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 anatomical regions, based on spatial patterns

10 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 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce

15 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project

16 will support the development of new ways to selectively target cortical areas, and it will support the development of a

17 method for identifying the cortical areal boundaries present in small tissue samples.

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

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

20 Background and significance

21 Aim 1

22 Machine learning terminology: supervised learning

23 The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the

24 expression level of those genes is known, then the locations of the regions can be inferred.

25 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we

26 are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to

27 which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned

28 to a class (namely, its region).

29 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of

30 the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels

31 within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs.

32 We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label

33 (or a class label).

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

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

36 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning

37 procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used

38 in the construction of the classifier is called training data.

39 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a

40 task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances

41 (voxels) for which the labels (regions) are known.

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

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

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

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

46 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

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

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

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

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

51 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to

52 each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or

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

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

55 method.

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

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

58 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be

59 identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene

60 included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at

61 combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary

62 Results). Therefore, each instance should contain multiple features (genes).

63 Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is

64 only allowed to look at the expression of the genes which have been selected as features. The more data that is available to

65 a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a

66 strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations

67 in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as

68 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the

69 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the

70 level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order

71 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as

72 features.

73 __________________________________

74 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

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 Principle 3: Use geometry in feature selection

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

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

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

82 Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.

83 Principle 4: Work in 2-D whenever possible

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

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

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

87 data.

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

89 Related work

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

91 which is not fundamentally spatial2.

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

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

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

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

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

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

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

99 [8 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of

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

101 GeneAtlas[3] and EMAGE [18] allow the user to construct a search query by demarcating regions and then specifing

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

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

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

105 whose expression is within four discretization levels. EMAGE uses Jaccard similarity, which is equal to the number of true

106 pixels in the intersection of the two images, divided by the number of pixels in their union. Neither GeneAtlas nor EMAGE

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

108 [10 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components:

109 ∙Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)

110 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists

111 of overexpressed genes for selected structures)

112 ∙Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene

113 expression profile of the seed voxel and every other voxel.

114 ∙Clusters: will be described later

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

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

117 search for underexpression. Third, Gene Finder uses a simple pointwise score4, whereas we will also use geometric scores

118 such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.

119 [4 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni

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

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

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

123 _________________________________________

124 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not

125 just data which has only a few different locations or which is indexed by anatomical label.

126 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.

127 4“Expression energy ratio”, which captures overexpression.

128 [7 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary

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

130 match score is Jaccard similarity.

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

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

133 scoring methods.

134 Aim 2

135 Machine learning terminology: clustering

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 are

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

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

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

144 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, if at all; perhaps

146 some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they

147 could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests

148 the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels.

149 This is called hierarchial clustering.

150 Similarity scores

151 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or

152 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and

153 scoring methods for similarity.

154 Spatially contiguous clusters; image segmentation

155 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have

156 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary

157 Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these

158 results against other methods which guarantee contiguous clusters.

159 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a

160 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into

161 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in

162 our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which

163 use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used

164 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting

165 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene

166 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of

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

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

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

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

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

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

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

174 set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features

175 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced

176 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene

177 expression levels.

178 Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the

179 reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second,

180 it is thought that some clustering algorithms may give better results on reduced data.

181 Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example,

182 one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions

183 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points

184 in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of

185 the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find

186 arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction

187 is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction

188 before clustering.

189 Clustering genes rather than voxels

190 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster

191 the features (genes). There are two ways that clusters of genes could be used.

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

193 have one reduced feature for each gene cluster.

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

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

196 interesting region will have multiple genes which each individually pick it out5. This suggests the following procedure:

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

198 In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”

199 formed by lumping together a few regions, are associated with gene clusters in this fashion.

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

201 algorithms.

202 Related work

203 We are aware of five existing efforts to cluster spatial gene expression data.

204 [15 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

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

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

207 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset6 and while the results are

208 promising (see Preliminary Data), we think that it will be possible to find an even better method.

209 AGEA[10] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation

210 as the similarity metric. EMAGE[18] allows the user to select a dataset from among a large number of alternatives, or by

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

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

213 [4 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were

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

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

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

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

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

219 clustering voxels

220 In an interesting twist, [7] applies their technique for finding combinations of marker genes for the purpose of clustering

221 genes around a “seed gene”. The way they do this is by using the pattern of expression of the seed gene as the target image,

222 and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found

223 are considered to be related to the seed. The same team also describes a method[17] for finding “association rules” such as,

224 “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene”. This could be

225 useful as part of a procedure for clustering voxels.

