAM
3.5.3. A laboratory may define other quantitative characteristics of mixtures
(e.g., mixture ratios) to aid in further refining the contributors.
• So don’t forget about proportion between
contributors (mixture ratio)
• (PHR is proportion within a contributor)
• We’ll mention 3.5.3.1 in a minute
All combinations for 2 people
• Grouped by number of alleles
• Sub-grouped by homozygotes/heterzygotes
and sharing/no-sharing
All combinations for 2 people
• Grouped as “family” or “category” of like types
• Highlighted top row is generic form
• Other possible combinations in white
All combinations for 2 people
Some don’t have much to calculate
All combinations for 2 people
Some have no sharing so easy to
calculate
All combinations for 2 people
We just saw two categories that take
a bit more effort to calculate
Proportional Allele Sharing Method
•
•
•
•
No crazy math
Easy to follow the logic of the model
Supported by numerous in-house studies
It just works
• All models are wrong, but some are wrong
more often than others
Rule 1 – AB BC Sharing
• Whenever possible,
shared alleles are
shared proportionately
500
1500 790
Rule 1 – AB BC Sharing
• First, consider the
alleles that are
unshared to get the
proportion of the two
donors
• Essentially, you
calculate the proportion
for two homozygotes
500
1500 790
Rule 1 – AB BC Sharing
• Proportion =
500
500 + 790 = 0.39 for 10(,12)
790
500 + 790 = 0.61 for (12,)13
500
1500 790
Rule 1 – AB BC Sharing
• So based 39%/61% ratio:
• For 10, 12 donor
.61
.39  1500 = 585 rfu
500 ÷ 585 = 0.85 PHR
• For 12, 13 donor
.61  1500 = 915 rfu
790 ÷ 915 = 0.85 PHR
.39
500
1500 790
Rule 1 – AB BC Sharing
• PHR = 0.85 for both
contributors
• PHR is always the same for
proportional sharing model
500
1500
790
• The enzyme doesn’t
arbitrarily give one person a
good PHR and the other a
bad PHR
AB BC Sharing Summary
• Test 1
• Test 2
• Proportional
• AB PHR = 0.5
• AB PHR = 0.5
• AB PHR = 0.85
• AB portion = 0.27 • AB portion = 0.54
• AB portion = 0.39
• BC PHR = 0.63
• BC PHR = 0.85
• BC PHR = 0.63
• BC portion = 0.73 • BC portion = 0.46
• BC portion = 0.61
• 1:4 mixture
• 1:2.5 mixture
• 1:1 mixture
Rule 2 – AA AB Sharing
• Whenever possible,
PHRs are assumed to be
1.0
Rule 2 – AA AB Sharing
• Which way?
• 50% “down”
• 50% “up”
Rule 2 – AA AB Sharing
• PHR = 1.0 is the middle
ground
Rule 2 – AA AB Sharing
1093/1320 = 0.82
823/1031 = 0.80
• PHR = 1.0 is the middle
ground
• Replicate amps
• Calculate the PHR
Ave PHR = 0.805
Ave PHR = 0.74
• Not very close to 1.0
797/1013 = 0.79
602/894 = 0.68
Rule 2 – AA AB Sharing
1093/1320 = 0.82
Ave = 1.04
1013/797 = 1.27
1031/823 = 1.25
Ave = 0.965
602/894 = 0.68
• PHR is (typically)
smallest/tallest
• Do it again with
first/second as the
smallest and tallest
switched
• Pretty close to 1.0 with
only 2 replicates
• (Some folks do
HMW/LMW)
Rule 2 – AA AB Sharing
• So two reasons for Rule 2
– PHR = 1.0 is the middle
ground
– PHR = 1.0 fits replicate
amps
• May not fit quite as well
at large loci and/or big
steps between alleles –
eg: 11,23 at D18
Rule 2 – AA AB Sharing
• For AB (heterozygote):
500 ÷
500 = 1.0
PHR
Defined
as PHR
1.0!
