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Note to the Reader This is a revised edition of a review published in Mouse Brain Development (Springer, ISBN 3540666648, $169 from Amazon.com). Text additions and modification are in brackets. [...]. Williams RW (2000) Mapping genes that modulate brain development: a quantitative genetic approach. In: Mouse brain development (Goffinet AF, Rakic P, eds). Springer Verlag, New York, pp 21–49.
Print Friendly Contents 1. Why brain weight and neuron number matter
In my opinion there are only quantitative differences, not qualitative differences, between the brain of a man and that of a mouse. Ramón y Cajal (1890)
The difference in behavioral capacity between man and chimpanzee may be no more than the addition of one cell generation in the segmentation of the neuroblasts which form the cerebral network. Lashley (1949)
IntroductionThe complexity of CNS development is staggering. In mice a total of
approximately 75 million neurons and 25 million glial cells are generated,
moved, connected, and integrated into hundreds of different circuits over
a period of one month. The process is coordinated by the expression of a
large fraction of the genome—as many as 40,000 genes may be involved
(Sutcliffe 1988; Adams et al. 1993). These same genes coordinate the
development of the human brain, but a thousand times more neurons are
generated (Williams and Herrup 1988) and their integration and training
take more than a decade. While 5,000 of these genes have common roles in
cellular metabolism, this still leaves a huge complement that have
selective, transient, and partially redundant roles in the development of
different parts of the brain (Usui et al. 1994; Gautvik et al. 1996).
Reductionist approaches that focus on isolated processes and molecules may
seem hopelessly inadequate, but they are an absolute necessity at this
early stage of analysis and understanding. Why brain weight and neuron number matter Metabolic constraints. There are several reasons why differences in brain size and neuron number are interesting and biologically significant. First, relative to its size, the brain with its large population of neurons consumes a disproportionate amount of energy (Clark 1994). The high cost of making, training, and maintaining this metabolically demanding organ has wide-ranging effects on an animal's development and behavior (Sacher and Staffeldt 1974; Eisenberg and Wilson 1978; Martin, 1981; Armstrong 1983; Hofman, 1983; Pagel and Harvey 1990; Allman et al. 1993). Humans are an extreme example, with a brain that is 10 times heavier than expected on the basis of body weight. We afford this luxury by developing slowly and by having an efficient diet (Aiello and Wheeler 1995). Given the fact that we are such a large-brained species, it may be a surprise to learn that mice have brains that are proportionally just as large as those of humans. A 22-gm adult mouse typically has a 450-mg brain, whereas a 66-kg human typically has a 1350-gm brain, 2% in both cases. Functional correlates. A second and almost self-evident reason to be interested in brain weight and neuron number is that variation in these simple parameters is associated with variation in behavior (Lashley 1949; Rensch 1956; Wimer and Prater 1966; Fuller and Herman 1972; Roderick et al. 1979; Fuller, 1979; Crusio et al. 1989; Jacobs et al. 1990; Belknap et al. 1992; Aboitiz 1996; Keverne et al. 1996). This is most clear-cut when specific regions of the brains of different species or individuals are compared. For example, in song birds the volume of song system nuclei and numbers of neurons tend to be positively correlated with different features of song production (e.g., DeVoogd et al. 1993; Ward et al. 1998). Another fine example—although strongly negative in this case—is the correlation in mice between avoidance learning and the size of the infrapyramidal projection from dentate gyrus to CA3 (Schwegler and Lipp 1983; Lipp et al. 1989). Insights into CNS development. My colleagues
and I are interested in brain weight and neuron number for a third reason:
as a means to map, clone, and characterize genes that control the
proliferation, differentiation, and death of cells in the CNS (Williams
and Herrup
1988; Williams et al.