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

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

228 none of these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first

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

230 _________________________________________

231 5This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

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

233 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

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

235 6We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

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

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

238 Aim 3

239 Background

240 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can

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

242 downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can

243 picture an area of the cortex as a slice of many-layered cake.

244 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,

245 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,

246 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of

247 their approximate location upon the cortical surface.

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

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

250 agreed-upon map can be seen by contrasting the recent maps given by Swanson[14] on the one hand, and Paxinos and

251 Franklin[11] on the other. While the maps are certainly very similar in their general arrangement, significant differences

252 remain in the details.

253 The Allen Mouse Brain Atlas dataset

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

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

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

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

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

259 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate

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

261 voxels in the 3D coordinate system, of which 51,533 are in the brain[10].

262 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[20]. The ABA contains

263 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our

264 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and

265 also has greater registration error[10]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes

266 of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[10].

267 The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[6],

268 GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress7, EADHB8, MAMEP9, Xenbase10,

269 ZFIN[13], Aniseed11, VisiGene12, GEISHA[2], Fruitfly.org[16], COMPARE13 GXD[12], GEO[1]14. With the exception of

270 the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH

271 images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of

272 data available for public download from the website15. Many of these resources focus on developmental gene expression.

273 Significance

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

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

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

277 target individual cortical areas.

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

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

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

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

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

283 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is

284 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s

285 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of

286 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been

287 _________________________________________

288 7http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE

289 8http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html

290 9http://mamep.molgen.mpg.de/index.php

291 10http://xenbase.org/

292 11http://aniseed-ibdm.univ-mrs.fr/

293 12http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources

294 13http://compare.ibdml.univ-mrs.fr/

295 14GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.

296 15without prior offline registration

297 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking

298 at the patterns of gene expression.

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

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

301 Related work

302 [10 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations

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

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

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

306 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas16.

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

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

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

310 from gene expression data.

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

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

313 _________________________________________

314 16In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are

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

316 correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not

317 find most cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have

318 many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for

319 most cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found,

320 and it creates that ROI by (pairwise voxel correlation) clustering around the seed.

321 Preliminary work

322

323

324 Figure 1: Top row: Genes Nfic and

325 A930001M12Rik are the most correlated with

326 area SS (somatosensory cortex). Bottom row:

327 Genes C130038G02Rik and Cacna1i are those

328 with the best fit using logistic regression. Within

329 each picture, the vertical axis roughly corresponds

330 to anterior at the top and posterior at the bot-

331 tom, and the horizontal axis roughly corresponds

332 to medial at the left and lateral at the right. The

333 red outline is the boundary of region SS. Pixels are

334 colored according to correlation, with red meaning

335 high correlation and blue meaning low. Format conversion between SEV, MATLAB, NIFTI

336 We have created software to (politely) download all of the SEV files from

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

338 between the SEV, MATLAB, and NIFTI file formats, as well as some of

339 Caret’s file formats.

340 Flatmap of cortex

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

342 voxels which belong to cerebral cortex. We divided the cortex into hemi-

343 spheres.

344 Using Caret[5], we created a mesh representation of the surface of the

345 selected voxels. For each gene, for each node of the mesh, we calculated

346 an average of the gene expression of the voxels “underneath” that mesh

347 node. We then flattened the cortex, creating a two-dimensional mesh.

348 We sampled the nodes of the irregular, flat mesh in order to create

349 a regular grid of pixel values. We converted this grid into a MATLAB

350 matrix.

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

352 the ABA coronal reference atlas slides. We then converted these manual

353 traces into Caret-format regional boundary data on the mesh surface.

354 We projected the regions onto the 2-d mesh, and then onto the grid, and

355 then we converted the region data into MATLAB format.

356 At this point, the data is in the form of a number of 2-D matrices,

357 all in registration, with the matrix entries representing a grid of points

358 (pixels) over the cortical surface:

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

360 each surface pixel

361 ∙ For each gene, a 2-D matrix whose entries represent the average expres-

362 sion level underneath each surface pixel

363

364 Figure 2: Gene Pitx2

365 is selectively underex-

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

367 expression level (over all surface pixels) and dividing each gene by its standard deviation.

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

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

370 which can be displayed on the flatmapped surface.

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

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

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

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

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

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

377 validation, we have manually demarcated the depth of the outer boundary of cortical layer 5

378 throughout the cortex.

379 Feature selection and scoring methods

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

381 for example, Figure 2.

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

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

384 surface pixels.

