1 Specific aims

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

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

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

5 regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:

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

7 anatomical regions

8 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns

9 in gene expression

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

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

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

13 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce

14 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project

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

16 method for identifying the cortical areal boundaries present in small tissue samples.

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

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

19 Background and significance

20 Aim 1

21 Machine learning terminology: supervised learning

22 The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the

23 expression level of those genes is known, then the locations of the regions can be inferred.

24 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we

25 are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to

26 which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned

27 to a class (namely, its region).

28 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of

29 the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels

30 within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs.

31 We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label

32 (or a class label).

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

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

35 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning

36 procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used

37 in the construction of the classifier is called training data.

38 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a

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

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

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

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

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

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

45 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

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

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

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

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

50 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to

51 each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If

52 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

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

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

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

56 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be

57 identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene

58 included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at

59 combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary

60 Results). Therefore, each instance should contain multiple features (genes).

61 Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is

62 only allowed to look at the expression of the genes which have been selected as features. The more data that is available to

63 a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a

64 strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations

65 in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as

66 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the

67 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the

68 level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order

69 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as

70 features.

71 Principle 3: Use geometry in feature selection

72 _________________________________________

73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.

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

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

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

77 Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.

78 Principle 4: Work in 2-D whenever possible

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

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

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

82 data.

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

84 Aim 2

85 Machine learning terminology: clustering

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

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

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

89 clustering or cluster analysis.

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

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

92 the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering

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

94 with similar gene expression.

95 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps

96 some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they

97 could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests

98 the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels.

99 This is called hierarchial clustering.

100 Similarity scores

101 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or

102 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and

103 scoring methods for similarity.

104 Spatially contiguous clusters; image segmentation

105 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have

106 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary

107 Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these

108 results against other methods which guarantee contiguous clusters.

109 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a

110 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into

111 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in

112 our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which

113 use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used

114 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting

115 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene

116 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of

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

118 Dimensionality reduction

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

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

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

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

123 set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features

124 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced

125 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene

126 expression levels.

127 Another use for dimensionality reduction is to visualize the relationships between regions. For example, one might want

128 to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar

129 gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot

130 should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on

131 a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find arrangements

132 of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied

133 after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.

134 Clustering genes rather than voxels

135 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster

136 the features (genes). There are two ways that clusters of genes could be used.

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

138 have one reduced feature for each gene cluster.

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

140 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically

141 interesting region will have multiple genes which each individually pick it out2. This suggests the following procedure:

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

143 In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”

144 formed by lumping together a few regions, are associated with gene clusters in this fashion.

145 Aim 3

146 Background

147 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can

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

149 downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can

150 picture an area of the cortex as a slice of many-layered cake.

151 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,

152 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,

153 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of

154 their approximate location upon the cortical surface.

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

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

157 single agreed-upon map can be seen by contrasting the recent maps given by Swanson[4] on the one hand, and Paxinos

158 and Franklin[3] on the other. While the maps are certainly very similar in their general arrangement, significant differences

159 remain in the details.

160 The Allen Mouse Brain Atlas dataset

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

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

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

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

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

166 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate

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

168 voxels in the 3D coordinate system, of which 51,533 are in the brain[2].

169 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[6]. The ABA contains

170 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our

171 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex,

172 and has greater registration error[2]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes of

173 known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[2].

174 The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[?],

175 GenePaint[?], its sister project GeneAtlas[?], BGEM[?], EMAGE[?], EurExpress (http://www.eurexpress.org/ee/; Eur-

176 Express data is also entered into EMAGE), todo. With the exception of the ABA, GenePaint, and EMAGE, most of these

177 resources, have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D

178 space, and only ABA and EMAGE make this form of data available for public download from the website. Many of these

179 resources focus on developmental gene expression.

180 _________________________________________

181 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is

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

183 perhaps there is some other way to map the cortex for which each region can be identified by single genes.

184 Significance

185 Themethod developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the

186 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for

187 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively

188 target individual cortical areas.

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

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

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

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

193 The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of

194 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is

195 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s

196 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of

197 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been

198 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking

199 at the patterns of gene expression.

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

201 develop could be used to suggest modifications to the human cortical map as well.

202 Related work

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

204 data which is not fundamentally spatial.

205 As noted above, there has been much work on both supervised learning and clustering, and there are many available

206 algorithms for each. However, the completion of Aims 1 and 2 involves more than just choosing between a set of existing

207 algorithms, and will constitute a substantial contribution to biology. The algorithms require the scientist to provide a

208 framework for representing the problem domain, and the way that this framework is set up has a large impact on performance.

209 Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical

210 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient

211 similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application.

