Note to the Reader
Quantitative Neuroanatomy: A Picture is Worth a Thousand Words, but a Number
is Worth a Thousand Pictures. Organizers: John H. Morrison and Patrick R.
Hof Society for Neuroscience Education Committee Saturday, November 7, 1998
(2:30–3:00 pm) Westin Bonaventure Hotel and Suites, Los Angeles, CA pp.
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Neuroscience Meets Quantitative Genetics: Using Morphometric Data to Map
Genes that Modulate CNS Architecture
Robert W. Williams
Center for Neuroscience, Department of Anatomy and Neurobiology,
University of Tennessee, Memphis, Tennessee 38163
Email questions and comments to
Prelude to Mapping
Mapping QTLs that Modulate
PCR protocols for mapping microsatellites
Types of Genetic
Crosses used to Map QTLs
The Highs and Lows of
Quantitative methods now pervade most aspects of neuroanatomical
research, whether the focus is on dendritic spines or the topography of
human neocortex. Sophisticated techniques to study cells in the CNS have
gained in importance as the field of neuroanatomy has matured beyond
qualitative analysis. Efficient methods to quantify cells in thick or thin
sections, particularly direct three-dimensional counting (Williams & Rakic,
1988) and several adaptations of the disector (Gundersen et al., 1988),
make it easier to obtain unbiased estimate of neuroanatomical traits. As a
practical matter, the most important advance in quantitative techniques has
been the rapid hybridization of microscopes, video systems, fast
microcomputers, and powerful application programs such as NIH Image (http://rsb.info.nih.gov/nih-image/Default.html).
These advances have given neuroscience a major boost, and investigators can
now use more trustworthy quantitative techniques to study large numbers of
The promise of quantitative genetics. This tutorial
illustrates how to exploit quantitative neuroanatomical datasets to map and
positively identify (clone) genes that generate the astonishing, but
nonetheless normal, variation in CNS architecture. The types of genes that I
am referring to are called quantitative trait loci or QTLs, and these
QTLs are responsible for much of the inheritable variation among individuals
within a species. For example, the volume and number of cells in visual
cortex of humans and other primates vary nearly 3-fold (Gilissen & Zilles,
1996; Suner & Rakic, 1996), and most of this remarkable variation is
generated by sets of still completely unknown neurogenic QTLs. You don't
need expertise in molecular biology to map these genes. In the near future
it should even be possible to clone QTLs without running gels. A solid
background in statistics and expertise in phenotyping is more helpful at
present than expertise in molecular biology. What you must have to pursue
complex trait analysis to study the nervous system is the ability, patience,
and resources to quantify large numbers of cases.
The QTL methods I describe in this paper have become available only in
the last few years (Tanksley, 1993; Lander & Schork, 1994, Kearsey & Pooni,
1996) and their applications in neuroscience are still largely restricted to
mice and human populations. These methods depend on the polymerase chain
reaction (PCR), high-density genetic maps, and sophisticated statistics
programs. The application of these methods in the next decades will
revolutionize our understanding of normal genetic mechanisms controlling CNS
development, susceptibility to disease, and even CNS evolution (Williams
2000; Greenspan 2001). Progress in QTL mapping is just as relentless as
in any other branch of genetics, and the application of new methods will
soon allow reseachers to achieve extremely high precision QTL
mapping—precision of better than 0.2 cM—with relatively modest total
phenotyping requirements and no genotyping at all within the next ten years
(cf., Williams et al., 2001).
The terrific feature of these new genetic tools is that specific categories
of genes can be targeted for analysis using a forward genetic approach. A
forward genetic approach starts with well-defined phenotypes and moves
toward single genes that contribute to those phenotypes (Takahashi et al.,
1994). It is therefore an ideal approach for neuroscientists, who typically
begin with specific problems and questions about specific CNS traits.
Forward genetics is not fishing; instead it is highly directed, like
harvesting fruit from a chosen tree in an orchard. The genes discovered
using QTL methods will usually be key controllers in molecular pathways that
normally influence CNS traits.
This chapter summarizes key principles and methods involved in a
quantitative genetic dissection of the mouse CNS. After reading this chapter
you may be interested in several papers that provide concrete examples of
how and why we are using these methods to map genes that control variation
in neuron number. A set of closely related papers on this topic (covering
olftactory bulb, striatum, hippocampus, and cerebellum) are available
without restriction on this web site and at
www.jneurosci.org/cgi/content/full/16/22/7193. A more general overview
of the genetics of brain weight is available at
What are QTLs? Quantitative trait loci are normal genes in every
sense of the word, but they are referred to using this somewhat unwieldy
term to highlight the fact that variant forms—or alleles—of QTLs have
relatively subtle quantitative effects on phenotypes (Lynch & Walsh, 1998).
In studies of human populations in clinical settings, QTLs are also referred
to as susceptibility genes, because humans who carry certain alleles are at
greater risk of developing disease. QTLs are often contrasted with Mendelian
loci that have pronounced, and usually discontinuous, qualitative effects on
phenotypes, but there is actually no sharp demarcation between quantitative
and qualitative traits. QTLs that have particularly large effects that verge
on producing Mendelian segregation patterns (e.g., 1:2:1) are major-factor
or major-effect QTLs. Their large effects make them the easiest QTLs to map.
Conversely, allelic variants at Mendelian loci can have graded effects, and
given a particular population or environment, they are also QTLs. The effect
size of a QTL is not in any way a measure of the importance of a gene in a
biological process or network; in fact some of the most important genes may
have only minor sequence variants.
In some instances a QTL may encompass two or more polymorphic genes that
are close to each other on a chromosome. "Close" in this sense means that
the two neighboring genes that modulate a trait have not been dissociated
sufficiently by recombination events. The collective effect of such linked
genes may be quite striking, and some effort may be required to dissect the
individual contributions of two of more QTLs apart. There are some
statistical short-cuts to help dissociate two polymorphic genes that
contribute to a "single" composite QTL, but the ultimate solution is simply
to use high resolution mapping panels (that is to say, groups of mice that
collectively harbor many recombination events) to resolve one composite QTL
into two or more constituents. An apt analogy is the differences of image
resolution achieved by light and electron microscopes—the higher the
frequency of the light source the better the resolution. In gene mapping,
the greater the number of recombination events, the better the resolution.
The ultimate goal is of course to resolve the effects of the single genes
that underlie QTLs; to turn QTLs into QTGs (quantitative trait genes) or
even QTNs (quantitative trait nucleotides).
Prelude to mapping
Four conditions. Methods used to map QTLs affecting the nervous
system can be applied widely, with the following provisions:
- The CNS trait must be variable. For example, to discover what genes
control variation in brain weight or in numbers of Purkinje cells in mice
(Fig. 1), we would first need to show that there are significant
differences among inbred strains.
- This variation must be heritable. Estimates of heritability should
usually be above 10% to begin mapping QTLs. Fortunately, there are methods
to boost the heritability of genetically controlled traits to very high
values using certain types of mapping resources, partcularly recombinant
- Methods used to phenotype CNS or behavioral traits must be efficient.
It will usually be necessary to phenotype several hundred cases to map one
or more QTLs.
- There must be a well-established linkage map for the species or genus
that is to be the focus of research. This currently restricts analysis to
laboratory mice and rats, and a half-wild outbred mammalian species (Homo
Fig. 1. Variation in brain weight between two inbred strains
and several generations of progeny can be used to estimate the minimum
number of genes that affect brain weight. Brain weights of two inbred
strains are shown to the far left. The upper left box is labeled BALB/cJ,
and the lower left box is labeled CAST/Ei. These are names of two
very different strains of mice. Each dot represents the brain weight
of an individual mouse; the short horizontal lines indicate group
means; the faint vertical bars within each box indicate the standard
deviation; and the horizontal line at 445 mg indicates the
mid-parental value (average of BALB/cJ and CAST/Ei). Brain weights of
genetically identical BALB/cJ mice vary from a low of 445 mg to a high of
580 mg. Brain weights of the much smaller CAST/Ei mice range from 320 mg to
415 mg. When BALB/cJ females are mated to CAST/Ei males, the F1 progeny have
brain weights between 450 and 560 mg. This does not differ greatly from the
weights of the BALB/cJ parental strain and indicates that BALB/cJ alleles
are likely to be dominant over CAST/Ei alleles (maternal effects may also be
at work). F2 mice are generated by crossing F1 males and females. Brain
weights of these F2 animals have a very wide range from 350 mg to 550 mg.
The increase is because these F2 mice are genetically heterogeneous. Note
that all F2 animals have genetically identical F1 mothers, so the
variability is not from maternal effects. The F1 animals can also be crossed
back to the parental strains, giving rise to the B1
progeny shown to the right. The equation at the bottom of the figure is the
Wright-Castle equation for estimating the minimum numbers of “effective
factors” (genes) that contribute to the genetic variance in a trait. Delta P
is the difference between parental strain means. VF2
and VF1 are the variances of the F2 and F1 values.
