BACKGROUND
cortex and cognition
the absolute and relative volumes of anatomically defined brain regions-such as the mammalian cerebral cortex-are of functional importance both within and across species  <cit> .
in humans, the volume of the cerebral hemispheres ranges between  <dig> and  <dig> cm <dig> in young adults  <cit> .
further, neocortical size is hereditarily specified, with over eighty percent of the variance of human neocortical gray matter volume being genetically determined  <cit> .
at present, little is known about the genomic determinants of such natural variation.
further, cognitive ability is related to neocortical size.
for example, reiss et al.
showed that iq is positively correlated with cerebral volume in children  <cit> .
thompson et al.
provided evidence based on quantitative mri volumetric measurements that not only is neocortical volume genetically determined , but that spearman's g, a measure of fluid intelligence, was significantly linked to frontal lobe neocortical volume.
similar findings also have been reported by posthuma et al.
<cit> .
these results provide evidence that neocortical volume is very much genetically determined and linked to cognitive abilities.
however, such studies provide no evidence concerning the genomic mechanisms that underlie these highly heritable traits.
for this all important question, quantitative neuroanatomical studies of the neocortex of recombinant inbred strains of mice provide one important path to unravelling the genomics of brain size.
the discovery of the genes that differentially regulate neocortical volume is a primary question for contemporary cognitive neuroscience.
the study of ri mice might provide some insight into this problem.
here, we report the first empirical study of this fundamental problem.
experimental strategy
we measured neocortex and total brain volume in  <dig> mice from  <dig> ri strains  as well as their two parental strains, c57bl/6j  and dba/2j , all strains being homozygous throughout their genomes.
from these measurements, both in vivo cortical brain and in vivo noncortical brain volumes were calculated.
RESULTS
reliability of measurement
to assess the reliability of the stereological measurements, cortical brain area was remeasured blindly in  <dig> brain sections.
the test-retest reliability coefficient indicated that the measurements were highly reliable .
similarly, reliability for total fixed brain volume remeasured for twenty mice was also very high .
regression analyses
the size of brain structure is not only regulated by structure-specific genes, but varies with other factors, which may include body weight , age, and sex.
to statistically remove these influences from our histological phenotypes, a multiple-regression analysis was performed using body weight, the logarithm of age, and sex as predictor variables, a standard procedure in qtl analysis.
body weight and the logarithm of age were the only significant predictor variables for in vivo cortical brain volume, yielding the following regression equation for adjusted cortical volume:
cxvreg =  <dig>  +  <dig>  -  <dig> ),
henceforth referred to as neocortex.
the same two predictor variables were used for the regression of in vivo noncortical brain volume, although body weight was the only significant predictor in that analysis.
the regression equation for in vivo noncortical brain volume was:
ncxvreg =  <dig>  +  <dig>  -  <dig> ),
termed noncortex in the following analyses.
qtl mapping
the linkage disequilibrium between a measured phenotypic trait, like regressed cortical volume or regressed noncortical volume, and any genomic marker can be measured using the likelihood ratio statistic .
this is a quantitative estimate of the probability that each individual marker does or does not overlie one of the polygenes regulating the phenotypic trait.
we computed the lrs for each of  <dig>  marker positions on chromosomes  <dig> through  <dig> as well as chromosome x, using webqtl as a genotype source and mapping engine  <cit> .
similar results were also obtain in preliminary analyses using the previous marker set containing  <dig> more sparsely distributed webqtl markers.
the lrs depends upon the ratio of a model not incorporating information about the marker in question  to a model incorporating genetic information , as shown in equation  <dig>  in marker regression, the lrs for a particular marker is a function of the ratio of the sum of squared deviations from the mean for the phenotypic variable x to the sum of the squared deviations of the variable from the submeans that are obtained when the phenotypes are segregated according to the parental allele value at that marker:
lrs=nln⁡ssreducedmodelssfullmodel=nln⁡∑2∑2+∑2
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaafaqadegadaaabagaemitawkaemouailaem4uamfabagaeyypa0dabagaemota4kagiibawmaeioba42aasaaaeaacqwgtbwucqwgtbwudawgaawcbaacbigae8nuailae8xzaumaemizaqmaemydaunaem4yammaemyzaumaemizaqmaemyta0kaem4ba8maemizaqmaemyzaumaemibawgabeaaaoqaaiabdofatjabdofatnaabaaaleaacqwggbgrcqwg1bqdcqwgsbabcqwgsbabcqwgnbqtcqwgvbwbcqwgkbazcqwglbqzcqwgsbabaeqaaaaaaoqaaaqaaiabg2da9aqaaiabd6eaojgbcygasjabc6gaunaalaaabawaaabqaeaaieaacqgfoaakcqwf4baedawgaawcbagae8xqaeeabeaakiabgkhitiqbdiha4zaarawaasbaasqaaiabdgeabbqabagccqggpaqkdaahaawcbeqaaiabikdayaaaaeqabeqdcqghris5aagcbawaaabqaeaacqggoaakcqwg4baedawgaawcbagaemoqaieabeaakiabgkhitiqbdiha4zaarawaasbaasqaaiabdkeacbqabagccqggpaqkdaahaawcbeqaaiabikdayaaakiabgucarmaaqaeabagaeiikagiaemieag3aasbaasqaaiabdseaebqabagccqghsislcuwg4baegaqeamaabaaaleaacqwgebaraeqaaaqabeqaniabgghildgccqggpaqkdaahaawcbeqaaiabikdayaaaaeqabeqdcqghris5aaaaaaaaaa@7e06@
where the subscripts a, b, and d indicate, respectively, all strains, strains with the c57bl/6j b-type, and strains with the dba/2j d-type allele at the marker, as shown above.
