1 Specific aims

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

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

4 locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expres-

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

6 maps based on gene expression patterns. We have three specific aims:

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

8 selectively target anatomical regions

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

10 based on spatial patterns in gene expression

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

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

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

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

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

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

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

18 from sets of tissues and disease states.

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

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

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

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

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

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

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

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

27 The challenge topic

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

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

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

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

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

33 The Challenge and Potential impact

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

35 thinking about the task, and we will present our strategy for solving it. Next we will discuss related work. At the

36 conclusion of each section, we will summarize why our strategy is different from what has been done before. At

37 the end of this section, we will describe the potential impact.

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

39

40 Figure 1: Gene Pitx2

41 is selectively underex-

42 pressed in area SS. Machine learning terminology: classifiers The task of looking for marker genes for

43 known anatomical regions means that one is looking for a set of genes such that, if

44 the expression level of those genes is known, then the locations of the regions can be

45 inferred.

46 If we define the regions so that they cover the entire anatomical structure to be

47 subdivided, we may say that we are using gene expression in each voxel to assign

48 that voxel to the proper area. We call this a classification task, because each voxel

49 is being assigned to a class (namely, its region). An understanding of the relationship

50 between the combination of their expression levels and the locations of the regions may

51 be expressed as a function. The input to this function is a voxel, along with the gene

52 expression levels within that voxel; the output is the regional identity of the target voxel,

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

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

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

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

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

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

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

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

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

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

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

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

65 with other aspects of training.

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

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

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

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

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

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

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

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

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

75 _________________________________________

76 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

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

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

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

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

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

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

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

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

85 robust to these kinds of errors.

86 Our strategy for Aim 1

87

88

89 Figure 2: Top row: Genes Nfic

90 and A930001M12Rik are the most

91 correlated with area SS (somatosen-

92 sory cortex). Bottom row: Genes

93 C130038G02Rik and Cacna1i are

94 those with the best fit using logistic

95 regression. Within each picture, the

96 vertical axis roughly corresponds to

97 anterior at the top and posterior at the

98 bottom, and the horizontal axis roughly

99 corresponds to medial at the left and

100 lateral at the right. The red outline is

101 the boundary of region SS. Pixels are

102 colored according to correlation, with

103 red meaning high correlation and blue

104 meaning low. Key questions when choosing a learning method are: What are the

105 instances? What are the features? How are the features chosen?

106 Here are four principles that outline our answers to these questions.

107 Principle 1: Combinatorial gene expression

108 It is too much to hope that every anatomical region of interest will be

109 identified by a single gene. For example, in the cortex, there are some

110 areas which are not clearly delineated by any gene included in the

111 Allen Brain Atlas (ABA) dataset. However, at least some of these areas

112 can be delineated by looking at combinations of genes (an example

113 of an area for which multiple genes are necessary and sufficient is

114 provided in Preliminary Studies, Figure 4). Therefore, each instance

115 should contain multiple features (genes).

116 Principle 2: Only look at combinations of small numbers of

117 genes

118 When the classifier classifies a voxel, it is only allowed to look at

119 the expression of the genes which have been selected as features.

120 The more data that are available to a classifier, the better that it can do.

121 For example, perhaps there are weak correlations over many genes

122 that add up to a strong signal. So, why not include every gene as a

123 feature? The reason is that we wish to employ the classifier in situations

124 in which it is not feasible to gather data about every gene. For example,

125 if we want to use the expression of marker genes as a trigger for some

126 regionally-targeted intervention, then our intervention must contain a

127 molecular mechanism to check the expression level of each marker

128 gene before it triggers. It is currently infeasible to design a molecular

129 trigger that checks the level of more than a handful of genes. Similarly,

130 if the goal is to develop a procedure to do ISH on tissue samples in

131 order to label their anatomy, then it is infeasible to label more than a

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

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

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

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

136 Principle 3: Use geometry in feature selection

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

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

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

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

141 pointwise and local scoring methods.

142 Principle 4: Work in 2-D whenever possible

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

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

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

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

147 not voxels.

148 Related work

149

150

151 Figure 3: The top row shows the two

152 genes which (individually) best predict

153 area AUD, according to logistic regres-

154 sion. The bottom row shows the two

155 genes which (individually) best match

156 area AUD, according to gradient sim-

157 ilarity. From left to right and top to

158 bottom, the genes are Ssr1, Efcbp1,

159 Ptk7, and Aph1a. There is a substantial body of work on the analysis of gene expres-

160 sion data, most of this concerns gene expression data which are not

161 fundamentally spatial2.