For this particular set of data, we estimate that no fewer than 4
polymorphic genes account for the increases variance in the F2 relative to
the isogenic F1. It is, of course, highly likely that far more than four
genes contribute to the genetic control of brain weight. Click on the image
to view a higher resolution copy in a separate window.
Getting a handle on the phenotype
"The importance of phenotype definition and delineation cannot be
overemphasized. For what we refer to now as "gene mapping" is actually
"phenotype mapping," with identificaiton of new gene loci merely a
by-product in our current age of ignorance. After the year 2005, when most
functional loci in the human genome will have been mapped and sequenced,
there will still remain huge gaps in our knowledge about
genotype-phenotype correlations. So as long as there is interest in
identifying alleles that cause human phenotypes, there will be continuing,
long-term interest in phenotype mapping." (from A. S. Aylsworth, 1998)
Sources of variance. Variation in the value of a trait or
phenotype is often thought of as an experimental annoyance. However, when
the aim is to map QTLs, the greater the genetic variance, the better the
prospects of success (Figure 1). The variance that is initially
measured in a quantitative neuroanatomical study (the square of the standard
deviation) has many sources (Falconer & Mackay, 1996; Lynch & Walsh, 1998,
chapters 5–7). For this reason, one of the first steps in a QTL analysis is
to partition this variance into its major components. Three especially
important components are (1) technical and sampling variance (Vt),
(2) environmental variance (Ve), and (3) additive genetic variance (Va).
There are several ways to separate them (Williams et al., 1996).
Technical error. Technical error can be estimated by repeated
analysis of a subset of cases. In one recent study, we used a quantitative
electron microscopic method to count retinal ganglion cells in mice. To
estimate the reliability of this method, we simply recounted cases (Williams
et al., 1996). Most cases were rephotographed and recounted by different lab
members to estimate inter-observer reliability. We discovered that technical
errors in our study were as important a source of variance as all
environmental sources of variance combined. In this study to get a reliable
strain average, we had to increase the number of cases to about 6 to 8
|Box 1: The
challenge of keeping records
Keeping records on sources of animals, their dates of birth, litter
size, sex, weight, and the many CNS traits that interest us can be
difficult. Difficulties are compounded when reliance is placed on
records scattered in different sets of notebooks kept by different
collaborators, technicians, and students. Add a host of Excel
spreadsheets and you have a recipe for data chaos. The efficiency and
accuracy of record keeping become major issues when several
investigators are collaborating and collecting data from as many as 100
animals per week. The solution is to maintain these types of records in a
We use an integrated relational database (FileMaker Pro:
www.filemaker.com/) to keep track of almost all of these types of
data. Data are entered directly into one of several interconnected
FileMaker files, all of which reside on a network server (a Mac G4),
backed up daily to a second hard drive, and archived on DVD-RAM at
weekly intervals. Networked computers (primarily iMacs and iBooks) on
small carts are kept in the mouse colony, near the hood, dissection
table, and by the electronic balances. Entering data directly into a
consolidated database greatly simplifies record keeping and minimizes
data loss and data transcription errors.
By typing in a case identification number we have immediate access to
information in any of the related databases. These data can be exported
easily for analysis in DataDesk, Excel, and Map Manager QTX.
Converting our laboratory from notebooks and a set of disjointed
Excel files to FileMaker took several months. Some of the more useful
databases are available at
Environmental and non-genetic developmental variance can be estimated by
phenotyping related individuals. For example, in (Figure A) the
variability in brain weight among BALB/cJ individuals is entirely due to
environmental differences and technical error. Once technical errors have
been factored out, the variance among inbred mice within a strain is almost
purely environmental and is a good estimate of Ve. Variation in age,
sex, body weight, litter size, age of mother and parity of her litters,
exposure to pathogens, temperature and humidity variation, the sometimes
amazing differences from bag to bag in non-synthetic mouse chows from major
vendors (Michael Tordoff of the
Chemical Senses Center finds 10-fold variation in calcium content between
bags), seasonal fluctuation in water quality, and a host of other
environmental factors can often be minimized or carefully controlled in
studies using mice. Failure to control for these factors can and will give
rise to variation within colonies and between laboratories. For studies of
robust Mendelian and quantitative traits, these sources of variation may not
matter much, but if you are trying to track down a host of genes that affect
the kinetics of neurogenesis in the hippocampus or of a sensitive behavioral
trait then go to the effort to control as much as possible. For example, if
practical feed animals a more expensive but much less variable synthetic
chow and provide your colony with a consistent source of deionized water. (Box
1: The challenge of keeping records provides advice on building and
maintaining a coherent and accurate laboratory database.) What we are left
with after accounting for technical and environmental sources of variance is
a large amount of unexplained or 'residual' variance. This is the genetic
variance that we will be trying to split apart into a neatly defined set of
precisely mapped QTLs.
Comparing strains. Before mapping QTLs, we need to know that the
trait is variable and that the variation is heritable. An easy way to go
about this is to phenotype 5–10 individuals from each of 10 or more common
inbred strains of mice, all raised in the same colony under closely matched
conditions. It is a good idea to gather cases from several different
litters. If all mice of a particular strain come from a single litter, then
the variance between strains could have as much to do with the health and
experience of the mother as with her genotype.
In our electron microscopic study of ganglion cells, we found that 70–80%
of the variance was heritable. Heritability, defined broadly to include all
sources of genetic variance, was estimated by comparing levels of variance
within and among 17 inbred strains. The average variance within a strain,
Vw, was 13.7 (variance units are x106cells2).
When the technical error, Vt, was subtracted, the average
environmental variance, Ve, was reduced to 4.65. In comparison, the
additive genetic variance, Va, computed across strains was 27.9. From
these values we computed the broad heritability, h2,
using the equation
h2 = 0.5Va / (0.5Va+Ve) (Hegmann
& Possidente, 1981).
Substituting values, heritability was estimated to be ~0.75—a relatively
high value, but one that will probably be typical of many quantitative
neuroanatomical traits (Wimer & Wimer, 1989).
Selecting strains. Which inbred strains or isogenic F1 hybrids
are appropriate for a preliminary analysis of the heritability of a variable
CNS trait in mice? My suggestions for an initial screen are in approximate
order of priority:
- C57BL/6J (the strains whose genome is being sequenced as part of a
public NIH-supported effort; used to generate most major mapping
- DBA/2J (key strain in behavior genetics, used to make many
recombinant inbred strains; this strain has been partly sequenced (1x
coverage by Celera; a parental strain of the BXD series)
- B6D2F1 (the F1 intercross of a female C57BL/6J and a male DBA/2J)
- A/J (key strain used to make the AXB and BXA recombinant inbreds, and
now consomic lines for QTL analysis; also sequenced 1X coverage by
- B6AF1 (the F1 intercross of a female C57BL/6J and a male A/J)
- BALB/cByJ (one of the parental strains of the CXB recombinant inbred
- C3H/HeJ (one of the parental strains of the BXH recombinant inbred
- 129X1/SvJ (used to be known as 129/SvJ, widely used in generating
transgenic and knockout lines, sequenced 1X by Celera)
- B6129PF1 (an F1 intercross used extensively in transgenic mouse
- BALB/cJ (key strain in behavior genetics, like A/J and BALB/cJ, this
strains is an albino)
- SM/J (parental strain of a very large RI set being made by Dr. James
Cheverud, Wash U)
- LG/J (parental strain of a very large RI set being made by Dr.
Cheverud, Wash U)
- CBA/J (one of the few strains with good hearing throughout life, key
in auditory research)
- FVB/NJ (key strain in transgenic research due to high fecundity and
ease of injecting oocytes with DNA)
- NOD/LtJ (use with caution, this is a non-obese diabetic mouse strain
- SWR/J (Swiss Webster inbred)
- CAST/Ei (wild inbred strain, small and frisky, hard to breed)
- SPRET/Ei (wild inbred strain, small and frisky, hard to breed)
- PANCEVO/Ei (wild inbred strain, small and frisky, hard to breed, a
colonial mound-building species from sourthern Eastern Europe and the
Note 1: As of January 2000, the genomes of four strains of mice have been
partly sequenced (C57BL/6J, DBA/2J, A/J, and 129X1/SvJ). The collected
sequence data should provide almost complete coverage of the mouse genome.
Sequence data for three of these strains is still proprietary data
belonging to Celera Genomics. You can keep up-to-date with the public
Note 2: If you need to determine the genetic difference between two
strains, then visit
http://pages.cidr.nhgri.nih.gov/mouse/mouse.html. The CIDR has
genotypes at a set of 300 MIT markers for a growing number of strains. For
a sophisticates comparison see Taylor (1972).
