1 Specific aims

2 Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic

3 reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared.

4 Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker

5 genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have

6 three specific aims:

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

8 anatomical regions

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

10 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 Mouse

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

13 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).

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

15 developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located in a low-dimensional

16 space.

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

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

19 the application of these methods to cortex will produce immediate benefits, because there are currently no known genetic

20 markers for most cortical areas. The results of the project will support the development of new ways to selectively target

21 cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small

22 tissue samples.

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

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

25 The challenge topic

26 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as in situ hybridiza-

27 tion (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others, allow the expression levels

28 of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in

29 gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical

30 maps based on gene expression patterns.

31 The Challenge and Potential impact

32 Now we will discuss each of our three aims in turn. For each aim, we will develop a conceptual framework for thinking

33 about the task, and we will present our strategy for solving it. Next we will discuss related work. At the conclusion of each

34 section, we will summarize why our strategy is different from what has been done before. At the end of this section, we will

35 describe the potential impact.

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

37 Machine learning terminology The task of looking for marker genes for known anatomical regions means that one is

38 looking for a set of genes such that, if the expression level of those genes is known, then the locations of the regions can be

39 inferred.

40 If we define the regions so that they cover the entire anatomical structure to be divided, we may say that we are using

41 gene expression to determine to which region each voxel within the structure belongs. We call this a classification task,

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

43 combination of their expression levels and the locations of the regions may be expressed as a function. The input to this

44 function is a voxel, along with the gene expression levels within that voxel; the output is the regional identity of the target

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

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

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

48 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be

49 analyzed in concert with an anatomical atlas in order to produce a classifier. The initial gene expression dataset used in

50 the construction of the classifier is called training data. In the machine learning literature, this sort of procedure may be

51 thought of as a supervised learning task, defined as a task in which the goal is to learn a mapping from instances to labels,

52 and the training data consists of a set of instances (voxels) for which the labels (regions) are known.

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

54 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with

55 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.

56 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then

57 chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic

58 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise

59 the score. Such procedures are called “stepwise” or “greedy”.

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

61 algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature selection

62 methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to each voxel,

63 and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or average). If

64 only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only

65 information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.

66 Our strategy for Aim 1

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

68 chosen? Here are four principles that outline our answers to these questions.

69 Principle 1: Combinatorial gene expression

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

71 cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset.

72 However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for

73 which multiple genes are necessary and sufficient is provided in Preliminary Studies, Figure 4). Therefore, each instance

74 should contain multiple features (genes).

75 _______

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

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

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

79 as features. The more data that are available to a classifier, the better that it can do. For example, perhaps there are weak

80 correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that

81 we wish to employ the classifier in situations in which it is not feasible to gather data about every gene. For example, if we

82 want to use the expression of marker genes as a trigger for some regionally-targeted intervention, then our intervention must

83 contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible

84 to design a molecular trigger that checks the level of more than a handful of genes. Similarly, if the goal is to develop a

85 procedure to do ISH on tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes.

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

87 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many

88 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task

89 combines feature selection with supervised learning.

90 Principle 3: Use geometry in feature selection

91 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of

92 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information

93 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See

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

95 Principle 4: Work in 2-D whenever possible

96 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When

97 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis

98 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D

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

100 Related work

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

102 which are not fundamentally spatial2.

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

104 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the

105 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively

106 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,

107 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Studies) may

108 be necessary in order to achieve the best results in this application.

109 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.

110 [11 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of

111 interest, computing what proportion of this structure is covered by the gene’s spatial region.

112 GeneAtlas[5] and EMAGE [23] allow the user to construct a search query by demarcating regions and then specifing

113 either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the

114 similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses

115 the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3

116 whose expression is within four discretization levels. EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE

117 allow one to search for combinations of genes that define a region in concert but not separately.

118 [13 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The user

119 selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list of genes which are

120 overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected

121 structures). Correlation: The user selects a seed voxel and the system then shows the user how much correlation there is

122 between the gene expression profile of the seed voxel and every other voxel. Clusters: will be described later

123 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we

124 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also

125 search for underexpression. Third, Gene Finder uses a simple pointwise score5, whereas we will also use geometric scores

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

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

128 _________________________________________

129 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not

130 just data which have only a few different locations or which is indexed by anatomical label.

