1 Specific aims

2 Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expres-

3 sion levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial

4 variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw

5 new anatomical maps based on gene expression patterns. We have three specific aims:

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

7 anatomical regions

8 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical subregions, based on spatial

9 patterns in gene expression

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

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

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

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

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

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

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

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

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

19 Background and significance

20 Aim 1

21 Machine learning terminology: supervised learning

22 The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if

23 the expression level of those genes is known, then the locations of the subregions can be inferred.

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

25 are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine

26 to which subregion each voxel within the structure belongs. We call this a classification task, because each voxel is being

27 assigned to a class (namely, its subregion).

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

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

30 within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel

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

32 a label (or a class label).

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

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

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

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

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

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

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

40 (voxels) for which the labels (subregions) are known.

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

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

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

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

45 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

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

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

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

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

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

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

52 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

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

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

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

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

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

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

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

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

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

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

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

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

65 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

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

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

68 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

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

70 features.

71 Principle 3: Use geometry in feature selection

72 _________________________________________

73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

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

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

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

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

78 Principle 4: Work in 2-D whenever possible

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

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

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

82 data.

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

84 Aim 2

85 Machine learning terminology: clustering

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

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

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

89 clustering or cluster analysis.

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

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

92 from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that

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

94 into clusters of voxels with similar gene expression.

95 It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all;

96 perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial

97 scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion.

98 This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which

99 partition the voxels. This is called hierarchial clustering.

100 Similarity scores

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

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

103 scoring methods for similarity.

104 Spatially contiguous clusters; image segmentation

105 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

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

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

108 results against other methods which guarantee contiguous clusters.

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

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

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

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

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

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

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

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

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

118 Dimensionality reduction

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

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

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

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

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

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

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

126 expression levels.

127 Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might

128 want tomake a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions

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

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

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

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

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

134 before clustering.

135 Clustering genes rather than voxels

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

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

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

139 have one reduced feature for each gene cluster.

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

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

142 interesting subregion will have multiple genes which each individually pick it out2. This suggests the following procedure:

143 cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the

144 final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some

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

146 Aim 3

147 Background

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

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

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

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

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

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

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

155 their approximate location upon the cortical surface.

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

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

158 single agreed-upon map can be seen by contrasting the recent maps given by Swanson[4] on the one hand, and Paxinos

159 and Franklin[3] on the other. While the maps are certainly very similar in their general arrangement, significant differences

160 remain in the details.

161 The Allen Mouse Brain Atlas dataset

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

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

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

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

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

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

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

169 voxels in the 3D coordinate system, of which 51,533 are in the brain[2].

170 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[6]. The ABA contains

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

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

173 and has greater registration error[2]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes of

174 known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[2].

175 Significance

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

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

178 _________________________________________

179 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

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

181 perhaps there is some other way to map the cortex for which each subregion can be identified by single genes.

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

183 target individual cortical areas.

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

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

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

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

188 The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of

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

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

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

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

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

194 at the patterns of gene expression.

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

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

197 Related work

198 There does not appear to be much work on the automated analysis of spatial gene expression data.

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

200 data which is not fundamentally spatial.

201 As noted above, there has been much work on both supervised learning and clustering, and there are many available

202 algorithms for each. However, the completion of Aims 1 and 2 involves more than just choosing between a set of existing

203 algorithms, and will constitute a substantial contribution to biology. The algorithms require the scientist to provide a

204 framework for representing the problem domain, and the way that this framework is set up has a large impact on performance.

205 Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical

206 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient

207 similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application.

208 We are aware of two existing efforts to relate spatial gene expression data to anatomy through computational methods.

209 [5 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

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

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

212 usefulness of such research. We have run NNMF on the cortical dataset3 and while the results are promising (see Preliminary

213 Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this

214 paper’s authors did manually will be possible).

215 [2 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA is an analysis tool for the ABA dataset. AGEA has

216 three components:

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

218 yields a list of genes which are overexpressed in that cluster.

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

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

221 * Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm

222 with correlation as the similarity metric.