1998a). These genes are entry points into molecular networks that
control brain development. Differences in brain weight are proportional to
total brain DNA content and consequently to total CNS cell numbers (Zamenhof
and von Marthens 1976). This is true even in neonatal mice, before
appreciable glial cell production (Zamenhof et al. 1971; Zamenhof and von
Marthens 1976). For this reason, brain weight is a surprisingly good
surrogate measure for total cell number in mice, as in humans (Pakkenberg
and Gundersen 1996).
The biometric analysis of the size and structure of the mouse CNS Precedents. In the late 1960s, Thomas Roderick, John Fuller, Douglas Wahlsten, and Richard and Cynthia Wimer began an ambitious program to manipulate neuroanatomical traits in mice by selective breeding (Roderick 1976). Their aim was to explore correlated changes in behavior. They gave the rapidly expanding field of behavioral neurogenetics a rigorous foundation in quantitative and statistical neuroanatomy (Wimer et al. 1969; Fuller and Geils 1972; Wahlsten 1975; Roderick et al. 1976; Fuller 1979; Wimer 1979; Wimer and Wimer 1985). Rather than relying on mutants, they exploited the substantial variation among standard inbred strains of mice. This work led to some important breakthroughs and some brick walls. One of the breakthroughs was successfully selecting for substantial differences in brain weight over less than 20 generations (Fuller 1979). An obvious limitation, highlighted by Roderick (1976), was that it was not possible to map gene loci responsible for the remarkable quantitative variation in CNS size, regional architecture, or behavior. A new opportunity. The situation has
changed radically in the past decade (Lander and Botstein 1989; Plomin et
al. 1991; Johnson et al. 1992; Belknap et al. 1992; Tanksley 1993; Frankel
1995; Crawley et al., 1997). Computational methods and molecular
reagents—particularly the polymerase chain reaction method—have become so
powerful and economical that it is now practical to systematically dissect
complex polygenic traits such as brain weight into sets of single
well-defined QTLs. Virtually any heritable trait in mice, whether
structural, physiological, pharmacological, or behavioral, can be targeted
for analysis. Recent examples in mice include epilepsy (Rise et al.,
1991), effects of ethanol and haloperidol (Plomin et al. 1993; Belknap et
al. 1993; Hitzemann et al. 1994; Kanes et al. 1996; Buck et al. 1997);
patterns of sleep and activity (Toth and Williams, 1998), and the mouse
equivalent of anxiety (Flint et al. 1995). As illustrated in the work of
Belknap and colleagues (1992), it is now feasible to continue the
systematic genetic dissection of the mouse CNS begun in the late 1960s and
to start identifying genes that underlie heritable variation in CNS size
and structure. Brain weight is highly variable. Brain weight is highly variable among strains reared in a common environment. For example, both A/J and DBA/2J have average brain weights close to 410 mg, whereas C57BL/6J and BALB/cJ have weights close to 510 mg. The variation within each strain is considerable even after compensating for differences in age, body weight, and sex by multiple regression (Williams et al. 1997). Two animals of the same sex and body weight taken from the same litter often have brain weights that differ by 10—20 mg. The coefficient of variation within isogenic groups shown in Table 1 averages about 5.5%, but when technical errors associated with fixation and dissection are taken into account, true non-genetic variation is close to 4%. In comparison, the retinal ganglion population of isogenic mice has a coefficient of variation that averages 3.6% (Williams et al. 1996a). We have explored the possibility that some of these differences in brain weight are due to variation in water content and the volume of the ventricles, and the short answer is that neither factor is important in mice older than 30 days. Wet and dry brain weights are very tightly correlated. Sex and age effects on brain weight. Both sexes and a wide range of ages were studied. Surprisingly, in mice sex has no detectable effect on adult brain weight (Williams et al. 1997) and this otherwise important trait can be neglected for most purposes. In some strains, there is a significant age-related increase in brain weight even after sexual maturity is reached. There is also a significant correlation between body weight and brain weight. The correlation across strains listed in Table 1 is merely 0.2, but in some crosses, such as that between CAST/Ei and BALB/cJ, the correlation can rise to 0.8. Information on over 5,000 mice and over 200 genotypes is available online at <http://www.nervenet.org>. [There are statistically significant mean sex differences in the size of several CNS regions, including the hippocampus (Lu et al., 2000), and the olfactory bulbs (Williams et al., 2000). These differences are relatively modest and certainly should not be thought of as sexual dimorphisms. The overlap in size between the sexes is very sustantial,, and sex only accounts a few percentage points of the total variance in either hipocampus or olfactory bulb size. (RW, June 2000)] Large differences between substrains. Perhaps the most remarkable aspect of the data summarized in Table 1 is the large differences in brain weight between several substrains of mice. For instance, brain weights of BALB/cByJ and BALB/cJ differ by 76 mg; C57L/J and C57BL/6J differ by 88 mg; C3H/HeJ and C3H/HeSnJ also differ by 88 mg. The closely matched and highly significant differences in these three pairs are intriguing. These differences were presumably generated by the recent fixation of variant alleles in a very small number of genes—probably one or two.