500 + 500
1300 + 500
800
= 0.56 P
• For AA (homozygote):
500
1300
No PHR
800
= 0.44 P
+
1300 500
500
AA AB Sharing Summary
• Test 1
• Test 2
• PHR = 1.0
• AB PHR = 0.5
• AB PHR = 0.5
• AB PHR = 0.5
• AB portion = 0.42 • AB portion = 0.83
• AB portion = 0.56
• AA portion = 0.58 • AA portion = 0.17
• AA portion = 0.44
• ≈1:1 mixture
• ≈1:1 mixture
• ≈1:6 mixture
Similar ratio, but major/minor (sort of) has flipped
An advantage of this approach
• The proportion of contributors calculated at a
specific locus is not dependent upon
something calculated at some other locus
• This allows for consideration of degradation
– (When we look at degraded samples using this
approach, they kind of “self-correct” meaning
with known mixtures, the true types are still
usually the best fit.)
An advantage of this approach
• Section 3.5.3.1 – SWGDAM
3.5.3. A laboratory may define other quantitative characteristics of
mixtures (e.g., mixture ratios) to aid in further refining the contributors.
3.5.3.1. Differential degradation of the contributors to a mixture may
impact the mixture ratio across the entire profile.
• But you can’t predict from one locus how
degradation will affect the next
• This approach helps, as each locus is
independent
Rule 3 – Minimum Peak Height
• Minimum peak heights (mph) are always
maintained and supersede Rules 1 and 2.
• We won’t discuss this much now
• Analogous to your peak calling threshold (75
rfu or 100 rfu, etc)
• Or based on the mixture ratio (proportions)
Rule 3 – Minimum Peak Height
• Comes into play for certain combinations
• Think of looking for an AB and BB contributor
– 12,12 homozygote? How many RFU?
– We just saw this example
– The other homozygote option
• MPH gives a starting point
Three Person Mixtures
• These simple rules work for three person
mixtures also
• Most (well, lots anyway) 3 person mixtures
break down into simple patterns that we just
discussed for 2 person mixtures
– Rule 1
– Rule 2
Three Person Mixtures
Donors 2 and 3
• PHR and P for Donor 1
is straight forward
– 6,7
Donor 1
• Donors 2 and 3 is AA AB
pattern (Rule 2)
– 9,9.3
– 9.3,9.3
Three Person Mixtures
Donors 2 and 3
are 21,22 and 22,25
• PHR and P for Donor 1
is straight forward
– 24,26
Donor 1 = 24,26
• Donors 2 and 3 is AB BC
pattern (Rule 1)
– 21,22
– 22,25
Three Person Mixtures
• You just have to realize some calculated PHR
and P results have two contributors added
together
– Victim ≈ 15%, Consensual ≈ 35%, Foreign ≈ 50%
– AB AB CD locus
(V and C are both AB)
• P for AB = 48% (combined known V and C)
• P for CD = 52% for F
Three Person Mixtures
• This is where it gets a bit tricky for three
person mixtures
Three Person Mixtures
• 4 types where we cannot calculate PHR and P
AA
AB
AB
AC
BC
BD
AB
AA
AC
AB
BC
BB
Three Person Mixtures
• Two alleles shared by two people (twice)
– “Circular” sharing
– “Double” sharing
• In these cases, upper and lower boundaries
can be calculated based on PHR to determine
if viable – “Not Excluded” result
– Increase PHR stringency to “test” fit
– If type with defined PHR and P dropout but not
the “Not Excluded” option…
A computer can help
• Calculate the PHR and P for every possible
combination using Rules 1, 2, and 3
– 3 Contributors in a 4 allele pattern:
• 6 “families” of types
• 52 total combinations
– 3 Contributors in a 5 allele pattern
• Only 2 “families”
• But one contains 30 combinations
A computer can help
• Filter the possibilities shown to the analyst:
– Don’t show combinations with low PHR (eg: <50%)
– Don’t show combinations with proportions of 5%
when you know your minor is at least 20% (4-fold
difference)
– Don’t show combinations that do not include a
known donor (V on own panties)
• Starts to become fairly manageable
A computer can help
• Assumes good data
– Can’t do much with a 3 person mixture that only
had 100pg of DNA in the first place
– Deconvolution works best when you are in a range
that your validation says PHR’s are robust
• Even if you can’t deconvolute the mixture, you
may be able to limit the possible types present
to a manageable number – (Statistics…)