n is the total number of strains analyzed, here  <dig>  the value of the lrs can be compared with values obtained from a permutation test to determine the genome-wide significance of the association  <cit> .
qtl boundaries
the boundaries of each qtl were determined by examination of the distribution of the lrs scores of the markers surrounding the qtl peak.
all peaks were well formed and sharp.
following van ooijen  <cit>  we located the nearest markers for which the value of the lrs was reduced by at least  <dig>  units, corresponding to the  <dig> percent confidence limits for the qtl.
kim et al.
has recently confirmed that this method is both accurate and unbiased  <cit> .
descriptive statistics
there was substantial variation in both in vivo neocortical and noncortical brain volume across strains.
in vivo neocortical volume ranged from a minimum of  <dig>  mm <dig> in bxd <dig> mice to  <dig>  mm <dig> in bxd <dig> mice.
the mean in vivo neocortical volume was  <dig>  mm <dig>  with a standard deviation of  <dig> .
in vivo noncortical brain volume ranged from  <dig>   to  <dig>  mm <dig> , with a mean of  <dig>  and a standard deviation of  <dig> .
the range of both phenotypic measurements is about  <dig> percent of the mean phenotypic value, which provides ample variation for a linkage disequilibrium analysis.
analysis of variance
the hypothesis that neocortical volume is in part genomically determined was assessed by analysis of variance , with inbred strain  as the independent variable and residual neocortical volume as the dependent variable, as shown in table  <dig>  the main effect of strain was highly significant .
significant strain differences were also observed for residual noncortical brain volume .
relative independence of cortical volume and body weight
brain size is known to vary with body size in a wide variety of species, including mice and other rodents  <cit> .
however, an examination of the regression analyses reported above for phenotype versus predictor variables suggests that the covariation between brain volume and body size is very much weaker for cerebral cortex than it is for noncortical brain volume.
we tested this relationship by first computing the pearson product moment correlation coefficients for body weight and in vivo cortical volume  and in vivo noncortical volume .
we then used fisher's r-to-z transformation  to statistically test for a significant difference between these correlations.
the result provides evidence that the mammalian cerebral cortex is significantly less regulated by factors related to body size than are most other regions of the central nervous system .
high heritability of brain size
the proportion of phenotypic variance that might be attributed to genomic factors was estimated as broad-sense heritability, or the total genetic determination of a phenotypic trait.
broad-sense heritability was estimated from an analysis of variance with strain as the independent variable and quantitative phenotype as the dependent variable, using the following formula:
ω2=f−1f+/dfb,
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwfjpwddaahaawcbeqaaiabikdayaaakiabg2da9maalaaabagaemoraykaeyoei0iaegymaedabagaemoraykaey4kasiaeiikagiaemizaqmaemozay2aasbaasqaaiabdeha3bqabagccqghrawkcqaixaqmcqggpaqkcqggvawlcqwgkbazcqwgmbgzdawgaawcbagaemoyaigabeaakiabcycasaaaaaa@436e@
where f is the ratio of the mean square deviation between strains to the mean square deviation within strains.
the value of ω <dig> varies between  <dig>  and  <dig> .
these analyses showed that a substantial fraction of phenotypic variance is genetically determined.
for regressed cortical volume, ω <dig> was  <dig> ; for regressed noncortical volume, ω <dig> was  <dig> .
qtls for cortical volume
given the high heritability of both residual cortical and noncortical brain volume, the genomic question is not if quantitative trait loci exist for these phenotypic anatomical variables , but rather where on the genome these qtls are located.
qtl analyses provide the mechanism for locating genomic regions in which allele values are closely associated with a phenotypic trait.
the results of the qtl analysis of  <dig>  markers across the mouse genome for association with regressed cortical volume are shown in figure  <dig>  there are two prominent spikes in the lrs profile for residual cortical volume.
table  <dig> shows the lrs values produced by marker regression.
the most significant marker  is d11mit <dig> at  <dig>  megabases  on chromosome  <dig>  two other nearby markers  also show suggestive association with regressed cortical volume.
because of the restricted genomic resolution afforded by the available number of recombinant inbred strains, we treat these three markers as reflective of a single qtl in the immediate vicinity of d11mit <dig>
there is a second, suggestive qtl for residual cortical volume on chromosome  <dig>  this is reflected by a linkage disequilibrium with two adjacent markers, d16mit <dig>  and d16mit <dig> .
these markers on proximal chromosome  <dig> also contribute to the genetic specification of neocortical volume.
to estimate the minimal proportion of phenotypic variance accounted for by each of these two qtl markers, we calculated the partial eta squared  from an analysis of variance with the markers d11mit <dig> and d16mit <dig> and their interaction as factors.
these proportions are  <dig>  for d11mit <dig> and  <dig>  for d16mit <dig>  the proportion attributable to the interaction of the two markers was negligible.