Table 1. Brain weights of 28 common inbred strains of laboratory mice with a comparison to two previous studies. Additional data on brain and body weights are availble for over 230 genotypes of mice. /P>
QTLs versus Mendelian loci. QTLs are conventional genes that have two or more alleles that contribute to quantitative variation of specific traits (Roff 1997; Lynch and Walsh 1998). A trait may be a concentration or number, a size, weight or density, an activity or behavior, a severity index or an age-of-onset. QTLs are often contrasted with Mendelian loci that have discontinuous effects on phenotypes and predictable segregation patterns. In contrast, individual QTLs usually have more modest effects on a particular phenotype and are associated with phenotypes in a probabilistic way. A QTL might account for as little as 2% or as much as 50% of the total phenotypic variance. QTLs come in sets that collectively define a polygene. For example, at least three QTLs are currently known to control part of the twofold variation in numbers of retinal ganglion cells (Williams et al. 1998a; Strom 1999), and at least 30 QTLs appear to modulate body size (Cheverud et al. 1996; Brockmann et al. 1998). In the next several pages I explain the process of mapping a QTL—in this case, one of the first QTLs demonstrated to modulate brain weight in the mouse. There are four key steps in mapping QTLs.
Step 1: Assessing trait variation. The
first step is to identify significant variation in phenotypes among
individuals, or, in the case of laboratory mice, among inbred strains.
Variation is an absolute necessity. It is the signal we are trying to
pinpoint on a map of the genome. The greater the heritable variation, the
better the prospects of success. Step 2: Estimating heritability. The second step in QTL mapping is to verify that a substantial fraction of the variability of the trait is heritable (Curcio 1992; Wahlsten 1992; Williams et al. 1996a). In a standard mouse colony, variation in brain weight has a heritability that ranges from 0.35 to 0.7 (Roderick et al., 1973; Roderick et al., 1976; Seyfried and Daniel 1977; Fuller 1979; Henderson 1979; Atchley et al. 1984; Williams et al. 1996b; Strom and Williams 1997; Strom 1999). Heritability estimates can admittedly be problematic (Lewontin 1957; Eleftheriou et al. 1975), and in the context of the heritability of human intelligence, Wahlsten (1994) comments that "I would feel more secure riding a three legged moose over thin ice than relying on a heritability coefficient to help me understand the origins of individual differences or predict future levels of intelligence." But it can still be useful to go through the process of computing heritability. The reason is that we need to have some idea of the approximate fraction of variance in our sample population that is due to heritable genetic factors before we attempt to map QTLs. The heritable variance is what we are trying to assign to a set of QTLs. While heritability estimates may be labile, the QTLs that we map are anchored in the genome itself.