223 Gene Finder is different from our Aim 1 in at least four ways. First, although the user chooses a seed voxel, Gene

224 Finder, not the user, chooses the cluster for which genes will be found, and in our experience it never chooses cortical areas,

225 instead preferring cortical layers4. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second,

226 Gene Finder finds only single genes, whereas we will also look for combinations of genes5. Third, gene finder can only use

227 overexpression as a marker, whereas in the Preliminary Data we show that underexpression can also be used. Fourth, Gene

228 Finder uses a simple pointwise score6, whereas we will also use geometric metrics such as gradient similarity.

229 _________________________________________

230 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

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

232 needed. The paper under discussion mentions that they also tried a hierarchial variant of NNMF, but since they didn’t report its results, we

233 assume that those result were not any more impressive than the results of the non-hierarchial variant.

234 4Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene

235 expression of voxels in different areas but the same layer are stronger than pairwise correlatios between the gene expression of voxels in different

236 layers but the same area. This appears to be the case.

237 5See Preliminary Data for an example of an area which cannot be marked by any single gene in the dataset, but which can be marked by a

238 combination.

239 6“Expression energy ratio”, which captures overexpression.

240 The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters cor-

241 responding to layers, but no clusters corresponding to areas7 8 Our Aim 2 will not be accomplished until a clustering is

242 produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does no

243 dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better

244 than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Third,

245 AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify intersting

246 spatial subregions such as cortical areas.

247 _______

248 7This is for the same reason as in footnote 4.

249 8There are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area

250 intersection clusters, further work is needed to make sense of these.

251 Preliminary work

252 Format conversion between SEV, MATLAB, NIFTI

253 We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created

254 software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file formats.

255 Flatmap of cortex

256 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided

257 the cortex into hemispheres.

258 Using Caret[1], we created a mesh representation of the surface of the selected region. For each gene, for each node of

259 the mesh, we used Caret to calculate an average of the gene expression of the voxels “underneath” that mesh node. We

260 then used Caret to flatten the cortex, creating a two-dimensional mesh.

261 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid

262 into a MATLAB matrix.

263 We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted

264 these manual traces into Caret-format regional boundary data on the mesh surface. Using Caret, we projected the regions

265 onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format.

266 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing

267 a grid of points (pixels) over the cortical surface:

268 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel

269 ∙For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel

270 We created a normalized version of the gene expression data by subtracting each gene’s mean expression level (over all

271 surface pixels) and dividing each gene by its standard deviation.

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

273 cortical layer to represent the average expression level within that layer. Cortical layers are found at different depths in

274 different parts of the cortex. In preparation for extracting the layer-specific datasets, we have extended Caret with routines

275 that allow the depth of the ROI for volume-to-surface projection to vary.

276 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually

277 demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.

278 Feature selection and scoring methods

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

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

281 surface pixels.

282 The features and the target area are both functions on the surface pixels; alternately, they can be thought of as images

283 which can be displayed on the flatmapped surface. One class of feature selection scoring method are those which calculate

284 some sort of “match” between each gene image and the target image. Those genes which match the best are good candidates

285 for features.

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

287 each gene and each cortical area.

288 Conditional entropy An information-theoretic scoring method is to find features such that, if the features (gene

289 expression levels) are known, uncertainty about the target (the regional identity) is reduced. Entropy measures uncertainty,

290 so what we want is to find features such that the conditional distribution of the target has minimal entropy. The distribution

291 to which we are referring is the probability distribution over the population of surface pixels.

292 The simplest way to use information theory is on discrete data, so we discretized our gene expression data by creating,

293 for each gene, five thresholded binary masks of the gene data. For each gene, we created a binary mask of its expression

294 levels over pixels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the mean

295 minus two standard deviations, the mean plus one standard deviation, the mean plus two standard deviations.

296 Now, for each region, we ran a forward stepwise procedure which attempted to find pairs of gene expression binary masks

297 such that the conditional entropy of the target area’s binary mask, conditioned upon the pair of gene expression binary

298 masks, is minimized.

299 This finds pairs of genes which are most informative, at least at these discretization thresholds.

300 Gradient similarity todo

301

302

303

304 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel’s value on the lower left is the sum

305 of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the

306 top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right.

307 The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells

308 underneath each pixel, with red meaning a lot of expression and blue meaning little.

