1 Specific aims

2 Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ

3 transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many loca-

4 tions to be compared. Our goal is to develop automated methods to relate spatial variation in gene expression to

5 anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical maps

6 based on gene expression patterns. We will validate these methods by applying them to 46 anatomical areas

7 within the cerebral cortex, by using the Allen Mouse Brain Atlas coronal dataset (ABA). This gene expression

8 dataset was generated using ISH, and contains over 4,000 genes. For each gene, a digitized 3-D raster of the

9 expression pattern is available: for each gene, the level of expression at each of 51,533 voxels is recorded.

10 We have three specific aims:

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

12 selectively target anatomical regions

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

14 based on spatial patterns in gene expression

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

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

17 the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the

18 methods developed in (1) and (2).

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

20 the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located

21 in a low-dimensional space. In particular, our method could be applied to genome-wide sequencing data derived

22 from sets of tissues and disease states.

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

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

25 of the algorithms, the application of these methods to cortex will produce immediate benefits, because there

26 are currently no known genetic markers for most cortical areas. The results of the project will support the

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

28 identifying the cortical areal boundaries present in small tissue samples.

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

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

31 The challenge topic

32 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as

33 in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others,

34 allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated

35 methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific

36 anatomical regions, and also to draw new anatomical maps based on gene expression patterns.

37 ______________

38 The Challenge and Potential impact

39 Each of our three aims will be discussed in turn. For each aim, we will develop a conceptual framework for

40 thinking about the task. Next we will discuss related work, and then summarize why our strategy is different from

41 what has been done before. After we have discussed all three aims, we will describe the potential impact.

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

43 Machine learning terminology: classifiers The task of looking for marker genes for known anatomical regions

44 means that one is looking for a set of genes such that, if the expression level of those genes is known, then the

45 locations of the regions can be inferred.

46 If we define the regions so that they cover the entire anatomical structure to be subdivided, we may say that

47 we are using gene expression in each voxel to assign that voxel to the proper area. We call this a classification

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

49 between the combination of their expression levels and the locations of the regions may be expressed as a

50 function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is

51 the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function

52 a classifier. In general, the input to a classifier is called an instance, and the output is called a label (or a class

53 label).

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

55 determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene

56 expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. The

57 initial gene expression dataset used in the construction of the classifier is called training data. In the machine

58 learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a task in

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

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

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

62 selection. Feature selection is one component of the task of learning a classifier. Some methods for learning

63 classifiers start out with a separate feature selection phase, whereas other methods combine feature selection

64 with other aspects of training.

65 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked

66 genes are then chosen. Some scoring measures can assign a score to a set of selected genes, not just to a

67 single gene; in this case, a dynamic procedure may be used in which features are added and subtracted from the

68 selected set depending on how much they raise the score. Such procedures are called “stepwise” or “greedy”.

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

70 that voxel, the algorithm which constructs the classifier may look over the entire dataset. We can categorize

71 score-based feature selection methods depending on how the score of calculated. Often the score calculation

72 consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the

73 aggregation is often a sum or a sum of squares or average). If only information from nearby voxels is used to

74 calculate a voxel’s sub-score, then we say it is a local scoring method. If only information from the voxel itself is

75 used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.

76 Both gene expression data and anatomical atlases have errors, due to a variety of factors. Individual subjects

77 have idiosyncratic anatomy. Subjects may be improperly registered to the atlas. The method used to measure

78 gene expression may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical

79 atlas are “wrong” in that they do not have the same shape as the natural domains of gene expression to which

80 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

81 they correspond. These sources of error can affect the displacement and the shape of both the gene expression

82 data and the anatomical target areas. Therefore, it is important to use feature selection methods which are

83 robust to these kinds of errors.

84 Our strategy for Aim 1

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

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

87 Principle 1: Combinatorial gene expression

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

89 in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas

90 (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes

91 (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies,

92 Figure 4). Therefore, each instance should contain multiple features (genes).

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

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

95 been selected as features. The more data that are available to a classifier, the better that it can do. For example,

96 perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every

97 gene as a feature? The reason is that we wish to employ the classifier in situations in which it is not feasible to

98 gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for

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

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

101 checks the level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on

102 tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we

103 must select only a few genes as features.

104 The requirement to find combinations of only a small number of genes limits us from straightforwardly ap-

105 plying many of the most simple techniques from the field of supervised machine learning. In the parlance of

106 machine learning, our task combines feature selection with supervised learning.