Step 3: Phenotyping and genotyping members of an experimental cross. The third step is to gather phenotype and genotype data from a set of animals appropriate for QTL mapping. Several different types of crosses can be used to map QTLs (Taylor 1978; Groot et al. 1992; Frankel 1995; Darvasi 1998; Vadasz et al. 1998; Williams 1998b). Figure 1 already introduced one the most common—the F2 intercross. The central idea behind the intercross is to allow high and low alleles of QTLs inherited from the two inbred strains to segregate and assort independently from unlinked marker loci. The only marker loci that will consistently be associated with high, intermediate, and low trait values in the set of F2 progeny are those marker loci that are closely linked to QTLs (Tanksley 1993; Williams 1998b). Phenotyping and regression analysis.
Weighing brain weight is quick and easy, but before we can use these
weights to map QTLs we need to deal with the issue of specificity of gene
action. The brain weight data we have considered so far have not been
corrected for significant differences in the mean body weight among mice.
The heritability that we blithely assigned to brain weight may actually be
a consequence of heritable variation in body size. Unless we adjust our
brain weight phenotype appropriately, we risk mapping body weight QTLs
(Hahn and Haber 1978; Lande 1979). To ensure that we are mapping what we
want to map, we need to factor out variation in brain weight that is
predictable from variation in body weight, sex, age, and other variable
for which we have data.
Table 2. Regression analysis of brain weight in an F2 intercross
r2 = 67.4% Genotyping. In a typical analysis of F2
progeny, three to five marker loci spaced about 15 to 25 centimorgans (cM)
apart are genotyped on each of the 20 chromosome pairs. These marker loci
are usually repetitive microsatellite DNA sequences that consist of
variable numbers of cytosine-adenine (CA) dinucleotide repeats. One strain
of mouse may have a microsatellite with 30 CA repeats, whereas another
strain may have a microsatellite with 40 CA repeats. The 5' and 3'
flanking sequences of each microsatellites are unique to that part of the
genome, but they are also highly conserved among strains of mice. This
makes it possible to design PCR primers that selectively amplify a
polymorphic microsatellite located at a precisely defined chromosomal
position (Dietrich et al. 1994).
Step 4: The statistics of mapping QTLs.
We now have all the necessary data and we are poised to assess whether
QTLs have been discovered, and if so, with what precision and confidence
(Lander and Schork 1994; Churchill and Doerge 1994). Mapping QTLs involves
finding marker loci for which the three genotypes match up well with
variation in the phenotype. BALB/cJ has a much larger brain than does
CAST/Ei. If a QTL modulating brain weight is located near one of the
microsatellites then F2 animals that are homozygous for B alleles
at that marker should have heavier brains than those homozygous for C
alleles. Referring to Table 3, we test whether or not there is a
significant correlation (or regression coefficient) between the numerical
values (–1, 0, and +1) in the sixth through eighth columns and brain
weight residuals in the fourth column. These correlations are listed at
the bottom of Table 3.
To refine the analysis of this QTL near D6Mit327 we could genotype neighboring markers to determine whether any have even stronger association with variation in brain weight. This additional genotyping is usually not necessary because we can infer the genotypes that are likely to be present between neighboring marker loci. For example, if a mouse has a BB genotype at one marker and a CC genotype at a flanking marker then half way between these markers the genotype will most probably split the difference and be BC. Comparing predicted genotypes with actual phenotypes in the interval between marker loci is referred to as interval mapping (Lander and Botstein 1989). This refinement can significantly improve the statistical power of a QTL search and makes it possible to distinguish between a weak QTL that is near to a marker and a strong QTL that is located farther away. In other words, interval mapping improves the ability to locate a QTL and to estimate the effects that it is likely to have on the phenotype.