385 One class of feature selection scoring method are those which calculate some sort of “match” between each gene image

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

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

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

389

390

391 Figure 3: The top row shows the two genes which

392 (individually) best predict area AUD, according

393 to logistic regression. The bottom row shows the

394 two genes which (individually) best match area

395 AUD, according to gradient similarity. From left

396 to right and top to bottom, the genes are Ssr1,

397 Efcbp1, Ptk7, and Aph1a. Conditional entropy An information-theoretic scoring method is

398 to find features such that, if the features (gene expression levels) are

399 known, uncertainty about the target (the regional identity) is reduced.

400 Entropy measures uncertainty, so what we want is to find features such

401 that the conditional distribution of the target has minimal entropy. The

402 distribution to which we are referring is the probability distribution over

403 the population of surface pixels.

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

405 we discretized our gene expression data by creating, for each gene, five

406 thresholded boolean masks of the gene data. For each gene, we created a

407 boolean mask of its expression levels using each of these thresholds: the

408 mean of that gene, the mean minus one standard deviation, the mean

409 minus two standard deviations, the mean plus one standard deviation,

410 the mean plus two standard deviations.

411 Now, for each region, we created and ran a forward stepwise pro-

412 cedure which attempted to find pairs of gene expression boolean masks

413 such that the conditional entropy of the target area’s boolean mask, con-

414 ditioned upon the pair of gene expression boolean masks, is minimized.

415 This finds pairs of genes which are most informative (at least at these

416 discretization thresholds) relative to the question, “Is this surface pixel

417 a member of the target area?”. Its advantage over linear methods such

418 as logistic regression is that it takes account of arbitrarily nonlinear re-

419 lationships; for example, if the XOR of two variables predicts the target,

420 conditional entropy would notice, whereas linear methods would not.

421

422

423 Figure 4: Upper left: wwc1. Upper right: mtif2.

424 Lower left: wwc1 + mtif2 (each pixel’s value on

425 the lower left is the sum of the corresponding pix-

426 els in the upper row). Gradient similarity We noticed that the previous two scoring

427 methods, which are pointwise, often found genes whose pattern of ex-

428 pression did not look similar in shape to the target region. For this

429 reason we designed a non-pointwise local scoring method to detect when

430 a gene had a pattern of expression which looked like it had a boundary

431 whose shape is similar to the shape of the target region. We call this

432 scoring method “gradient similarity”.

433 One might say that gradient similarity attempts to measure how

434 much the border of the area of gene expression and the border of the

435 target region overlap. However, since gene expression falls off continu-

436 ously rather than jumping from its maximum value to zero, the spatial

437 pattern of a gene’s expression often does not have a discrete border.

438 Therefore, instead of looking for a discrete border, we look for large

439 gradients. Gradient similarity is a symmetric function over two images

440 (i.e. two scalar fields). It is is high to the extent that matching pixels

441 which have large values and large gradients also have gradients which

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

443 ∑

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

445 2 &#x22C5; pixel_value1 + pixel_value2

446 2

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

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

449 i at the current pixel; and pixel_valuei is the value of the current pixel in image i.

450 The intuition is that we want to see if the borders of the pattern in the two images are similar; if the borders are similar,

451 then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a

452 similar direction (because the borders are similar).

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

454 Gradient similarity provides information complementary to correlation

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

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

457 _________________________________________

458 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

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

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

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

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

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

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

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

466

467

468

469

470 Figure 5: From left to right and top to bot-

471 tom, single genes which roughly identify ar-

472 eas SS (somatosensory primary + supplemen-

473 tal), SSs (supplemental somatosensory), PIR (pir-

474 iform), FRP (frontal pole), RSP (retrosplenial),

475 COApm (Cortical amygdalar, posterior part, me-

476 dial zone). Grouping some areas together, we

477 have also found genes to identify the groups

478 ACA+PL+ILA+DP+ORB+MO (anterior cingu-

479 late, prelimbic, infralimbic, dorsal peduncular, or-

480 bital, motor), posterior and lateral visual (VISpm,

481 VISpl, VISI, VISp; posteromedial, posterolateral,

482 lateral, and primary visual; the posterior and lat-

483 eral visual area is distinguished from its neigh-

484 bors, but not from the entire rest of the cortex).

485 The genes are Pitx2, Aldh1a2, Ppfibp1, Slco1a5,

486 Tshz2, Trhr, Col12a1, Ets1. Areas which can be identified by single genes Using gradient

487 similarity, we have already found single genes which roughly identify

488 some areas and groupings of areas. For each of these areas, an example

489 of a gene which roughly identifies it is shown in Figure 5. We have not

490 yet cross-verified these genes in other atlases.

491 In addition, there are a number of areas which are almost identified

492 by single genes: COAa+NLOT (anterior part of cortical amygdalar area,

493 nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral

494 anterior cingulate), VIS (visual), AUD (auditory).