107 Principle 3: Use geometry in feature selection

108 When doing feature selection with score-based methods, the simplest thing to do would be to score the per-

109 formance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach

110 is to also use information about the geometric relations between each voxel and its neighbors; this requires non-

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

112 pointwise and local scoring methods.

113 Principle 4: Work in 2-D whenever possible

114 There are many anatomical structures which are commonly characterized in terms of a two-dimensional

115 manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be

116 improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for

117 humans to visualize and work with 2-D data. Therefore, when possible, the instances should represent pixels,

118 not voxels.

119 Related work

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

121 sion data which are not fundamentally spatial2.

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

123 algorithms for each. However, the algorithms require the scientist to provide a framework for representing the

124 problem domain, and the way that this framework is set up has a large impact on performance. Creating a

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

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

127 _________________________________________

128 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;

129 not just data which have only a few different locations or which is indexed by anatomical label.

130 as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best

131 results in this application.

132 We now turn to efforts to find marker genes using spatial gene expression data using automated methods.

133 GeneAtlas[3] and EMAGE [19] allow the user to construct a search query by demarcating regions and then

134 specifying either the strength of expression or the name of another gene or dataset whose expression pattern

135 is to be matched. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes that define a

136 region in concert but not separately.

137 [12 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The

138 user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list of

139 genes which are overexpressed in that cluster. Correlation: The user selects a seed voxel and the system then

140 shows the user how much correlation there is between the gene expression profile of the seed voxel and every

141 other voxel. Clusters: will be described later. [4] looks at the mean expression level of genes within anatomical

142 regions, and applies a Student’s t-test with Bonferroni correction to determine whether the mean expression

143 level of a gene is significantly higher in the target region. [12] and [4] differ from our Aim 1 in at least three

144 ways. First, [12] and [4] find only single genes, whereas we will also look for combinations of genes. Second,

145 [12 ] and [4] can only use overexpression as a marker, whereas we will also search for underexpression. Third,

146 [12 ] and [4] use scores based on pointwise expression levels, whereas we will also use geometric scores such

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

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

149 [8 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use

150 an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to

151 match a target image.

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

153 explores combinations of marker genes, and none of these publications compare the results obtained by using

154 different algorithms or scoring methods.

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

156 Machine learning terminology: clustering

157 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is

158 referred to as unsupervised learning in the jargon of machine learning. One thing that you can do with such a

159 dataset is to group instances together. A set of similar instances is called a cluster, and the activity of finding

160 grouping the data into clusters is called clustering or cluster analysis.

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

162 instances are once again voxels (or pixels) along with their associated gene expression profiles. We make

163 the assumption that voxels from the same anatomical region have similar gene expression profiles, at least

164 compared to the other regions. This means that clustering voxels is the same as finding potential regions; we

165 seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.

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

167 outcome of clustering may be a hierarchical tree of clusters, rather than a single set of clusters which partition

168 the voxels. This is called hierarchical clustering.

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

170 either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature

171 selection (discussed above under Aim 1) and scoring methods for similarity.

172 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering

173 task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels

174 grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get

175 reasonable results without enforcing this constraint; however, we plan to compare these results against other

176 methods which guarantee contiguous clusters.

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

178 clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are

179 thousands of color channels (one for each gene), rather than just three3. A more crucial difference is that there

180 are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not

181 appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation

182 algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these

183 algorithms are specialized for visual images.

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

185 feature vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying

186 data.

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

188 in the instances. However, some clustering algorithms perform better on small numbers of features4. There are

189 techniques which “summarize” a larger number of features using a smaller number of features; these techniques

190 go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique

191 yields is called the reduced feature set. Note that the features in the reduced feature set do not necessarily

192 correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.

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

194 one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes

195 could be used.

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

197 we could have one reduced feature for each gene cluster.

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

199 an expression pattern which seems to pick out a single, spatially contiguous region. This suggests the following

200 procedure: cluster together genes which pick out similar regions, and then to use the more popular common

201 regions as the final clusters. In Preliminary Studies, Figure 7, we show that a number of anatomically recognized

202 cortical regions, as well as some “superregions” formed by lumping together a few regions, are associated with

203 gene clusters in this fashion.