131 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.

132 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.

133 5“Expression energy ratio”, which captures overexpression.

134 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni

135 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,

136 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for

137 underexpression, and does not look for combinations of genes.

138 [9 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary

139 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their

140 match score is Jaccard similarity.

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

142 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or

143 scoring methods.

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

145 Machine learning terminology: clustering

146 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as

147 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances

148 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called

149 clustering or cluster analysis.

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

151 are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels

152 from the same anatomical region have similar gene expression profiles, at least compared to the other regions. This means

153 that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into

154 clusters of voxels with similar gene expression.

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

156 clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called

157 hierarchial clustering.

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

159 of instances, or clusters, or both. There is much overlap between scoring methods for feature selection (discussed above

160 under Aim 1) and scoring methods for similarity.

161 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering task. In fact,

162 it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a

163 cluster must be spatially contiguous. In Preliminary Studies, we show that one can get reasonable results without enforcing

164 this constraint; however, we plan to compare these results against other methods which guarantee contiguous clusters.

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

166 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels

167 (one for each gene), rather than just three6. A more crucial difference is that there are various cues which are appropriate

168 for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data

169 such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other

170 sorts of spatially arranged data, some of these algorithms are specialized for visual images.

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

172 vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.

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

174 instances. However, some clustering algorithms perform better on small numbers of features7. There are techniques which

175 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature

176 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature

177 set. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set

178 may be any function of the set of gene expression levels.

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

180 strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes could be used.

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

182 have one reduced feature for each gene cluster.

183 __

184 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are often

185 used to process satellite imagery.

186 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering algorithms

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

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

189 patternwhich seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically

190 interesting region will have multiple genes which each individually pick it out8. This suggests the following procedure:

191 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.

192 In Preliminary Studies, Figure 7, we show that a number of anatomically recognized cortical regions, as well as some

193 “superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion.

194 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering

195 algorithms.

196 Related work

197 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example, [15], [2], [16],

198 and [1 ] associate spots on the cortex with the radial profile9 of response to some stain ([10] uses MRI), extract features from

199 this profile, and then use similarity between surface pixels to cluster. Features used include statistical moments, wavelets,

200 and the excess mass functional. Some of these features are motivated by the presence of tangential lines of stain intensity

201 which correspond to laminar structure. Some methods use standard clustering procedures, whereas others make use of the

202 spatial nature of the data to look for sudden transitions, which are identified as areal borders.

203 [20 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

204 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive

205 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving

206 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset10 and while the results are

207 promising, they also demonstrate that NNMF is not necessarily the best dimensionality reduction method for this application

208 (see Preliminary Studies, Figure 6).

209 AGEA[13] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation

210 as the similarity metric. EMAGE[23] allows the user to select a dataset from among a large number of alternatives, or by

211 running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage

212 clustering with un-centred correlation as the similarity score.

213 [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were

214 highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and

215 ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between

216 the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing

217 similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial

218 expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without

219 clustering voxels.

220 [9 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes around a “seed

221 gene”. They do this by using the pattern of expression of the seed gene as the target image, and then searching for other

222 genes which can be combined to reproduce this pattern. Other genes which are found are considered to be related to the

223 seed. The same team also describes a method[22] for finding “association rules” such as, “if this voxel is expressed in by

224 any gene, then that voxel is probably also expressed in by the same gene”. This could be useful as part of a procedure for

225 clustering voxels.

226 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-

227 rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. The

228 projects using gene expression on cortex did not attempt to make use of the radial profile of gene expression. Also, none of

229 these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first in order

230 to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.

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

232 Background

233 The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation of the cortex

234 into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the

235 _________________________________________

236 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

237 possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;

238 perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although

239 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.

240 9A radial profile is a profile along a line perpendicular to the cortical surface.

241 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

242 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was

243 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.