212 We are aware of four existing efforts to relate spatial gene expression data to anatomy through computational methods.

213 [? ] refers to GeneAtlas. GeneAtlas allows the user to construct a search query by freely demarcating one or two 2-D

214 regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression

215 pattern is to be matched. GeneAtlas differs from our Aim 1 in at least two ways. First, GeneAtlas finds only single genes,

216 whereas we will also look for combinations of genes3. Second, at least for the custom spatial search, Gene Atlas appears to

217 use a simple pointwise scoring method (strength of expression), whereas we will also use geometric metrics such as gradient

218 similarity.

219 [? ] todo

220 [5 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,

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

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

223 usefulness of such research. We have run NNMF on the cortical dataset4 and while the results are promising (see Preliminary

224 Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this

225 paper’s authors did manually will be possible).

226 [2 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA is an analysis tool for the ABA dataset. AGEA has

227 three components:

228 * Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)

229 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of

230 overexpressed genes for selected structures)

231 * Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene

232 expression profile of the seed voxel and every other voxel.

233 * Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm

234 with correlation as the similarity metric.

235 Gene Finder is different from our Aim 1 in at least four ways. First, although the user chooses a seed voxel, Gene

236 Finder, not the user, chooses the cluster for which genes will be found, and in our experience it never chooses cortical areas,

237 _________________________________________

238 3See Preliminary Data for an example of an area which cannot be marked by any single gene in the dataset, but which can be marked by a

239 combination.

240 4We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

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

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

243 instead preferring cortical layers5. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second,

244 Gene Finder finds only single genes, whereas we will also look for combinations of genes6. Third, gene finder can only use

245 overexpression as a marker, whereas in the Preliminary Data we show that underexpression can also be used. Fourth, Gene

246 Finder uses a simple pointwise score7, whereas we will also use geometric metrics such as gradient similarity.

247 The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters corre-

248 sponding to layers, but no clusters corresponding to cortical areas8 9 Our Aim 2 will not be accomplished until a clustering

249 is produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does

250 no dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any

251 better than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted.

252 Third, AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify

253 intersting spatial regions such as cortical areas.

254 Finally, with the except of [5], none of the publications discussed above compare the results obtained by using different

255 algorithms or scoring methods. [5] reports that both mNNMF and hierarchial mNNMF clustering were useful, and that

256 hierarchial recursive bifurcation gave similar results.

257 To summarize, in comparison to our Aim 1, none of the previous projects explores combinations of marker genes, and

258 w/r/t both aims, there has been almost no experimentation with or comparison of different algorithms or scoring methods.

259 todo

260 _________________________________________

261 5Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene

262 expression of voxels in different areas but the same layer are stronger than pairwise correlatios between the gene expression of voxels in different

263 layers but the same area. This appears to be the case.

264 6See Preliminary Data for an example of an area which cannot be marked by any single gene in the dataset, but which can be marked by a

265 combination.

266 7“Expression energy ratio”, which captures overexpression.

267 8This is for the same reason as in footnote 5.

268 9There are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area

269 intersection clusters, further work is needed to make sense of these.

270 Preliminary work

271 Format conversion between SEV, MATLAB, NIFTI

272 We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created

273 software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file formats.

274 Flatmap of cortex

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

276 the cortex into hemispheres.

277 Using Caret[1], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of

278 the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened

279 the cortex, creating a two-dimensional mesh.

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

281 into a MATLAB matrix.

282 We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted

283 these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d

284 mesh, and then onto the grid, and then we converted the region data into MATLAB format.

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

286 a grid of points (pixels) over the cortical surface:

287 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel

288 ∙For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel

289 We created a normalized version of the gene expression data by subtracting each gene’s mean expression level (over all

290 surface pixels) and dividing each gene by its standard deviation.

291 The features and the target area are both functions on the surface pixels. They can be referred to as scalar fields over

292 the space of surface pixels; alternately, they can be thought of as images which can be displayed on the flatmapped surface.

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

294 cortical layer to represent the average expression level within that layer. Cortical layers are found at different depths in

295 different parts of the cortex. In preparation for extracting the layer-specific datasets, we have extended Caret with routines

296 that allow the depth of the ROI for volume-to-surface projection to vary.

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

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

299 Feature selection and scoring methods

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

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

302 surface pixels.

303 One class of feature selection scoring method are those which calculate some sort of “match” between each gene image

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

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

306 each gene and each cortical area.

307 todo: fig

308 Conditional entropy An information-theoretic scoring method is to find features such that, if the features (gene

309 expression levels) are known, uncertainty about the target (the regional identity) is reduced. Entropy measures uncertainty,

310 so what we want is to find features such that the conditional distribution of the target has minimal entropy. The distribution

311 to which we are referring is the probability distribution over the population of surface pixels.