204 Related work

205 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example,

206 [15 ], [2 ], [16], and [1] associate spots on the cortex with the radial profile5 of response to some stain ([10] uses

207 MRI), extract features from this profile, and then use similarity between surface pixels to cluster.

208 [18 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual

209 analysis, two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and

210 a hierarchical recursive bifurcation clustering scheme based on correlation as the similarity score. The paper

211 yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on

212 the cortical dataset

213 AGEA[12] includes a preset hierarchical clustering of voxels based on a recursive bifurcation algorithm with

214 correlation as the similarity metric. EMAGE[19] allows the user to select a dataset from among a large number

215 of alternatives, or by running a search query, and then to cluster the genes within that dataset. EMAGE clusters

216 via hierarchical complete linkage clustering.

217 [4 ] clusters genes. For each cluster, prototypical spatial expression patterns were created by averaging the

218 genes in the cluster. The prototypes were analyzed manually, without clustering voxels.

219 [8 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes

220 around a “seed gene”.

221 In summary, although these projects obtained clusterings, there has not been much comparison between

222 different algorithms or scoring methods, so it is likely that the best clustering method for this application has not

223 yet been found. The projects using gene expression on cortex did not attempt to make use of the radial profile

224 of gene expression. Also, none of these projects did a separate dimensionality reduction step before clustering

225 _________________________________________

226 3There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are

227 often used to process satellite imagery.

228 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering

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

230 5A radial profile is a profile along a line perpendicular to the cortical surface.

231 pixels, none tried to cluster genes first in order to guide automated clustering of pixels into spatial regions, and

232 none used co-clustering algorithms.

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

234

235

236 Figure 1: Top row: Genes Nfic

237 and A930001M12Rik are the most

238 correlated with area SS (somatosen-

239 sory cortex). Bottom row: Genes

240 C130038G02Rik and Cacna1i are

241 those with the best fit using logistic

242 regression. Within each picture, the

243 vertical axis roughly corresponds to

244 anterior at the top and posterior at the

245 bottom, and the horizontal axis roughly

246 corresponds to medial at the left and

247 lateral at the right. The red outline is

248 the boundary of region SS. Pixels are

249 colored according to correlation, with

250 red meaning high correlation and blue

251 meaning low. Background

252 The cortex is divided into areas and layers. Because of the cortical

253 columnar organization, the parcellation of the cortex into areas can be

254 drawn as a 2-D map on the surface of the cortex. In the third dimension,

255 the boundaries between the areas continue downwards into the cortical

256 depth, perpendicular to the surface. The layer boundaries run parallel

257 to the surface. One can picture an area of the cortex as a slice of a

258 six-layered cake6.

259 It is known that different cortical areas have distinct roles in both

260 normal functioning and in disease processes, yet there are no known

261 marker genes for most cortical areas. When it is necessary to divide a

262 tissue sample into cortical areas, this is a manual process that requires

263 a skilled human to combine multiple visual cues and interpret them in

264 the context of their approximate location upon the cortical surface.

265 Even the questions of how many areas should be recognized in

266 cortex, and what their arrangement is, are still not completely settled.

267 A proposed division of the cortex into areas is called a cortical map.

268 In the rodent, the lack of a single agreed-upon map can be seen by

269 contrasting the recent maps given by Swanson[17] on the one hand,

270 and Paxinos and Franklin[14] on the other. While the maps are cer-

271 tainly very similar in their general arrangement, significant differences

272 remain.

273 The Allen Mouse Brain Atlas dataset

274 The Allen Mouse Brain Atlas (ABA) data[11] were produced by do-

275 ing in-situ hybridization on slices of male, 56-day-old C57BL/6J mouse

276 brains. Pictures were taken of the processed slice, and these pictures

277 were semi-automatically analyzed to create a digital measurement of

278 gene expression levels at each location in each slice. Per slice, cellular

279 spatial resolution is achieved. Using this method, a single physical slice

280 can only be used to measure one single gene; many different mouse brains were needed in order to measure

281 the expression of many genes.

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

283 about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections.

284 Our dataset is derived from only the coronal subset of the ABA7. An automated nonlinear alignment procedure

285 located the 2D data from the various slices in a single 3D coordinate system. In the final 3D coordinate system,

286 voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326 voxels, of which 51,533 are in the

287 brain[12]. For each voxel and each gene, the expression energy[11] within that voxel is made available.