I have chosen these strains for four reasons: (1) most are readily
available, (2) these strains differ greatly in both phenotypes and
genotypes, (3) their genomes have been characterized extensively, and (4)
many of these strains have been used to generate recombinant inbred strains
that are proving to be especially useful to neurogeneticists. Some of these
mice will not be suitable for certain studies–for example, C3H/HeJ, CBA/J,
and SWR/J all carry the mutant rd1 allele of the Pdeb gene
that causes photoreceptor degeneration, so none would not be appropriate for
an analysis of retinal cell populations. For an excellent synopsis of
strains of mice that are suitable for different types of neurogenetic/behavioral
analysis see Crawley et al. (1997)
Level of genetic variation between strains. One key to
successfully mapping QTLs is a high level of genetic variation among mice.
Many strains listed above have now been genotyped ~6400 loci (Dietrich et
al., 1994). It is therefore possible to determine at an early stage how
feasible it will be to map QTLs using a cross between any two of these
strains. For most pairs of strains, more than 30% of marker loci have
reliable and easily scored differences (Fig. 1). In contrast, it would not
be practical to map QTLs responsible for the heritable 100 mg difference in
brain weight between BALB/cJ and BALB/cByJ because these strains are closely
related, and just finding suitable marker loci would be a major undertaking.
In this particular case a complementary analysis of differences in
expression levels of genes or proteins might be extremely fruitful (Sandberg
et al., (2000)).
Resources for regression analysis
Neuroanatomists are generally not familiar with regression analysis
and its applications in quantitative neuroscience. Chapters 14–16 of
Biometry provide a solid introduction to the topic. Genetics and
Analysis of Quantitative Traits covers regression from a rigorous
genetic perspective. Our group’s favorites are still The Cartoon
Guide to Statistics and Data Reduction and Error Analysis for the
There are numerous pitfalls in performing regression analysis.
Mismeasured cases, runts, and hydrocephalic animals can ruin an
analysis. It is essential to explore the data graphically, to handle or
discard outliers, and to normalize distributions before plunging ahead.
For advanced, yet practical, advice on applying regression analysis, see
Data Analysis and Regression.
The program DataDesk 6.0 is extremely well adapted for performing
multiple regression analysis (linear and non-linear), as well as an
armada of other statistical procedures. DataDesk allows sets of
variables to be added or removed using a simple drag-and-drop interface.
The program comes with an excellent and pragmatic statistics guide by
The DataDesk web site at:
http://www.lightlink.com/datadesk/ is a treat. Trial versions are
available for Macintosh or Windows operating systems.
- Sokal RR, Rohlf FJ (1981) Biometry. The Principle and Practice
of Statistics in Biological Research, 2nd ed. WH Freeman, New
- Lynch M, Walsh B (1998) Genetic Analysis of Quantitative
Traits. Sinauer, Sunderland MA.
- Mosteller F, Tukey JW (1977) Data Analysis and Regression. A
Second Course in Statistics. Addison-Wesley, Reading MA.
- Gonick L, Smith W (1993) The Cartoon Guide to Statistics.
HarperCollins, New York.
- Bevington PR, Robinson DK (1992) Data Reduction and Error
Analysis for the Physical Sciences. 2nd ed. McGraw-Hill, New York.
Using multiple regression analysis to improve specificity of QTL
mapping. Quantitative neuroanatomical methods can be used to generate
unbiased estimates, but before these estimates can be employed to map genes,
they will need to be fine-tuned using multiple regression techniques (Box
2: Resources for regression analysis). The reason is that a trait may be
tightly correlated with other traits, and if care is not taken, it is
possible to map the wrong QTLs or no QTLs at all. For example, assume that
we are interested in mapping genes that specifically control normal
variation in numbers of Purkinje cells in the cerebellum. If we count these
neurons in a large sample of animals and use these raw numbers to map QTLs,
we will almost certainly, and inadvertently, map genes that affect the
entire cerebellum, the entire brain, or perhaps even the entire body. To
sidestep this problem, and to map QTLs that have selective effects on
Purkinje cells, we need to have data on body, brain, and cerebellar weight.
The more data we have on what might be called “higher-order” phenotypes, the
In this particular example, we should perform a multiple regression
analysis of Purkinje cell number against cerebellar weight, brain weight,
body weight, sex, age, fixation quality, the identity of the investigator
who carried out the dissection and counted the tissue, method of processing,
and whatever other parameters we can demonstrate are statistically
associated with our estimates of Purkinje cell number. If an individual
parameter is not significant in this multiple regression, then it should be
eliminated from the analysis. David Airey, Lu Lu, and I carried out an
analysis like this, and after stripping away extraneous variance generated
by many general factors we were able to map four QTLs that specifically
control the size of the mouse cerebellum (Airey
et al., 2001). The phenotype values used in this analysis were multiple
regression residuals—the differences between expected and observed
cerebellar weights. With this background on the genetics of cerebellar size,
we are now poised to study particular cell populations within cerebellum. In
almost any study of cell number in the nervous system, it will help to
factor out global effects.
Mapping QTLs that modulate CNS traits
A QTL mapping study is in essence a search for statistically significant
associations between variation in a quantitative trait such as Purkinje cell
number and variation in genotypes at particular gene loci (Tanksley, 1993).
If our aim is to map QTLs using a set of F2 intercross progeny, then we
would compare the residuals computed by regression analysis to the genotypes
that we have obtained at 70 to 100 marker loci (Fig. 1). To simplify the
explanation of how we compare phenotypes and genotypes I will describe a
hypothetical experiment and use this experiment to review some useful
genetics. It will help those who are unfamiliar with the methods to spend a
few minutes looking over Figure 3, which summarizes graphically, much of
The QTL mapping experiment starts with a morphometric analysis of
Purkinje cells in two inbred strains of mice: C57BL/6 (B type; named
for its black coat color) and DBA/2 (D type; named for its
dilute brown coat color). These strains are fully inbred, meaning that
alleles at all autosomal gene loci in mice of a given strain are identical.
Pairs of chromosomes have precisely the same DNA sequence–imagine each
chromosome as a string of 4000 Bs, with each B representing
the B-type allele at each of 4000 genes on an average mouse
Generating an F2 intercross. Assume that Purkinje cells in these
two inbred strains have now been counted and that the majority of C57BL/6
mice have low counts (a residual -11,500 ± 2,700, as shown in Fig. 2),
whereas the majority of DBA/2 mice have high counts (a residual of +12,300 ±
3,000, as shown in Fig. 2). There isn't much overlap between estimates, and
our analysis demonstrates that heritability is high. We mate these mice,
producing the first filial or F1 generation of progeny. Individual F1 mice
are hybrids with BD genotypes, but these hybrids are also isogenic
because each F1 mouse inherits one complete set of B chromosomes from
its mother and one complete set of D chromosomes from its father.
That is, all F1 offspring have precisely the same BD genotype at all
autosomal loci. With the exception of sex differences, the quantitative
variation among these F1 animals is purely environmental and technical (Ve
We breed the F1 mice to generate an F2 generation. Half of the
chromosomes packaged into gametes of the F1 mice are themselves hybrids,
with long alternating stretches of B and D alleles generated
during meiosis by reciprocal crossovers (recombinations) between aligned
B and D chromatids. Furthermore, at any autosomal gene locus in
the F2 generation, the ratio of BB, BD, and DD
genotypes will be close to the expected Mendelian binomial ratio of 1:2:1.
Now the total quantitative variation in cell number among F2 progeny is due
both to environmental factors—the same environmental factors measured in
parental strains and F1s—and to the random segregation of allelic variants
at QTLs that affect Purkinje cell numbers. The total variance among F2
progeny—the variance we intend to assign to well-defined QTLs—is simply the
total phenotypic variance, Vp, minus Ve + Vt.
Linkage and haplotypes. We do not know the genotype of a
particular F2 animal at a particular gene locus unless we type that animal's
DNA. However, we don't need to sequence or analyze each gene individually.
We can infer genotypes of entire chromosomal regions quite reliably by
typing only a few marker loci per chromosome. The reason this can be done is
that during meiosis there is on average only one crossover per chromosome.
In fact, the genetic length of a chromosome is defined by the frequency of
recombination. A chromosome that is 50 centimorgans (cM) long experiences an
average of one crossover event per meiosis, generating two recombinant
chromosomes and two non-recombinant or parental-type chromosomes. (Note that
in contrast to genetic length measured in cM units, the physical length of a
chromosome is measured in bases or basepairs and because recombination
frequencies are quite variable there is only a loose correspondence between
physical and genetic lengths.) The closer two neighboring genes are to each
other on a chromosome, the less likely it is that they will be separated by
a recombination event (Tanksley, 1993). If genes are within 1 centimorgan (cM)
of each other (about 2 million basepairs of DNA in mice but only 1 million
basepairs in humans), they will be split apart only about 1 in 100 times,
and as a result neighboring genes of particular types on a single chromosome
(referred to as a haplotype) will tend to stay together from
generation to generation. Geneticists refer to this association using the
more imposing terms linkage disequilibrium or gametic phase
disequilibrium. The greater the disequilibrium, the higher the
probability that particular strings of genes or alleles present on a
particular chromosome–the haplotype–will be inherited as a non-recombinant
or parental-type unit in the F2 progeny.