244 areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the

245 surface.One can picture an area of the cortex as a slice of a six-layered cake11.

246 It is known that different cortical areas have distinct roles in both normal functioning and in disease processes, yet there

247 are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is

248 a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their

249 approximate location upon the cortical surface.

250 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not

251 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single

252 agreed-upon map can be seen by contrasting the recent maps given by Swanson[19] on the one hand, and Paxinos and

253 Franklin[14] on the other. While the maps are certainly very similar in their general arrangement, significant differences

254 remain.

255 The Allen Mouse Brain Atlas dataset

256 The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, 56-day-old

257 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed

258 to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution

259 is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse

260 brains were needed in order to measure the expression of many genes.

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

262 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326

263 voxels in the 3D coordinate system, of which 51,533 are in the brain[13].

264 Mus musculus is thought to contain about 22,000 protein-coding genes[25]. The ABA contains data on about 20,000

265 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from

266 only the coronal subset of the ABA12.

267 The ABA is not the only large public spatial gene expression dataset13. With the exception of the ABA, GenePaint, and

268 EMAGE, most of the other resources have not (yet) extracted the expression intensity from the ISH images and registered

269 the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public

270 download from the website14. Many of these resources focus on developmental gene expression.

271 Related work

272 [13 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations

273 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either

274 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of

275 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes

276 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas15.

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

278 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally

279 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo

280 from gene expression data.

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

282 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.

283 _________________________________________

284 11Outside of isocortex, the number of layers varies.

285 12The sagittal data do not cover the entire cortex, and also have greater registration error[13]. Genes were selected by the Allen Institute for

286 coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression

287 pattern”[13].

288 13Other such resources include GENSAT[8], GenePaint[24], its sister project GeneAtlas[5], BGEM[12], EMAGE[23], EurExpress (http://www.

289 eurexpress.org/ee/; EurExpress data are also entered into EMAGE), EADHB (http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.

290 html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[18], Aniseed (http://aniseed-ibdm.

291 univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some of the other listed data sources), GEISHA[4],

292 Fruitfly.org[21], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[17], GEO[3] (GXD and GEO contain spatial data but also non-spatial

293 data. All GXD spatial data are also in EMAGE.)

294 14without prior offline registration

295 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger

296 than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation

297 clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters which presumably correspond to the

298 intersection of a layer and an area, but since one area will have many layer-area intersection clusters, further work is needed to make sense of

299 these). The reason that Gene Finder cannot the find marker genes for cortical areas is that, although the user chooses a seed voxel, Gene Finder

300 chooses the ROI for which genes will be found, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.

301 Significance

302 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the combinatorial

303 expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for drug discovery

304 as well as for experimentation because marker genes can be used to design interventions which selectively target individual

305 cortical areas.

306 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom-

307 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can

308 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that

309 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.

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

311 better map. The development of present-day cortical maps was driven by the application of histological stains. If a different

312 set of stains had been available which identified a different set of features, then today’s cortical maps may have come out

313 differently. It is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been

314 captured by any stain. Therefore, cortical anatomy needs to incorporate what we can learn from looking at the patterns of

315 gene expression.

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

317 to develop could be used to suggest modifications to the human cortical map as well. In fact, the methods we will develop

318 will be applicable to other datasets beyond the brain. We will provide an open-source toolbox to allow other researchers

319 to easily use our methods. With these methods, researchers with gene expression for any area of the body will be able to

320 efficiently find marker genes for anatomical regions, or to use gene expression to discover new anatomical patterning. As

321 described above, marker genes have a variety of uses in the development of drugs and experimental manipulations, and in

322 the anatomical characterization of tissue samples. The discovery of new ways to carve up anatomical structures into regions

323 will widely impact all areas of biology.

324 The approach: Preliminary Studies

325

326

327 Figure 1: Top row: Genes Nfic and

328 A930001M12Rik are the most correlated

329 with area SS (somatosensory cortex). Bot-

330 tom row: Genes C130038G02Rik and

331 Cacna1i are those with the best fit using

332 logistic regression. Within each picture, the

333 vertical axis roughly corresponds to anterior

334 at the top and posterior at the bottom, and

335 the horizontal axis roughly corresponds to

336 medial at the left and lateral at the right.