288 The ABA is not the only large public spatial gene expression dataset. However, with the exception of the ABA,

289 GenePaint, and EMAGE, most of the other resources have not (yet) extracted the expression intensity from the

290 ISH images and registered the results into a single 3-D space.

291 Related work

292 [12 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure

293 of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort

294 _________________________________________

295 6Outside of isocortex, the number of layers varies.

296 7The sagittal data do not cover the entire cortex, and also have greater registration error[12]. Genes were selected by the Allen

297 Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked

298 non-ubiquitous expression pattern”[12].

299 of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical

300 map based on gene expression data. Neither of the other components of AGEA can be applied to cortical

301 areas; AGEA’s Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA’s hierarchical

302 clustering does not produce clusters corresponding to the cortical areas8.

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

304 (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no

305 work on computationally finding marker genes for cortical areas, or on finding a hierarchical clustering that will

306 yield a map of cortical areas de novo from gene expression data.

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

308 find marker genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing

309 different methods.

310 Significance

311

312 Figure 2: Gene Pitx2

313 is selectively underex-

314 pressed in area SS. The method developed in aim (1) will be applied to each cortical area to find a set of

315 marker genes such that the combinatorial expression pattern of those genes uniquely

316 picks out the target area. Finding marker genes will be useful for drug discovery as

317 well as for experimentation because marker genes can be used to design interventions

318 which selectively target individual cortical areas.

319 The application of the marker gene finding algorithm to the cortex will also support

320 the development of new neuroanatomical methods. In addition to finding markers for

321 each individual cortical areas, we will find a small panel of genes that can find many of

322 the areal boundaries at once. This panel of marker genes will allow the development of

323 an ISH protocol that will allow experimenters to more easily identify which anatomical

324 areas are present in small samples of cortex.

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

326 of a better map. The development of present-day cortical maps was driven by the application of histological

327 stains. If a different set of stains had been available which identified a different set of features, then today’s

328 cortical maps may have come out differently. It is likely that there are many repeated, salient spatial patterns

329 in the gene expression which have not yet been captured by any stain. Therefore, cortical anatomy needs to

330 incorporate what we can learn from looking at the patterns of gene expression.

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

332 we propose to develop could be used to suggest modifications to the human cortical map as well. In fact, the

333 methods we will develop will be applicable to other datasets beyond the brain.

334 _______________________________

335 The approach: Preliminary Studies

336 Format conversion between SEV, MATLAB, NIFTI

337 We have created software to (politely) download all of the SEV files9 from the Allen Institute website. We have

338 also created software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s

339 file formats.

340 Flatmap of cortex

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

342 We divided the cortex into hemispheres. Using Caret[5], we created a mesh representation of the surface of the

343 selected voxels. For each gene, and for each node of the mesh, we calculated an average of the gene expression

344 of the voxels “underneath” that mesh node. We then flattened the cortex, creating a two-dimensional mesh. We

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

346 grid into a MATLAB matrix. We manually traced the boundaries of each of 46 cortical areas from the ABA coronal

347 reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the

348 8In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer

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

350 pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas.

351 9SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

352 mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the

353 region data into MATLAB format.

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

355 representing a grid of points (pixels) over the cortical surface. There is one 2-D matrix whose entries represent

356 the regional label associated with each surface pixel. And for each gene, there is a 2-D matrix whose entries

357 represent the average expression level underneath each surface pixel. We created a normalized version of the

358 gene expression data by subtracting each gene’s mean expression level (over all surface pixels) and dividing the

359 expression level of each gene by its standard deviation. The features and the target area are both functions on

360 the surface pixels. They can be referred to as scalar fields over the space of surface pixels; alternately, they can

361 be thought of as images which can be displayed on the flatmapped surface.

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

363 for each cortical layer to represent the average expression level within that layer. Cortical layers are found at

364 different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have

365 extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary. In the

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

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

368 Feature selection and scoring methods

369

370

371 Figure 3: The top row shows the two

372 genes which (individually) best predict

373 area AUD, according to logistic regres-

374 sion. The bottom row shows the two

375 genes which (individually) best match

376 area AUD, according to gradient sim-

377 ilarity. From left to right and top to

378 bottom, the genes are Ssr1, Efcbp1,

379 Ptk7, and Aph1a. Underexpression of a gene can serve as a marker Underexpression

380 of a gene can sometimes serve as a marker. See, for example, Figure

381 2.

382 Correlation Recall that the instances are surface pixels, and con-

383 sider the problem of attempting to classify each instance as either a

384 member of a particular anatomical area, or not. The target area can be

385 represented as a boolean mask over the surface pixels.