309 Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas

310 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi-

311 natorially. according to logistic regression, gene wwc19 is the best fit single gene for predicting whether or not a pixel on

312 the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure shows wwc1’s spatial expression

313 pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene

314 overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the

315 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo).

316 Gene mtif210 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right

317 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these

318 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene.

319 Geometric and pointwise scoring methods provide complementary information

320 To show that local geometry can provide useful information that cannot be detected via pointwise analyses, consider Fig.

321 . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method11. The bottom

322 row displays the 3 genes which most match AUD according to a method which considers local geometry12 The pointwise

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

324 includes many areas which don’t have a salient border matching the areal border. The geometric method identifies genes

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

326 which don’t express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as

327 Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD;

328 we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods.

329 Areas which can be identified by single genes

330 todo

331 Areas can sometimes be marked by underexpression

332 todo

333 Specific to Aim 1 (and Aim 3)

334 Forward stepwise logistic regression todo

335 __

336 9“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652

337 10“mitochondrial translational initiation factor 2”; EntrezGene ID 76784

338 11For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor

339 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

340 they predict area AUD.

341 12For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the

342 shape of area AUD, was calculated, and this was used to rank the genes.

343

344

345

346 Figure 2: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.

347 The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From

348 left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr

349 SVM on all genes at once

350 In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical

351 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%13. As noted above,

352 however, a classifier that looks at all the genes at once isn’t practically useful.

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

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

355 combines feature selection with supervised learning.

356 Decision trees

357 todo

358 Specific to Aim 2 (and Aim 3)

359 Raw dimensionality reduction results

360 todo

361 (might want to incld nnMF since mentioned above)

362 Dimensionality reduction plus K-means or spectral clustering

363 Many areas are captured by clusters of genes

364 todo

365 todo

366 _________________________________________

367 135-fold cross-validation.

368 Research plan

369 todo amongst other things:

370 Develop algorithms that find genetic markers for anatomical regions

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

372 geometric, and information-theoretic measures.

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

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

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

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

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

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

379 machines.

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

381 to identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the

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

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

384 a larger area which can be fit.

385 Apply these algorithms to the cortex

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

387 between SEV, NIFTI and MATLAB formats.

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

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

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

391 that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once.

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

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

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

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

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

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

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

399 Bibliography & References Cited

400 [1]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite for surface-

401 based analyses of cerebral cortex. Journal of the American Medical Informatics Association: JAMIA, 8(5):443–59, 2001.

402 PMID: 11522765.

403 [2]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M Sunkin,

404 Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann, David J Anderson, Ed S

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

406 12(3):356–362, March 2009.

407 [3]George Paxinos and Keith B.J. Franklin. The Mouse Brain in Stereotaxic Coordinates. Academic Press, 2 edition, July

408 2001.

409 [4]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.

410 [5]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T. Mortrud,

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

412 Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the hippocampus. Neuron, 60(6):1010–

413 1021, December 2008.

