1 Specific aims

2 Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic

3 reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared.

4 Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker

5 genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have

6 three specific aims:

7 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target

8 anatomical regions

9 (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, based on

10 spatial patterns in gene expression

11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse

12 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of

13 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).

14 Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that the methods

15 developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional

16 space.

17 In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker genes,

18 and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness of the algorithms,

19 the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic

20 markers for most cortical areas. The results of the project will support the development of new ways to selectively target

21 cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small

22 tissue samples.

23 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the

24 machine-readable datasets developed in aim (3), will be published and freely available for others to use.

25 Background and significance

26 Aim 1: Given a map of regions, find genes that mark the regions

27 Machine learning terminology The task of looking for marker genes for known anatomical regions means that one is

28 looking for a set of genes such that, if the expression level of those genes is known, then the locations of the regions can be

29 inferred.

30 If we define the regions so that they cover the entire anatomical structure to be divided, we may say that we are using

31 gene expression to determine to which region each voxel within the structure belongs. We call this a classification task,

32 because each voxel is being assigned to a class (namely, its region). An understanding of the relationship between the

33 combination of their expression levels and the locations of the regions may be expressed as a function. The input to this

34 function is a voxel, along with the gene expression levels within that voxel; the output is the regional identity of the target

35 voxel, that is, the region to which the target voxel belongs. We call this function a classifier. In general, the input to a

36 classifier is called an instance, and the output is called a label (or a class label).

37 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a

38 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be

39 analyzed in concert with an anatomical atlas in order to produce a classifier. The initial gene expression dataset used in

40 the construction of the classifier is called training data. In the machine learning literature, this sort of procedure may be

41 thought of as a supervised learning task, defined as a task in which the goal is to learn a mapping from instances to labels,

42 and the training data consists of a set of instances (voxels) for which the labels (regions) are known.

43 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection.

44 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with

45 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.

46 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then

47 chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic

48 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise

49 the score. Such procedures are called “stepwise” or “greedy”.

50 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the

51 algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature selection

52 methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to each voxel,

53 and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or average). If

54 only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only

55 information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.

56 Our strategy for Aim 1

57 Key questions when choosing a learning method are: What are the instances? What are the features? How are the features

58 chosen? Here are four principles that outline our answers to these questions.

59 Principle 1: Combinatorial gene expression

60 It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the

61 cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset.

62 However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for

63 which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure 4). Therefore, each instance

64 should contain multiple features (genes).

65 Principle 2: Only look at combinations of small numbers of genes

66 When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected

67 as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak

68 correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that

69 we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we

70 want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must

71 contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible

72 to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a

73 procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes.

74 Therefore, we must select only a few genes as features.

75 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many

76 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task

77 combines feature selection with supervised learning.

78 _________________________________________

79 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

80 Principle 3: Use geometry in feature selection

81 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of

82 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information

83 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See

84 Preliminary Studies, figure 3 for evidence of the complementary nature of pointwise and local scoring methods.

85 Principle 4: Work in 2-D whenever possible

86 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When

87 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis

88 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D

89 data. Therefore, when possible, the instances should represent pixels, not voxels.

90 Related work

91 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data

92 which are not fundamentally spatial2.

93 As noted above, there has been much work on both supervised learning and there are many available algorithms for

94 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the

95 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively

96 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,

97 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may

98 be necessary in order to achieve the best results in this application.

99 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.

100 [11 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of

101 interest, computing what proportion of this structure is covered by the gene’s spatial region.

102 GeneAtlas[5] and EMAGE [23] allow the user to construct a search query by demarcating regions and then specifing

103 either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the

104 similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses

105 the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3

106 whose expression is within four discretization levels. EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE

107 allow one to search for combinations of genes that define a region in concert but not separately.

108 [13 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The user

109 selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list of genes which are

110 overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected

111 structures). Correlation: The user selects a seed voxel and the system then shows the user how much correlation there is

112 between the gene expression profile of the seed voxel and every other voxel. Clusters: will be described later

113 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we

114 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also

115 search for underexpression. Third, Gene Finder uses a simple pointwise score5, whereas we will also use geometric scores

116 such as gradient similarity (described in Preliminary Studies). Figures 4, 2, and 3 in the Preliminary Studies section contains

117 evidence that each of our three choices is the right one.

118 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni

119 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,

120 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for

121 underexpression, and does not look for combinations of genes.

122 [9 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary

123 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their

124 match score is Jaccard similarity.

125 In summary, there has been fruitful work on finding marker genes, but only one of the previous projects explores

126 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or

127 scoring methods.

128 Aim 2: From gene expression data, discover a map of regions

129 Machine learning terminology: clustering

130 _

131 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not

132 just data which have only a few different locations or which is indexed by anatomical label.

133 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.

134 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.

135 5“Expression energy ratio”, which captures overexpression.

136 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as

137 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances

138 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called

139 clustering or cluster analysis.

140 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances

141 are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels

142 from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means

143 that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into

144 clusters of voxels with similar gene expression.

145 It is desirable to determine not just one set of regions, but also how these regions relate to each other. The outcome of

146 clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called

147 hierarchial clustering.