386 We calculated the correlation between each gene and each cortical

387 area. The top row of Figure 1 shows the three genes most correlated

388 with area SS.

389 Conditional entropy

390 For each region, we created and ran a forward stepwise procedure

391 which attempted to find pairs of gene expression boolean masks such

392 that the conditional entropy of the target area’s boolean mask, condi-

393 tioned upon the pair of gene expression boolean masks, is minimized.

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

395 these discretization thresholds) relative to the question, “Is this surface

396 pixel a member of the target area?”. Its advantage over linear methods

397 such as logistic regression is that it takes account of arbitrarily nonlin-

398 ear relationships; for example, if the XOR of two variables predicts the

399 target, conditional entropy would notice, whereas linear methods would

400 not.

401 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found

402 genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed

403 a non-pointwise scoring method to detect when a gene had a pattern of expression which looked like it had a

404 boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient

405 similarity”. The formula is:

406 ∑

407 pixel<img src="cmsy8-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|

408 2 &#x22C5; pixel_value1 + pixel_value2

409 2

410 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current pixel; &#x2220;&#x2207;i is the angle of the

411 gradient of image i at the current pixel; |&#x2207;i| is the magnitude of the gradient of image i at the current pixel; and

412 pixel valuei is the value of the current pixel in image i.

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

414 are similar, then both images will have corresponding pixels with large gradients (because this is a border) which

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

416 Gradient similarity provides information complementary to correlation

417

418

419 Figure 4: Upper left: wwc1. Upper

420 right: mtif2. Lower left: wwc1 + mtif2

421 (each pixel&#8217;s value on the lower left is

422 the sum of the corresponding pixels in

423 the upper row). To show that gradient similarity can provide useful information that

424 cannot be detected via pointwise analyses, consider Fig. 3. The

425 pointwise method in the top row identifies genes which express more

426 strongly in AUD than outside of it; its weakness is that this includes

427 many areas which don&#8217;t have a salient border matching the areal bor-

428 der. The geometric method identifies genes whose salient expression

429 border seems to partially line up with the border of AUD; its weakness

430 is that this includes genes which don&#8217;t express over the entire area.

431 Areas which can be identified by single genes Using gradient

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

433 some areas and groupings of areas. For each of these areas, an ex-

434 ample of a gene which roughly identifies it is shown in Figure 5. We

435 have not yet cross-verified these genes in other atlases.

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

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

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

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

440 These results validate our expectation that the ABA dataset can be

441 exploited to find marker genes for many cortical areas, while also validating the relevancy of our new scoring

442 method, gradient similarity.

443 Combinations of multiple genes are useful and necessary for some areas

444 In Figure 4, we give an example of a cortical area which is not marked by any single gene, but which

445 can be identified combinatorially. According to logistic regression, gene wwc1 is the best fit single gene for

446 predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left

447 picture in Figure 4 shows wwc1&#8217;s spatial expression pattern over the cortex. The lower-right boundary of MO is

448 represented reasonably well by this gene, but the gene overshoots the upper-left boundary. This flattened 2-D

449 representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex.

450 MO is only found on the dorsal surface. Gene mtif2 is shown in the upper-right. Mtif2 captures MO&#8217;s upper-left

451 boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding

452 together the values at each pixel in these two figures, we get the lower-left image. This combination captures

453 area MO much better than any single gene.

454 This shows that our proposal to develop a method to find combinations of marker genes is both possible and

455 necessary.

456 Multivariate supervised learning

457 Forward stepwise logistic regression Logistic regression is a popular method for predictive modeling of cate-

458 gorical data. As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise

459 logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. This is

460 an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes

461 found were shown in various figures throughout this document, and Figure 4 shows a combination of genes

462 which was found.

463 SVM on all genes at once

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

465 classify cortical surface pixels based on their gene expression profiles. We achieved classification accuracy of

466 about 81%10. This shows that the genes included in the ABA dataset are sufficient to define much of cortical

467 anatomy. However, as noted above, a classifier that looks at all the genes at once isn&#8217;t as practically useful as a

468 classifier that uses only a few genes.

