Applied Mendelian Statistics!
Stefan Tarnawsky Feb 14, 2014
In December I wrote how my grad courses taught me skills that I could apply directly to my research. This week, I took advantage of those skills to determine if my mice colonies were breeding a Mendelian ratios.
Mice are the most commonly used animal in biomedical research. They are small, breed quickly, and are relatively inexpensive to house. They are also very amenable to genetic manipulations. A variety of techniques allow researchers to model human diseases by modifying mouse genes. However, many of these genes are essential, meaning that a deletion or mutation will cause the mouse to die prior to birth. The circumvent these ‘embryonic lethal’ genes researchers have developed a system that activates the mutations in adulthood. Thereby, the gene remains relatively undisturbed during the crucial periods of development in utero. This method relies on the activation of the Cre Recombinase gene. Cre is a DNA modifying enzyme that can be used to turn on a mutant gene. However, it is not normally present in the mouse genome—just like the mutant gene, Cre must be introduced into the mouse. Once a mouse has both Cre and the mutant gene, you have a model that expresses an embryonic lethal mutation in adulthood.
The mating strategy in this case is straightforward (see figure). You cross a male who has one allele of the mutation to a female who has one allele of Cre. Each will pass along the desired gene (Cre+ or Mut+) to ½ of their offspring. So we expect ¼ to be both Cre+ and Mut+.
The statistical test that is used to evaluate ratios is called the Chi Squared test. It compares the expected probability of an event (in this case: ¼) to the observed number of events. It then determines how likely your result is to occur by chance if probability expected = probability observed.
The test is both powerful and useful by translating one’s hunches into a definite answer. For instance, I was disappointed to see that only 4 of my 31 animals were both Cre+ and Mut+. My instinct was to conclude that these animals were becoming sick in utero and that were being born at sub-Mendelian ratios. However, the Chi Squared test gave me a p-value of 0.24. The technical meaning of this value is: if my mice are being born proportionately and I randomly selected 31 mice for genotyping 100 times, then 24 out of those 100 times I would see four or fewer Cre+ / Mut+.
Translation: there is a high likelihood that the disappointingly low # of Cre+/Mut+ mice I saw is purely due to chance. As such, I conclude there is no basis to conclude that my mutant mice are being born at lower than expected ratios.
Now, that doesn’t mean that they are being born at normal Mendelian ratios either. If just means that I will need to continue tracking the birth ratio of my mouse colony before I am able to draw a definitive conclusion.