162 As noted above, there has been much work on both supervised

163 learning and there are many available algorithms for each. However,

164 the algorithms require the scientist to provide a framework for repre-

165 senting the problem domain, and the way that this framework is set

166 up has a large impact on performance. Creating a good framework

167 can require creatively reconceptualizing the problem domain, and is

168 not merely a mechanical “fine-tuning” of numerical parameters. For

169 example, we believe that domain-specific scoring measures (such as

170 gradient similarity, which is discussed in Preliminary Studies) may be

171 necessary in order to achieve the best results in this application.

172 We are aware of six existing efforts to find marker genes using spa-

173 tial gene expression data using automated methods.

174 [13] mentions the possibility of constructing a spatial region for each

175 gene, and then, for each anatomical structure of interest, computing

176 what proportion of this structure is covered by the gene’s spatial region.

177 GeneAtlas[5] and EMAGE [26] allow the user to construct a search

178 query by demarcating regions and then specifying either the strength of

179 expression or the name of another gene or dataset whose expression

180 pattern is to be matched. Neither GeneAtlas nor EMAGE allow one to

181 search for combinations of genes that define a region in concert but not separately.

182 [15 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The

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

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

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

186 other voxel. Clusters: will be described later

187 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with

188 Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in the

189 target region.

190 [15 ] and [6] differ from our Aim 1 in at least three ways. First, [15] and [6] find only single genes, whereas

191 we will also look for combinations of genes. Second, [15] and [6] can only use overexpression as a marker,

192 whereas we will also search for underexpression. Third, [15] and [6] use scores based on pointwise expression

193 levels, whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies).

194 Figures 4, 1, and 3 in the Preliminary Studies section contain evidence that each of our three choices is the right

195 one.

196 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use

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

198 match a target image.

199 _____________________

200 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;

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

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

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

204 different algorithms or scoring methods.

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

206

207

208 Figure 4: Upper left: wwc1. Upper

209 right: mtif2. Lower left: wwc1 + mtif2

210 (each pixel’s value on the lower left is

211 the sum of the corresponding pixels in

212 the upper row). Machine learning terminology: clustering

213 If one is given a dataset consisting merely of instances, with no

214 class labels, then analysis of the dataset is referred to as unsupervised

215 learning in the jargon of machine learning. One thing that you can do

216 with such a dataset is to group instances together. A set of similar

217 instances is called a cluster, and the activity of finding grouping the

218 data into clusters is called clustering or cluster analysis.

219 The task of deciding how to carve up a structure into anatomical

220 regions can be put into these terms. The instances are once again

221 voxels (or pixels) along with their associated gene expression profiles.

222 We make the assumption that voxels from the same anatomical region

223 have similar gene expression profiles, at least compared to the other

224 regions. This means that clustering voxels is the same as finding po-

225 tential regions; we seek a partitioning of the voxels into regions, that is,

226 into clusters of voxels with similar gene expression.

227 It is desirable to determine not just one set of regions, but also how

228 these regions relate to each other. The outcome of clustering may be

229 a hierarchical tree of clusters, rather than a single set of clusters which

230 partition the voxels. This is called hierarchical clustering.

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

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

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

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

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

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

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

238 methods which guarantee contiguous clusters.

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

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

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

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

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

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

245 algorithms are specialized for visual images.

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

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

248 data.

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

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

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

252 _________________________________________

253 3There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are

254 often used to process satellite imagery.

255 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering

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

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

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

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

260

261

262

263

264 Figure 5: From left to right and top

265 to bottom, single genes which roughly

266 identify areas SS (somatosensory pri-

267 mary + supplemental), SSs (supple-

268 mental somatosensory), PIR (piriform),

269 FRP (frontal pole), RSP (retrosple-

270 nial), COApm (Cortical amygdalar, pos-

271 terior part, medial zone). Grouping

272 some areas together, we have also

273 found genes to identify the groups

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

275 cingulate, prelimbic, infralimbic, dor-

276 sal peduncular, orbital, motor), poste-

277 rior and lateral visual (VISpm, VISpl,

278 VISI, VISp; posteromedial, posterolat-

279 eral, lateral, and primary visual; the

280 posterior and lateral visual area is dis-

281 tinguished from its neighbors, but not

282 from the entire rest of the cortex). The

283 genes are Pitx2, Aldh1a2, Ppfibp1,

284 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. Clustering genes rather than voxels Although the ultimate goal is

285 to cluster the instances (voxels or pixels), one strategy to achieve this

286 goal is to first cluster the features (genes). There are two ways that

287 clusters of genes could be used.