469 Data-driven redrawing of the cortical map

470

471

472

473

474 Figure 5: From left to right and top

475 to bottom, single genes which roughly

476 identify areas SS (somatosensory pri-

477 mary + supplemental), SSs (supple-

478 mental somatosensory), PIR (piriform),

479 FRP (frontal pole), RSP (retrosple-

480 nial), COApm (Cortical amygdalar, pos-

481 terior part, medial zone). Grouping

482 some areas together, we have also

483 found genes to identify the groups

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

485 cingulate, prelimbic, infralimbic, dor-

486 sal peduncular, orbital, motor), poste-

487 rior and lateral visual (VISpm, VISpl,

488 VISI, VISp; posteromedial, posterolat-

489 eral, lateral, and primary visual; the

490 posterior and lateral visual area is dis-

491 tinguished from its neighbors, but not

492 from the entire rest of the cortex). The

493 genes are Pitx2, Aldh1a2, Ppfibp1,

494 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. We have applied the following dimensionality reduction algorithms

495 to reduce the dimensionality of the gene expression profile associ-

496 ated with each pixel: Principal Components Analysis (PCA), Simple

497 PCA, Multi-Dimensional Scaling, Isomap, Landmark Isomap, Laplacian

498 eigenmaps, Local Tangent Space Alignment, Stochastic Proximity Em-

499 bedding, Fast Maximum Variance Unfolding, Non-negative Matrix Fac-

500 torization (NNMF). Space constraints prevent us from showing many of

501 the results, but as a sample, PCA, NNMF, and landmark Isomap are

502 shown in the first, second, and third rows of Figure 6.

503 After applying the dimensionality reduction, we ran clustering algo-

504 rithms on the reduced data. To date we have tried k-means and spec-

505 tral clustering. The results of k-means after PCA, NNMF, and landmark

506 Isomap are shown in the last row of Figure 6. To compare, the leftmost

507 picture on the bottom row of Figure 6 shows some of the major subdivi-

508 sions of cortex. These results clearly show that different dimensionality

509 reduction techniques capture different aspects of the data and lead to

510 different clusterings, indicating the utility of our proposal to produce a

511 detailed comparison of these techniques as applied to the domain of

512 genomic anatomy.

513 Many areas are captured by clusters of genes We also clustered

514 the genes using gradient similarity to see if the spatial regions defined

515 by any clusters matched known anatomical regions. Figure 7 shows, for

516 ten sample gene clusters, each cluster&#8217;s average expression pattern,

517 compared to a known anatomical boundary. This suggests that it is

518 worth attempting to cluster genes, and then to use the results to cluster

519 pixels.

520 The approach: what we plan to do

521 Flatmap cortex and segment cortical layers

522 There are multiple ways to flatten 3-D data into 2-D. We will compare

523 mappings from manifolds to planes which attempt to preserve size

524 (such as the one used by Caret[5]) with mappings which preserve an-

525 gle (conformal maps). Our method will include a statistical test that

526 warns the user if the assumption of 2-D structure seems to be wrong.

527 We have not yet made use of radial profiles. While the radial pro-

528 files may be used &#8220;raw&#8221;, for laminar structures like the cortex another

529 strategy is to group together voxels in the same cortical layer; each sur-

530 face pixel would then be associated with one expression level per gene

531 per layer. We will develop a segmentation algorithm to automatically

532 identify the layer boundaries.

533 Develop algorithms that find genetic markers for anatomical re-

534 gions

535 Scoring measures and feature selection We will develop scoring

536 methods for evaluating how good individual genes are at marking ar-

537 eas. We will compare pointwise, geometric, and information-theoretic

538 _________________________________________

539 105-fold cross-validation.

540 measures. We already developed one entirely new scoring method (gradient similarity), but we may develop

541 more. Scoring measures that we will explore will include the L1 norm, correlation, expression energy ratio, con-

542 ditional entropy, gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such

543 as Student&#8217;s t-test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a

544 scoring measure on genes by taking the prediction error when using that gene to predict the target.

545

546

547

548

549 Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec-

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

551 the first six reduced dimensions, using landmark Isomap. Bottom

552 row: examples of kmeans clustering applied to reduced datasets

553 to find 7 clusters. Left: 19 of the major subdivisions of the cortex.

554 Second from left: PCA. Third from left: NNMF. Right: Landmark

555 Isomap. Additional details: In the third and fourth rows, 7 dimen-

556 sions were found, but only 6 displayed. In the last row: for PCA,

557 50 dimensions were used; for NNMF, 6 dimensions were used; for

558 landmark Isomap, 7 dimensions were used. Using some combination of these mea-

559 sures, we will develop a procedure to

560 find single marker genes for anatomical

561 regions: for each cortical area, we will

562 rank the genes by their ability to delineate

563 each area. We will quantitatively compare

564 the list of single genes generated by our

565 method to the lists generated by previous

566 methods which are mentioned in Aim 1 Re-

567 lated Work.