337 The red outline is the boundary of region

338 SS. Pixels are colored according to correla-

339 tion, with red meaning high correlation and

340 blue meaning low. Format conversion between SEV, MATLAB, NIFTI

341 We have created software to (politely) download all of the SEV files16 from

342 the Allen Institute website. We have also created software to convert between

343 the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file

344 formats.

345 Flatmap of cortex

346 We downloaded the ABA data and applied a mask to select only those voxels

347 which belong to cerebral cortex. We divided the cortex into hemispheres.

348 Using Caret[7], we created a mesh representation of the surface of the se-

349 lected voxels. For each gene, for each node of the mesh, we calculated an

350 average of the gene expression of the voxels “underneath” that mesh node. We

351 then flattened the cortex, creating a two-dimensional mesh.

352 We sampled the nodes of the irregular, flat mesh in order to create a regular

353 grid of pixel values. We converted this grid into a MATLAB matrix.

354 We manually traced the boundaries of each of 49 cortical areas from the

355 ABA coronal reference atlas slides. We then converted these manual traces

356 into Caret-format regional boundary data on the mesh surface. We projected

357 the regions onto the 2-d mesh, and then onto the grid, and then we converted

358 the region data into MATLAB format.

359 At this point, the data are in the form of a number of 2-D matrices, all in

360 registration, with the matrix entries representing a grid of points (pixels) over

361 the cortical surface:

362 ∙ A 2-D matrix whose entries represent the regional label associated with each

363 surface pixel

364 ∙ For each gene, a 2-D matrix whose entries represent the average expression

365 level underneath each surface pixel

366 _________________________________________

367 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.

368

369

370 Figure 2: Gene Pitx2

371 is selectively underex-

372 pressed in area SS. We created a normalized version of the gene expression data by subtracting each gene’s mean

373 expression level (over all surface pixels) and dividing the expression level of each gene by its

374 standard deviation.

375 The features and the target area are both functions on the surface pixels. They can be referred

376 to as scalar fields over the space of surface pixels; alternately, they can be thought of as images

377 which can be displayed on the flatmapped surface.

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

379 separate matrix for each cortical layer to represent the average expression level within that layer.

380 Cortical layers are found at different depths in different parts of the cortex. In preparation for

381 extracting the layer-specific datasets, we have extended Caret with routines that allow the depth

382 of the ROI for volume-to-surface projection to vary.

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

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

385 Feature selection and scoring methods

386 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a marker. See,

387 for example, Figure 2.

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

389 as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the

390 surface pixels.

391 One class of feature selection scoring methods contains methods which calculate some sort of “match” between each gene

392 image and the target image. Those genes which match the best are good candidates for features.

393 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between

394 each gene and each cortical area. The top row of Figure 1 shows the three genes most correlated with area SS.

395

396

397 Figure 3: The top row shows the two genes

398 which (individually) best predict area AUD,

399 according to logistic regression. The bot-

400 tom row shows the two genes which (indi-

401 vidually) best match area AUD, according

402 to gradient similarity. From left to right and

403 top to bottom, the genes are Ssr1, Efcbp1,

404 Ptk7, and Aph1a. Conditional entropy An information-theoretic scoring method is to find

405 features such that, if the features (gene expression levels) are known, uncer-

406 tainty about the target (the regional identity) is reduced. Entropy measures

407 uncertainty, so what we want is to find features such that the conditional dis-

408 tribution of the target has minimal entropy. The distribution to which we are

409 referring is the probability distribution over the population of surface pixels.

410 The simplest way to use information theory is on discrete data, so we

411 discretized our gene expression data by creating, for each gene, five thresholded

412 boolean masks of the gene data. For each gene, we created a boolean mask of

413 its expression levels using each of these thresholds: the mean of that gene, the

414 mean minus one standard deviation, the mean minus two standard deviations,

415 the mean plus one standard deviation, the mean plus two standard deviations.