qtls for noncortical brain volume
there are significant and suggestive qtls for regressed noncortical brain volume as well, two of which do not affect cortical volume, and the third affects both, but to differing degrees.
figure  <dig> presents the corresponding qtl analysis for regressed noncortical brain volume.
a significant association between this regressed noncortical volume and the mammalian genotype may be seen on proximal chromosome  <dig>  this is most evident at marker d19mit <dig> , which reaches genome-wide significance on many – but not all – permutation tests.
because the results of all permutation tests vary slightly from sample to sample, any lrs score that lies within this narrow range will reach significance with some instances of the permutation test, but not others.
thus, we conclued that this qtl neither greatly exceeds nor falls far short of the genome-wide  <dig>  significance level.
this qtl extends to neighboring markers d19mit <dig>  and d19mit <dig> .
these markers appear to be indicative of a single qtl harboring one or more genes that regulate noncortical, but not cortical, brain size.
d11mit <dig> on chromosome  <dig>  which is significantly related to regressed cortical volume, also shows a suggestive, but not significant, association with noncortical brain volume.
there is also a marker on chromosome  <dig> with a borderline lrs in marker regression, d15mit <dig> , which exceeds the criterion for a suggestive lrs on some permutation tests, but not on others.
the minimal proportion of phenotypic variance accounted for by these three markers was estimated by ηp2
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwf3oaadaqhaawcbagaemicaahabagaegomaidaaaaa@30e7@.
the obtained values were  <dig>  for d19mit <dig>   <dig>  for d11mit <dig>  and  <dig>  for d15mit <dig>  all interactions produced negligible values of ηp2
mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwf3oaadaqhaawcbagaemicaahabagaegomaidaaaaa@30e7@.
composite interval mapping
composite interval mapping  <cit>  can increase the sensitivity of a search for additional qtls associated with a phenotype by incorporating the variance associated with previously identified significant qtls to the background of the additive model.
composite interval maps were constructed for both residual phenotypes, but no additional qtls emerged from these analyses.
epistasis
epistasis is the interaction of two or more genes at different chromosomal sites, which can either be suppressive or facilitative.
it is important to test for epistasis, as it indicates a departure from additivity in polygene action.
we tested for epistasis between all the possible marker pairs for the regressed neocortical and noncortical volume phenotypes, respectively, using ljungberg's direct global optimization algorithm as implemented in webqtl with phenotype data from the recombinant inbred strains  <cit> .
there were no significant interactions for either phenotypic variable.
discussion
these results have several implications for understanding the genetic specification of neocortical development.
relative independence of cortical size from body size
the various strains of bxd mice differ considerably from each other in both cortical and noncortical brain volume.
however, these two compartments of the mouse brain show quite different dependencies on body size.
nearly  <dig> percent of the variance in noncortical brain volume can be accounted for by body size in our data .
in contrast, our measurements suggest that neocortical brain volume is much less dependent on body size, with only about  <dig> percent of that compartment being predictable from body weight.
neocortex appears to be regulated by factors that differ substantially from those regulating other regions of the central nervous system, a conclusion that complements recent observations made by bush and allman  <cit> .
thus, one might expect different genomic regions to regulate the heritable factors that determine size of the neocortex and noncortical brain regions, which proves to be the case.
a cortex-dependent qtl on chromosome 11
one qtl with genome-wide significance for regressed cortical volume emerged from our analyses.
it was located at the dna marker d11mit <dig> and flanked by two suggestive markers.
a qtl associated near this location  was reported previously in a doctoral dissertation in which the phenotype was total brain weight, controlling for the effects of sex, age, body weight, litter size, and parity by multiple regression  <cit> .
the qtl was interpreted as one that controls neuron number throughout the brain.
our data suggest a more specific interpretation.
using our phenotypic data we can compare the the proportion of variance accounted for r <dig> on chromosome  <dig> at d11mit <dig> for neocortex alone , whole brain volume or brain weight , and noncortex , all regressed for body weight and the logarithm of age.
the r <dig> values are highest for neocortex, lowest for noncortex, and intermediate for the whole brain.
it is clear that this qtl is not a generic determinant of brain size, but rather selectively exerts its effects on the neocortex and perhaps some adjacent forebrain structures such as the olfactory bulb.
candidate genes for a cerebral cortex volume modulator
the qtl analyses presented above describe chromosomal regions in which a phenotypic measurement – here cortical or noncortical brain volume – are statistically linked with chromosomal markers.
but the true endgame of neurogenomics is the discovery of specific genes that mediate these associations.
we describe three approaches for narrowing this search.
the mouse chromosome  <dig> is slightly less than  <dig> megabases  in length.
the strongest linkage between cortical volume and any marker in the murine genome is at d11mit <dig> at  <dig>  mbp on chromosome  <dig>  the ± 95% confidence intervals for this qtl are between  <dig> and  <dig> mb.
using the criteria described above, snp filtering revealed polymorphisms in the coding or untranslated regulatory regions of twenty known genes.
the filtered known genes within the chromosome  <dig> confidence interval for neocortex are e030025d05rik, aw <dig>  4931428d14rik, c330012f17rik, 2010316f05rik, 2510006c20rik, stc <dig>  il9r, 3300001g02rik, rhbdf <dig>  mpg, hba-x, a230090e <dig>  stk <dig>  fbxw1b, fgf <dig>  gabrp, kcnmb <dig>  dock <dig>  and vrk <dig>  however, a detailed examination of these genes suggests that they are not uniquely expressed in brain and thus are less likely to provide an explanation of the neocortex qtl.