568 Some cortical areas have no single

569 marker genes but can be identified by com-

570 binatorial coding. This requires multivari-

571 ate scoring measures and feature selec-

572 tion procedures. Many of the measures,

573 such as expression energy, gradient sim-

574 ilarity, Jaccard, Dice, Hough, Student&#8217;s t,

575 and Mann-Whitney U are univariate. We

576 will extend these scoring measures for use

577 in multivariate feature selection, that is, for

578 scoring how well combinations of genes,

579 rather than individual genes, can distin-

580 guish a target area. There are existing

581 multivariate forms of some of the univariate

582 scoring measures, for example, Hotelling&#8217;s

583 T-square is a multivariate analog of Stu-

584 dent&#8217;s t.

585 We will develop a feature selection pro-

586 cedure for choosing the best small set of

587 marker genes for a given anatomical area. In addition to using the scoring measures that we develop, we will

588 also explore (a) feature selection using a stepwise wrapper over &#8220;vanilla&#8221; classifiers such as logistic regression,

589 (b) supervised learning methods such as decision trees which incrementally/greedily combine single gene mark-

590 ers into sets, and (c) supervised learning methods which use soft constraints to minimize number of features

591 used, such as sparse support vector machines (SVMs).

592 Since errors of displacement and of shape may cause genes and target areas to match less than they should,

593 we will consider the robustness of feature selection methods in the presence of error. Some of these methods,

594 such as the Hough transform, are designed to be resistant in the presence of error, but many are not. We will

595 consider extensions to scoring measures that may improve their robustness; for example, a wrapper that runs a

596 scoring method on small displacements and distortions of the data adds robustness to registration error at the

597 expense of computation time.

598 An area may be difficult to identify because the boundaries are misdrawn in the atlas, or because the shape

599 of the natural domain of gene expression corresponding to the area is different from the shape of the area as

600 recognized by anatomists. We will extend our procedure to handle difficult areas by combining areas or redrawing

601 their boundaries. We will develop extensions to our procedure which (a) detect when a difficult area could be

602 fit if its boundary were redrawn slightly11, and (b) detect when a difficult area could be combined with adjacent

603 _________________________________________

604 11Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by

605 multiple sources of evidence. Interestingly, the need to detect &#8220;natural spatial domains of gene expression&#8221; in a data-driven fashion

606 means that the methods of Aim 2 might be useful in achieving Aim 1, as well &#8211; particularly discriminative dimensionality reduction.

607 areas to create a larger area which can be fit.

608 A future publication on the method that we develop in Aim 1 will review the scoring measures and quantita-

609 tively compare their performance in order to provide a foundation for future research of methods of marker gene

610 finding. We will measure the robustness of the scoring measures as well as their absolute performance on our

611 dataset.

612 Classifiers We will explore and compare different classifiers. As noted above, this activity is not separate

613 from the previous one, because some supervised learning algorithms include feature selection, and any clas-

614 sifier can be combined with a stepwise wrapper for use as a feature selection method. We will explore logistic

615 regression (including spatial models[13]), decision trees12, sparse SVMs, generative mixture models (including

616 naive bayes), kernel density estimation, instance-based learning methods (such as k-nearest neighbor), genetic

617 algorithms, and artificial neural networks.

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

619

620 Figure 7: Prototypes corresponding to sample gene

621 clusters, clustered by gradient similarity. Region bound-

622 aries for the region that most matches each prototype

623 are overlaid. Dimensionality reduction on gene expression pro-

624 files We have already described the application of

625 ten dimensionality reduction algorithms for the pur-

626 pose of replacing the gene expression profiles, which

627 are vectors of about 4000 gene expression levels,

628 with a smaller number of features. We plan to fur-

629 ther explore and interpret these results, as well as to

630 apply other unsupervised learning algorithms, includ-

631 ing independent components analysis, self-organizing

632 maps, and generative models such as deep Boltz-

633 mann machines. We will explore ways to quantitatively

634 compare the relevance of the different dimensionality

635 reduction methods for identifying cortical areal bound-

636 aries.

