October 1995: DNA Goes to Court

While modern DNA technology is assisting prosecutors to convict rapists and murderers in the courtroom, it is also helping medical sleuths track down and convict the culprits of the microbial world. A recent example was the identification of the agent responsible for a mysterious outbreak of fatal pneumonia in the Southwest. Scientists at the Centers for Disease Control (CDC) showed the culprit to be a "new" strain of hantavirus by using PCR-amplified DNA in tissue extracts from infected patients. Hantavirus is virtually uncultivatable, making its isolation and characterization by conventional tissue culture techniques virtually impossible. More detailed DNA sequence analysis showed that the American isolate was closely related to a deadly hantavirus strain that had swept across Korea in the 1970s.

Shuffling the Genetic Deck

This exercise provides an excellent opportunity to remind your students that mathematics plays a key role in forensic DNA identification. DNA typing is very much a numbers game. Because absolute certainty in DNA identification is not possible in practice, the next best thing is to claim virtual certainty due to the extremely small probabilities of a coincidental match.

Objectives

After completing this lesson, students should be able to:

Determine the predicted frequency of an allele.
Apply the multiplication rule to calculate the frequency of a set of alleles occuring together.
Explain why probabilities are influenced by the makeup of the database.
Discuss whether DNA evidence alone is sufficient to convict a suspect of murder in the absence of supporting evidence.

Material

Photocopies of the feature article for the class.
Decks of playing cards (preferably one for each student).
Calculators

Procedure

Tell your students they will use decks of cards to demonstrate the multiplication rule as it is applied to calculating probabilities in DNA-profiling. Each card dealt represents a LOCUS. The color of the card (red or black), or the suit (Spade, Diamond, Heart, Club), or a specific value (e.g., Queen of Hearts) represent ALLELES (see Fig. 3).

Here is one suggested game: display a predetermined card or group of cards. Announce to the class that this card (or group of cards) represents the DNA profile of evidence found at a crime scene. Tell your students that they all are "suspects" in the crime. The question is: how many of them have DNA profiles that match the evidence? Have your students calculate the probability of a match before they deal. Then, have each student deal the same number of card(s) from their decks as you did. Count how many "suspect" profiles match the evidence profile. If matches occur, compare the experimental results to their calculated probability.

Start with high-probability events and work toward lower-probability events. This strategy will help your students understand that lower probabilities of a chance match result from choosing low-frequency alleles, and including more cards (loci) in the game. Point out to your students that including more cards in the game is similar to using more than one DNA probe in a RFLP experiment.

Figure 3 Card suit, color, or value represents alleles.

A Possible Sequence

1. Turn over a RED card. How many students should do the same? ans. 1 in 2. [Half the cards in the deck are RED, the allele frequency for RED is 0.5; 1/0.5=1 in 2].

2. Turn over a CLUB. How many students should match that allele? ans. 1 in 4. [The allele frequency for CLUBs is 0.25, 1/0.25=1 in 4]. So far, too many "suspects" match the evidence by chance, so let's lower the probability of a coincidental match.

3. Turn over 4 RED cards in succession. How many students should match that sequence? ans. 1 in 16. [ 0.5 x 0.5 x 0.5 x 0.5=0.0625; 1/0.0625=1 in 16].

4. Remove all of the HEARTs from each deck. Now answer Question #3. ans. 1 in 84. [0.33 x 0.33 x 0.33 x 0.33=0.01186, 1/0.01186=1 in 84]. Note how altering the database has significantly changed the probability of this match compared to the allele set posed in Question #3.

5. Turn over 4 RED cards in succession; one card being an ACE. How many "suspects" should match that sequence? ans. 1 in 213. [0.5 x 0.5 x 0.5 x 0.038=0.0047; 1/0.0047=1 in 213]. Note how the inclusion of the relatively low-frequency allele-RED ACE-makes the probability of this match much lower than the one posed in Question #3.

Hints

In the case of low-probability sequences, such as the one posed in Question #5, students should deal a hand, score it, then reshuffle those cards back into the deck before dealing another hand. However, the exercise should work fine, especially for high-probability alleles, if you choose to skip the reshuffling step for the sake of time or convenience.

Sometimes an "unlikely" combination is dealt in the first two or three hands. When this occurs, have your students continue to deal hands in order to validate the observed frequency. It should become obvious that observed probabilities only match calculated probabilities when sufficient trials are made.