148 Similarity scores A crucial choice when designing a clustering method is how to measure similarity, across either pairs

149 of instances, or clusters, or both. There is much overlap between scoring methods for feature selection (discussed above

150 under Aim 1) and scoring methods for similarity.

151 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering task. In fact,

152 it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a

153 cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing

154 this constraint; however, we plan to compare these results against other methods which guarantee contiguous clusters.

155 Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim

156 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels

157 (one for each gene), rather than just three6. A more crucial difference is that there are various cues which are appropriate

158 for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data

159 such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other

160 sorts of spatially arranged data, some of these algorithms are specialized for visual images.

161 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature

162 vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.

163 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the

164 instances. However, some clustering algorithms perform better on small numbers of features7. There are techniques which

165 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature

166 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature

167 set. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set

168 may be any function of the set of gene expression levels.

169 Clustering genes rather than voxels Although the ultimate goal is to cluster the instances (voxels or pixels), one

170 strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes could be used.

171 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could

172 have one reduced feature for each gene cluster.

173 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression

174 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically

175 interesting region will have multiple genes which each individually pick it out8. This suggests the following procedure:

176 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.

177 In Preliminary Studies, Figure 7, we show that a number of anatomically recognized cortical regions, as well as some

178 “superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion.

179 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering

180 algorithms.

181 ________________________________

182 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often

183 used to process satellite imagery.

184 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering algorithms

185 may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.

186 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

187 possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;

188 perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although

189 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.

190 Related work

191 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example, [15], [2], [16],

192 and [1 ] associate spots on the cortex with the radial profile9 of response to some stain ([10] uses MRI), extract features from

193 this profile, and then use similarity between surface pixels to cluster. Features used include statistical moments, wavelets,

194 and the excess mass functional. Some of these features are motivated by the presence of tangential lines of stain intensity

195 which correspond to laminar structure. Some methods use standard clustering procedures, whereas others make use of the

196 spatial nature of the data to look for sudden transitions, which are identified as areal borders.

197 [20 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

198 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive

199 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving

200 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset10 and while the results are

201 promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application

202 (see Preliminary Studies, Figure 6).

203 AGEA[13] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation

204 as the similarity metric. EMAGE[23] allows the user to select a dataset from among a large number of alternatives, or by

205 running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage

206 clustering with un-centred correlation as the similarity score.

207 [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were

208 highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and

209 ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between

210 the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing

211 similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial

212 expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without

213 clustering voxels.

214 [9 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes around a “seed

215 gene”. They do this by using the pattern of expression of the seed gene as the target image, and then searching for other

216 genes which can be combined to reproduce this pattern. Other genes which are found are considered to be related to the

217 seed. The same team also describes a method[22] for finding “association rules” such as, “if this voxel is expressed in by

218 any gene, then that voxel is probably also expressed in by the same gene”. This could be useful as part of a procedure for

219 clustering voxels.

220 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-

221 rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. The

222 projects using gene expression on cortex did not attempt to make use of the radial profile of gene expression. Also, none of

223 these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first in order

224 to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.

225 Aim 3: apply the methods developed to the cerebral cortex

226 Background

227 The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex

228 into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the

229 areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the

230 surface. One can picture an area of the cortex as a slice of a six-layered cake11.

231 It is known that different cortical areas have distinct roles in both normal functioning and in disease processes, yet there

232 are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is

233 a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their

234 approximate location upon the cortical surface.

235 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not

236 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single

237 agreed-upon map can be seen by contrasting the recent maps given by Swanson[19] on the one hand, and Paxinos and

238 Franklin[14] on the other. While the maps are certainly very similar in their general arrangement, significant differences

239 remain.

240 The Allen Mouse Brain Atlas dataset

241 __

242 9A radial profile is a profile along a line perpendicular to the cortical surface.

243 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

244 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was

245 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.

246 11Outside of isocortex, the number of layers varies.

247 The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old

248 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed

249 to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution

250 is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse

251 brains were needed in order to measure the expression of many genes.

252 An automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate

253 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326

254 voxels in the 3D coordinate system, of which 51,533 are in the brain[13].

255 Mus musculus is thought to contain about 22,000 protein-coding genes[25]. The ABA contains data on about 20,000

256 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from

257 only the coronal subset of the ABA12.

258 The ABA is not the only large public spatial gene expression dataset13. With the exception of the ABA, GenePaint, and

259 EMAGE, most of the other resources have not (yet) extracted the expression intensity from the ISH images and registered

260 the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public

261 download from the website14. Many of these resources focus on developmental gene expression.

262 Significance

263 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the

264 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for

265 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively

266 target individual cortical areas.

267 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom-

268 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can

269 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that

270 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.

271 The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation of a

272 better map. The development of present-day cortical maps was driven by the application of histological stains. If a different

273 set of stains had been available which identified a different set of features, then today’s cortical maps may have come out

274 differently. It is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been

275 captured by any stain. Therefore, cortical anatomy needs to incorporate what we can learn from looking at the patterns of

276 gene expression.

277 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to

278 develop could be used to suggest modifications to the human cortical map as well.

279 Related work

280 [13 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations

281 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either

282 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of

283 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes

284 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas15.

285 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has

286 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally

287 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo

288 from gene expression data.

289 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker

290 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.

