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 ______________

34 The Challenge and Potential impact

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

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

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

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

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

40

41 Figure 1: Gene Pitx2

42 is selectively underex-

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

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

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

46 inferred.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

66 with other aspects of training.

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

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

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

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

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

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

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

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

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

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

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

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

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

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 now turn to efforts to find marker genes using spatial gene ex-

173 pression data using automated methods.

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

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

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

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

178 search for combinations of genes that define a region in concert but not

179 separately.

180 [15] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA

181 has three components. Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which

182 includes the seed voxel, (2) yields a list of genes which are overexpressed in that cluster. Correlation: The

183 user selects a seed voxel and the system then shows the user how much correlation there is between the gene

184 expression profile of the seed voxel and every other voxel. Clusters: will be described later. [6] looks at the mean

185 expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni correction to

186 determine whether the mean expression level of a gene is significantly higher in the target region. [15] and [6]

187 differ from our Aim 1 in at least three ways. First, [15] and [6] find only single genes, whereas we will also look

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

189 search for underexpression. Third, [15] and [6] use scores based on pointwise expression levels, whereas we

190 will also use geometric scores such as gradient similarity (described in Preliminary Studies). Figures 4, 1, and 3

191 in the Preliminary Studies section contain evidence that each of our three choices is the right one.

192 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use

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

194 match a target image.

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

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

197 different algorithms or scoring methods.

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

199 Machine learning terminology: clustering

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

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

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

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

204 _________________________________________

205 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;

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

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

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

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

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

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

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

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

214 the voxels. This is called hierarchical clustering.

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

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

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

218

219

220 Figure 4: Upper left: wwc1. Upper

221 right: mtif2. Lower left: wwc1 + mtif2

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

223 the sum of the corresponding pixels in

224 the upper row). Spatially contiguous clusters; image segmentation We have

225 shown that aim 2 is a type of clustering task. In fact, it is a special

226 type of clustering task because we have an additional constraint on

227 clusters; voxels grouped together into a cluster must be spatially con-

228 tiguous. In Preliminary Studies, we show that one can get reasonable

229 results without enforcing this constraint; however, we plan to compare

230 these results against other methods which guarantee contiguous clus-

231 ters.

232 Image segmentation is the task of partitioning the pixels in a digital

233 image into clusters, usually contiguous clusters. Aim 2 is similar to an

234 image segmentation task. There are two main differences; in our task,

235 there are thousands of color channels (one for each gene), rather than

236 just three3. A more crucial difference is that there are various cues

237 which are appropriate for detecting sharp object boundaries in a visual

238 scene but which are not appropriate for segmenting abstract spatial

239 data such as gene expression. Although many image segmentation

240 algorithms can be expected to work well for segmenting other sorts of

241 spatially arranged data, some of these algorithms are specialized for

242 visual images.

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

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

245 data.

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

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

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

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

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

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

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

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

254 could be used.

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

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

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

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

259 _________________________________________

260 3There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are

261 often used to process satellite imagery.

262 4First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering

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

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

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

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

267 gene clusters in this fashion.

268

269

270

271

272 Figure 5: From left to right and top

273 to bottom, single genes which roughly

274 identify areas SS (somatosensory pri-

275 mary + supplemental), SSs (supple-

276 mental somatosensory), PIR (piriform),

277 FRP (frontal pole), RSP (retrosple-

278 nial), COApm (Cortical amygdalar, pos-

279 terior part, medial zone). Grouping

280 some areas together, we have also

281 found genes to identify the groups

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

283 cingulate, prelimbic, infralimbic, dor-

284 sal peduncular, orbital, motor), poste-

285 rior and lateral visual (VISpm, VISpl,

286 VISI, VISp; posteromedial, posterolat-

287 eral, lateral, and primary visual; the

288 posterior and lateral visual area is dis-

289 tinguished from its neighbors, but not

290 from the entire rest of the cortex). The

291 genes are Pitx2, Aldh1a2, Ppfibp1,

292 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. Related work

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

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

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

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

297 similarity between surface pixels to cluster.

298 [23] describes an analysis of the anatomy of the hippocampus us-

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

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

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

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

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

304 We have run NNMF on the cortical dataset

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

306 on a recursive bifurcation algorithm with correlation as the similarity

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

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

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

310 complete linkage clustering.

311 [6] clusters genes. For each cluster, prototypical spatial expression

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

313 totypes were analyzed manually, without clustering voxels.

314 [10] applies their technique for finding combinations of marker genes

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

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

317 not been much comparison between different algorithms or scoring

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

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

320 on cortex did not attempt to make use of the radial profile of gene ex-

321 pression. Also, none of these projects did a separate dimensionality

322 reduction step before clustering pixels, none tried to cluster genes first

323 in order to guide automated clustering of pixels into spatial regions, and

324 none used co-clustering algorithms.

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

326 Background

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

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

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

330 the boundaries between the areas continue downwards into the cortical

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

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

333 six-layered cake6.

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

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

336 _________________________________________

337 5A radial profile is a profile along a line perpendicular to the cortical surface.

338 6Outside of isocortex, the number of layers varies.