The utility of linkage. This linkage between neighboring genes
means that we do not need to analyze every gene in an individual F2 mouse to
deduce the probable genotype at a particular locus. In fact, linkage
disequilibrium is high enough in an F2 intercross that we can confidently
infer the genotype at any of approximately 80,000 genes in the 3 billion
basepair (bp) mouse genome by typing only 70 to 100 well-distributed marker
loci that collectively sample less than 20,000 bp, or 0.006% of the genome.
The closer a particular marker is to a QTL, the better the inference (Weiss
and Terwilliger, 2000). A single marker locus will effectively sample a
chromosomal interval of about 15 cM on either side. This region is called
the marker's swept radius. As few as 3 to 4 markers will sweep an
entire chromosome in an F2 intercross.
The first aim of QTL mapping is to find one or more marker loci, such as
D5Mit294 shown in Figure 2, for which patterns of the three
genotypes match those of phenotypes. We hope to find markers that are
statistically associated and physically linked to QTLs that modulates
Fig. 2. Genotypes at a microsatellite locus on chromosome 5 (D5Mit294).
The left lane is a DNA size standard, and the next two lanes are PCR samples
from the parental strains B (higher band at 198 bp) and D
(lowest band at 176 bp). Lanes 4 to 25 are the F2 samples. The bottom
band—or bands, in the case of heterozygotes—define the genotype of each
animal. The bands at the top of the figure are caused by DNA retained in the
pipetting wells. Figure from work by G. Zhou (Zhou & Williams, 1997; see
Detailed PCR protocols for mapping microsatellites.)
Purkinje cell numbers. Given that the parental strain, C57BL/6J, has
fewer Purkinje cells, we expect that BB individuals will on average
have fewer cells than DD individuals at marker loci linked to
important QTLs. But for a trait controlled by as many as 10 or 20 QTLs we
can also expect to find markers at which DD individuals have fewer
cells. BD heterozygotes will typically have intermediate numbers of
cells, but if either the B or D allele at a particular QTL is
dominant, then heterozygotes as a group will have either high or low cell
In a QTL analysis it is important to realize that we are concerned with
group means, not individuals. Some BB individuals may have more cells
than BD or even DD individuals. In contrast to Mendelian
traits, quantitative traits are controlled by numerous genes, and except in
unusual circumstances, no single QTL is responsible for more than a
relatively small fraction of the phenotypic variance. A major-effect locus
may account for 20% of the genetic variance, but values less than 10% are
far more common (Tanksley, 1993; Roff, 1997). Environmental and
developmental perturbations will also generate exceptional phenotypes.
Interval mapping. If a QTL has a small effect or if a QTL has a
large effect but is located far from flanking markers, then the statistical
association between genotypes and phenotypes will be weak. In either case,
we may fail to detect Purkinje cell QTLs (an error of omission, or Type II
error). However, we often have data on markers that flank both sides of the
QTL. Using genotype data at these flanking markers we can predict the most
likely genotypes at any intermediate position between markers and compare
these inferred genotypes with Purkinje cell numbers. This can greatly
improve our ability to detect QTLs and it also allows us to statistically
distinguish between nearby QTLs with small effects and more distant QTLs
with large effects. The statistical method used to infer QTL genotypes and
then compare them with actual phenotypes is called interval mapping
(Lander & Botstein, 1989)
Figure 3. See the legend at the bottom of the figure.
Fig. 3. Summary of mapping QTLs using F2 intercross progeny.
At the top of the figure I have illustrated pairs of homologous chromosomes
from two inbred parental strains (C57BL/6J with thin black lines, DBA/2J
with wider gray lines). The two chromosomes within each parent are identical
and have identical alleles (B- or D-type) at each of the four marker loci,
M1, M2, M3, and M4. A single QTL maps in the interval between M1 and M2. F1
hybrids are mated to produce a set of 500 F2 progeny. Some of the
chromosomes in the F2s are recombinants and are made up of long segments of
both parental strain chromosomes. The genotypes of the F2 at the four makers
are shown at the bottom of the figure along with a simple scoring scheme
based on numbers of B-type alleles each F2 animal has at each marker
(also see Fig. 1). Gray regions throughout the figure contain data on
phenotypes of the parental strains, the F1 hybrids, and the individual F2
cases. In the bottom right corner of the figure is a summary of
correlations between genotype scores (0, 1, 2, or -1, 0, and +1) for the
four F2 cases and their respective quantitative trait values (2.4, -1.9,
-8.6, and 7.3). In this case the best correlation is to marker M1. As
expected, the correlation is negative because B alleles are
associated with lower values (compare the parental strains). Marker M4 has a
reasonably high positive correlation, and it is possible that a second QTL
in which a B allele is associated with a higher mean phenotype is located in
this interval. With an n of only 4 even a correlation of 1.0 is
insignificant. Unless a QTL has a very large effect it will usually be
necessary to genotype and phenotype several hundred animals.
Genotyping microsatellite marker loci. We can determine the
genotype of each F2 animal by measuring differences in the number of
basepairs of DNA in highly variable repeat sequences called
microsatellites (Fig. 2). Many thousands of these variable repeat
sequences are scattered throughout the mammalian genome. Most
microsatellites are in anonymous, non-coding stretches of DNA, but some map
within introns, and more rarely, within exons. (This latter group can
produce severe neurodegenerative diseases in humans, most notably
spinocerebellar ataxia, Friedrich's ataxia, and Huntington's disease.)
A set of ~6700 highly polymorphic microsatellites called simple
sequence length polymorphisms (SSLPs) have been mapped in mouse by
Dietrich et al. (1994). When we say that microsatellites are polymorphic, we
simply mean that different strains of mice—in our example, C57BL/6 and DBA/2—have
alleles that differ in number of repeats. Fifty-two percent of all
microsatellite loci in C57BL/6 and DBA/2 are polymorphic and differ by 2 bp
or more (Dietrich et al, 1996). As illustrated in Figure 2, differences in
the length of these DNA sequences are easy to detect and score by
electrophoresing PCR products through agarose or polyacrylamide gels. The
DNA is visualized using a fluorescent DNA–binding dye such as ethidium
|Box 3: Programs
for mapping QTLs
Map Manager QTX is one of several programs that can be used to map
QTLs. The program has a well-designed, almost intuitive, interface
(Manly, 1993), and is available free at
http://mapmgr.roswellpark.org/mmQT.html. Map Manager QTX is
available for Macintosh and \Windows OS. It is one of the few programs
that computes genetic maps for you; all you do is enter the genotypes
for your cases. To take full advantage of the permutation test that is
built into Map Manager QTX, install this program on a computer with a
Map Manager QTX is accompanied by an informative tutorial and manual
that is well worth downloading, printing, and perusing. I also recommend
highly a short review by Tanksley (1993) on QTL mapping strategies and
The QTL Cafe at
http://web.bham.ac.uk/g.g.seaton/ links to a Java applet that will
help you carry out an online QTL analysis. You will need Netscape
Navigator 4.05 or higher and you will need to have 3 data files before
starting: a map file with information on the names and locations of
markers, a file with genotypes, and a file with the case IDs and trait
QTL Cartographer is a highly capable mapping program—one that may be
particularly suitable for those with a background in UNIX and who are
comfortable with advanced statistical analysis. The program is available
for three operating systems at
MAPMAKER/QTL is a powerful program that implements a maximum
likelihood method to map QTLs. This program and a tutorial are available
from the Center for Genome Research at
Numerous free or inexpensive programs for mapping QTLs are listed at
QTLs are defined by strong statistical associations. We are now
ready to return to the question posed earlier: how do we compare variation
in Purkinje cell number (or any other phenotype) with genotypes in the F2
generation? At any particular gene locus, each F2 animal will have BB,
BD, or DD genotypes. In Figure 2, reading from left to right,
the first 22 F2 genotypes, starting with lane 4, are HBHBD HBBBH HHDBH HHHBH HH
(H for heterozygotes). After all F2s have been genotyped at
several markers on each chromosome, we need to evaluate the data and
determine the likelihood that we have mapped one or more QTLs to particular
chromosomal intervals. Information on several of the programs that are used
for this purpose is provided in Box 3: Programs for mapping QTLs.