291 _________________________________________

292 12The sagittal data do not cover the entire cortex, and also have greater registration error[13]. Genes were selected by the Allen Institute for

293 coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression

294 pattern”[13].

295 13Other such resources include GENSAT[8], GenePaint[24], its sister project GeneAtlas[5], BGEM[12], EMAGE[23], EurExpress (http://www.

296 eurexpress.org/ee/; EurExpress data are also entered into EMAGE), EADHB (http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.

297 html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[18], Aniseed (http://aniseed-ibdm.

298 univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some of the other listed data sources), GEISHA[4],

299 Fruitfly.org[21], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[17], GEO[3] (GXD and GEO contain spatial data but also non-spatial

300 data. All GXD spatial data are also in EMAGE.)

301 14without prior offline registration

302 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger

303 than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation

304 clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters which presumably correspond to the

305 intersection of a layer and an area, but since one area will have many layer-area intersection clusters, further work is needed to make sense of

306 these). The reason that Gene Finder cannot the find marker genes for cortical areas is that, although the user chooses a seed voxel, Gene Finder

307 chooses the ROI for which genes will be found, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.

308 Preliminary Studies

309

310

311 Figure 1: Top row: Genes Nfic and

312 A930001M12Rik are the most correlated

313 with area SS (somatosensory cortex). Bot-

314 tom row: Genes C130038G02Rik and

315 Cacna1i are those with the best fit using

316 logistic regression. Within each picture, the

317 vertical axis roughly corresponds to anterior

318 at the top and posterior at the bottom, and

319 the horizontal axis roughly corresponds to

320 medial at the left and lateral at the right.

321 The red outline is the boundary of region

322 SS. Pixels are colored according to correla-

323 tion, with red meaning high correlation and

324 blue meaning low. Format conversion between SEV, MATLAB, NIFTI

325 We have created software to (politely) download all of the SEV files16 from

326 the Allen Institute website. We have also created software to convert between

327 the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file

328 formats.

329 Flatmap of cortex

330 We downloaded the ABA data and applied a mask to select only those voxels

331 which belong to cerebral cortex. We divided the cortex into hemispheres.

332 Using Caret[7], we created a mesh representation of the surface of the se-

333 lected voxels. For each gene, for each node of the mesh, we calculated an

334 average of the gene expression of the voxels “underneath” that mesh node. We

335 then flattened the cortex, creating a two-dimensional mesh.

336 We sampled the nodes of the irregular, flat mesh in order to create a regular

337 grid of pixel values. We converted this grid into a MATLAB matrix.

338 We manually traced the boundaries of each of 49 cortical areas from the

339 ABA coronal reference atlas slides. We then converted these manual traces

340 into Caret-format regional boundary data on the mesh surface. We projected

341 the regions onto the 2-d mesh, and then onto the grid, and then we converted

342 the region data into MATLAB format.

343 At this point, the data are in the form of a number of 2-D matrices, all in

344 registration, with the matrix entries representing a grid of points (pixels) over

345 the cortical surface:

346 ∙ A 2-D matrix whose entries represent the regional label associated with each

347 surface pixel

348 ∙ For each gene, a 2-D matrix whose entries represent the average expression

349 level underneath each surface pixel

350

351 Figure 2: Gene Pitx2

352 is selectively underex-

353 pressed in area SS. We created a normalized version of the gene expression data by subtracting each gene’s mean

354 expression level (over all surface pixels) and dividing the expression level of each gene by its

355 standard deviation.

356 The features and the target area are both functions on the surface pixels. They can be referred

357 to as scalar fields over the space of surface pixels; alternately, they can be thought of as images

358 which can be displayed on the flatmapped surface.

359 To move beyond a single average expression level for each surface pixel, we plan to create a

360 separate matrix for each cortical layer to represent the average expression level within that layer.

361 Cortical layers are found at different depths in different parts of the cortex. In preparation for

362 extracting the layer-specific datasets, we have extended Caret with routines that allow the depth

363 of the ROI for volume-to-surface projection to vary.

364 In the Research Plan, we describe how we will automatically locate the layer depths. For

365 validation, we have manually demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.

366 Feature selection and scoring methods

367 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See,

368 for example, Figure 2.

369 Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance

370 as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the

371 surface pixels.

372 One class of feature selection scoring methods contains methods which calculate some sort of “match” between each gene

373 image and the target image. Those genes which match the best are good candidates for features.

374 _________________________________________

375 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

376 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between

377 each gene and each cortical area. The top row of Figure 1 shows the three genes most correlated with area SS.

378

379

380 Figure 3: The top row shows the two genes

381 which (individually) best predict area AUD,

382 according to logistic regression. The bot-

383 tom row shows the two genes which (indi-

384 vidually) best match area AUD, according

385 to gradient similarity. From left to right and

386 top to bottom, the genes are Ssr1, Efcbp1,

387 Ptk7, and Aph1a. Conditional entropy An information-theoretic scoring method is to find

388 features such that, if the features (gene expression levels) are known, uncer-

389 tainty about the target (the regional identity) is reduced. Entropy measures

390 uncertainty, so what we want is to find features such that the conditional dis-

391 tribution of the target has minimal entropy. The distribution to which we are

392 referring is the probability distribution over the population of surface pixels.

