1 Specific aims

2 Massive new datasets obtained with techniques such as in situ hybridization

3 (ISH) and BAC-transgenics allow the expression levels of many genes at many

4 locations to be compared. Our goal is to develop automated methods to relate

5 spatial variation in gene expression to anatomy. We want to find marker genes

6 for specific anatomical regions, and also to draw new anatomical maps based on

7 gene expression patterns. We have three specific aims:

8 (1) develop an algorithm to screen spatial gene expression data for combina-

9 tions of marker genes which selectively target anatomical regions

10 (2) develop an algorithm to suggest new ways of carving up a structure into

11 anatomical subregions, based on spatial patterns in gene expression

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

13 a flattened version of the Allen Mouse Brain Atlas ISH data, as well as

14 the boundaries of cortical anatomical areas. Use this dataset to validate

15 the methods developed in (1) and (2).

16 In addition to validating the usefulness of the algorithms, the application of

17 these methods to cerebral cortex will produce immediate benefits, because there

18 are currently no known genetic markers for many cortical areas. The results

19 of the project will support the development of new ways to selectively target

20 cortical areas, and it will support the development of a method for identifying

21 the cortical areal boundaries present in small tissue samples.

22 All algorithms that we develop will be implemented in an open-source soft-

23 ware toolkit. The toolkit, as well as the machine-readable datasets developed

24 in aim (3), will be published and freely available for others to use.

25 Background and significance

26 Aim 1

27 Machine learning terminology: supervised learning

28 The task of looking for marker genes for anatomical subregions means that

29 one is looking for a set of genes such that, if the expression level of those genes

30 is known, then the locations of the subregions can be inferred.

31 If we define the subregions so that they cover the entire anatomical structure

32 to be divided, then instead of saying that we are using gene expression to find

33 the locations of the subregions, we may say that we are using gene expression to

34 determine to which subregion each voxel within the structure belongs. We call

35 this a classification task, because each voxel is being assigned to a class (namely,

36 its subregion).

37 Therefore, an understanding of the relationship between the combination of

38 their expression levels and the locations of the subregions may be expressed as

39 a function. The input to this function is a voxel, along with the gene expression

40 1

41

42 levels within that voxel; the output is the subregional identity of the target

43 voxel, that is, the subregion to which the target voxel belongs. We call this

44 function a classifier. In general, the input to a classifier is called an instance,

45 and the output is called a label (or a class label).

46 The object of aim 1 is not to produce a single classifier, but rather to develop

47 an automated method for determining a classifier for any known anatomical

48 structure. Therefore, we seek a procedure by which a gene expression dataset

49 may be analyzed in concert with an anatomical atlas in order to produce a

50 classifier. Such a procedure is a type of a machine learning procedure. The

51 construction of the classifier is called training (also learning), and the initial

52 gene expression dataset used in the construction of the classifier is called training

53 data.

54 In the machine learning literature, this sort of procedure may be thought

55 of as a supervised learning task, defined as a task in whcih the goal is to learn

56 a mapping from instances to labels, and the training data consists of a set of

57 instances (voxels) for which the labels (subregions) are known.

58 Each gene expression level is called a feature, and the selection of which

59 genes to include is called feature selection. Feature selection is one component

60 of the task of learning a classifier. Some methods for learning classifiers start

61 out with a separate feature selection phase, whereas other methods combine

62 feature selection with other aspects of training.

63 One class of feature selection methods assigns some sort of score to each

64 candidate gene. The top-ranked genes are then chosen. Some scoring measures

65 can assign a score to a set of selected genes, not just to a single gene; in this

66 case, a dynamic procedure may be used in which features are added and sub-

67 tracted from the selected set depending on how much they raise the score. Such

68 procedures are called “stepwise” or “greedy”.

69 Although the classifier itself may only look at the gene expression data within

70 each voxel before classifying that voxel, the learning algorithm which constructs

71 the classifier may look over the entire dataset. We can categorize score-based

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

73 the score calculation consists of assigning a sub-score to each voxel, and then

74 aggregating these sub-scores into a final score (the aggregation is often a sum or

75 a sum of squares). If only information from nearby voxels is used to calculate a

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

77 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a

78 pointwise scoring method.

79 Key questions when choosing a learning method are: What are the instances?

80 What are the features? How are the features chosen? Here are four principles

81 that outline our answers to these questions.

82 Principle 1: Combinatorial gene expression

83 Above, we defined an “instance” as the combination of a voxel with the

84 “associated gene expression data”. In our case this refers to the expression level

85 of genes within the voxel, but should we include the expression levels of all

86 genes, or only a few of them?