637 Dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene expression

638 profiles, the same techniques can be applied instead to the pixels. It is possible that the features generated in

639 this way by some dimensionality reduction techniques will directly correspond to interesting spatial regions.

640 Clustering and segmentation on pixels We will explore clustering and segmentation algorithms in order to

641 segment the pixels into regions. We will explore k-means, spectral clustering, gene shaving[7], recursive division

642 clustering, multivariate generalizations of edge detectors, multivariate generalizations of watershed transforma-

643 tions, region growing, active contours, graph partitioning methods, and recursive agglomerative clustering with

644 various linkage functions. These methods can be combined with dimensionality reduction.

645 Clustering on genes We have already shown that the procedure of clustering genes according to gradient

646 similarity, and then creating an averaged prototype of each cluster&#8217;s expression pattern, yields some spatial

647 patterns which match cortical areas. We will further explore the clustering of genes.

648 In addition to using the cluster expression prototypes directly to identify spatial regions, this might be useful

649 as a component of dimensionality reduction. For example, one could imagine clustering similar genes and then

650 replacing their expression levels with a single average expression level, thereby removing some redundancy from

651 the gene expression profiles. One could then perform clustering on pixels (possibly after a second dimensionality

652 reduction step) in order to identify spatial regions. It remains to be seen whether removal of redundancy would

653 help or hurt the ultimate goal of identifying interesting spatial regions.

654 Co-clustering There are some algorithms which simultaneously incorporate clustering on instances and on

655 features (in our case, genes and pixels), for example, IRM[9]. These are called co-clustering or biclustering

656 _________________________________________

657 12Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision

658 tree for that area. We achieved good classification accuracy on our training set, but the number of genes that appeared in each tree was

659 too large. We plan to implement a pruning procedure to generate trees that use fewer genes.

660 algorithms.

661 Radial profiles We wil explore the use of the radial profile of gene expression under each pixel.

662 Compare different methods In order to tell which method is best for genomic anatomy, for each experimental

663 method we will compare the cortical map found by unsupervised learning to a cortical map derived from the Allen

664 Reference Atlas. We will explore various quantitative metrics that purport to measure how similar two clusterings

665 are, such as Jaccard, Rand index, Fowlkes-Mallows, variation of information, Larsen, Van Dongen, and others.

666 Discriminative dimensionality reduction In addition to using a purely data-driven approach to identify

667 spatial regions, it might be useful to see how well the known regions can be reconstructed from a small number

668 of features, even if those features are chosen by using knowledge of the regions. For example, linear discriminant

669 analysis could be used as a dimensionality reduction technique in order to identify a few features which are the

670 best linear summary of gene expression profiles for the purpose of discriminating between regions. This reduced

671 feature set could then be used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the

672 reference atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is.

673 Apply the new methods to the cortex

674 Using the methods developed in Aim 1, we will present, for each cortical area, a short list of markers to identify

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

676 Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible for an unrelated

677 combination of genes to seem to identify an area when in fact it is only coincidence. There are two ways we will

678 validate our marker genes to guard against this. First, we will confirm that putative combinations of marker genes

679 express the same pattern in both hemispheres. Second, we will manually validate our final results on other gene

680 expression datasets such as EMAGE, GeneAtlas, and GENSAT[6].

681 Using the methods developed in Aim 2, we will present one or more hierarchical cortical maps. We will identify

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

683 of these maps, and we will provide biological hypotheses to interpret any new cortical areas, or groupings of

684 areas, which are discovered.

685 ____________________________________________________________________________

686 Timeline and milestones

687 Finding marker genes

688 September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers

689 November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information

690 for each layer

691 October 2009-April 2010: Develop scoring and supervised learning methods.

692 January 2010 (milestone): Submit a publication on single marker genes for cortical areas

693 February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Extend tech-

694 niques for robustness. Compare the performance of techniques. Validate marker genes. Prepare software

695 toolbox for Aim 1.

696 June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.

697 July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a

698 small number of marker genes that can, in combination, define most of the areas at once

699 Revealing new ways to parcellate a structure into regions

700 June 2010-March 2011: Explore dimensionality reduction algorithms. Explore clustering algorithms. Adapt

701 clustering algorithms to use radial profile information. Compare the performance of techniques.

702 March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.

703 February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex,

704 interpret the results. Prepare software toolbox for Aim 2.

705 May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in

706 Aim 2

707 May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1.

708 Possibly submit another paper.

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