416 Now, for each region, we created and ran a forward stepwise procedure

417 which attempted to find pairs of gene expression boolean masks such that the

418 conditional entropy of the target area’s boolean mask, conditioned upon the

419 pair of gene expression boolean masks, is minimized.

420 This finds pairs of genes which are most informative (at least at these dis-

421 cretization thresholds) relative to the question, “Is this surface pixel a member

422 of the target area?”. Its advantage over linear methods such as logistic regres-

423 sion is that it takes account of arbitrarily nonlinear relationships; for example,

424 if the XOR of two variables predicts the target, conditional entropy would

425 notice, whereas linear methods would not.

426 Gradient similarity We noticed that the previous two scoring methods,

427 which are pointwise, often found genes whose pattern of expression did not look similar in shape to the target region. For

428 this reason we designed a non-pointwise local scoring method to detect when a gene had a pattern of expression which

429 looked like it had a boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient

430 similarity”.

431 One might say that gradient similarity attempts to measure how much the border of the area of gene expression and

432 the border of the target region overlap. However, since gene expression falls off continuously rather than jumping from its

433 maximum value to zero, the spatial pattern of a gene’s expression often does not have a discrete border. Therefore, instead

434 of looking for a discrete border, we look for large gradients. Gradient similarity is a symmetric function over two images

435 (i.e. two scalar fields). It is is high to the extent that matching pixels which have large values and large gradients also have

436 gradients which are oriented in a similar direction. The formula is:

437 ∑

438 pixel<img src="cmsy7-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|

439 2 &#x22C5; pixel_value1 + pixel_value2

440 2

441

442

443 Figure 4: Upper left: wwc1. Upper right:

444 mtif2. Lower left: wwc1 + mtif2 (each

445 pixel&#8217;s value on the lower left is the sum of

446 the corresponding pixels in the upper row). where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current

447 pixel; &#x2220;&#x2207;i is the angle of the gradient of image i at the current pixel; |&#x2207;i| is

448 the magnitude of the gradient of image i at the current pixel; and pixel_valuei

449 is the value of the current pixel in image i.

450 The intuition is that we want to see if the borders of the pattern in the

451 two images are similar; if the borders are similar, then both images will have

452 corresponding pixels with large gradients (because this is a border) which are

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

454 Most of the genes in Figure 5 were identified via gradient similarity.

455 Gradient similarity provides information complementary to cor-

456 relation

457 To show that gradient similarity can provide useful information that cannot

458 be detected via pointwise analyses, consider Fig. 3. The top row of Fig. 3

459 displays the 3 genes which most match area AUD, according to a pointwise

460 method17. The bottom row displays the 3 genes which most match AUD ac-

461 cording to a method which considers local geometry18 The pointwise method

462 in the top row identifies genes which express more strongly in AUD than out-

463 side of it; its weakness is that this includes many areas which don&#8217;t have a

464 salient border matching the areal border. The geometric method identifies

465 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes

466 genes which don&#8217;t express over the entire area. Genes which have high rankings using both pointwise and border criteria,

467 such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker

468 for AUD; we deliberately chose a &#8220;difficult&#8221; area in order to better contrast pointwise with geometric methods.

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

470 roughly identify some areas and groupings of areas. For each of these areas, an example of a gene which roughly identifies

471 it is shown in Figure 5. We have not yet cross-verified these genes in other atlases.

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

473 cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS

474 (visual), AUD (auditory).

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

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

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

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

479 combinatorially. Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a

480 pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1&#8217;s spatial

481 expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, but the

482 gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding

483 to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. Gene mtif2 is shown in the

484 upper-right. Mtif2 captures MO&#8217;s upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much

485 on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This

486 combination captures area MO much better than any single gene.

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

488 Feature selection integrated with prediction As noted earlier, in general, any predictive method can be used for

489 feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number

490 of features used. Examples of both of these will be seen in the section &#8220;Multivariate Predictive methods&#8221;.

491 _________________________________________

492 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor

493 variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well

494 they predict area AUD.