495 These results validate our expectation that the ABA dataset can

496 be exploited to find marker genes for many cortical areas, while also

497 validating the relevancy of our new scoring method, gradient similarity.

498 Combinations of multiple genes are useful and necessary for

499 some areas

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

501 by any single gene, but which can be identified combinatorially. Acc-

502 cording to logistic regression, gene wwc1 is the best fit single gene for

503 predicting whether or not a pixel on the cortical surface belongs to the

504 motor area (area MO). The upper-left picture in Figure 4 shows wwc1&#8217;s

505 spatial expression pattern over the cortex. The lower-right boundary of

506 MO is represented reasonably well by this gene, however the gene over-

507 shoots the upper-left boundary. This flattened 2-D representation does

508 not show it, but the area corresponding to the overshoot is the medial

509 surface of the cortex. MO is only found on the lateral surface. Gene mtif2

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

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

512 the medial surface. By adding together the values at each pixel in these

513 two figures, we get the lower-left image. This combination captures area

514 MO much better than any single gene.

515 This shows that our proposal to develop a method to find combina-

516 tions of marker genes is both possible and necessary.

517 Feature selection integrated with prediction As noted earlier,

518 in general, any predictive method can be used for feature selection by

519 running it inside a stepwise wrapper. Also, some predictive methods

520 integrate soft constraints on number of features used. Examples of both

521 of these will be seen in the section &#8220;Multivariate Predictive methods&#8221;.

522 Multivariate Predictive methods

523 Forward stepwise logistic regression Logistic regression is a popu-

524 lar method for predictive modeling of categorial data. As a pilot run,

525 for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed

526 forward stepwise logistic regression to find single genes, pairs of genes,

527 and triplets of genes which predict areal identify. This is an example

528 of feature selection integrated with prediction using a stepwise wrapper.

529 Some of the single genes found were shown in various figures throughout

530 _________________________________________

531 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

532 they predict area AUD.

533 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,

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

535 this document, and Figure 4 shows a combination of genes which was

536 found.

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

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

539

540

541

542

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

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

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

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

547 19 of the major subdivisions of the cortex. Second from left: PCA. Third

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

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

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

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

552 In order to see how well one can do when

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

554 vector machine to classify cortical surface pix-

555 els based on their gene expression profiles. We

556 achieved classification accuracy of about 81%19.

557 This shows that the genes included in the ABA

558 dataset are sufficient to define much of cortical

559 anatomy. As noted above, however, a classifier

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

561 tically useful as a classifier that uses only a few

562 genes.

563 Data-driven redrawing of the cor-

564 tical map

565 We have applied the following dimensional-

566 ity reduction algorithms to reduce the dimen-

567 sionality of the gene expression profile associ-

568 ated with each voxel: Principal Components

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

570 Dimensional Scaling (MDS), Isomap, Land-

571 mark Isomap, Laplacian eigenmaps, Local Tan-

572 gent Space Alignment (LTSA), Hessian locally

573 linear embedding, Diffusion maps, Stochastic

574 Neighbor Embedding (SNE), Stochastic Prox-

575 imity Embedding (SPE), Fast Maximum Vari-

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

577 trix Factorization (NNMF). Space constraints

578 prevent us from showing many of the results,

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

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

581 rows of Figure 6.

582

583 Figure 7: Prototypes corresponding to sample gene clusters, clustered by

584 gradient similarity. Region boundaries for the region that most matches

585 each prototype are overlayed. After applying the dimensionality reduc-

586 tion, we ran clustering algorithms on the re-

587 duced data. To date we have tried k-means and

588 spectral clustering. The results of k-means after

589 PCA, NNMF, and landmark Isomap are shown

590 in the last row of Figure 6. To compare, the

591 leftmost picture on the bottom row of Figure

592 6 shows some of the major subdivisions of cor-

593 tex. These results clearly show that different di-

594 mensionality reduction techniques capture dif-

595 ferent aspects of the data and lead to differ-

596 ent clusterings, indicating the utility of our pro-

597 posal to produce a detailed comparion of these

598 techniques as applied to the domain of genomic

599 anatomy.

600 Many areas are captured by clusters of genes We also clustered the genes using gradient similarity to see if the

601 spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten sample gene clusters, each

602 cluster&#8217;s average expression pattern, compared to a known anatomical boundary. This suggests that it is worth attempting

603 to cluster genes, and then to use the results to cluster voxels.

604 _________________________________________

605 195-fold cross-validation.

