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

• Two sources combined and looks like a two person mixture

Male Ref

Female Ref

Mixture

Same references mixed differently

• Two sources combined that looks like a single source profile

• Her birthday is at Thanksgiving

Dad

Mom

Ellie

• Start with the mixture, and then go backwards to the single source profiles.

What is deconvolution?

Deconvolution

• Some loci are easy to deconvolute• Major/minor contributors

Deconvolution

• Some loci are harder to deconvolute

• But if you can assume a contributor…• It can become easier

Mixture - Victim = Foreign

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?

• So for 10,12 type:

500 1500 790

250250

500

÷ = 0.5 PHR

250

500+

500 +1500 +790= 0.27 P(proportion)

250 500

250 500500 1500 790



500 1500 790

1250

790

1250

÷ = 0.63 PHR

1250

+

790500

+

1500

+

790

= 0.73 P

790790

790

12501250

500 1500


• Or• Assume 1000 rfu of the

12 goes with the 10


• Note the PHR is the same, but P is double500 1500 790

1000

500

÷

1000

= 0.5 PHR

1000

+

500500

+

1500

+

790

= 0.54 P500500

500

1500 790

10001000


• 12,13 type is now:

• Note that PHR is the same as Test 1

• Proportion is about 1/3 less than Test 1

500 1500 790

500500

÷

790

= 0.5 PHR

500

+

790500 1500 790

+ += 0.46 P

500500

500

1500 790790

790

AB BC Sharing Summary

• Test 1

• AB PHR = 0.5

• AB portion = 0.27

• BC PHR = 0.63

• BC portion = 0.73

• 1:4 mixture

• Test 2

• AB PHR = 0.5


• BC PHR = 0.63


• 1:1 mixture

Time to Vote

1 2 3 4 5

20% 20% 20%20%20%1. Test 1 is correct2. Test 2 is correct3. The truth is

somewhere in between

4. You cannot make a determination at all

5. I just want lunch

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?


250

1300 500

250÷

500

= 0.5 PHR250

+

5001300

+

500

= 0.42 P250250

500500

5001300



1050

1300 500

No PHR

1050

1300

+

500

= 0.58 P1050

1300 500


• Or• Assume 1000 rfu from

the 8 goes with the 12?• So for 8,12 type:

• Note PHR is the same, but P doubles

1000

1300 500

= 0.5 PHR÷1000

500

1000

500

+

1300

+

500

= 0.83 P500500

500

13001000

1000



• Note that P is smaller by a factor of ~3 ½

300

1300 500

No PHR

300

5001300

+ = 0.17 P1300 500

300

AA AB Sharing Summary

• Test 1

• AB PHR = 0.5


• AA portion = 0.58

• ≈1:1 mixture

• Test 2

• AB PHR = 0.5



• ≈1:6 mixture

Time to Vote

1 2 3 4 5

20% 20% 20%20%20%1. Test 1 is correct2. Test 2 is correct3. The truth is out

there4. Who cares, a 1:1

mixture looks like a 1:6 mixture anyway

5. I said I wanted lunch

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

• 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

3.5.3. A laboratory may define other quantitative characteristics of mixtures (e.g., mixture ratios) to aid in further refining the contributors.

All combinations for 2 people

• Grouped by number of alleles• Sub-grouped by homozygotes/heterzygotes

and sharing/no-sharing


• Grouped as “family” or “category” of like types• Highlighted top row is generic form• Other possible combinations in white


Some don’t have much to calculate


Some have no sharing so easy to calculate


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


• 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


• Proportion =

500 1500 790500

+

500 790

= 0.39 for 10(,12)

790500

+

790

= 0.61 for (12,)13

500500

500

790

790790


• So based 39%/61% ratio:• For 10, 12 donor

• For 12, 13 donor

500 1500 790

.61

.39

1500

.39

= 585 rfu

500

÷585

= 0.85 PHR

÷

790

.61

= 915 rfu

1500

915= 0.85 PHR

.39 1500500 585

.61 1500915790


• PHR = 0.85 for both contributors

• PHR is always the same for proportional sharing model

• The enzyme doesn’t arbitrarily give one person a good PHR and the other a bad PHR500 1500 790

AB BC Sharing Summary

• Test 1

• AB PHR = 0.5


• BC PHR = 0.63


• 1:4 mixture

• Test 2

• AB PHR = 0.5


• BC PHR = 0.63


• 1:1 mixture

• Proportional

• AB PHR = 0.85


• BC PHR = 0.85


• 1:2.5 mixture

Rule 2 – AA AB Sharing

• Whenever possible, PHRs are assumed to be 1.0


• Which way?

• 50% “down”

• 50% “up”


• PHR = 1.0 is the middle ground


• PHR = 1.0 is the middle ground

• Replicate amps

• Calculate the PHR

• Not very close to 1.0

1093/1320 = 0.82

797/1013 = 0.79

823/1031 = 0.80

602/894 = 0.68

Ave PHR = 0.805 Ave PHR = 0.74


• 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)

1093/1320 = 0.82

1013/797 = 1.27

1031/823 = 1.25

602/894 = 0.68

Ave = 1.04 Ave = 0.965


• 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


• For AB (heterozygote):

• For AA (homozygote):

1300 500

800

500

= 1.0 PHR÷+ = 0.56 P

500

= 0.44 P

5001300

+

500

No PHR

800

1300

+

500

500

500500500

1300

1300

800

500500PHR Defined as 1.0!

AA AB Sharing Summary

• Test 1

• AB PHR = 0.5



• ≈1:1 mixture

• Test 2

• AB PHR = 0.5



• ≈1:6 mixture

• PHR = 1.0

• AB PHR = 0.5



• ≈1:1 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

• But you can’t predict from one locus how degradation will affect the next

• This approach helps, as each locus is independent

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.

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


• PHR and P for Donor 1 is straight forward– 6,7

• Donors 2 and 3 is AA AB pattern (Rule 2)– 9,9.3– 9.3,9.3

Donor 1

Donors 2 and 3


• PHR and P for Donor 1 is straight forward– 24,26

• Donors 2 and 3 is AB BC pattern (Rule 1)– 21,22– 22,25

Donor 1 = 24,26

Donors 2 and 3are 21,22 and 22,25


• 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


• This is where it gets a bit tricky for three person mixtures


• 4 types where we cannot calculate PHR and P

B CA A A B A B A C B C

A B A C B DB BA A A B


• 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…)

Documents

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