393 The simplest way to use information theory is on discrete data, so we

394 discretized our gene expression data by creating, for each gene, five thresholded

395 boolean masks of the gene data. For each gene, we created a boolean mask of

396 its expression levels using each of these thresholds: the mean of that gene, the

397 mean minus one standard deviation, the mean minus two standard deviations,

398 the mean plus one standard deviation, the mean plus two standard deviations.

399 Now, for each region, we created and ran a forward stepwise procedure

400 which attempted to find pairs of gene expression boolean masks such that the

401 conditional entropy of the target area’s boolean mask, conditioned upon the

402 pair of gene expression boolean masks, is minimized.

403 This finds pairs of genes which are most informative (at least at these dis-

404 cretization thresholds) relative to the question, “Is this surface pixel a member

405 of the target area?”. Its advantage over linear methods such as logistic regres-

406 sion is that it takes account of arbitrarily nonlinear relationships; for example,

407 if the XOR of two variables predicts the target, conditional entropy would

408 notice, whereas linear methods would not.

409 Gradient similarity We noticed that the previous two scoring methods,

410 which are pointwise, often found genes whose pattern of expression did not look similar in shape to the target region. For

411 this reason we designed a non-pointwise local scoring method to detect when a gene had a pattern of expression which

412 looked like it had a boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient

413 similarity”.

414

415

416 Figure 4: Upper left: wwc1. Upper right:

417 mtif2. Lower left: wwc1 + mtif2 (each

418 pixel’s value on the lower left is the sum of

419 the corresponding pixels in the upper row). One might say that gradient similarity attempts to measure how much the

420 border of the area of gene expression and the border of the target region over-

421 lap. However, since gene expression falls off continuously rather than jumping

422 from its maximum value to zero, the spatial pattern of a gene’s expression often

423 does not have a discrete border. Therefore, instead of looking for a discrete

424 border, we look for large gradients. Gradient similarity is a symmetric function

425 over two images (i.e. two scalar fields). It is is high to the extent that matching

426 pixels which have large values and large gradients also have gradients which

427 are oriented in a similar direction. The formula is:

428 ∑

429 pixel<img src="cmsy7-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|

430 2 &#x22C5; pixel_value1 + pixel_value2

431 2

432 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current

433 pixel; &#x2220;&#x2207;i is the angle of the gradient of image i at the current pixel; |&#x2207;i| is

434 the magnitude of the gradient of image i at the current pixel; and pixel_valuei

435 is the value of the current pixel in image i.

436 The intuition is that we want to see if the borders of the pattern in the

437 two images are similar; if the borders are similar, then both images will have

438 corresponding pixels with large gradients (because this is a border) which are

439 oriented in a similar direction (because the borders are similar).

440 Most of the genes in Figure 5 were identified via gradient similarity.

441 Gradient similarity provides information complementary to correlation

442 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider

443 Fig. 3. The top row of Fig. 3 displays the 3 genes which most match area AUD, according to a pointwise method17. The

444 _________________________________________

445 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor

446 variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well

447 they predict area AUD.

448 bottom row displays the 3 genes which most match AUD according to a method which considers local geometry18 The

449 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is

450 that this includes many areas which don&#8217;t have a salient border matching the areal border. The geometric method identifies

451 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes

452 genes which don&#8217;t express over the entire area. Genes which have high rankings using both pointwise and border criteria,

453 such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker

454 for AUD; we deliberately chose a &#8220;difficult&#8221; area in order to better contrast pointwise with geometric methods.

455

456

457

458

459 Figure 5: From left to right and top

460 to bottom, single genes which roughly

461 identify areas SS (somatosensory primary

462 + supplemental), SSs (supplemental so-

463 matosensory), PIR (piriform), FRP (frontal

464 pole), RSP (retrosplenial), COApm (Corti-

465 cal amygdalar, posterior part, medial zone).

466 Grouping some areas together, we have

467 also found genes to identify the groups

468 ACA+PL+ILA+DP+ORB+MO (anterior

469 cingulate, prelimbic, infralimbic, dorsal pe-

470 duncular, orbital, motor), posterior and lat-

471 eral visual (VISpm, VISpl, VISI, VISp; pos-

472 teromedial, posterolateral, lateral, and pri-

473 mary visual; the posterior and lateral vi-

474 sual area is distinguished from its neigh-

475 bors, but not from the entire rest of the

476 cortex). The genes are Pitx2, Aldh1a2,

477 Ppfibp1, Slco1a5, Tshz2, Trhr, Col12a1,

478 Ets1. Areas which can be identified by single genes Using gradient simi-

479 larity, we have already found single genes which roughly identify some areas

480 and groupings of areas. For each of these areas, an example of a gene which

481 roughly identifies it is shown in Figure 5. We have not yet cross-verified these

482 genes in other atlases.

483 In addition, there are a number of areas which are almost identified by single

484 genes: COAa+NLOT (anterior part of cortical amygdalar area, nucleus of the

485 lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate),

486 VIS (visual), AUD (auditory).

487 These results validate our expectation that the ABA dataset can be ex-

488 ploited to find marker genes for many cortical areas, while also validating the

489 relevancy of our new scoring method, gradient similarity.