The initial mapping analysis will typically involve what is now referred
to as simple interval mapping. Simple interval mapping assumes that
we do not already know of any particular QTLs that influence variation in
Purkinje cell number. However, if QTLs are successfully mapped in the first
round of analysis (see Statistical criteria), then we may
advance to composite interval mapping. This refinement is really
nothing more than the extension of the multiple regression analysis we have
already discussed, but instead of compensating for environmental effects or
global variables like body size and brain weight, we compensate for the
presence of one or more well defined QTLs.
The strength of association between variation in a phenotype and the F2
genotypes at marker loci can be assessed using a F statistic, the logarithm
of the odds ratio (the LOD score), the likelihood ratio statistic (LRS), or
a conventional probability of linkage. These statistics are interconvertable.
LRS scores have a conventional chi-square distribution and are relatively
easy to interpret. The LOD score is equal to the LRS divided by 4.61. Both
statistics are ratios of probabilities (or likelihoods) that a QTL is, or is
not, located within a tested chromosomal interval. But this really does not
explain what these statistics are doing. Let me explain the idea using more
familiar statistics: analysis of variance (ANOVA), Pearson product-moment
correlations, and linear regression.
ANOVA. To perform a statistical analysis and to test the
likelihood that there is a QTL linked to the locus D5Mit294 in Figure
2 above, we could simply divide cases into categories by genotype and
perform a single-factor ANOVA. With two degrees of freedom among the three
genotypes and a total of more than 100 progeny, we would need an F
statistic above 3 to suspect that D5Mit294 might be linked to a QTL.
In our example, we have been fortunate and the F statistic is 9.4,
with an associated p of 0.00014. This would seem to be strong
evidence that there is a QTL near this marker, but this statistic alone does
not tell us much about differences among the genotypes.
Correlation and regression. To obtain additional information we
could score genotypes by numbers of B alleles: BB = 2, BD
= 1, and DD = 0 (computationally, it is sometimes preferable to score
genotypes as -1, 0, and +1). It would then be possible to compute a
correlation between phenotypes and genotypes to assess the strength of
linkage. The correlation in this example is –0.28. The negative sign
indicates that B alleles are typically associated with cases that
have lower cell numbers. The amount of variance that this putative QTL
generates can be estimated by squaring the correlation. In this example,
r2, the coefficient of determination, is
0.076. In other words, approximately 7.6% of the variance is associated with
a QTL on chromosome (Chr) 5 near D5Mit294. We can also regress
phenotype values against genotype values and determine whether the
regression coefficient is significantly different from zero. In this case,
the slope of the regression equation (–3700 cells per allele) is
significantly different from zero. This analysis indicates that the
substitution of a B allele for a D allele typically lowers the
trait value in the F2 sample by 3700 Purkinje cells.
A series of these types of tests are carried out at many points along
each chromosome generating a profile of the strength of the statistic as a
function of position—a LOD score map. The region of the chromosome in which
LOD scores are within 2 LOD of the peak defines a >95% confidence interval
of the QTL's position (Darvasi, 1997a). In our imaginary Purkinje cell
example, the LOD score reaches a peak of 4.2 between D5Mit294 and
D5Mit346. The confidence interval is about 12 cM. Figure 4, is an
example of a LOD score map in which a gene that specifically modulates brain
weight has been discovered on the proximal half of Chr 11. The likelihood
ratio statistic (4.6 times the LOD score) is shown on the y-axis. The
linkage statistic reaches a peak of 22.8 at about 12 cM. The 2-LOD
confidence interval for this QTL (Bsc1 for brain size control 1)
extends from 10 to 20 cM.
Fig. 4. Interval mapping results for a QTL that controls
brain weight in the mouse. The x-axis represents the full length of Chr 11,
from the centromere at 0 cM to the left, to the telomere at about 72 cM to
the right. The y-axis represents the strength of linkage of the brain weight
phenotype data (BXD recombinant inbred strains) to different intervals on
Chr 11. The brain weight data has a peak linkage with an LRS of 22.8 at
about 12 cM. Fifteen genes or markers are labeled along the x-axis. Data are
from Williams et al., (1997, in preparation).
In practice, QTL analysis is carried out along these lines but using
statistical procedures that can assess more than just the statistical
strength and position of QTLs (Lynch & Walsh, 1998; Liu, 1998). Several
genetic models are usually tested to assess the ways in which alleles are
likely to interact with each other (linear-additive interactions, non-linear
dominance interactions, and combinations of both types). More sophisticated
models may also explore whether QTLs on different chromosomes interact—again
linearly or non-linearly. Non-linear interactions between loci is referred
to as epistasis. It is premature to worry about epistasic
interactions before any QTLs have been mapped, but it is worth stressing
that a realistic understanding of genetic sources of variation in CNS
structure and function will ultimately demand attention to complex
interactions of networks of variant gene products.
Statistical criteria. What statistical criteria should be used
to decide whether a QTL has been successfully mapped? Is the LOD score of
4.2 good enough? Lander and Schork (1994) deal with this issue at length and
emphasize the need for stringent criteria. The main reason is that a
genome-wide search of QTLs involves comparing phenotypes with many
independent sets of genotypes. Remember that the gel shown in Figure 2 is
just one of 50 or more gels of this type. This gel is used to test a single
point in the genome (a point-wise test), but we actually test many points
(or chromosomal intervals) and we are naturally much more interested in the
genome-wide significance of our result. We have a classic
multiple-comparisons problem, and a conventional point-wise criterion
level of p = 0.05 is far too lenient. If we divide 0.05 by the 50
independent comparisons we are likely to make then we arrive at a safer
estimate of the genome-wide criterion level we need to achieve with a single
test. In other words, the point-wise p must to be less than 0.001 to
be associated with an effective genome-wise p of less than 0.05.
There has been a heated debate among quantitative geneticists regarding
appropriate criteria, but there is general agreement that a QTL should not
be claimed until the genome-wide significance of making a type I statistical
error (an error of commission; declaring the presence of a QTL when there is
really nothing there) is under 5% (Elston,
Permutation tests. In our own work we use a robust
non-parametric method to determine the genome-wide 5% level for each trait
that we map (Churchill & Doerge, 1994). The idea behind the permutation
method is simple: we randomly reassign trait values to genotypes and then we
treat these permuted datasets in the same way as the original data. We then
see how often QTLs are "successfully" mapped with disordered data. If many
of the permuted datasets produce LOD scores that are as good or better than
that generated by the correctly ordered data, then we cannot place much, if
any, confidence in our putative QTL. In contrast, if fewer than 1 in 100 of
the permuted datasets reaches the level of correctly ordered data, then we
can be confident that the probability of having made a type I error is under
0.01. In our studies, we typically run more than 10,000 permutations, and
make a histogram of the single best scores from each permutation. Using
these permutation histograms we can accurately estimate the strength of
association between a trait and newly discovered QTLs (Fig. B).
Returning to the Purkinje cell example one last time: the permutation
analysis of cell counts reveals that the probability of obtaining a LOD
score of 4.2 by chance is <0.008. We can now state with reasonable certainty
that there is a QTL on proximal Chr 5 that controls Purkinje cell number. In
a similar way, a permuation analysis for the brain weight dataset shown in
Figure 4 demonstrates that a LOD score of 4.3 (or an LRS score of 19.7) is
required to reach a genome-wide p at the 0.05 level.
Selective genotyping and phenotyping. The most extreme
cases—those with highest and lowest trait values—are most informative for
mapping QTLs (Taylor et al., 1994). These cases are more likely than others
to be homozygous for alleles that increase or decrease trait values. It is
therefore possible to improve the efficiency and power of detecting QTLs by
initially genotyping only extreme cases. The choice of what fraction of
cases to genotype depends on the relative cost of phenotyping and genotyping
(Darvasi, 1997c). If phenotyping is relatively economical, one may be able
to afford to generate large sets of progeny and initially genotype only 5%
to 10% of cases from both tails of the distribution. In our laboratory the
fraction of cases that we initially genotype is also influenced by the
particular PCR and gel equipment that we use. Reactions are run in 96-well
microtiter plates. We select 23 high and 22 low cases and run these with DNA
from the two parental strains and the F1 hetrozygote (n = 48 samples). In
this way, we are able to test two microsatellites per PCR run. Seventy
markers can be analyzed in a week. Most of our F2 crosses contain 200 to 500
animals, so we are limiting our analysis to the extreme 5–10% in both tails.
It is also possible to pool DNA from high and low groups and compare the
relative intensity of alleles at markers that sample the entire genome
(Taylor et al., 1994). When we find a chromosomal interval that harbors a
suspected QTL, we then genotype all cases at these hot markers. This last
step is particularly important because the initial analysis of the tails of
the distribution may be influenced greatly by epistatic interactions between
the main QTL and unlinked loci. Until all individuals have been typed, we
will not have any good idea of the independent effects of the main QTL or of
its actually chromosomal location (Darvasi, 1997c).