288 Gene clusters could be used as part of dimensionality reduction:

289 rather than have one feature for each gene, we could have one reduced

290 feature for each gene cluster.

291 Gene clusters could also be used to directly yield a clustering on

292 instances. This is because many genes have an expression pattern

293 which seems to pick out a single, spatially contiguous region. This

294 suggests the following procedure: cluster together genes which pick

295 out similar regions, and then to use the more popular common regions

296 as the final clusters. In Preliminary Studies, Figure 7, we show that a

297 number of anatomically recognized cortical regions, as well as some

298 “superregions” formed by lumping together a few regions, are associ-

299 ated with gene clusters in this fashion.

300 Related work

301 Some researchers have attempted to parcellate cortex on the basis of

302 non-gene expression data. For example, [18], [2], [19], and [1] asso-

303 ciate spots on the cortex with the radial profile5 of response to some

304 stain ([12] uses MRI), extract features from this profile, and then use

305 similarity between surface pixels to cluster.

306 [23] describes an analysis of the anatomy of the hippocampus us-

307 ing the ABA dataset. In addition to manual analysis, two clustering

308 methods were employed, a modified Non-negative Matrix Factoriza-

309 tion (NNMF), and a hierarchical recursive bifurcation clustering scheme

310 based on correlation as the similarity score. The paper yielded impres-

311 sive results, proving the usefulness of computational genomic anatomy.

312 We have run NNMF on the cortical dataset

313 AGEA[15] includes a preset hierarchical clustering of voxels based

314 on a recursive bifurcation algorithm with correlation as the similarity

315 metric. EMAGE[26] allows the user to select a dataset from among a

316 large number of alternatives, or by running a search query, and then to

317 cluster the genes within that dataset. EMAGE clusters via hierarchical

318 complete linkage clustering.

319 [6] clusters genes. For each cluster, prototypical spatial expression

320 patterns were created by averaging the genes in the cluster. The pro-

321 totypes were analyzed manually, without clustering voxels.

322 [10] applies their technique for finding combinations of marker

323 genes for the purpose of clustering genes around a “seed gene”.

324 In summary, although these projects obtained clusterings, there has

325 not been much comparison between different algorithms or scoring

326 methods, so it is likely that the best clustering method for this appli-

327 cation has not yet been found. The projects using gene expression on

328 cortex did not attempt to make use of the radial profile of gene expression. Also, none of these projects did a

329 _________________________________________

330 5A radial profile is a profile along a line perpendicular to the cortical surface.

331 separate dimensionality reduction step before clustering pixels, none tried to cluster genes first in order to guide

332 automated clustering of pixels into spatial regions, and none used co-clustering algorithms.

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

334

335

336

337

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

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

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

341 row: examples of kmeans clustering applied to reduced datasets

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

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

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

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

346 50 dimensions were used; for NNMF, 6 dimensions were used; for

347 landmark Isomap, 7 dimensions were used. Background

348 The cortex is divided into areas and lay-

349 ers. Because of the cortical columnar or-

350 ganization, the parcellation of the cortex

351 into areas can be drawn as a 2-D map on

352 the surface of the cortex. In the third di-

353 mension, the boundaries between the ar-

354 eas continue downwards into the cortical

355 depth, perpendicular to the surface. The

356 layer boundaries run parallel to the sur-

357 face. One can picture an area of the cortex

358 as a slice of a six-layered cake6.

359 It is known that different cortical areas

360 have distinct roles in both normal function-

361 ing and in disease processes, yet there are

362 no known marker genes for most cortical

363 areas. When it is necessary to divide a

364 tissue sample into cortical areas, this is a

365 manual process that requires a skilled hu-

366 man to combine multiple visual cues and

367 interpret them in the context of their ap-

368 proximate location upon the cortical sur-

369 face.

370 Even the questions of how many ar-

371 eas should be recognized in cortex, and

372 what their arrangement is, are still not com-

373 pletely settled. A proposed division of the

374 cortex into areas is called a cortical map.

375 In the rodent, the lack of a single agreed-

376 upon map can be seen by contrasting the recent maps given by Swanson[22] on the one hand, and Paxinos

377 and Franklin[17] on the other. While the maps are certainly very similar in their general arrangement, significant

378 differences remain.

379 The Allen Mouse Brain Atlas dataset

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

381 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-

382 automatically analyzed to create a digital measurement of gene expression levels at each location in each slice.