490 Combinations of multiple genes are useful and necessary for some

491 areas

492 In Figure 4, we give an example of a cortical area which is not marked by

493 any single gene, but which can be identified combinatorially. Acccording to

494 logistic regression, gene wwc1 is the best fit single gene for predicting whether

495 or not a pixel on the cortical surface belongs to the motor area (area MO).

496 The upper-left picture in Figure 4 shows wwc1&#8217;s spatial expression pattern over

497 the cortex. The lower-right boundary of MO is represented reasonably well by

498 this gene, but the gene overshoots the upper-left boundary. This flattened 2-D

499 representation does not show it, but the area corresponding to the overshoot is

500 the medial surface of the cortex. MO is only found on the dorsal surface. Gene

501 mtif2 is shown in the upper-right. Mtif2 captures MO&#8217;s upper-left boundary,

502 but not its lower-right boundary. Mtif2 does not express very much on the

503 medial surface. By adding together the values at each pixel in these two figures,

504 we get the lower-left image. This combination captures area MO much better

505 than any single gene.

506 This shows that our proposal to develop a method to find combinations of

507 marker genes is both possible and necessary.

508 Feature selection integrated with prediction As noted earlier, in gen-

509 eral, any predictive method can be used for feature selection by running it

510 inside a stepwise wrapper. Also, some predictive methods integrate soft con-

511 straints on number of features used. Examples of both of these will be seen in

512 the section &#8220;Multivariate Predictive methods&#8221;.

513 Multivariate Predictive methods

514 Forward stepwise logistic regression Logistic regression is a popular

515 method for predictive modeling of categorial data. As a pilot run, for five

516 cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise

517 logistic regression to find single genes, pairs of genes, and triplets of genes

518 which predict areal identify. This is an example of feature selection integrated

519 with prediction using a stepwise wrapper. Some of the single genes found

520 were shown in various figures throughout this document, and Figure 4 shows

521 a combination of genes which was found.

522 We felt that, for single genes, gradient similarity did a better job than

523 logistic regression at capturing our subjective impression of a &#8220;good gene&#8221;.

524 _________________________________________

525 18For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD,

526 was calculated, and this was used to rank the genes.

527

528

529

530

531

532 Figure 6: First row: the first 6 reduced dimensions, using PCA. Second

533 row: the first 6 reduced dimensions, using NNMF. Third row: the first

534 six reduced dimensions, using landmark Isomap. Bottom row: examples

535 of kmeans clustering applied to reduced datasets to find 7 clusters. Left:

536 19 of the major subdivisions of the cortex. Second from left: PCA. Third

537 from left: NNMF. Right: Landmark Isomap. Additional details: In the

538 third and fourth rows, 7 dimensions were found, but only 6 displayed. In

539 the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions

540 were used; for landmark Isomap, 7 dimensions were used. SVM on all genes at once

541 In order to see how well one can do when

542 looking at all genes at once, we ran a support

543 vector machine to classify cortical surface pix-

544 els based on their gene expression profiles. We

545 achieved classification accuracy of about 81%19.

546 This shows that the genes included in the ABA

547 dataset are sufficient to define much of cortical

548 anatomy. However, as noted above, a classifier

549 that looks at all the genes at once isn&#8217;t as prac-

550 tically useful as a classifier that uses only a few

551 genes.

552 Data-driven redrawing of the cor-

553 tical map

554 We have applied the following dimensional-

555 ity reduction algorithms to reduce the dimen-

556 sionality of the gene expression profile associ-

557 ated with each voxel: Principal Components

558 Analysis (PCA), Simple PCA (SPCA), Multi-

559 Dimensional Scaling (MDS), Isomap, Land-

560 mark Isomap, Laplacian eigenmaps, Local Tan-

561 gent Space Alignment (LTSA), Hessian locally

562 linear embedding, Diffusion maps, Stochastic

563 Neighbor Embedding (SNE), Stochastic Prox-

564 imity Embedding (SPE), Fast Maximum Vari-

565 ance Unfolding (FastMVU), Non-negative Ma-

566 trix Factorization (NNMF). Space constraints

567 prevent us from showing many of the results,

568 but as a sample, PCA, NNMF, and landmark

569 Isomap are shown in the first, second, and third

570 rows of Figure 6.

571

572 Figure 7: Prototypes corresponding to sample gene clusters,

573 clustered by gradient similarity. Region boundaries for the

574 region that most matches each prototype are overlayed. After applying the dimensionality reduction, we ran clus-

575 tering algorithms on the reduced data. To date we have tried

576 k-means and spectral clustering. The results of k-means af-

577 ter PCA, NNMF, and landmark Isomap are shown in the

578 last row of Figure 6. To compare, the leftmost picture on

579 the bottom row of Figure 6 shows some of the major sub-

580 divisions of cortex. These results clearly show that differ-

581 ent dimensionality reduction techniques capture different as-

582 pects of the data and lead to different clusterings, indicating

583 the utility of our proposal to produce a detailed comparion

584 of these techniques as applied to the domain of genomic

585 anatomy.

586 Many areas are captured by clusters of genes We

587 also clustered the genes using gradient similarity to see if

588 the spatial regions defined by any clusters matched known

589 anatomical regions. Figure 7 shows, for ten sample gene clusters, each cluster&#8217;s average expression pattern, compared to

590 a known anatomical boundary. This suggests that it is worth attempting to cluster genes, and then to use the results to

591 cluster voxels.