495 18For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD,

496 was calculated, and this was used to rank the genes.

497

498

499

500

501

502 Figure 5: From left to right and top

503 to bottom, single genes which roughly

504 identify areas SS (somatosensory primary

505 + supplemental), SSs (supplemental so-

506 matosensory), PIR (piriform), FRP (frontal

507 pole), RSP (retrosplenial), COApm (Corti-

508 cal amygdalar, posterior part, medial zone).

509 Grouping some areas together, we have

510 also found genes to identify the groups

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

512 cingulate, prelimbic, infralimbic, dorsal pe-

513 duncular, orbital, motor), posterior and lat-

514 eral visual (VISpm, VISpl, VISI, VISp; pos-

515 teromedial, posterolateral, lateral, and pri-

516 mary visual; the posterior and lateral vi-

517 sual area is distinguished from its neigh-

518 bors, but not from the entire rest of the

519 cortex). The genes are Pitx2, Aldh1a2,

520 Ppfibp1, Slco1a5, Tshz2, Trhr, Col12a1,

521 Ets1. Multivariate Predictive methods

522

523

524

525

526 Figure 6: First row: the first 6 reduced dimensions, using PCA. Second

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

528 six reduced dimensions, using landmark Isomap. Bottom row: examples

529 of kmeans clustering applied to reduced datasets to find 7 clusters. Left:

530 19 of the major subdivisions of the cortex. Second from left: PCA. Third

531 from left: NNMF. Right: Landmark Isomap. Additional details: In the

532 third and fourth rows, 7 dimensions were found, but only 6 displayed. In

533 the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions

534 were used; for landmark Isomap, 7 dimensions were used. Forward stepwise logistic regression Lo-

535 gistic regression is a popular method for pre-

536 dictive modeling of categorial data. As a pi-

537 lot run, for five cortical areas (SS, AUD, RSP,

538 VIS, and MO), we performed forward stepwise

539 logistic regression to find single genes, pairs of

540 genes, and triplets of genes which predict areal

541 identify. This is an example of feature selec-

542 tion integrated with prediction using a stepwise

543 wrapper. Some of the single genes found were

544 shown in various figures throughout this doc-

545 ument, and Figure 4 shows a combination of

546 genes which was found.

547 We felt that, for single genes, gradient simi-

548 larity did a better job than logistic regression at

549 capturing our subjective impression of a &#8220;good

550 gene&#8221;.

551 SVM on all genes at once

552 In order to see how well one can do when

553 looking at all genes at once, we ran a support

554 vector machine to classify cortical surface pix-

555 els based on their gene expression profiles. We

556 achieved classification accuracy of about 81%19.

557 This shows that the genes included in the ABA

558 dataset are sufficient to define much of cortical

559 anatomy. However, as noted above, a classifier

560 that looks at all the genes at once isn&#8217;t as prac-

561 tically useful as a classifier that uses only a few

562 genes.

563 Data-driven redrawing of the cor-

564 tical map

565

566 Figure 7: Prototypes corresponding to sample gene clusters,

567 clustered by gradient similarity. Region boundaries for the

568 region that most matches each prototype are overlayed. We have applied the following dimensionality reduction al-

569 gorithms to reduce the dimensionality of the gene expression

570 profile associated with each voxel: Principal Components

571 Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional

572 Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigen-

573 maps, Local Tangent Space Alignment (LTSA), Hessian lo-

574 cally linear embedding, Diffusion maps, Stochastic Neigh-

575 bor Embedding (SNE), Stochastic Proximity Embedding

576 (SPE), Fast Maximum Variance Unfolding (FastMVU),

577 Non-negative Matrix Factorization (NNMF). Space con-

578 straints prevent us from showing many of the results, but as

579 a sample, PCA, NNMF, and landmark Isomap are shown in

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

581 After applying the dimensionality reduction, we ran clus-

582 tering algorithms on the reduced data. To date we have tried

583 k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last

584 row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some of the major subdivisions of

585 cortex. These results clearly show that different dimensionality reduction techniques capture different aspects of the data

586 and lead to different clusterings, indicating the utility of our proposal to produce a detailed comparion of these techniques

587 as applied to the domain of genomic anatomy.