87 It is too much to hope that every anatomical region of interest will be iden-

88 2

89

90 tified by a single gene. For example, in the cortex, there are some areas which

91 are not clearly delineated by any gene included in the Allen Brain Atlas (ABA)

92 dataset. However, at least some of these areas can be delineated by looking

93 at combinations of genes (an example of an area for which multiple genes are

94 necessary and sufficient is provided in Preliminary Results).

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

96 When the classifier classifies a voxel, it is only allowed to look at the expres-

97 sion of the genes which have been selected as features. The more data that is

98 available to a classifier, the better that it can do. For example, perhaps there

99 are weak correlations over many genes that add up to a strong signal. So, why

100 not include every gene as a feature? The reason is that we wish to employ

101 the classifier in situations in which it is not feasible to gather data about every

102 gene. For example, if we want to use the expression of marker genes as a trigger

103 for some regionally-targeted intervention, then our intervention must contain a

104 molecular mechanism to check the expression level of each marker gene before

105 it triggers. It is currently infeasible to design a molecular trigger that checks

106 the level of more than a handful of genes. Similarly, if the goal is to develop a

107 procedure to do ISH on tissue samples in order to label their anatomy, then it

108 is infeasible to label more than a few genes. Therefore, we must select only a

109 few genes as features.

110 Principle 3: Use geometry in feature selection

111 When doing feature selection with score-based methods, the simplest thing

112 to do would be to score the performance of each voxel by itself and then com-

113 bine these scores (pointwise scoring). A more powerful approach is to also use

114 information about the geometric relations between each voxel and its neighbors;

115 this requires non-pointwise, local scoring methods. See Preliminary Results for

116 evidence of the complementary nature of pointwise and local scoring methods.

117 Principle 4: Work in 2-D whenever possible

118 There are many anatomical structures which are commonly characterized in

119 terms of a two-dimensional manifold. When it is known that the structure that

120 one is looking for is two-dimensional, the results may be improved by allowing

121 the analysis algorithm to take advantage of this prior knowledge. In addition,

122 it is easier for humans to visualize and work with 2-D data.

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

124 Aim 2

125 Machine learning terminology: clustering

126 If one is given a dataset consisting merely of instances, with no class labels,

127 then analysis of the dataset is referred to as unsupervised learning in the jargon

128 of machine learning. One thing that you can do with such a dataset is to group

129 instances together. A set of similar instances is called a cluster, and the activity

130 of finding grouping the data into clusters is called clustering or cluster analysis.

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

132 can be put into these terms. The instances are once again voxels (or pixels)

133 along with their associated gene expression profiles. We make the assumption

134 3

135

136 that voxels from the same subregion have similar gene expression profiles, at

137 least compared to the other subregions. This means that clustering voxels is

138 the same as finding potential subregions; we seek a partitioning of the voxels

139 into subregions, that is, into clusters of voxels with similar gene expression.

140 It is desirable to determine not just one set of subregions, but also how

141 these subregions relate to each other, if at all; perhaps some of the subregions

142 are more similar to each other than to the rest, suggesting that, although at a

143 fine spatial scale they could be considered separate, on a coarser spatial scale

144 they could be grouped together into one large subregion. This suggests the

145 outcome of clustering may be a hierarchial tree of clusters, rather than a single

146 set of clusters which partition the voxels. This is called hierarchial clustering.

147 Similarity scores

148 todo

149 Spatially contiguous clusters; image segmentation

150 We have shown that aim 2 is a type of clustering task. In fact, it is a

151 special type of clustering task because we have an additional constraint on

152 clusters; voxels grouped together into a cluster must be spatially contiguous.

153 In Preliminary Results, we show that one can get reasonable results without

154 enforcing this constraint, however, we plan to compare these results against

155 other methods which guarantee contiguous clusters.

156 Perhaps the biggest source of continguous clustering algorithms is the field

157 of computer vision, which has produced a variety of image segmentation algo-

158 rithms. Image segmentation is the task of partitioning the pixels in a digital

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

160 segmentation task. There are two main differences; in our task, there are thou-

161 sands of color channels (one for each gene), rather than just three. There are

162 imaging tasks which use more than three colors, however, for example multispec-

163 tral imaging and hyperspectral imaging, which are often used to process satellite

164 imagery. A more crucial difference is that there are various cues which are ap-

165 propriate for detecting sharp object boundaries in a visual scene but which are

166 not appropriate for segmenting abstract spatial data such as gene expression.