nonetheless, several possibilities remain.
first, and most obvious, is that the gene controlling neocortical volume have simply not yet been discovered, a possibility that can not be excluded, particularly since the study of the genome is still young.
another possibility is that the gene may have been "discovered" but its effects on the developing forebrain are not yet known.
in this case, the known gene would not be selected in the literature search.
a third possibility is that the gene is known, but was excluded in snp filtering.
thus, it is of interest that there is a known gene within the qtl on chromosome  <dig> that is specifically related to neocortex development.
otx <dig>  plays a major and selective role in the development of the mammalian neocortex  <cit> .
otx <dig> is expressed early in development and provides a molecular basis for the development of the deep layers of the cerebral cortex, as well as in the development of the eye, olfactory system, and cochlea.
otx <dig> is closely related to otx <dig>  which modulates the development of the mammalian brainstem.
interestingly, the expression of otx <dig> is regulated by two distant enhancers, one located  <dig> kb upstream and the other  <dig> kb downstream from otx <dig> itself on chromosome  <dig>  <cit> .
if similar enhancers exist for otx <dig>  they would have been excluded by our snp filtering procedure.
a search of the celera database reveals that there are  <dig> d/b snps within ±  <dig> kb of otx <dig>  if any of these snps lay within a putative otx <dig> enhancer, it could provide a molecular basis for the qtl.
thus, otx <dig> may still be a reasonable candidate gene mediating the effects of the chromosome  <dig> qtl for neocortical volume.
a noncortex-dependent qtl on chromosome 19
in the analysis of regressed noncortical volume, the single qtl detected with genome-wide significance was on proximal chromosome  <dig>  this genomic region had absolutely no effect on regressed cortical volume.
thus, the data display a classical pattern of double dissociation: one factor that affects cortical volume more than noncortical volume and a second factor that shows the mirror image pattern.
double dissociation is an important criterion in neuropsychology, because it provides positive logical proof of the specificity of effects.
the same argument can be made in the present case as well.
candidate genes for a noncortical volume modulator
in an analysis similar to that performed for neocortex we carried out a snp filtered celera search of chromosome  <dig>  which is about  <dig> mb in length, in the vicinity of d19mit <dig>  using a qtl confidence interval  <dig> to  <dig> mb.
this search produced  <dig> known genes with snps differentiating the two parental strains.
the filtered known genes within the chromosome  <dig> confidence interval for noncortex are 5730596k20rik, d630002g <dig>  slc22a <dig>  chrm <dig>  slc3a <dig>  4930563m09rik, gng <dig>  b3gat <dig>  0710001o03rik, bc <dig>  1110006i15rik, zp <dig>  mor239- <dig>  a33000e03rik, mor202- <dig>  keg <dig>  cntf, mor202- <dig>  mor202- <dig>  mor202- <dig>  mor266- <dig>  mor2127- <dig>  and mor212- <dig>
examination of expression information for these  <dig> known genes in the ncbi entrez gene database revealed one gene that was particularly promising as a candidate to mediate the qtl's effect on noncortical brain volume.
that gene is ciliary neurotrophic factor .
ctnf is a one of the gp <dig> family of cytokines and acts as a survival factor for a number of different neuronal cell types.
originally discovered as a factor that supports the survival of parasympathetic nerve fibers in the ciliary ganglia, ctnf is now known to play an active role in neuronal maintenance within the central nervous system  <cit> .
recent reports have also shown that ctnf modulates central nervous system neurogenesis as well  <cit> .
thus, it is not unreasonable to conclude the genetically controlled natural variations in ctnf expression might modulate brain size in bxd recombinant inbred mice.
ctnf is indeed a strong candidate gene for understanding the qtl on chromosome  <dig> related to noncortical brain volume.
other suggestive qtls
the other suggestive qtls reported above should be noted, although the evidence for them is not exceptionally strong.
these include possible cortex-dependent qtl on proximal  <dig> and the noncortex dependent qtl on chromosome  <dig>  suggestive qtls in today's analyses can provide guidance and support for other, more sensitive, analyses in the future if they are replicated.
CONCLUSIONS
our localization of qtls regulating neocortical size may have broader, more cognitive implications.
gibson, in a recent theoretical paper on brain size and mental capacity , concludes: perhaps "those genetic factors that control enhanced brain size, especially the size of the sensori-motor control for the oral and manual organs, the neocortical association areas, the basal ganglia, and the cerebellum would emerge as the prime genetic determinants of the mental abilities of human infants."
properly designed qtl analyses using the appropriate behavioral phenotypic measures in recombinant inbred mice could help resolve this question.
since there is ample conservation in the mammalian genome over species, one hopes that findings obtained using well-developed recombinant inbred strains of mice will be applicable to understanding primate and human neurogenomics in a straightforward manner as well.