606 Research plan

607 Further work on flatmapping

608 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),

609 or by the surface of the structure (as is the case with the cortex). In the former case, the manifold of interest is a plane, but

610 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.

611 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal

612 for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[5]) with

613 mappings which preserve angle (conformal maps).

614 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.

615 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D

616 structure seems to be wrong.

617 todo amongst other things:

618 layerfinding

619 Develop algorithms that find genetic markers for anatomical regions

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

621 geometric, and information-theoretic measures.

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

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

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

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

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

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

628 machines.

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

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

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

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

633 a larger area which can be fit.

634 # Linear discriminant analysis

635 Decision trees todo

636 For each cortical area, we used the C4.5 algorithm to find a pruned decision tree and ruleset for that area. We achieved

637 estimated classification accuracy of more than 99.6% on each cortical area (as evaluated on the training data without

638 cross-validation; so actual accuracy is expected to be lower). However, the resulting decision trees each made use of many

639 genes.

640 Apply these algorithms to the cortex

641 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert

642 between SEV, NIFTI and MATLAB formats.

643 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.

644 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.

645 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify

646 that area; and we will also present lists of &#8220;panels&#8221; of genes that can be used to delineate many areas at once.

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

648 # mixture models, etc

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

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

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

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

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

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

655 # Linear discriminant analysis

656 # jbt, coclustering

657 # self-organizing map

658 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting

659 # compare using clustering scores

660 # multivariate gradient similarity

661 # deep belief nets

662 # note: slice artifact

663 Bibliography &amp; References Cited

664 [1]Tanya Barrett, Dennis B. Troup, Stephen E. Wilhite, Pierre Ledoux, Dmitry Rudnev, Carlos Evangelista, Irene F.

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

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

667 [2]George W. Bell, Tatiana A. Yatskievych, and Parker B. Antin. GEISHA, a whole-mount in situ hybridization gene

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

669 [3]James P Carson, Tao Ju, Hui-Chen Lu, Christina Thaller, Mei Xu, Sarah L Pallas, Michael C Crair, Joe Warren, Wah

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

671 2005.

672 [4]Mark H. Chin, Alex B. Geng, Arshad H. Khan, Wei-Jun Qian, Vladislav A. Petyuk, Jyl Boline, Shawn Levy, Arthur W.

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

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

675 [5]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite for surface-

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

677 PMID: 11522765.

678 [6]Shiaoching Gong, Chen Zheng, Martin L. Doughty, Kasia Losos, Nicholas Didkovsky, Uta B. Schambra, Norma J.

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

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

681 [7]Jano Hemert and Richard Baldock. Matching Spatial Regions with Combinations of Interacting Gene Expression Pat-

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

683 2008.

684 [8]Erh-Fang Lee, Jyl Boline, and Arthur W. Toga. A High-Resolution anatomical framework of the neonatal mouse brain

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

686 [9]Susan Magdaleno, Patricia Jensen, Craig L. Brumwell, Anna Seal, Karen Lehman, Andrew Asbury, Tony Cheung,

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

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

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

690 [10]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M

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

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

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

694 [11]George Paxinos and Keith B.J. Franklin. The Mouse Brain in Stereotaxic Coordinates. Academic Press, 2 edition, July

695 2001.

696 [12]Constance M. Smith, Jacqueline H. Finger, Terry F. Hayamizu, Ingeborg J. McCright, Janan T. Eppig, James A.

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

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

699 [13]Judy Sprague, Leyla Bayraktaroglu, Dave Clements, Tom Conlin, David Fashena, Ken Frazer, Melissa Haendel, Dou-

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

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

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

703 [14]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.

704 [15]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T. Mortrud,

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

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

707 1021, December 2008.

708 [16]Pavel Tomancak, Amy Beaton, Richard Weiszmann, Elaine Kwan, ShengQiang Shu, Suzanna E Lewis, Stephen

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

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

711 PMC151190.

712 [17]Jano van Hemert and Richard Baldock. Mining Spatial Gene Expression Data for Association Rules, volume 4414/2007

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

714 [18]Shanmugasundaram Venkataraman, Peter Stevenson, Yiya Yang, Lorna Richardson, Nicholas Burton, Thomas P. Perry,

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

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

717 [19]Axel Visel, Christina Thaller, and Gregor Eichele. GenePaint.org: an atlas of gene expression patterns in the mouse

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

719 [20]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agar-

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

752

753 _______________________________________________________________________________________________________

754 stuff i dunno where to put yet (there is more scattered through grant-oldtext):

755 Principle 4: Work in 2-D whenever possible

756 &#8212;

757 note:

758 two hemis

759

760