167 Although many image segmentation algorithms can be expected to work well

168 for segmenting other sorts of spatially arranged data, some of these algorithms

169 are specialized for visual images.

170 Dimensionality reduction

171 Unlike aim 1, there is no externally-imposed need to select only a handful

172 of informative genes for inclusion in the instances. However, some clustering

173 algorithms perform better on small numbers of features. There are techniques

174 which “summarize” a larger number of features using a smaller number of fea-

175 tures; these techniques go by the name of feature extraction or dimensionality

176 reduction. The small set of features that such a technique yields is called the

177 reduced feature set. After the reduced feature set is created, the instances may

178 be replaced by reduced instances, which have as their features the reduced fea-

179 ture set rather than the original feature set of all gene expression levels. Note

180 that the features in the reduced feature set do not necessarily correspond to

181 genes; each feature in the reduced set may be any function of the set of gene

182 4

183

184 expression levels.

185 Another use for dimensionality reduction is to visualize the relationships

186 between subregions. For example, one might want to make a 2-D plot upon

187 which each subregion is represented by a single point, and with the property

188 that subregions with similar gene expression profiles should be nearby on the

189 plot (that is, the property that distance between pairs of points in the plot

190 should be proportional to some measure of dissimilarity in gene expression). It

191 is likely that no arrangement of the points on a 2-D plan will exactly satisfy

192 this property – however, dimensionality reduction techniques allow one to find

193 arrangements of points that approximately satisfy that property. Note that

194 in this application, dimensionality reduction is being applied after clustering;

195 whereas in the previous paragraph, we were talking about using dimensionality

196 reduction before clustering.

197 Clustering genes rather than voxels

198 Although the ultimate goal is to cluster the instances (voxels or pixels), one

199 strategy to achieve this goal is to first cluster the features (genes). There are

200 two ways that clusters of genes could be used.

201 Gene clusters could be used as part of dimensionality reduction: rather than

202 have one feature for each gene, we could have one reduced feature for each gene

203 cluster.

204 Gene clusters could also be used to directly yield a clustering on instances.

205 This is because many genes have an expression pattern which seems to pick

206 out a single, spatially continguous subregion. Therefore, it seems likely that an

207 anatomically interesting subregion will have multiple genes which each individ-

208 ually pick it out1. This suggests the following procedure: cluster together genes

209 which pick out similar subregions, and then to use the more popular common

210 subregions as the final clusters. In the Preliminary Data we show that a num-

211 ber of anatomically recognized cortical regions, as well as some “superregions”

212 formed by lumping together a few regions, are associated with gene clusters in

213 this fashion.

214 Aim 3

215 Background

216 The cortex is divided into areas and layers. To a first approximation, the

217 parcellation of the cortex into areas can be drawn as a 2-D map on the surface of

218 the cortex. In the third dimension, the boundaries between the areas continue

219 downwards into the cortical depth, perpendicular to the surface. The layer

220 boundaries run parallel to the surface. One can picture an area of the cortex as

221 a slice of many-layered cake.

222 ___

223 1This would seem to contradict our finding in aim 1 that some cortical areas are combina-

224 torially coded by multiple genes. However, it is possible that the currently accepted cortical

225 maps divide the cortex into subregions which are unnatural from the point of view of gene

226 expression; perhaps there is some other way to map the cortex for which each subregion can

227 be identified by single genes.

228 5

229

230 Although it is known that different cortical areas have distinct roles in both

231 normal functioning and in disease processes, there are no known marker genes

232 for many cortical areas. When it is necessary to divide a tissue sample into

233 cortical areas, this is a manual process that requires a skilled human to combine

234 multiple visual cues and interpret them in the context of their approximate

235 location upon the cortical surface.

236 Even the questions of how many areas should be recognized in cortex, and

237 what their arrangement is, are still not completely settled. A proposed division

238 of the cortex into areas is called a cortical map. In the rodent, the lack of a

239 single agreed-upon map can be seen by contrasting the recent maps given by

240 Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While

241 the maps are certainly very similar in their general arrangement, significant

242 differences remain in the details.

243 Significance

244 The method developed in aim (1) will be applied to each cortical area to find

245 a set of marker genes such that the combinatorial expression pattern of those

246 genes uniquely picks out the target area. Finding marker genes will be useful

247 for drug discovery as well as for experimentation because marker genes can be

248 used to design interventions which selectively target individual cortical areas.