 cortex and cognition the absolute and relative volumes of anatomically defined brain regions-such as the mammalian cerebral cortex-are of functional importance both within and across species. in humans, the volume of the cerebral hemispheres ranges between and cm in young adults. further, neocortical size is hereditarily specified, with over eighty percent of the variance of human neocortical gray matter volume being genetically determined. at present, little is known about the genomic determinants of such natural variation. further, cognitive ability is related to neocortical size. for example, reiss et al. showed that iq is positively correlated with cerebral volume in children. thompson et al. provided evidence based on quantitative mri volumetric measurements that not only is neocortical volume genetically determined, but that spearman's g, a measure of fluid intelligence, was significantly linked to frontal lobe neocortical volume. similar findings also have been reported by posthuma et al.. these results provide evidence that neocortical volume is very much genetically determined and linked to cognitive abilities. however, such studies provide no evidence concerning the genomic mechanisms that underlie these highly heritable traits. for this all important question, quantitative neuroanatomical studies of the neocortex of recombinant inbred strains of mice provide one important path to unravelling the genomics of brain size. the discovery of the genes that differentially regulate neocortical volume is a primary question for contemporary cognitive neuroscience. the study of ri mice might provide some insight into this problem. here, we report the first empirical study of this fundamental problem. experimental strategy we measured neocortex and total brain volume in mice from ri strains as well as their two parental strains, c57bl/6j and dba/2j, all strains being homozygous throughout their genomes. from these measurements, both in vivo cortical brain and in vivo noncortical brain volumes were calculated.  reliability of measurement to assess the reliability of the stereological measurements, cortical brain area was remeasured blindly in brain sections. the test-retest reliability coefficient indicated that the measurements were highly reliable. similarly, reliability for total fixed brain volume remeasured for twenty mice was also very high. regression analyses the size of brain structure is not only regulated by structure-specific genes, but varies with other factors, which may include body weight, age, and sex. to statistically remove these influences from our histological phenotypes, a multiple-regression analysis was performed using body weight, the logarithm of age, and sex as predictor variables, a standard procedure in qtl analysis. body weight and the logarithm of age were the only significant predictor variables for in vivo cortical brain volume, yielding the following regression equation for adjusted cortical volume: cxvreg = + - ), henceforth referred to as neocortex. the same two predictor variables were used for the regression of in vivo noncortical brain volume, although body weight was the only significant predictor in that analysis. the regression equation for in vivo noncortical brain volume was: ncxvreg = + - ), termed noncortex in the following analyses. qtl mapping the linkage disequilibrium between a measured phenotypic trait, like regressed cortical volume or regressed noncortical volume, and any genomic marker can be measured using the likelihood ratio statistic. this is a quantitative estimate of the probability that each individual marker does or does not overlie one of the polygenes regulating the phenotypic trait. we computed the lrs for each of marker positions on chromosomes through as well as chromosome x, using webqtl as a genotype source and mapping engine. similar results were also obtain in preliminary analyses using the previous marker set containing more sparsely distributed webqtl markers. the lrs depends upon the ratio of a model not incorporating information about the marker in question to a model incorporating genetic information, as shown in equation in marker regression, the lrs for a particular marker is a function of the ratio of the sum of squared deviations from the mean for the phenotypic variable x to the sum of the squared deviations of the variable from the submeans that are obtained when the phenotypes are segregated according to the parental allele value at that marker: lrs=nln⁡ssreducedmodelssfullmodel=nln⁡∑2∑2+∑2 mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaafaqadegadaaabagaemitawkaemouailaem4uamfabagaeyypa0dabagaemota4kagiibawmaeioba42aasaaaeaacqwgtbwucqwgtbwudawgaawcbaacbigae8nuailae8xzaumaemizaqmaemydaunaem4yammaemyzaumaemizaqmaemyta0kaem4ba8maemizaqmaemyzaumaemibawgabeaaaoqaaiabdofatjabdofatnaabaaaleaacqwggbgrcqwg1bqdcqwgsbabcqwgsbabcqwgnbqtcqwgvbwbcqwgkbazcqwglbqzcqwgsbabaeqaaaaaaoqaaaqaaiabg2da9aqaaiabd6eaojgbcygasjabc6gaunaalaaabawaaabqaeaaieaacqgfoaakcqwf4baedawgaawcbagae8xqaeeabeaakiabgkhitiqbdiha4zaarawaasbaasqaaiabdgeabbqabagccqggpaqkdaahaawcbeqaaiabikdayaaaaeqabeqdcqghris5aagcbawaaabqaeaacqggoaakcqwg4baedawgaawcbagaemoqaieabeaakiabgkhitiqbdiha4zaarawaasbaasqaaiabdkeacbqabagccqggpaqkdaahaawcbeqaaiabikdayaaakiabgucarmaaqaeabagaeiikagiaemieag3aasbaasqaaiabdseaebqabagccqghsislcuwg4baegaqeamaabaaaleaacqwgebaraeqaaaqabeqaniabgghildgccqggpaqkdaahaawcbeqaaiabikdayaaaaeqabeqdcqghris5aaaaaaaaaa@7e06@ where the subscripts a, b, and d indicate, respectively, all strains, strains with the c57bl/6j b-type, and strains with the dba/2j d-type allele at the marker, as shown above. n is the total number of strains analyzed, here the value of the lrs can be compared with values obtained from a permutation test to determine the genome-wide significance of the association. qtl boundaries the boundaries of each qtl were determined by examination of the distribution of the lrs scores of the markers surrounding the qtl peak. all peaks were well formed and sharp. following van ooijen we located the nearest markers for which the value of the lrs was reduced by at least units, corresponding to the percent confidence limits for the qtl. kim et al. has recently confirmed that this method is both accurate and unbiased. descriptive statistics there was substantial variation in both in vivo neocortical and noncortical brain volume across strains. in vivo