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 one

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

30 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 1

40

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

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 “asso-

84 ciated gene expression data”. In our case this refers to the expression level of

85 2

86

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

88 or only a few of them?

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

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 expression of

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

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

99 correlations over many genes that add up to a strong signal. So, why not include

100 every gene as a feature? The reason is that we wish to employ the classifier in

101 situations in which it is not feasible to gather data about every gene. For

102 example, if we want to use the expression of marker genes as a trigger for some

103 regionally-targeted intervention, then our intervention must contain a molecular

104 mechanism to check the expression level of each marker gene before it triggers.

105 It is currently infeasible to design a molecular trigger that checks the level of

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

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

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

109 features.

110 Principle 3: Use geometry in feature selection

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

112 would be to score the performance of each voxel by itself and then combine these

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

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

115 non-pointwise, local scoring methods. See Preliminary Results for evidence of

116 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 3

125

126 Aim 2

127 Machine learning terminology: clustering

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

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

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

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

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

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

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

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

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 special type

151 of clustering task because we have an additional constraint on clusters; voxels

152 grouped together into a cluster must be spatially contiguous. In Preliminary

153 Results, we show that one can get reasonable results without enforcing this

154 constraint, however, we plan to compare these results against other methods

155 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 4

168

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

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

171 are specialized for visual images.

172 Dimensionality reduction

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

174 informative genes for inclusion in the instances. However, some clustering al-

175 gorithms perform better on small numbers of features. There are techniques

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

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

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

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

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

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

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

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

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 __________________________

210 1This would seem to contradict our finding in aim 1 that some cortical areas are combina-

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

212 5

213

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

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

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

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

218 this fashion.

219 Aim 3

220 Background

221 The cortex is divided into areas and layers. To a first approximation, the par-

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

223 of the cortex. In the third dimension, the boundaries between the areas con-

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

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

226 a slice of many-layered cake.

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

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

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

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

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

232 location upon the cortical surface.

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

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

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

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

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

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

239 differences remain in the details.

240 Significance

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

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

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

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

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

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

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

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

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

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

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

252 small samples of cortex.

253 ______

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

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

256 be identified by single genes.

257 6

258

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

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

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

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

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

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

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

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

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

268 from looking at the patterns of gene expression.

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

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

271 modifications to the human cortical map as well.

272 Related work

273 todo

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

275 Preliminary work

276 Format conversion between SEV, MATLAB, NIFTI

277 todo

278 Flatmap of cortex

279 todo

280 Using combinations of multiple genes is necessary and sufficient to

281 delineate some cortical areas

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

283 gene, but which can be identified combinatorially. according to logistic regres-

284 sion, gene wwc12 is the best fit single gene for predicting whether or not a pixel

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

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

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

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

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

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

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

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

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

294 __________________________

295 2“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652

296 3“mitochondrial translational initiation factor 2”; EntrezGene ID 76784

297 7

298

299

300

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

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

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

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

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

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

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

308 expression and blue meaning little.

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

310 area MO much better than any single gene.

311 Geometric and pointwise scoring methods provide complementary

312 information

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

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

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

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

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

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

319 __________________________

320 4For each gene, a logistic regression in which the response variable was whether or not a

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

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

323 of how well they predict area AUD.

324 5For each gene the gradient similarity (see section ??) between (a) a map of the expression

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

326 was used to rank the genes.

327 8

328

329

330

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

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

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

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

335 Ptk7, Aph1a again, and Lepr

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

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

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

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

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

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

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

343 better contrast pointwise with geometric methods.

344 Areas which can be identified by single genes

345 todo

346 Aim 1 (and Aim 3)

347 SVM on all genes at once

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

349 a support vector machine to classify cortical surface pixels based on their gene

350 expression profiles. We achieved classification accuracy of about 81%6. As noted

351 above, however, a classifier that looks at all the genes at once isn’t practically

352 useful.

353 _____________________

354 6Using the Shogun SVM package (todo:cite), with parameters type=GMNPSVM (multi-

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

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

357 parameters. 5-fold cross-validation.

358 9

359

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

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

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

363 our task combines feature selection with supervised learning.

364 Decision trees

365 todo

366 Aim 2 (and Aim 3)

367 Raw dimensionality reduction results

368 Dimensionality reduction plus K-means or spectral clus-

369 tering

370 Many areas are captured by clusters of genes

371 todo

372 todo

373 Research plan

374 todo

375 amongst other thigns:

376 Develop algorithms that find genetic markers for anatomical regions

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

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

379 theoretic measures.

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

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

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

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

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

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

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

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

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

389 such as sparse support vector machines.

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

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

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

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

394 10

395

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

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

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

399 Apply these algorithms to the cortex

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

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

402 LAB formats.

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

404 the cortical area boundaries onto it.

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

406 matically find the cortical layer boundaries.

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

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

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

410 at once.

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

412 ical parts

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

414 TODO

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

416 TODO

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

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

419 TODO

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

421 clustering to create anatomical maps

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

423 map of the cortex

424 ______________________________________________

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

426 oldtext):

427 11

428

429 Principle 4: Work in 2-D whenever possible

430 In anatomy, the manifold of interest is usually either defined by a combination

431 of two relevant anatomical axes (todo), or by the surface of the structure (as is

432 the case with the cortex). In the former case, the manifold of interest is a plane,

433 but in the latter case it is curved. If the manifold is curved, there are various

434 methods for mapping the manifold into a plane.

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

436 2-D plane. Although the manifold that characterized cortical areas is known

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

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

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

440 which preserve angle (conformal maps).

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

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

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

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

445 12

446

447