592 _____________________________

593 195-fold cross-validation.

594 Research Design and Methods

595 Flatmapping and segmentation of cortical layers**

596 There are multiple ways to flatten 3-D data into 2-D. We will compare mappings from manifolds to planes which attempt

597 to preserve size (such as the one used by Caret[7]) with mappings which preserve angle (conformal maps). Our method will

598 include a statistical test that warns the user if the assumption of 2-D structure seems to be wrong.

599 We have not yet made use of radial profiles. While the radial profiles may be used &#8220;raw&#8221;, for laminar structures like the

600 cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would then be associated

601 with one expression level per gene per layer. We will develop a segmentation algorithm to automatically identify the layer

602 boundaries.

603 Develop algorithms that find genetic markers for anatomical regions

604 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise,

605 geometric, and information-theoretic measures.

606 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining

607 the scoring measures developed, we will rank the genes by their ability to delineate each area.

608 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any

609 single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily

610 combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised

611 learning techniques which use soft constraints to minimize the number of features, such as sparse support vector

612 machines.

613 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult

614 to identify because the boundaries are misdrawn, or because it does not &#8220;really&#8221; exist as a single area, at least on the

615 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its

616 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create

617 a larger area which can be fit.

618 # Linear discriminant analysis

619 Decision trees todo

620 20.

621 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting, two hemis

622 # mixture models, etc

623 Develop algorithms to suggest a division of a structure into anatomical parts

624 1.Explore dimensionality reduction algorithms applied to pixels: including TODO

625 2.Explore dimensionality reduction algorithms applied to genes: including TODO

626 3.Explore clustering algorithms applied to pixels: including TODO

627 4.Explore clustering algorithms applied to genes: including gene shaving, TODO

628 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps

629 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex

630 # Linear discriminant analysis

631 # jbt, coclustering

632 # self-organizing map

633 # compare using clustering scores

634 # multivariate gradient similarity

635 # deep belief nets

636 Apply these algorithms to the cortex Using the methods developed in Aim 1, we will present, for each cortical area,

637 a short list of markers to identify that area; and we will also present lists of &#8220;panels&#8221; of genes that can be used to delineate

638 _________________________________________

639 20Already, for each cortical area, we have used the C4.5 algorithm to find a decision tree for that area. We achieved good classification accuracy

640 on our training set, but the number of genes that appeared in each tree was too large. We plan to implement a pruning procedure to generate

641 trees that use fewer genes

642 many areas at once. Using the methods developed in Aim 2, we will present one or more hierarchial cortical maps. We will

643 identifyand explain how the statistical structure in the gene expression data led to any unexpected or interesting features

644 of thesemaps.

645 Bibliography &amp; References Cited

646 [1]Chris Adamson, Leigh Johnston, Terrie Inder, Sandra Rees, Iven Mareels, and Gary Egan. A Tracking Approach to

647 Parcellation of the Cerebral Cortex, volume Volume 3749/2005 of Lecture Notes in Computer Science, pages 294&#8211;301.

648 Springer Berlin / Heidelberg, 2005.

649 [2]J. Annese, A. Pitiot, I. D. Dinov, and A. W. Toga. A myelo-architectonic method for the structural classification of

650 cortical areas. NeuroImage, 21(1):15&#8211;26, 2004.

651 [3]Tanya Barrett, Dennis B. Troup, Stephen E. Wilhite, Pierre Ledoux, Dmitry Rudnev, Carlos Evangelista, Irene F.

652 Kim, Alexandra Soboleva, Maxim Tomashevsky, and Ron Edgar. NCBI GEO: mining tens of millions of expression

653 profiles&#8211;database and tools update. Nucl. Acids Res., 35(suppl_1):D760&#8211;765, 2007.

654 [4]George W. Bell, Tatiana A. Yatskievych, and Parker B. Antin. GEISHA, a whole-mount in situ hybridization gene

655 expression screen in chicken embryos. Developmental Dynamics, 229(3):677&#8211;687, 2004.

656 [5]James P Carson, Tao Ju, Hui-Chen Lu, Christina Thaller, Mei Xu, Sarah L Pallas, Michael C Crair, Joe Warren, Wah

657 Chiu, and Gregor Eichele. A digital atlas to characterize the mouse brain transcriptome. PLoS Comput Biol, 1(4):e41,

658 2005.

659 [6]Mark H. Chin, Alex B. Geng, Arshad H. Khan, Wei-Jun Qian, Vladislav A. Petyuk, Jyl Boline, Shawn Levy, Arthur W.

660 Toga, Richard D. Smith, Richard M. Leahy, and Desmond J. Smith. A genome-scale map of expression for a mouse

661 brain section obtained using voxelation. Physiol. Genomics, 30(3):313&#8211;321, August 2007.

662 [7]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite for surface-

663 based analyses of cerebral cortex. Journal of the American Medical Informatics Association: JAMIA, 8(5):443&#8211;59, 2001.

664 PMID: 11522765.

665 [8]Shiaoching Gong, Chen Zheng, Martin L. Doughty, Kasia Losos, Nicholas Didkovsky, Uta B. Schambra, Norma J.