neocortical volume ranged from a minimum of mm in bxd mice to mm in bxd mice. the mean in vivo neocortical volume was mm with a standard deviation of. in vivo noncortical brain volume ranged from to mm, with a mean of and a standard deviation of. the range of both phenotypic measurements is about percent of the mean phenotypic value, which provides ample variation for a linkage disequilibrium analysis. analysis of variance the hypothesis that neocortical volume is in part genomically determined was assessed by analysis of variance, with inbred strain as the independent variable and residual neocortical volume as the dependent variable, as shown in table the main effect of strain was highly significant. significant strain differences were also observed for residual noncortical brain volume. relative independence of cortical volume and body weight brain size is known to vary with body size in a wide variety of species, including mice and other rodents. however, an examination of the regression analyses reported above for phenotype versus predictor variables suggests that the covariation between brain volume and body size is very much weaker for cerebral cortex than it is for noncortical brain volume. we tested this relationship by first computing the pearson product moment correlation coefficients for body weight and in vivo cortical volume and in vivo noncortical volume. we then used fisher's r-to-z transformation to statistically test for a significant difference between these correlations. the result provides evidence that the mammalian cerebral cortex is significantly less regulated by factors related to body size than are most other regions of the central nervous system. high heritability of brain size the proportion of phenotypic variance that might be attributed to genomic factors was estimated as broad-sense heritability, or the total genetic determination of a phenotypic trait. broad-sense heritability was estimated from an analysis of variance with strain as the independent variable and quantitative phenotype as the dependent variable, using the following formula: ω2=f−1f+/dfb, mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwfjpwddaahaawcbeqaaiabikdayaaakiabg2da9maalaaabagaemoraykaeyoei0iaegymaedabagaemoraykaey4kasiaeiikagiaemizaqmaemozay2aasbaasqaaiabdeha3bqabagccqghrawkcqaixaqmcqggpaqkcqggvawlcqwgkbazcqwgmbgzdawgaawcbagaemoyaigabeaakiabcycasaaaaaa@436e@ where f is the ratio of the mean square deviation between strains to the mean square deviation within strains. the value of ω varies between and. these analyses showed that a substantial fraction of phenotypic variance is genetically determined. for regressed cortical volume, ω was; for regressed noncortical volume, ω was. qtls for cortical volume given the high heritability of both residual cortical and noncortical brain volume, the genomic question is not if quantitative trait loci exist for these phenotypic anatomical variables, but rather where on the genome these qtls are located. qtl analyses provide the mechanism for locating genomic regions in which allele values are closely associated with a phenotypic trait. the results of the qtl analysis of markers across the mouse genome for association with regressed cortical volume are shown in figure there are two prominent spikes in the lrs profile for residual cortical volume. table shows the lrs values produced by marker regression. the most significant marker is d11mit at megabases on chromosome two other nearby markers also show suggestive association with regressed cortical volume. because of the restricted genomic resolution afforded by the available number of recombinant inbred strains, we treat these three markers as reflective of a single qtl in the immediate vicinity of d11mit there is a second, suggestive qtl for residual cortical volume on chromosome this is reflected by a linkage disequilibrium with two adjacent markers, d16mit and d16mit. these markers on proximal chromosome also contribute to the genetic specification of neocortical volume. to estimate the minimal proportion of phenotypic variance accounted for by each of these two qtl markers, we calculated the partial eta squared from an analysis of variance with the markers d11mit and d16mit and their interaction as factors. these proportions are for d11mit and for d16mit the proportion attributable to the interaction of the two markers was negligible. qtls for noncortical brain volume there are significant and suggestive qtls for regressed noncortical brain volume as well, two of which do not affect cortical volume, and the third affects both, but to differing degrees. figure presents the corresponding qtl analysis for regressed noncortical brain volume. a significant association between this regressed noncortical volume and the mammalian genotype may be seen on proximal chromosome this is most evident at marker d19mit, which reaches genome-wide significance on many – but not all – permutation tests. because the results of all permutation tests vary slightly from sample to sample, any lrs score that lies within this narrow range will reach significance with some instances of the permutation test, but not others. thus, we conclued that this qtl neither greatly exceeds nor falls far short of the genome-wide significance level. this qtl extends to neighboring markers d19mit and d19mit. these markers appear to be indicative of a single qtl harboring one or more genes that regulate noncortical, but not cortical, brain size. d11mit on chromosome which is significantly related to regressed cortical volume, also shows a suggestive, but not significant, association with noncortical brain volume. there is also a marker on chromosome with a borderline lrs in marker regression, d15mit, which exceeds the criterion for a suggestive lrs on some permutation tests, but not on others. the minimal proportion of phenotypic variance accounted for by these three markers was estimated by ηp2 mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwf3oaadaqhaawcbagaemicaahabagaegomaidaaaaa@30e7@. the obtained values were for d19mit for d11mit and for d15mit all interactions produced negligible values of ηp2 mathtype@mtef@5@5@+=feaafiart1ev1aaatcvaufkttlearuwrp9mdh5mbpbiqv92aaexatlxbi9gbaebbnrfifhhdyfgasaach8aky=wiffydh8gipec8eeeu0xxdbba9frfj0=oqffea0dxdd9vqai=hguq8kuc9pgc9s8qqaq=dirpe0xb9q8qilsfr0=vr0=vr0dc8meaabaqaciaacagaaeqabaqabegadaaakeaaiigacqwf3oaadaqhaawcbagaemicaahabagaegomaidaaaaa@30e7@. composite