Once a QTL has been identified the procedure can be reversed–it is now
possible to save time and money by phenotyping selectively. For example, it
is possible to generate a very large sample of animals, genotype DNA taken
from the tips of their tails when they are still pups, and then only
phenotype particular genotypes as adults. Selective procedures like this
have risks because they depend on the tails of the distribution being "well
behaved." But tails of distributions are often the havens of unrecognized
measurement errors, developmental flukes, and as mentioned above, of rare
epistatic interactions. It is also good practice to sample from both tails
of the distribution. An example of the power (and risk) of selective
phenotyping is an interesting study by Chorney and colleagues (1998). They
report that the insulin growth factor 2 receptor (IGF2R) is a marker for
very slightly higher intelligence (4 IQ points) in a mixed population of
Caucasians in the Cleveland area. Their analysis is based on a comparison of
allelic differences between groups of very bright children (a selection as
intense as 1 in 30,000 based on test scores) and groups of normal children.
There are serious interpretive difficulties related both to the intense
selection of individuals more than four standard deviations away from the
mean and to the intentionally unbalanced sampling design that excludes
humans with low or low-normal scores. What is often not appreciated is that
QTLs can have their primary effects on the variance of a trait, rather than
the mean of a trait, and obviously if only one tail of a distribution is
sampled one runs the risk of confounding these types of QTLs. There is
therefore still no direct evidence that a QTL near IGF2R actually influences
mean intelligence. A simple analysis of patterns of IGF2R alleles in a
large, normally distributed, sample would resolve this issue, but
indications from the within-sample correlations performed by Chorney et al.,
do not give any cause for optimism (r = –0.07).
The major crosses for mapping QTLs
Web Resources for Mapping QTLs
http://www.nervenet.org and the
Mouse Brain Library.
My research group's web sites. Full texts of papers, grants, and an
extended description of the 3D cell counting protocol. The Portable
Dictionary of the Mouse Genome also available at
http://www.nervenet.org, is a FileMaker database that includes
current mapping information for more than 20,000 loci in mouse. The 10
MB database can be downloaded and used as a local resource. It contains
data on all MIT microsatellite loci.
http://www.nervenet.org/main/databases.html Our lab's database
server. You can currently obtain data on fixed and fresh brain weights,
sex, age, and body weights of >8000 animals belonging to >200 strains of
http://www.jax.org/ The Jackson Laboratory is the primary provider
of mice for biomedical and genetic research. Their web site provides
detailed information on a huge assortment of mice (inbred, transgenic,
knockouts, recombinant inbred strains), gene mapping resources, and
other tools. This site will also lead you to the Mouse Genome Database (MGD)—the
definitive repository for mouse locus data.
http://www.resgen.com/ Research Genetics Inc. is the primary source
for microsatellite primers.
http://www-genome.wi.mit.edu/ The Center for Genome Research at the
Whitehead Institute includes a searchable databases of all MIT
microsatellite loci and numerous other genetics resources for mapping in
mouse and human populations.
http://linkage.rockefeller.edu/ The Laboratory of Statistical
Genetics at Rockefeller University includes a comprehensive links to
linkage analysis software.
http://nitro.biosci.arizona.edu/zbook/book.html A site associated
with the superb text by Lynch and Walsh, Genetics and Analysis of
Quantitative Traits. Many related QTL links. Supplementary material is
organized by chapter.
http://www.sfbr.org/nigms/Report.html A synopsis of the current
status of quantitative genetics and prospects for funding at the federal
level in the USA. The report highlights some of major conceptual
problems we can expect to encounter, and perhaps resolve, in the next
Bruce Weir's lecture at Dartmouth (Chance Lecture series) on the
statistics of DNA forensic analysis.
What type of cross is best suited for different types of studies? There
are currently five common types of line crosses that are commonly used to
map QTLs in mice.
F2 intercross progeny. The F2 intercross (described briefly in
our Purkinje cell example) is currently used in the first phase of the
majority of QTL studies. The advantage of this cross between lines is that
it is usually possible to scan the entire genome for QTLs by typing only 70
to 90 well-spaced marker loci. This used to be a major advantage, but
genotyping is getting much easier, and other factors, such as precision and
power of the analysis are now more important considerations. For most
purposes a group of 200 or more F2 animals will need to be generated and
typed. (One person working full time can genotype approximately 200 animals
at 100 marker loci in one month. You would need four 96-well thermal cyclers;
each run twice a day.) The more animals one can tolerate to type, the
greater the power of the analysis and the greater the number of detected
QTLs (Darvasi, 1998). In general, the efficiency of phenotyping is far more
critical than that of genotyping, so be sure you spend time reviewing all
data collection methods from start to finish and make those changes that
will allow you to generated more numbers, more accurately, more quickly.
Although the F2 is a very common cross, I don't recommend it anymore. It
lacks adequate positional precision. One way to improve the F2 cross without
much more work is to extend the cross for two more generations, out to
generation 4 (F2 to G3 to G4). This will double the precision with which
QTLs are mapped. The downside is that you will need to type twice as many
marker loci, as many as 200 per animal. In carrying out a four generation
cross be sure NOT to mate littermates when possible.
Backcross progeny. Mating F1 animals back to either or both
parental strain generates one or two panels of backcross progeny. Backcross
progeny are commonly used in mapping Mendelian traits, especially recessive
mutations. There are only two genotype classes to contend with at any
locus—the homozygote and the heterozgyote. The reduced number of genotypes
simplifies scoring of genotypes and may allow QTLs to be detected more
easily (Darvasi, 1998). An N2 cross may be particularly helpful in cases in
which the F1 generation has an average phenotype very close to one of the
parental strains; in other words, a case in which one set of parental
alleles behaves in a dominant fashion. The F1 is then backcrossed to the
"recessive" parental strain.
The main problem with both the F2 intercross and the backcross is that
QTLs usually cannot be mapped precisely. Recombination events between nearby
loci will be relatively uncommon in these animals, and even with large
numbers of progeny it will often be difficult to pin down a QTL to a
chromosomal interval of 10 cM—roughly 20 million bp of DNA. This is a long
stretch of DNA that will typically contain hundreds of genes. Fishing for
good candidate genes will be tough. If we can get down to a 1–2 cM interval
then we may only have to contend with a few dozen candidate genes. There are
now several ways to to greatly improve the precision with which QTLs are
mapped (Darvasi & Soller, 1995; Darvasi, 1997b, 1998). The most simple
method is the recombinant inbred intercross method that exploits a set of
more than 102 very well mapped recombinant inbred strains now available from
the Jackson Laboratory (Williams et al,
Advanced intercross progeny. An advanced intercross is generated
by crossing F2 males and females to produce a third generation, referred to
as G3 (G rather than F because filial matings are
intentionally avoided). G3 individuals from different litters are then
intercrossed in a way that minimizes inbreeding to produce a G4 generation (Darvasi,
1998). This process is repeated for several generations. Assuming that
inbreeding can be minimized during this process, the cumulative amount of
recombination between the original parental genomes doubles with each
doubling of the generation number. Since all genetic maps are measured in
units of recombination, not in basepairs, this process greatly increases the
length of the genetic map. The consequence is a twofold improvement in the
precision with which QTLs can be mapped for every twofold increase in
generation number using a fixed number of offspring. Obviously, making an
advanced intercross is a lot of work; in each generation 20 or more breeding
cages need to be maintained (ideally 50 or more cages). The payoff is that
at G8 the precision of mapping will be roughly four times greater than that
of the F2 intercross. Because the genetic map is stretched so much, the
number of marker loci that we need to use to scan the entire genetic map
will also be increased four-fold. Each marker still only samples a region of
30 cM (the so-called swept radius), but the total length of the genome has
now been stretched from 1400 cM to as much as 6000 cM. While we may have
managed with 80 markers using an F2, we will need 320 markers to have the
same assurance of detecting QTLs in a G8 cross. However, if we have already
mapped QTLs using the F2 generation, or any of the subsequent generations,
then we do not actually need to scan the entire genome of the G8 progeny. We
need to remap only those chromosomal intervals that have been shown to
harbor QTLs using earlier generations. The advanced intercross then can be
used to map QTLs across the entire genome to a 95% confidence interval of ±2
cM. Even so this may require an analysis of 500 to 2000 cases (Darvasi,
1998). It is also practical to backcross an advanced intercross to one of
the oroginal parental strains to generate an advanced backcross. The
advanced backcross may have some advantages when traits are controlled by
QTLs with dominant alleles or when the trait is influenced strongly by
A problem with an advanced intercross is that some chromosomal intervals
will drift or be selected far from the Hardy-Weinberg genotype expectation.