666 Nowak, Alexandra Joyner, Gabrielle Leblanc, Mary E. Hatten, and Nathaniel Heintz. A gene expression atlas of the

667 central nervous system based on bacterial artificial chromosomes. Nature, 425(6961):917&#8211;925, October 2003.

668 [9]Jano Hemert and Richard Baldock. Matching Spatial Regions with Combinations of Interacting Gene Expression Pat-

669 terns, volume 13 of Communications in Computer and Information Science, pages 347&#8211;361. Springer Berlin Heidelberg,

670 2008.

671 [10]F. Kruggel, M. K. Brckner, Th. Arendt, C. J. Wiggins, and D. Y. von Cramon. Analyzing the neocortical fine-structure.

672 Medical Image Analysis, 7(3):251&#8211;264, September 2003.

673 [11]Erh-Fang Lee, Jyl Boline, and Arthur W. Toga. A High-Resolution anatomical framework of the neonatal mouse brain

674 for managing gene expression data. Frontiers in Neuroinformatics, 1:6, 2007. PMC2525996.

675 [12]Susan Magdaleno, Patricia Jensen, Craig L. Brumwell, Anna Seal, Karen Lehman, Andrew Asbury, Tony Cheung,

676 Tommie Cornelius, Diana M. Batten, Christopher Eden, Shannon M. Norland, Dennis S. Rice, Nilesh Dosooye, Sundeep

677 Shakya, Perdeep Mehta, and Tom Curran. BGEM: an in situ hybridization database of gene expression in the embryonic

678 and adult mouse nervous system. PLoS Biology, 4(4):e86 EP &#8211;, April 2006.

679 [13]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M

680 Sunkin, Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann, David J Anderson,

681 Ed S Lein, Allan R Jones, and Michael Hawrylycz. An anatomic gene expression atlas of the adult mouse brain. Nat

682 Neurosci, 12(3):356&#8211;362, March 2009.

683 [14]George Paxinos and Keith B.J. Franklin. The Mouse Brain in Stereotaxic Coordinates. Academic Press, 2 edition, July

684 2001.

685 [15]A. Schleicher, N. Palomero-Gallagher, P. Morosan, S. Eickhoff, T. Kowalski, K. Vos, K. Amunts, and K. Zilles. Quanti-

686 tative architectural analysis: a new approach to cortical mapping. Anatomy and Embryology, 210(5):373&#8211;386, December

687 2005.

688 [16]Oliver Schmitt, Lars Hmke, and Lutz Dmbgen. Detection of cortical transition regions utilizing statistical analyses of

689 excess masses. NeuroImage, 19(1):42&#8211;63, May 2003.

690 [17]Constance M. Smith, Jacqueline H. Finger, Terry F. Hayamizu, Ingeborg J. McCright, Janan T. Eppig, James A.

691 Kadin, Joel E. Richardson, and Martin Ringwald. The mouse gene expression database (GXD): 2007 update. Nucl.

692 Acids Res., 35(suppl_1):D618&#8211;623, 2007.

693 [18]Judy Sprague, Leyla Bayraktaroglu, Dave Clements, Tom Conlin, David Fashena, Ken Frazer, Melissa Haendel, Dou-

694 glas G Howe, Prita Mani, Sridhar Ramachandran, Kevin Schaper, Erik Segerdell, Peiran Song, Brock Sprunger, Sierra

695 Taylor, Ceri E Van Slyke, and Monte Westerfield. The zebrafish information network: the zebrafish model organism

696 database. Nucleic Acids Research, 34(Database issue):D581&#8211;5, 2006. PMID: 16381936.

697 [19]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.

698 [20]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T. Mortrud,

699 Allison Cusick, Zackery L. Riley, Susan M. Sunkin, Amy Bernard, Ralph B. Puchalski, Fred H. Gage, Allan R. Jones,

700 Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the hippocampus. Neuron, 60(6):1010&#8211;

701 1021, December 2008.

702 [21]Pavel Tomancak, Amy Beaton, Richard Weiszmann, Elaine Kwan, ShengQiang Shu, Suzanna E Lewis, Stephen

703 Richards, Michael Ashburner, Volker Hartenstein, Susan E Celniker, and Gerald M Rubin. Systematic determina-

704 tion of patterns of gene expression during drosophila embryogenesis. Genome Biology, 3(12):research008818814, 2002.

705 PMC151190.

706 [22]Jano van Hemert and Richard Baldock. Mining Spatial Gene Expression Data for Association Rules, volume 4414/2007

707 of Lecture Notes in Computer Science, pages 66&#8211;76. Springer Berlin / Heidelberg, 2007.

708 [23]Shanmugasundaram Venkataraman, Peter Stevenson, Yiya Yang, Lorna Richardson, Nicholas Burton, Thomas P. Perry,

709 Paul Smith, Richard A. Baldock, Duncan R. Davidson, and Jeffrey H. Christiansen. EMAGE edinburgh mouse atlas

710 of gene expression: 2008 update. Nucl. Acids Res., 36(suppl_1):D860&#8211;865, 2008.

711 [24]Axel Visel, Christina Thaller, and Gregor Eichele. GenePaint.org: an atlas of gene expression patterns in the mouse

712 embryo. Nucl. Acids Res., 32(suppl_1):D552&#8211;556, 2004.