interval mapping composite interval mapping can increase the sensitivity of a search for additional qtls associated with a phenotype by incorporating the variance associated with previously identified significant qtls to the background of the additive model. composite interval maps were constructed for both residual phenotypes, but no additional qtls emerged from these analyses. epistasis epistasis is the interaction of two or more genes at different chromosomal sites, which can either be suppressive or facilitative. it is important to test for epistasis, as it indicates a departure from additivity in polygene action. we tested for epistasis between all the possible marker pairs for the regressed neocortical and noncortical volume phenotypes, respectively, using ljungberg's direct global optimization algorithm as implemented in webqtl with phenotype data from the recombinant inbred strains. there were no significant interactions for either phenotypic variable. discussion these results have several implications for understanding the genetic specification of neocortical development. relative independence of cortical size from body size the various strains of bxd mice differ considerably from each other in both cortical and noncortical brain volume. however, these two compartments of the mouse brain show quite different dependencies on body size. nearly percent of the variance in noncortical brain volume can be accounted for by body size in our data. in contrast, our measurements suggest that neocortical brain volume is much less dependent on body size, with only about percent of that compartment being predictable from body weight. neocortex appears to be regulated by factors that differ substantially from those regulating other regions of the central nervous system, a conclusion that complements recent observations made by bush and allman. thus, one might expect different genomic regions to regulate the heritable factors that determine size of the neocortex and noncortical brain regions, which proves to be the case. a cortex-dependent qtl on chromosome 11 one qtl with genome-wide significance for regressed cortical volume emerged from our analyses. it was located at the dna marker d11mit and flanked by two suggestive markers. a qtl associated near this location was reported previously in a doctoral dissertation in which the phenotype was total brain weight, controlling for the effects of sex, age, body weight, litter size, and parity by multiple regression. the qtl was interpreted as one that controls neuron number throughout the brain. our data suggest a more specific interpretation. using our phenotypic data we can compare the the proportion of variance accounted for r on chromosome at d11mit for neocortex alone, whole brain volume or brain weight, and noncortex, all regressed for body weight and the logarithm of age. the r values are highest for neocortex, lowest for noncortex, and intermediate for the whole brain. it is clear that this qtl is not a generic determinant of brain size, but rather selectively exerts its effects on the neocortex and perhaps some adjacent forebrain structures such as the olfactory bulb. candidate genes for a cerebral cortex volume modulator the qtl analyses presented above describe chromosomal regions in which a phenotypic measurement – here cortical or noncortical brain volume – are statistically linked with chromosomal markers. but the true endgame of neurogenomics is the discovery of specific genes that mediate these associations. we describe three approaches for narrowing this search. the mouse chromosome is slightly less than megabases in length. the strongest linkage between cortical volume and any marker in the murine genome is at d11mit at mbp on chromosome the ± 95% confidence intervals for this qtl are between and mb. using the criteria described above, snp filtering revealed polymorphisms in the coding or untranslated regulatory regions of twenty known genes. the filtered known genes within the chromosome confidence interval for neocortex are e030025d05rik, aw 4931428d14rik, c330012f17rik, 2010316f05rik, 2510006c20rik, stc il9r, 3300001g02rik, rhbdf mpg, hba-x, a230090e stk fbxw1b, fgf gabrp, kcnmb dock and vrk however, a detailed examination of these genes suggests that they are not uniquely expressed in brain and thus are less likely to provide an explanation of the neocortex qtl. nonetheless, several possibilities remain. first, and most obvious, is that the gene controlling neocortical volume have simply not yet been discovered, a possibility that can not be excluded, particularly since the study of the genome is still young. another possibility is that the gene may have been "discovered" but its effects on the developing forebrain are not yet known. in this case, the known gene would not be selected in the literature search. a third possibility is that the gene is known, but was excluded in snp filtering. thus, it is of interest that there is a known gene within the qtl on chromosome that is specifically related to neocortex development. otx plays a major and selective role in the development of the mammalian neocortex. otx is expressed early in development and provides a molecular basis for the development of the deep layers of the cerebral cortex, as well as in the development of the eye, olfactory system, and cochlea. otx is closely related to otx which modulates the development of the mammalian brainstem. interestingly, the expression of otx is regulated by two distant enhancers, one located kb upstream and the other kb downstream from otx itself on chromosome. if similar enhancers exist for otx they would have been excluded by our snp filtering procedure. a search of the celera database reveals that there are d/b snps within ± kb of otx if any of these snps lay within a putative otx enhancer, it could provide a molecular basis for the qtl. thus, otx may still be a reasonable candidate gene mediating the effects of the chromosome qtl for neocortical volume. a noncortex-dependent qtl on chromosome 19 in the analysis of regressed noncortical volume, the single qtl detected with genome-wide significance was on proximal chromosome this genomic region had absolutely no effect on regressed cortical volume. thus, the data display a classical pattern of double dissociation: one factor that affects cortical volume