383 Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used

384 to measure one single gene; many different mouse brains were needed in order to measure the expression of

385 many genes.

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

387 coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are

388 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain[15].

389 Mus musculus is thought to contain about 22,000 protein-coding genes[28]. The ABA contains data on about

390 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our

391 _________________________________________

392 6Outside of isocortex, the number of layers varies.

393 dataset is derived from only the coronal subset of the ABA7.

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

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

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

397 Related work

398 [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure

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

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

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

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

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

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

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

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

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

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

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

410 different methods.

411 Significance

412

413 Figure 7: Prototypes corresponding to sample gene

414 clusters, clustered by gradient similarity. Region bound-

415 aries for the region that most matches each prototype

416 are overlaid. The method developed in aim (1) will be applied to

417 each cortical area to find a set of marker genes such

418 that the combinatorial expression pattern of those

419 genes uniquely picks out the target area. Finding

420 marker genes will be useful for drug discovery as well

421 as for experimentation because marker genes can be

422 used to design interventions which selectively target

423 individual cortical areas.

424 The application of the marker gene finding algo-

425 rithm to the cortex will also support the development

426 of new neuroanatomical methods. In addition to find-

427 ing markers for each individual cortical areas, we will

428 find a small panel of genes that can find many of the

429 areal boundaries at once. This panel of marker genes

430 will allow the development of an ISH protocol that will allow experimenters to more easily identify which anatom-

431 ical areas are present in small samples of cortex.

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

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

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

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

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

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

438 _________________________________________

439 7The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen

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

441 non-ubiquitous expression pattern”[15].

442 8In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer

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

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

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

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

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

448 The approach: Preliminary Studies

449 Format conversion between SEV, MATLAB, NIFTI

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

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

452 file formats.

453 Flatmap of cortex

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

455 We divided the cortex into hemispheres. Using Caret[7], we created a mesh representation of the surface of the

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

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

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

459 grid into a MATLAB matrix. We manually traced the boundaries of each of 49 cortical areas from the ABA coronal

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

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

462 region data into MATLAB format.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

477 Feature selection and scoring methods

478 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a

479 marker. See, for example, Figure 1.

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

481 each instance as either a member of a particular anatomical area, or not. The target area can be represented

482 as a boolean mask over the surface pixels.

483 We calculated the correlation between each gene and each cortical area. The top row of Figure 2 shows the

484 three genes most correlated with area SS.

485 Conditional entropy

486 __________________

487 9SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

488 For each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene

489 expression boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned

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

491 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the

492 question, “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic

493 regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables

494 predicts the target, conditional entropy would notice, whereas linear methods would not.

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

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

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

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

499 similarity”. The formula is:

500 ∑

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

502 2 &#x22C5; pixel_value1 + pixel_value2

503 2

504 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

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

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

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

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

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

510 Gradient similarity provides information complementary to correlation

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

512 consider Fig. 3. The pointwise method in the top row identifies genes which express more strongly in AUD than

513 outside of it; its weakness is that this includes many areas which don&#8217;t have a salient border matching the areal

514 border. The geometric method identifies genes whose salient expression border seems to partially line up with

515 the border of AUD; its weakness is that this includes genes which don&#8217;t express over the entire area.

516 Areas which can be identified by single genes Using gradient similarity, we have already found single

517 genes which roughly identify some areas and groupings of areas. For each of these areas, an example of

518 a gene which roughly identifies it is shown in Figure 5. We have not yet cross-verified these genes in other

519 atlases.

520 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior

521 part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior

522 cingulate), VIS (visual), AUD (auditory).

523 These results validate our expectation that the ABA dataset can be exploited to find marker genes for many

524 cortical areas, while also validating the relevancy of our new scoring method, gradient similarity.

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

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

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

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

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

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

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

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

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

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

535 area MO much better than any single gene.

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

537 necessary.

538 Multivariate supervised learning

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

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

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

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

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

544 which was found.

545 SVM on all genes at once

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

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

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

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

550 classifier that uses only a few genes.

551 Data-driven redrawing of the cortical map

552 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene ex-

553 pression profile associated with each pixel: Principal Components Analysis (PCA), Simple PCA, Multi-Dimensional

554 Scaling, Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment, Stochastic Proximity

555 Embedding, Fast Maximum Variance Unfolding, Non-negative Matrix Factorization (NNMF). Space constraints

556 prevent us from showing many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in

557 the first, second, and third rows of Figure 6.