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

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

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

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

343

344

345

346

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

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

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

350 row: examples of kmeans clustering applied to reduced datasets

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

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

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

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

355 50 dimensions were used; for NNMF, 6 dimensions were used; for

356 landmark Isomap, 7 dimensions were used. Even the questions of how many ar-

357 eas should be recognized in cortex, and

358 what their arrangement is, are still not com-

359 pletely settled. A proposed division of the

360 cortex into areas is called a cortical map.

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

362 upon map can be seen by contrasting the

363 recent maps given by Swanson[22] on the

364 one hand, and Paxinos and Franklin[17] on

365 the other. While the maps are certainly

366 very similar in their general arrangement,

367 significant differences remain.

368 The Allen Mouse Brain Atlas dataset

369 The Allen Mouse Brain Atlas (ABA)

370 data were produced by doing in-situ hy-

371 bridization on slices of male, 56-day-old

372 C57BL/6J mouse brains. Pictures were

373 taken of the processed slice, and these pic-

374 tures were semi-automatically analyzed to

375 create a digital measurement of gene ex-

376 pression levels at each location in each

377 slice. Per slice, cellular spatial resolution

378 is achieved. Using this method, a single

379 physical slice can only be used to measure

380 one single gene; many different mouse

381 brains were needed in order to measure

382 the expression of many genes.

383 An automated nonlinear alignment pro-

384 cedure located the 2D data from the var-

385 ious slices in a single 3D coordinate system. In the final 3D coordinate system, voxels are cubes with 200

386 microns on a side. There are 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in

387 the brain[15].

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

389 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our

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

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

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

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

394 Related work

395 [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure

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

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

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

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

400 _________________________________________

401 7The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen

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

403 non-ubiquitous expression pattern”[15].

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

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

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

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

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

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

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

411 different methods.

412 Significance

413

414 Figure 7: Prototypes corresponding to sample gene

415 clusters, clustered by gradient similarity. Region bound-

416 aries for the region that most matches each prototype

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

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

419 that the combinatorial expression pattern of those

420 genes uniquely picks out the target area. Finding

421 marker genes will be useful for drug discovery as well

422 as for experimentation because marker genes can be

423 used to design interventions which selectively target

424 individual cortical areas.

425 The application of the marker gene finding algo-

426 rithm to the cortex will also support the development

427 of new neuroanatomical methods. In addition to find-

428 ing markers for each individual cortical areas, we will

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

430 areal boundaries at once. This panel of marker genes

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

432 ical areas are present in small samples of cortex.

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

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

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

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

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

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

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

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

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

442 _______________________________

443 The approach: Preliminary Studies

444 Format conversion between SEV, MATLAB, NIFTI

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

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

447 file formats.

448 Flatmap of cortex

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

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

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

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

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

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

455 8In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer

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

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

458 9SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

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

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

461 region data into MATLAB format.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

476 Feature selection and scoring methods

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

478 marker. See, for example, Figure 1.

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

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

481 as a boolean mask over the surface pixels.

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

483 three genes most correlated with area SS.

484 Conditional entropy

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

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

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

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

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

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

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

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

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

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

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

496 similarity”. The formula is:

497 ∑

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

499 2 &#x22C5; pixel_value1 + pixel_value2

500 2

501 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

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

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

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

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

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

507 Gradient similarity provides information complementary to correlation

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

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

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

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

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

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

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

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

516 atlases.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

532 area MO much better than any single gene.

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

534 necessary.

535 Multivariate supervised learning

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

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

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

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

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

541 which was found.

542 SVM on all genes at once

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

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

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

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

547 classifier that uses only a few genes.

548 Data-driven redrawing of the cortical map

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

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

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

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

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

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

555 _

556 105-fold cross-validation.

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

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

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

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

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

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

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

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

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

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

567 The approach: what we plan to do

568 Flatmap cortex and segment cortical layers

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

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

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

572 be wrong.

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

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

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

576 automatically identify the layer boundaries.

577 Develop algorithms that find genetic markers for anatomical regions

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

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

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

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

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

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

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

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

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

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

588 methods which are mentioned in Aim 1 Related Work.

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

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

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

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

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

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

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

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

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

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

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

600 support vector machines (SVMs).

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

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

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

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

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

606 expense of computation time.

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

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

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

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

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

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

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

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

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

616 dataset.

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

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

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

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

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

622 algorithms, and artificial neural networks.

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

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

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

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

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

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

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

630 areal boundaries.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

650 _________________________________________

651 11Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by

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

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

654 12Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision

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

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

657 algorithms.

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

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

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

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

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

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

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

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

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

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

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

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

670 Apply the new methods to the cortex

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

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

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

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

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

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

677 expression datasets such as EMAGE, GeneAtlas, and GENSAT[8].

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

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

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

681 areas, which are discovered.

682 ____________________________________________________________________________

683 Timeline and milestones

684 Finding marker genes

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

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

687 for each layer

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

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

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

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

692 toolbox for Aim 1.

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

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

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

696 Revealing new ways to parcellate a structure into regions

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

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

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

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

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

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

703 Aim 2

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

705 Possibly submit another paper.

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