We expect a 1:2:1 ratio of BB, BD, and DD genotypes. But if B alleles on
distal Chr 1 are significantly more advantageous then D alleles for
fertility and survival then by the eighth generation there may be few
animals with the DD genotype. This distortion will result in non-syntenic
(literally, "not on the same string or chromosome") gene loci being closely
linked or associated in a statistical sense. For example two regions on Chr 1
and Chr 9 that are both enriched for the BB genotype will be in linkage
disequilibrium and thus seem to be linked despite their separation on
different chromosomes. If uncorrected, such non-sytenic disequilibrium will
generate spurious mapping results.
[A caution to anyone setting up an advanced intercross: Make sure to use
as many possible parents in the penultimate generation as possible and only
generate single litters from particular breeding pairs of mice. Rotate males
in the the last generations rather than letting a single mating pair
generate a large number of litters. Failure to rotate partners will result
in marked inequities in the representation of haplotypes in the final
generation used for mapping.]
Recombinant inbred strains: a neuroscientist's first choice.
Recombinant inbred (RI) strains are the easiest means for neuroscientists to
get started mapping QTLs. They have several significant advantages, the
foremost being that isolating and typing DNA is not required. RI strains are
generated in the same way as an advanced intercross with the important
exception that at each generation, siblings are intentionally mated (Belknap
et al., 1992; Silver, 1995, p. 207–213; Williams et al.,
2001). By the 20th generation, progeny are almost entirely inbred. In
each of these fully inbred strains, chromosomes of the original parental
strains have recombined extensively: hence the name, recombinant inbred
Unlike the case in the other genetic crosses we have considered, an
entire strain rather than just a single mouse represents each recombinant
genome. This feature is an obvious advantage for studies in which reliable
neuroanatomical or behavioral traits are hard to generate from single
animals. Accurate averages for each genotype can be obtained simply by
phenotyping more animals. The absence of any heterozygotes also increases
the phenotypic and genotypic variance for a given sample size, while at the
same time reducing the number of genotype classes. This can make it easier
to resolve QTLs.
Mapping QTLs in human populations
Nuclear magnetic resonance imaging (MRI) makes it feasible to map
QTLs that control variation in the size of CNS compartments in humans
(Bartley et al., 1997). The general strategy of mapping QTLs is the same
as that outlined in the main text, but obviously the complex genetic
structure of human populations demands different tactics and is somewhat
harder to accomplish since environmental factors cannot be eeasily
controlled (Lynch & Walsh, 1998, chapter 16; Ott and Hoh, 2000; Weiss
and Terwilliger, 2000). Kruglyak (1997) provides an introduction to one
of several powerful new methods called linkage disequilibrium mapping.
Several methods require information from related individuals, but the
allele association method (Risch & Merikangas, 1996) can be used to map
QTLs without any pedigree data. These mapping techniques could be
readily combined with MRI and new chip-based methods to genotype single
nucleotide polymorphisms (SNPs) to map quantitative neuroanatomical
trait in humans. Allele association methods would be particularly
adaptable to the analysis of postmortem brain tissues.
- Bartley AJ, Jones DW, Weinberger DR (1997) Genetic variability of
human brain size and cortical gyral patterns. Brain 120:257–269.
- Kruglyak L (1997) What is significant in whole-genome linkage
disequilibrium studies. Am J Hum Genet 61:810–812.
- Risch N, Merikangas K (1996) The future of genetic studies of
complex human disease loci in humans. Science 273:1516–1517.
The advantage of replicated recombinant genotypes. But for
neuroscientists the most compelling advantage of RI strains is that it
becomes possible to study relationships and correlations between many CNS
traits. One can carry out immunocytochemical analyses using dozens of
antibodies, then add receptor-binding studies, and finish with counts of
cells using unbiased stereological methods. These structural parameters can
then be compared with multiple behavioral traits (Dains et al., 1996). The
accumulation of phenotypic data for these replicated genotypes, adds
tremendous power to RI strains. If a QTL controls numbers of retinal
ganglions, then does it also control variation in numbers of cells in the
dorsal lateral geniculate nucleus, superior colliculus, or even a
functionaly unrelated structure like the olfactory bulb? Do single QTLs have
pleiotropic effects on multiple structures and cell populations? RI strains
can be used to answer these questions. In comparison to other crosses in
which each genotype is represented by a single mouse, RI strains are ideal
for long-term correlative, collaborative, and corroborative studies of the
genetic control of CNS structure.
At present there is little information on the CNS of RI strains (Belknap
et al., 1992; Dains et al.; 1996, Williams et al., 1998a). My colleague
Glenn Rosen and I have begun to redress this deficiency by systematically
processing brains of many of RI strains with the idea of producing a library
of sectioned material to be used specifically for 3D-counting of cell
populations (see <www.mbl.org>).
All the tissue is embedded in celloidin, cut in coronal or horizontal planes
at 30 µm, and stained with cresyl violet. The current collection consists of
~350 cases, representing more than 40 strains.
If one of these recombinant inbred mice is genotyped, then the entire
strain has been genotyped. For this reason, genotype data also accumulates
as more researchers type these strains. We maintain a large database of
error-checked and curated genotypes for five of the most common RI sets
(AXB, BXA, BXD, BXH, and CXB). One of the largest and best-characterized RI
sets consists of 35 BXD strains generated by Benjamin Taylor of the Jackson
Laboratory by crossing C57BL/6J to DBA/2J (Taylor, 1989). Over 1750 gene and
marker loci have now been genotyped in the majority of these strains. To map
a QTL using these RI strains, we simply phenotype a sample from each of the
35 strains and then compare the pattern of strain averages or residuals with
the distribution pattern of alleles at a subset of approximately 1000 loci.
The procedure is explained in detail in Williams et al. (1998a) and complete
genotype databases for BXD and other RI strains are available at
www.nervenet.org. One last advantage of RI strains is that the genetic
maps have a resolution that is 4-fold greater than that in an F2 cross. Like
maps of an advanced intercross, those of RI strains are expanded, and in
some cases it is possible to map a QTL with a precision of ± 2 cM (Williams
et al., 1998a; Williams et al.,
2001). This also means that QTLs mapped with RI strains will usually be
associated with single genes, rather than sets of linked genes.
The main disadvantage of RI strains. At present the major
disadvantage of RI strains is that there are still too few of them, and as a
result only QTLs that have comparatively large effects can be mapped. This
is not a serious problem at an early stage of analysis, before any QTLs have
been mapped. In our work we have consistently been able to use the BXD
strains to map at least one QTL controlling each of the following traits:
ganglion cell number, eye size, brain weight, and cerebellar weight. But
there are many other QTLs controlling each of these traits, and mapping QTLs
with less robust effects will usually require larger numbers of recombinant
genotypes. This has usually involved a second phase in which N2, F2 or
advanced intercross progeny are used to confirm and extend the genetic
analysis. To provide a better solution we have recently genotyped a set of
100 RI strains that all share one common parent (C57BL/6J). It is
straightforward to pool data from multiple RI sets and to statistically
assemble an RI super set to improve statistical power. Combining data from
several sets of RI strains should double or triple the yield of QTLs.
Another reported disadvantage of RI strains is that gene dominance effects
can not be assayed since all of the RI strains are fully inbred. The absense
of heterozygotes prevents one from determining the effects of a single
allele on a trait. However, this is a trivial problem to overcome since it
is easy to generate F1 intercrosses between RI strains and thereby make
large numbers of obligate heterozygotes on any interval desired.
Congenic strains. Congenic strains are generated by crossing two
inbred strains (generating an F1 hybrid) and then backcrossing repeatedly to
one parental strains (Morel et al., 1997; Wakeland et al., 1997). The idea
is to transfer and isolate a specific chromosomal interval from one strain
(the donor) to another strain (the recipient). For example, we might wish to
transfer an allele that is associated with a low Purkinje cell population
from the genome of C57BL/6 onto the DBA/2J strain. To do this we would
backcross the F1 progeny to DBA/2J. The backcross progeny—refered to as the
N2 progeny—must then be genotyped at markers on both sides of the QTL and
perhaps one additional marker half way between. (If the QTL is poorly
localized three or even more markers may need to be typed to insure that the
entire interval that may harbor the QTL is heterozygous in animals chosen
for breeding.) On average 50% of the genome of the N2 progeny will be
homozygous for DBA/2 alleles. Animals that have inherited one B allele at
both markers M1 and M2 (Fig. 2) are then crossed back to the DBA/2 parental
strain again. In this N3 backcross generation 75% of the genome will be
homozygous for the DBA/2 genotype, but because we intentionally bred animals
that were heterozygotes between M1 and M2, an average of half of the N3
progeny will still be heterozygous in this interval.