Figure 4. Linkage of the QTL Bsc5 to chromosome 6 in a cross between BALB/cJ and CAST/Ei. The x-axis represents position along Chr 6. The most proximal marker that we typed (D6Mit273) maps at 19 centiMorgans (cM), whereas the most distal maps at 70 cM. The Bsc5 locus is most likely to map about 1 cM proximal to the microsatellite marker D6Mit32. The confidence interval (CI) of this estimate (bold black lines) is wide–from 37 to 61 cM for a two-LOD CI (95% probability), and from 41 to 56 cM for a one-LOD CI. Genome-wide probability thresholds (Fig. 5) are marked by fine horizontal lines. The right scale and the two lower curves indicate the approximate additive effect and dominance deviations generated by Bsc5. The substitution of a single BALB/cJ allele for a CAST/Ei allele at Bsc5 may be responsible for a 15-mg gain in brain weight.
Permutation analysis. The process of mapping QTLs involves computing hundreds of linkage statistics across the entire set of chromosomes. Given the large number of statistical tests there is a strong probability of getting a "significant" association by chance alone. The nominal probabilities listed in Table 4 tell us little about the genome-wide probability that we have discovered a QTL (Lander and Kruglyak 1997). We need to compensate for these multiple tests. The appropriate correction factor depends on the particular distribution of trait values and the quality and quantity of genotype data.
A conceptual simple but computationally tedious permutation test can be used to estimate the distribution of best LRS scores that one might expect to get by chance with a given dataset (Churchill and Doerge 1994). This procedure reassigns phenotype values listed in Table 3, and then remaps the jumbled dataset to get a new version of Table 4. For each permutation the program keeps track of the single highest LRS score. The process is carried out another 9,999 times. Figure 5 shows a histogram of the peak LRS scores that resulted from a permutation of the data in Table 3. The peak LRS score was typically near 10. This non-parametric distribution of peak LRS scores can now be used to gauge the probability of obtaining an LRS of 18.3 by chance alone. Only 2% of permutations do this well or better. We can therefore be reasonably confident that we have mapped a QTL modulating brain weight to Chr 6. This is the fifth QTL that Richelle Strom and I have mapped (Strom 1999, R. C. Strom and R. W. Williams, in progress), and we have named it brain size control 5 (Bsc5). Bsc5 maps on Chr 6, approximately 1 cM proximal to D6Mit327. Bsc5 has not been mapped with much precision: the 95% confidence interval is defined by the width of the map profile 2 LOD units (or 9.2 LRS units) to either side of the peak—in this case between 37 and 61 cM. This 24-cM interval contains approximately 1,200 genes, and perusing a list of candidates at this point is little more than an entertaining exercise in optimism. A quick scan of this region using the Mouse Genome Database reveals one interesting candidate—the thyrotropin releasing hormone gene that maps at 43 cM. Cloning QTLs. Mapping QTLs is the initial
reconnaissance stage in a systematic effort to explore mechanisms that
modulate the development of the CNS. The next step is to match each QTL
with a single gene and its alternative alleles. QTLs will generally need
to be mapped with a precision of 1 to 2 cM—a chromosomal interval that
will typically harbor 50–100 genes. Achieving this level of accuracy is
not impractical, although it will often require an analysis of 1000 or
more animals (Darvasi 1997, 1998). A small subset of positional candidate
genes can then be chosen for further analysis on the basis of expression
patterns, known function, and differences in DNA sequence among strains.
The efficiency of the candidate gene approach will improve greatly in the
next decade. The genome of C57BL/6J will have been sequenced within five
years, and it is also likely that the utility of this code will be
enhanced with sequence data from other major inbred strains such as 129,
A, BALB/c, C3H, DBA/2, CAST/Ei, SPRET/Ei. Once sequence data have been
combined with expression maps for different parts of the mouse brain, it
should be possible to winnow a set of candidate genes to a very short
list. If the thyrotropin releasing hormone gene survives this filtration,
then we may then be justified in comparing its sequence among strains with
different phenotypes. The conversion of quantitative phenotypes (e.g., low
to high) by substituting alleles of one strain with that of another strain
will provide the final and most compelling support that the identity
between a QTL and a particular sequence variant has been made correctly
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