558 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we

559 have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are

560 shown in the last row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some

561 of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques

562 capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to

563 produce a detailed comparison of these techniques as applied to the domain of genomic anatomy.

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

565 see if the spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten

566 sample gene clusters, each cluster&#8217;s average expression pattern, compared to a known anatomical boundary.

567 This suggests that it is worth attempting to cluster genes, and then to use the results to cluster pixels.

568 The approach: what we plan to do

569 Flatmap cortex and segment cortical layers

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

571 attempt to preserve size (such as the one used by Caret[7]) with mappings which preserve angle (conformal

572 maps). Our method will include a statistical test that warns the user if the assumption of 2-D structure seems to

573 be wrong.

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

575 like the cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would

576 then be associated with one expression level per gene per layer. We will develop a segmentation algorithm to

577 automatically identify the layer boundaries.

578 __

579 105-fold cross-validation.

580 Develop algorithms that find genetic markers for anatomical regions

581 Scoring measures and feature selection We will develop scoring methods for evaluating how good individual

582 genes are at marking areas. We will compare pointwise, geometric, and information-theoretic measures. We

583 already developed one entirely new scoring method (gradient similarity), but we may develop more. Scoring

584 measures that we will explore will include the L1 norm, correlation, expression energy ratio, conditional entropy,

585 gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such as Student&#8217;s t-

586 test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring measure

587 on genes by taking the prediction error when using that gene to predict the target.

588 Using some combination of these measures, we will develop a procedure to find single marker genes for

589 anatomical regions: for each cortical area, we will rank the genes by their ability to delineate each area. We

590 will quantitatively compare the list of single genes generated by our method to the lists generated by previous

591 methods which are mentioned in Aim 1 Related Work.

592 Some cortical areas have no single marker genes but can be identified by combinatorial coding. This requires

593 multivariate scoring measures and feature selection procedures. Many of the measures, such as expression

594 energy, gradient similarity, Jaccard, Dice, Hough, Student&#8217;s t, and Mann-Whitney U are univariate. We will extend

595 these scoring measures for use in multivariate feature selection, that is, for scoring how well combinations of

596 genes, rather than individual genes, can distinguish a target area. There are existing multivariate forms of some

597 of the univariate scoring measures, for example, Hotelling&#8217;s T-square is a multivariate analog of Student&#8217;s t.

598 We will develop a feature selection procedure for choosing the best small set of marker genes for a given

599 anatomical area. In addition to using the scoring measures that we develop, we will also explore (a) feature

600 selection using a stepwise wrapper over &#8220;vanilla&#8221; classifiers such as logistic regression, (b) supervised learning

601 methods such as decision trees which incrementally/greedily combine single gene markers into sets, and (c)

602 supervised learning methods which use soft constraints to minimize number of features used, such as sparse

603 support vector machines (SVMs).

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

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

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

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

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

609 expense of computation time.

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

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

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

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

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

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

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

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

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

619 dataset.

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

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

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

623 regression (including spatial models[16]), decision trees12, sparse SVMs, generative mixture models (including

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

625 _________________________________________

626 11Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by

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

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

629 12Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision

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

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

632 algorithms, and artificial neural networks.

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

634 Dimensionality reduction on gene expression profiles We have already described the application of ten

635 dimensionality reduction algorithms for the purpose of replacing the gene expression profiles, which are vectors

636 of about 4000 gene expression levels, with a smaller number of features. We plan to further explore and interpret

637 these results, as well as to apply other unsupervised learning algorithms, including independent components

638 analysis, self-organizing maps, and generative models such as deep Boltzmann machines. We will explore ways

639 to quantitatively compare the relevance of the different dimensionality reduction methods for identifying cortical

640 areal boundaries.

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

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

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

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

645 segment the pixels into regions. We will explore k-means, spectral clustering, gene shaving[9], recursive division

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

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

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

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

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

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

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

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

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

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

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

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

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

659 features (in our case, genes and pixels), for example, IRM[11]. These are called co-clustering or biclustering

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[8].

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 Timeline and milestones

686 Finding marker genes

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

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

689 for each layer

690 October 2009-April 2010: Develop scoring methods, dimensionality reduction, and supervised learning meth-

691 ods.

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 for Aim 2. Explore clustering algorithms.

701 Adapt 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. If

704 new ways of organizing the cortex into areas are discovered, interpret the results. Prepare software toolbox for

705 Aim 2.

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

707 Aim 2

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

709 Possibly submit another paper.

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