The process of genotyping a few specific markers in a small number of
progeny and then crossing mice that carry B alleles back to DBA/2 is
repeated for eight or more generations. Homozygosity for DBA/2 alleles
increases from 75% at N3, to 87.5% at N4, and to 99.8% at N10. N10 progeny
that are heterozygous for markers M1 and M2 are mated. Some of their
offspring will be homozygous for C57 alleles in the M1–M2 interval and these
mice and their offspring are used produce a constant stream of congenic
animals that are homozygous for the C57 allele of our Purkinje cell QTL, but
which are otherwise almost entirely DBA/2 type. We have transferred the low
allele from one strain to another. We should probably also transfer the high
Purkinje cell allele from DBA/2 to C57BL/6, generating what is called the
reciprocal congenic strain. We have in essence turned a complex polygenic
trait into a more tractable single gene trait. Now it is possible to
phenotype many of these reciprocal congenic mice and compare Purkinje cells
populations. Differences are due to the QTL in the M1–M2 interval. We can do
this at any stage of development to determine when and where the allelic
differences begins to affect Purkinje cell proliferation or survival.
Congenic strains are presently the main tool used to fine-map QTLs. This
is accomplished by making sets of strains that are congenic for overlapping
intervals that collectively define intervals that can be as short as 1 cM
across the QTL's presumed location. Phenotypes of congenic strains are
compared, and those that differ from parental strains are presumed to harbor
the QTL (Darvasi, 1997b). Once a QTL has been mapped to this level of
precision it become feasible to test candidate genes that map to the 2-LOD
There can be problems with a congenic approach to mapping QTLs. The
primary problem is that as a QTL is introgressed into a recipient strain, it
may lose its effects on phenotypes. To minimize frustration, the phenotype
should be monitored during the process of introgressing the QTL (see Vadasz
et al., 1998 for a beautiful example). QTLs can evaporate because key
epistatic interactions upon which a phenotype depends are lost. In this
predicament, it may be possible to identify and conserve intervals that
appear to be critical for the penetrance of the QTL's effects.
Recombinant inbred intercross (RIX) progeny. This powerful yet
simple QTL mapping method was devised by David Threadgill and colleagues and
involves generating all or a subset of the many pairs of intercrosses (hence
RIXs) between a set of recombinant inbred strains (Williams et al
2000). The derived RIX set extends the number of genomes available for
phenotyping by a factor of n(n-1)/2, where n is the number of
original RI strains. For example, the 13 CXB/By strains and the 35 BXD/Ty
that have been used heavily can be supplemented by 6 and 17 times as many
novel recombinant RIX genotypes, respectively. Each individual RIX strain
has a unique but entirely predictable genome and like RI strains, many
genetically defined RIX individuals can be phenotyped to greatly improve
trait reliability. However, unlike an RI set, an RIX set closely resembles
an F2 intercross, with a 1:2:1 segregation ratio of genotypes at marker
loci. Furthermore, none of the RIX progeny are inbred, resulting in more
robust mice from which more reliable traits can be extracted. Parental
effects can be controlled to some extent by changing the polarity of the RIX;
in other words, the maternal and paternal strains can be switched to produce
reciprocal RIX progeny which are genetically identical. Any significant
differences between these reciprocal crosses are due to parental effects.
The statistical properties of RIX sets, that is, their power to detect
QTLs, the positional precision of mapping data, and the accuracy of
estimates of allelic effects of the trait of interest, are significantly
better than those of the original RI set. For example, the statistical power
of a complete RIX set (n = 561 RIXs) derived from the 34 BXD/Ty RI strains
will typically be boosted 4- to 6-fold. QTLs that control as little as 5% of
the phenotypic variance will often be detected with a power of better than
0.8. The 2-LOD confidence interval will also be somewhat smaller. Given the
already extensive phenotypic data for RI strains of mice, the RIX method
provides a highly effective means to confirm and extend existing QTL mapping
data. And no genotyping is required! Selective analysis of specific RIX
strains can also be a powerful method to test models of gene action and
interaction effects among multiple QTLs. For an example of the application
of this method see our recent abstract (Williams
et al., 2000).
Like the other crosses, there are drawbacks to the RIX approach. The
current problem with RIX mapping is that non-syntenic associations, that is,
statistical linkage between different chromosomal segments, can be high.
This problemin was already eluded to in the context of RI mapping (and see
Williams et al.,
2001), but in RIX mapping this problem has more obvious effects and will
generate spurious QTLs. To exploit RIX mapping effectively will require
carefully contructed RIX panels in which non-sytenic association has been
controlled either by selection or by sophisticated statistical control.
Combining results from two or more mapping studies. It is not
difficult to perform a meta-analysis of multile independent sets of mapping
results using a method explained in Sokal and Rohlf (1996, section 18.1). In
brief, one computes the combined probabilities of linkage in a number of
crosses. This method was used to help map the Nnc1 locus (Williams et al.,
1998, see equation in the methods) by combining data from two sets of RI
strains, BXD and BXH. The same method can be used to combine an apparent
hodge-podge of RI, F2, and N2 and advanced intercross data sets. This is
most productive when the same sets of alleles are segregating in the
different crosses (i.e., BXD, B6D2F2), but can even work in crosses that do
not share the same parental genomes. The main difficulty in applying this
method is deciding what values to actually combine. We have settled on a
simple procedure in which all markers used in each cross are assigned a
single "genome-wide" position value. These values have units of Morgans, and
the range of values extends from 0.00 for the most centromeric marker on Chr
1 to 15.9 for the distal-most marker on Chr X. These uniform genome-position
values provide a common framework map for every cross. The point-wise P
values are computed for all markers, and values between markers are
interpolated in 1 cM bins. The P values of identical 1 cM bins are then
combined. This pooling procedure (BXD plus and F2) was essential in mapping
the first set of QTLs affecting olfactory bulb weight (Williams
et al., 2001). (This paragraph added Oct 27, 2000 by RW)
The highs and lows of QTL analysis
QTL mapping is initially done at a level of analysis that is far removed
from cellular and molecular mechanisms, and it may at times seem that the
research has lost touch with biology. But keep in mind that this QTL
analysis is itself just a prelude to a renewed molecular and cellular
analysis—that the first aim is simply to determine where key regulatory
genes are located. In some ways this first stage is like air reconnaissance:
At high altitude, we hope to succeed in discerning the outlines of roads and
walls marking lost cities in the desert. We now know the approximate
locations, but we need to get on the ground to explore, to survey, and
ultimately, to excavate these sites. The payoff can be great, and in QTL
analysis the exploration on the ground does not need to be delayed for long.
As soon as QTLs have been mapped, and long before candidate genes have been
identified or cloned, QTLs can be used as "reagents" to probe neuronal
development and function.
In our own work on neuron number control 1 (Nnc1)—a QTL
that has pronounced effects on numbers of retinal ganglion cell populations—Richelle
Strom and I have been able to show that this QTL modulates neurogenesis
rather than cell death (Strom
& Williams, 1999). We now also suspect that Nnc1 may be the
thyroid hormone alpha receptor gene, and in collaboration with Guomin Zhou,
Douglas Forrest, and Bjorn Vennström, we are now examining effects of
inactivating this gene on the ganglion cell population.
There are several other powerful ways to exploit QTLs prior to cloning.
Chromosomal segments containing QTL alleles associated with high or low
phenotypes can be transferred to well-characterized inbred strains of
mice—producing the congenic strains mentioned above (Darvasi, 1997b). Once a
set of congenic mice has been generated, it becomes possible to explore
developmental, pathological, and even environmental mechanisms that lead to
differences between strains that carry the alleles associated with high and
low traits. Furthermore, sets of high and low alleles at genes on different
chromosomes can be combined in different combinations to test how QTLs
interact to modify CNS architecture.
The near future of QTL mapping. The principal goal of QTL
analysis is to identify the polymorphic sequences associated with each QTL.
As the genomes of both humans and mice are sequenced in the next decade, the
still arduous process of identifying genes will become progressively easier.
We can soon expect to have detailed maps and databases of genes expressed in
different tissue and cell types at different stages of development. It will
then be possible to combine data on well-mapped QTLs with precise data on
chromosomal positions of particular types of genes and expressed sequence
tags (ESTs) to quickly winnow the list of candidate genes. This future
belongs to those who start weighing, counting, measuring, and mapping now.
This work was supported in part by grants from the NEI (EY08868
and EY6627) and NINDS (NS35485) to RW. I thank Dr. Benjamin Taylor, James
Cheverud, Ty Vaughn, and Robert Hitzeman for corrections and comments. I
thank my colleagues Drs. Guomin Zhou, Richelle Strom, David Airey, and Glenn
Rosen for their help. My thanks to Kathryn Graehl for editing, Alexander
Williams for building internet sites, and to Drs. John Morrison and Patrick
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