414 [6]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agarwala,

415 Rachel Ainscough, Marina Alexandersson, Peter An, Stylianos E Antonarakis, John Attwood, Robert Baertsch, Jonathon

416 Bailey, Karen Barlow, Stephan Beck, Eric Berry, Bruce Birren, Toby Bloom, Peer Bork, Marc Botcherby, Nicolas Bray,

417 Michael R Brent, Daniel G Brown, Stephen D Brown, Carol Bult, John Burton, Jonathan Butler, Robert D Campbell,

418 Piero Carninci, Simon Cawley, Francesca Chiaromonte, Asif T Chinwalla, Deanna M Church, Michele Clamp, Christopher

419 Clee, Francis S Collins, Lisa L Cook, Richard R Copley, Alan Coulson, Olivier Couronne, James Cuff, Val Curwen, Tim

420 Cutts, Mark Daly, Robert David, Joy Davies, Kimberly D Delehaunty, Justin Deri, Emmanouil T Dermitzakis, Colin

421 Dewey, Nicholas J Dickens, Mark Diekhans, Sheila Dodge, Inna Dubchak, Diane M Dunn, Sean R Eddy, Laura Elnitski,

422 Richard D Emes, Pallavi Eswara, Eduardo Eyras, Adam Felsenfeld, Ginger A Fewell, Paul Flicek, Karen Foley, Wayne N

423 Frankel, Lucinda A Fulton, Robert S Fulton, Terrence S Furey, Diane Gage, Richard A Gibbs, Gustavo Glusman, Sante

424 Gnerre, Nick Goldman, Leo Goodstadt, Darren Grafham, Tina A Graves, Eric D Green, Simon Gregory, Roderic Guig,

425 Mark Guyer, Ross C Hardison, David Haussler, Yoshihide Hayashizaki, LaDeana W Hillier, Angela Hinrichs, Wratko

426 Hlavina, Timothy Holzer, Fan Hsu, Axin Hua, Tim Hubbard, Adrienne Hunt, Ian Jackson, David B Jaffe, L Steven

427 Johnson, Matthew Jones, Thomas A Jones, Ann Joy, Michael Kamal, Elinor K Karlsson, Donna Karolchik, Arkadiusz

428 Kasprzyk, Jun Kawai, Evan Keibler, Cristyn Kells, W James Kent, Andrew Kirby, Diana L Kolbe, Ian Korf, Raju S

429 Kucherlapati, Edward J Kulbokas, David Kulp, Tom Landers, J P Leger, Steven Leonard, Ivica Letunic, Rosie Levine, Jia

430 Li, Ming Li, Christine Lloyd, Susan Lucas, Bin Ma, Donna R Maglott, Elaine R Mardis, Lucy Matthews, Evan Mauceli,

431 John H Mayer, Megan McCarthy, W Richard McCombie, Stuart McLaren, Kirsten McLay, John D McPherson, Jim

432 Meldrim, Beverley Meredith, Jill P Mesirov, Webb Miller, Tracie L Miner, Emmanuel Mongin, Kate T Montgomery,

433 Michael Morgan, Richard Mott, James C Mullikin, Donna M Muzny, William E Nash, Joanne O Nelson, Michael N

434 Nhan, Robert Nicol, Zemin Ning, Chad Nusbaum, Michael J O’Connor, Yasushi Okazaki, Karen Oliver, Emma Overton-

435 Larty, Lior Pachter, Gens Parra, Kymberlie H Pepin, Jane Peterson, Pavel Pevzner, Robert Plumb, Craig S Pohl, Alex

436 Poliakov, Tracy C Ponce, Chris P Ponting, Simon Potter, Michael Quail, Alexandre Reymond, Bruce A Roe, Krishna M

437 Roskin, Edward M Rubin, Alistair G Rust, Ralph Santos, Victor Sapojnikov, Brian Schultz, Jrg Schultz, Matthias S

438 Schwartz, Scott Schwartz, Carol Scott, Steven Seaman, Steve Searle, Ted Sharpe, Andrew Sheridan, Ratna Shownkeen,

439 Sarah Sims, Jonathan B Singer, Guy Slater, Arian Smit, Douglas R Smith, Brian Spencer, Arne Stabenau, Nicole Stange-

440 Thomann, Charles Sugnet, Mikita Suyama, Glenn Tesler, Johanna Thompson, David Torrents, Evanne Trevaskis, John

441 Tromp, Catherine Ucla, Abel Ureta-Vidal, Jade P Vinson, Andrew C Von Niederhausern, Claire M Wade, Melanie Wall,

442 Ryan J Weber, Robert B Weiss, Michael C Wendl, Anthony P West, Kris Wetterstrand, Raymond Wheeler, Simon

443 Whelan, Jamey Wierzbowski, David Willey, Sophie Williams, Richard K Wilson, Eitan Winter, Kim C Worley, Dudley

444 Wyman, Shan Yang, Shiaw-Pyng Yang, Evgeny M Zdobnov, Michael C Zody, and Eric S Lander. Initial sequencing and

445 comparative analysis of the mouse genome. Nature, 420(6915):520–62, December 2002. PMID: 12466850.

446

447 _______________________________________________________________________________________________________

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

449 Principle 4: Work in 2-D whenever possible

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

451 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

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

453 The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that

454 characterized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold

455 into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used

456 by Caret[1]) with mappings which preserve angle (conformal maps).

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

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

459 structure seems to be wrong.

460 —

461 note:

462 do we need to cite: no known markers, impressive results?

463 two hemis

464

465