713 [25]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agar-

714 wala, Rachel Ainscough, Marina Alexandersson, Peter An, Stylianos E Antonarakis, John Attwood, Robert Baertsch,

715 Jonathon Bailey, Karen Barlow, Stephan Beck, Eric Berry, Bruce Birren, Toby Bloom, Peer Bork, Marc Botcherby,

716 Nicolas Bray, Michael R Brent, Daniel G Brown, Stephen D Brown, Carol Bult, John Burton, Jonathan Butler,

717 Robert D Campbell, Piero Carninci, Simon Cawley, Francesca Chiaromonte, Asif T Chinwalla, Deanna M Church,

718 Michele Clamp, Christopher Clee, Francis S Collins, Lisa L Cook, Richard R Copley, Alan Coulson, Olivier Couronne,

719 James Cuff, Val Curwen, Tim Cutts, Mark Daly, Robert David, Joy Davies, Kimberly D Delehaunty, Justin Deri,

720 Emmanouil T Dermitzakis, Colin Dewey, Nicholas J Dickens, Mark Diekhans, Sheila Dodge, Inna Dubchak, Diane M

721 Dunn, Sean R Eddy, Laura Elnitski, Richard D Emes, Pallavi Eswara, Eduardo Eyras, Adam Felsenfeld, Ginger A

722 Fewell, Paul Flicek, Karen Foley, Wayne N Frankel, Lucinda A Fulton, Robert S Fulton, Terrence S Furey, Diane Gage,

723 Richard A Gibbs, Gustavo Glusman, Sante Gnerre, Nick Goldman, Leo Goodstadt, Darren Grafham, Tina A Graves,

724 Eric D Green, Simon Gregory, Roderic Guig, Mark Guyer, Ross C Hardison, David Haussler, Yoshihide Hayashizaki,

725 LaDeana W Hillier, Angela Hinrichs, Wratko Hlavina, Timothy Holzer, Fan Hsu, Axin Hua, Tim Hubbard, Adrienne

726 Hunt, Ian Jackson, David B Jaffe, L Steven Johnson, Matthew Jones, Thomas A Jones, Ann Joy, Michael Kamal,

727 Elinor K Karlsson, Donna Karolchik, Arkadiusz Kasprzyk, Jun Kawai, Evan Keibler, Cristyn Kells, W James Kent,

728 Andrew Kirby, Diana L Kolbe, Ian Korf, Raju S Kucherlapati, Edward J Kulbokas, David Kulp, Tom Landers, J P

729 Leger, Steven Leonard, Ivica Letunic, Rosie Levine, Jia Li, Ming Li, Christine Lloyd, Susan Lucas, Bin Ma, Donna R

730 Maglott, Elaine R Mardis, Lucy Matthews, Evan Mauceli, John H Mayer, Megan McCarthy, W Richard McCombie,

731 Stuart McLaren, Kirsten McLay, John D McPherson, Jim Meldrim, Beverley Meredith, Jill P Mesirov, Webb Miller,

732 Tracie L Miner, Emmanuel Mongin, Kate T Montgomery, Michael Morgan, Richard Mott, James C Mullikin, Donna M

733 Muzny, William E Nash, Joanne O Nelson, Michael N Nhan, Robert Nicol, Zemin Ning, Chad Nusbaum, Michael J

734 O&#8217;Connor, Yasushi Okazaki, Karen Oliver, Emma Overton-Larty, Lior Pachter, Gens Parra, Kymberlie H Pepin, Jane

735 Peterson, Pavel Pevzner, Robert Plumb, Craig S Pohl, Alex Poliakov, Tracy C Ponce, Chris P Ponting, Simon Potter,

736 Michael Quail, Alexandre Reymond, Bruce A Roe, Krishna M Roskin, Edward M Rubin, Alistair G Rust, Ralph San-

737 tos, Victor Sapojnikov, Brian Schultz, Jrg Schultz, Matthias S Schwartz, Scott Schwartz, Carol Scott, Steven Seaman,

738 Steve Searle, Ted Sharpe, Andrew Sheridan, Ratna Shownkeen, Sarah Sims, Jonathan B Singer, Guy Slater, Arian

739 Smit, Douglas R Smith, Brian Spencer, Arne Stabenau, Nicole Stange-Thomann, Charles Sugnet, Mikita Suyama,

740 Glenn Tesler, Johanna Thompson, David Torrents, Evanne Trevaskis, John Tromp, Catherine Ucla, Abel Ureta-Vidal,

741 Jade P Vinson, Andrew C Von Niederhausern, Claire M Wade, Melanie Wall, Ryan J Weber, Robert B Weiss, Michael C

742 Wendl, Anthony P West, Kris Wetterstrand, Raymond Wheeler, Simon Whelan, Jamey Wierzbowski, David Willey,

743 Sophie Williams, Richard K Wilson, Eitan Winter, Kim C Worley, Dudley Wyman, Shan Yang, Shiaw-Pyng Yang,

744 Evgeny M Zdobnov, Michael C Zody, and Eric S Lander. Initial sequencing and comparative analysis of the mouse

745 genome. Nature, 420(6915):520&#8211;62, December 2002. PMID: 12466850.

746

747