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

589 _________________________________________

590 195-fold cross-validation.

591 spatial regions defined by any clusters matched known anatomical regions. Figure 7 shows, for ten sample gene clusters, each

592 cluster&#8217;s average expression pattern, compared to a known anatomical boundary. This suggests that it is worth attempting

593 to cluster genes, and then to use the results to cluster voxels.

594 The approach: what we plan to do

595 Flatmap and segment cortical layers

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

597 to preserve size (such as the one used by Caret[7]) with mappings which preserve angle (conformal maps). Our method will

598 include a statistical test that warns the user if the assumption of 2-D structure seems to be wrong.

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

600 cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would then be associated

601 with one expression level per gene per layer. We will develop a segmentation algorithm to automatically identify the layer

602 boundaries.

603 Develop algorithms that find genetic markers for anatomical regions

604 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise,

605 geometric, and information-theoretic measures.

606 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining

607 the scoring measures developed, we will rank the genes by their ability to delineate each area.

608 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any

609 single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily

610 combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised

611 learning techniques which use soft constraints to minimize the number of features, such as sparse support vector

612 machines.

613 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult

614 to identify because the boundaries are misdrawn, or because it does not &#8220;really&#8221; exist as a single area, at least on the

615 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its

616 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create

617 a larger area which can be fit.

618 # Linear discriminant analysis

619 Decision trees todo

620 20.

621 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting, two hemis

622 # mixture models, etc

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

624 1.Explore dimensionality reduction algorithms applied to pixels: including TODO

625 2.Explore dimensionality reduction algorithms applied to genes: including TODO

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

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

628 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps

629 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex

630 # Linear discriminant analysis

631 # jbt, coclustering

632 # self-organizing map

633 # compare using clustering scores

634 __________

635 20Already, for each cortical area, we have used the C4.5 algorithm to find a decision tree for that area. We achieved good classification accuracy

636 on our training set, but the number of genes that appeared in each tree was too large. We plan to implement a pruning procedure to generate

637 trees that use fewer genes

638 # multivariate gradient similarity

639 # deep belief nets

640 Apply these algorithms to the cortex

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

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

643 developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify and explain how the statistical

644 structure in the gene expression data led to any unexpected or interesting features of these maps.

645 Timeline and milestones

646 Aim 1

647 &#x2219;September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers

648 &#x2219;November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information for each

649 layer

650 &#x2219;October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks. Also

651 test out various dimensionality reduction schemes in combination with supervised learning. create or extend supervised

652 learning frameworks which use multivariate versions of the best scoring methods.

653 &#x2219;January 2010 (milestone): Submit a publication on single marker genes for cortical areas

654 &#x2219;February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the best way

655 to integrate radial profiles with supervised learning. Explore the best way to make supervised learning techniques

656 robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly off). Quantitatively

657 compare the performance of different supervised learning techniques. Validate marker genes found in the ABA dataset

658 by checking against other gene expression datasets. Create documentation and unit tests for software toolbox for Aim

659 1. Respond to user bug reports for Aim 1 software toolbox.

660 &#x2219;June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.

661 &#x2219;July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a small

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

663 Aim 2

664 &#x2219;April-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial clustering

665 algorithms, used in combination with dimensionality reduction, for Aim 2. Explore co-clustering algorithms. Think

666 about how radial profile information can be used for Aim 2. Adapt clustering algorithms to use radial profile in-

667 formation. Quantitatively compare the performance of different dimensionality reduction and clustering techniques.

668 Quantitatively compare the value of different flatmapping methods and ways of representing radial profiles.

669 &#x2219;March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.

670 &#x2219;February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If new ways

671 of organizing the cortex into areas are discovered, read the literature and talk to people to learn about research related

672 to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2. Respond to user bug

673 reports for Aim 1 software toolbox.

674 &#x2219;May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in Aim 2

675 &#x2219;May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1. Follow

676 up on responses to our papers. Possibly submit another paper.

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