249 The application of the marker gene finding algorithm to the cortex will

250 also support the development of new neuroanatomical methods. In addition to

251 finding markers for each individual cortical areas, we will find a small panel

252 of genes that can find many of the areal boundaries at once. This panel of

253 marker genes will allow the development of an ISH protocol that will allow

254 experimenters to more easily identify which anatomical areas are present in

255 small samples of cortex.

256 The method developed in aim (3) will provide a genoarchitectonic viewpoint

257 that will contribute to the creation of a better map. The development of present-

258 day cortical maps was driven by the application of histological stains. It is

259 conceivable that if a different set of stains had been available which identified

260 a different set of features, then the today’s cortical maps would have come out

261 differently. Since the number of classes of stains is small compared to the number

262 of genes, it is likely that there are many repeated, salient spatial patterns in

263 the gene expression which have not yet been captured by any stain. Therefore,

264 current ideas about cortical anatomy need to incorporate what we can learn

265 from looking at the patterns of gene expression.

266 While we do not here propose to analyze human gene expression data, it is

267 conceivable that the methods we propose to develop could be used to suggest

268 modifications to the human cortical map as well.

269 Related work

270 todo

271 vs. AGEA – i wrote something on this but i’m going to rewrite it

272 6

273

274 Preliminary work

275 Format conversion between SEV, MATLAB, NIFTI

276 todo

277 Flatmap of cortex

278 todo

279 Using combinations of multiple genes is necessary and sufficient to

280 delineate some cortical areas

281 Here we give an example of a cortical area which is not marked by any

282 single gene, but which can be identified combinatorially. according to logistic

283 regression, gene wwc12 is the best fit single gene for predicting whether or not a

284 pixel on the cortical surface belongs to the motor area (area MO). The upper-left

285 picture in Figure shows wwc1’s spatial expression pattern over the cortex. The

286 lower-right boundary of MO is represented reasonably well by this gene, however

287 the gene overshoots the upper-left boundary. This flattened 2-D representation

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

289 surface of the cortex. MO is only found on the lateral surface (todo).

290 Gnee mtif23 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s

291 upper-left boundary, but not its lower-right boundary. Mtif2 does not express

292 very much on the medial surface. By adding together the values at each pixel

293 in these two figures, we get the lower-left of Figure . This combination captures

294 area MO much better than any single gene.

295 Geometric and pointwise scoring methods provide complementary

296 information

297 To show that local geometry can provide useful information that cannot be

298 detected via pointwise analyses, consider Fig. . The top row of Fig. displays the

299 3 genes which most match area AUD, according to a pointwise method4. The

300 bottom row displays the 3 genes which most match AUD according to a method

301 which considers local geometry5 The pointwise method in the top row identifies

302 genes which express more strongly in AUD than outside of it; its weakness is that

303 this includes many areas which don’t have a salient border matching the areal

304 border. The geometric method identifies genes whose salient expression border

305 seems to partially line up with the border of AUD; its weakness is that this

306 includes genes which don’t express over the entire area. Genes which have high

307 rankings using both pointwise and border criteria, such as Aph1a in the example,

308 __________________________

309 2“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652

310 3“mitochondrial translational initiation factor 2”; EntrezGene ID 76784

311 4For each gene, a logistic regression in which the response variable was whether or not a

312 surface pixel was within area AUD, and the predictor variable was the value of the expression

313 of the gene underneath that pixel. The resulting scores were used to rank the genes in terms

314 of how well they predict area AUD.

315 5For each gene the gradient similarity (see section ??) between (a) a map of the expression

316 of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this

317 was used to rank the genes.

318 7

319

320

321

322 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2

323 (each pixel’s value on the lower left is the sum of the corresponding pixels in

324 the upper row). Within each picture, the vertical axis roughly corresponds to

325 anterior at the top and posterior at the bottom, and the horizontal axis roughly

326 corresponds to medial at the left and lateral at the right. The red outline is

327 the boundary of region MO. Pixels are colored approximately according to the

328 density of expressing cells underneath each pixel, with red meaning a lot of

329 expression and blue meaning little.

330 8

331

332

333

334 Figure 2: The top row shows the three genes which (individually) best predict

335 area AUD, according to logistic regression. The bottom row shows the three

336 genes which (individually) best match area AUD, according to gradient similar-

337 ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a,

338 Ptk7, Aph1a again, and Lepr

339 may be particularly good markers. None of these genes are, individually, a

340 perfect marker for AUD; we deliberately chose a “difficult” area in order to

341 better contrast pointwise with geometric methods.