more than noncortical volume and a second factor that shows the mirror image pattern. double dissociation is an important criterion in neuropsychology, because it provides positive logical proof of the specificity of effects. the same argument can be made in the present case as well. candidate genes for a noncortical volume modulator in an analysis similar to that performed for neocortex we carried out a snp filtered celera search of chromosome which is about mb in length, in the vicinity of d19mit using a qtl confidence interval to mb. this search produced known genes with snps differentiating the two parental strains. the filtered known genes within the chromosome confidence interval for noncortex are 5730596k20rik, d630002g slc22a chrm slc3a 4930563m09rik, gng b3gat 0710001o03rik, bc 1110006i15rik, zp mor239- a33000e03rik, mor202- keg cntf, mor202- mor202- mor202- mor266- mor2127- and mor212- examination of expression information for these known genes in the ncbi entrez gene database revealed one gene that was particularly promising as a candidate to mediate the qtl's effect on noncortical brain volume. that gene is ciliary neurotrophic factor. ctnf is a one of the gp family of cytokines and acts as a survival factor for a number of different neuronal cell types. originally discovered as a factor that supports the survival of parasympathetic nerve fibers in the ciliary ganglia, ctnf is now known to play an active role in neuronal maintenance within the central nervous system. recent reports have also shown that ctnf modulates central nervous system neurogenesis as well. thus, it is not unreasonable to conclude the genetically controlled natural variations in ctnf expression might modulate brain size in bxd recombinant inbred mice. ctnf is indeed a strong candidate gene for understanding the qtl on chromosome related to noncortical brain volume. other suggestive qtls the other suggestive qtls reported above should be noted, although the evidence for them is not exceptionally strong. these include possible cortex-dependent qtl on proximal and the noncortex dependent qtl on chromosome suggestive qtls in today's analyses can provide guidance and support for other, more sensitive, analyses in the future if they are replicated.  our localization of qtls regulating neocortical size may have broader, more cognitive implications. gibson, in a recent theoretical paper on brain size and mental capacity, concludes: perhaps "those genetic factors that control enhanced brain size, especially the size of the sensori-motor control for the oral and manual organs, the neocortical association areas, the basal ganglia, and the cerebellum would emerge as the prime genetic determinants of the mental abilities of human infants." properly designed qtl analyses using the appropriate behavioral phenotypic measures in recombinant inbred mice could help resolve this question. since there is ample conservation in the mammalian genome over species, one hopes that findings obtained using well-developed recombinant inbred strains of mice will be applicable to understanding primate and human neurogenomics in a straightforward manner as well. 
to determine the regions of the mammalian genome responsible for natural variations in cortical volume, we conducted a complex trait analysis using strains of recombinant inbred strains of mice, as well as their two parental strains. we located genomic regions in which a linkage disequilibrium was present using webqtl as both a mapping engine and genomic database. an analysis of single nucleotide polymorphisms in these regions indicated that ciliary neurotrophic factor is quite possibly the gene underlying the noncortical qtl. for neocortex, we found a genome-wide significant quantitative trait locus on chromosome, as well as a suggestive qtl on chromosome. marker regression and interval mapping were computed using webqtl. we measured both neocortical volume and total brain volume in coronally sectioned mouse brains that were nissl stained and embedded in celloidin. evidence for a candidate gene modulating neocortical volume was much weaker, but otx deserves further consideration. after correction for shrinkage, the measured cortical and noncortical brain volumes were entered into a multiple regression analysis, which removed the effects of body size and age from the measurements. this classic pattern of double dissociation argues strongly for different genetic factors regulating relative cortical size, as opposed to brain volume more generally.
 the relative growth of the neocortex parallels the emergence of complex cognitive functions across species. to determine the regions of the mammalian genome responsible for natural variations in cortical volume, we conducted a complex trait analysis using strains of recombinant inbred strains of mice, as well as their two parental strains. we measured both neocortical volume and total brain volume in coronally sectioned mouse brains that were nissl stained and embedded in celloidin. after correction for shrinkage, the measured cortical and noncortical brain volumes were entered into a multiple regression analysis, which removed the effects of body size and age from the measurements. marker regression and interval mapping were computed using webqtl.  an anova revealed that more than half of the variance of these regressed phenotypes is genetically determined. we then identified the regions of the genome regulating this heritability. we located genomic regions in which a linkage disequilibrium was present using webqtl as both a mapping engine and genomic database. for neocortex, we found a genome-wide significant quantitative trait locus on chromosome, as well as a suggestive qtl on chromosome. in contrast, for noncortex the effect of chromosome was markedly reduced, and a significant qtl appeared on chromosome.  this classic pattern of double dissociation argues strongly for different genetic factors regulating relative cortical size, as opposed to brain volume more generally. it is likely, however, that the effects of proximal chromosome extend beyond the neocortex strictly defined. an analysis of single nucleotide polymorphisms in these regions indicated that ciliary neurotrophic factor is quite possibly the gene underlying the noncortical qtl. evidence for a candidate gene modulating neocortical volume was much weaker, but otx deserves further consideration. 