342 Areas which can be identified by single genes

343 todo

344 Aim 1 (and Aim 3)

345 SVM on all genes at once

346 In order to see how well one can do when looking at all genes at once, we

347 ran a support vector machine to classify cortical surface pixels based on their

348 gene expression profiles. We achieved classification accuracy of about 81%6.

349 As noted above, however, a classifier that looks at all the genes at once isn’t

350 practically useful.

351 The requirement to find combinations of only a small number of genes limits

352 us from straightforwardly applying many of the most simple techniques from

353 the field of supervised machine learning. In the parlance of machine learning,

354 our task combines feature selection with supervised learning.

355 Decision trees

356 todo

357 ____________________

358 6Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multi-

359 class b-SVM), kernal = gaussian with sigma = 0.1, c = 10, epsilon = 1e-1 – these are the

360 first parameters we tried, so presumably performance would improve with different choices of

361 parameters. 5-fold cross-validation.

362 9

363

364 Aim 2 (and Aim 3)

365 Raw dimensionality reduction results

366 Dimensionality reduction plus K-means or spectral clus-

367 tering

368 Many areas are captured by clusters of genes

369 todo

370 todo

371 Research plan

372 todo

373 amongst other thigns:

374 Develop algorithms that find genetic markers for anatomical re-

375 gions

376 1. Develop scoring measures for evaluating how good individual genes are at

377 marking areas: we will compare pointwise, geometric, and information-

378 theoretic measures.

379 2. Develop a procedure to find single marker genes for anatomical regions: for

380 each cortical area, by using or combining the scoring measures developed,

381 we will rank the genes by their ability to delineate each area.

382 3. Extend the procedure to handle difficult areas by using combinatorial cod-

383 ing: for areas that cannot be identified by any single gene, identify them

384 with a handful of genes. We will consider both (a) algorithms that incre-

385 mentally/greedily combine single gene markers into sets, such as forward

386 stepwise regression and decision trees, and also (b) supervised learning

387 techniques which use soft constraints to minimize the number of features,

388 such as sparse support vector machines.

389 4. Extend the procedure to handle difficult areas by combining or redrawing

390 the boundaries: An area may be difficult to identify because the bound-

391 aries are misdrawn, or because it does not “really” exist as a single area,

392 at least on the genetic level. We will develop extensions to our procedure

393 which (a) detect when a difficult area could be fit if its boundary were

394 redrawn slightly, and (b) detect when a difficult area could be combined

395 with adjacent areas to create a larger area which can be fit.

396 Apply these algorithms to the cortex

397 1. Create open source format conversion tools: we will create tools to bulk

398 download the ABA dataset and to convert between SEV, NIFTI and MAT-

399 LAB formats.

400 10

401

402 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw

403 the cortical area boundaries onto it.

404 3. Find layer boundaries: cluster similar voxels together in order to auto-

405 matically find the cortical layer boundaries.

406 4. Run the procedures that we developed on the cortex: we will present, for

407 each area, a short list of markers to identify that area; and we will also

408 present lists of “panels” of genes that can be used to delineate many areas

409 at once.

410 Develop algorithms to suggest a division of a structure into anatom-

411 ical parts

412 1. Explore dimensionality reduction algorithms applied to pixels: including

413 TODO

414 2. Explore dimensionality reduction algorithms applied to genes: including

415 TODO

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

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

418 TODO

419 5. Develop an algorithm to use dimensionality reduction and/or hierarchial

420 clustering to create anatomical maps

421 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic

422 map of the cortex

423 ______________________________________________

424 stuff i dunno where to put yet (there is more scattered through grant-

425 oldtext):

426 Principle 4: Work in 2-D whenever possible

427 In anatomy, the manifold of interest is usually either defined by a combina-

428 tion of two relevant anatomical axes (todo), or by the surface of the structure

429 (as is the case with the cortex). In the former case, the manifold of interest is

430 a plane, but in the latter case it is curved. If the manifold is curved, there are

431 various methods for mapping the manifold into a plane.

432 The method that we will develop will begin by mapping the data into a

433 2-D plane. Although the manifold that characterized cortical areas is known

434 to be the cortical surface, it remains to be seen which method of mapping the

435 manifold into a plane is optimal for this application. We will compare mappings

436 which attempt to preserve size (such as the one used by Caret??) with mappings

437 which preserve angle (conformal maps).

438 Although there is much 2-D organization in anatomy, there are also struc-

439 tures whose shape is fundamentally 3-dimensional. If possible, we would like

440 the method we develop to include a statistical test that warns the user if the

441 assumption of 2-D structure seems to be wrong.

442 11

443

444