312 The simplest way to use information theory is on discrete data, so we discretized our gene expression data by creating,

313 for each gene, five thresholded binary masks of the gene data. For each gene, we created a binary mask of its expression

314 levels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the mean minus two

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

316 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene expression

317 binary masks such that the conditional entropy of the target area’s binary mask, conditioned upon the pair of gene expression

318 binary masks, is minimized.

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

320 “Is this surface pixel a member of the target area?”.

321

322

323

324 Figure 1: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.

325 The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From

326 left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr

327 todo: fig

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

329 pattern of expression did not look similar in shape to the target region. Fort his reason we designed a non-pointwise local

330 scoring method to detect when a gene had a pattern of expression which looked like it had a boundary whose shape is similar

331 to the shape of the target region. We call this scoring method “gradient similarity”.

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

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

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

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

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

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

338 ∑

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

340 2 &#x22C5; pixel_value1 + pixel_value2

341 2

342 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current pixel; &#x2220;&#x2207;i is the angle of the gradient of

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

344 value of the current pixel in image i.

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

346 then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a

347 similar direction (because the borders are similar).

348 Geometric and pointwise scoring methods provide complementary information

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

350 Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method10. The

351 bottom row displays the 3 genes which most match AUD according to a method which considers local geometry11 The

352 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is

353 that this includes many areas which don&#8217;t have a salient border matching the areal border. The geometric method identifies

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

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

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

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

358 Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas

359 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi-

360 natorially. according to logistic regression, gene wwc112 is the best fit single gene for predicting whether or not a pixel on

361 _________________________________________

362 10For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor

363 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

364 they predict area AUD.

365 11For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the

366 shape of area AUD, was calculated, and this was used to rank the genes.

367 12&#8220;WW, C2 and coiled-coil domain containing 1&#8221;; EntrezGene ID 211652

368

369

370

371 Figure 2: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel&#8217;s value on the lower left is the sum

372 of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the

373 top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right.

374 The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells

375 underneath each pixel, with red meaning a lot of expression and blue meaning little.

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

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

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

379 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo).

380 Gene mtif213 is shown in figure the upper-right of Fig. . Mtif2 captures MO&#8217;s upper-left boundary, but not its lower-right

381 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these

382 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene.

383 Areas which can be identified by single genes

384 todo

385 Areas can sometimes be marked by underexpression

386 todo

387 Specific to Aim 1 (and Aim 3)

388 Forward stepwise logistic regression todo

389 SVM on all genes at once

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

391 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%14. As noted above,

392 however, a classifier that looks at all the genes at once isn&#8217;t practically useful.

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

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

395 combines feature selection with supervised learning.

396 Decision trees

397 todo

398 Specific to Aim 2 (and Aim 3)

399 Raw dimensionality reduction results

400 todo

401 (might want to incld nnMF since mentioned above)

402 _________________________________________

403 13&#8220;mitochondrial translational initiation factor 2&#8221;; EntrezGene ID 76784

404 145-fold cross-validation.

405 Dimensionality reduction plus K-means or spectral clustering

406 Many areas are captured by clusters of genes

407 todo

408 todo

409 Research plan

410 Further work on flatmapping

411 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),

412 or by the surface of the structure (as is the case with the cortex). In the former case, the manifold of interest is a plane, but

413 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.

414 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal

415 for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[1]) with

416 mappings which preserve angle (conformal maps).

417 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.

418 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D

419 structure seems to be wrong.

420 todo amongst other things:

421 Develop algorithms that find genetic markers for anatomical regions

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

423 geometric, and information-theoretic measures.

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

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

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

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

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

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

430 machines.

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

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

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

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

435 a larger area which can be fit.

436 Apply these algorithms to the cortex

437 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert

438 between SEV, NIFTI and MATLAB formats.

439 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.

440 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.

441 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify

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

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

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

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

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

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

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

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

450 Bibliography &amp; References Cited

451 [1]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite for surface-

452 based analyses of cerebral cortex. Journal of the American Medical Informatics Association: JAMIA, 8(5):443&#8211;59, 2001.

453 PMID: 11522765.

454 [2]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M Sunkin,

455 Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann, David J Anderson, Ed S

456 Lein, Allan R Jones, and Michael Hawrylycz. An anatomic gene expression atlas of the adult mouse brain. Nat Neurosci,

457 12(3):356&#8211;362, March 2009.

458 [3]George Paxinos and Keith B.J. Franklin. The Mouse Brain in Stereotaxic Coordinates. Academic Press, 2 edition, July

459 2001.

460 [4]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.

461 [5]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T. Mortrud,

462 Allison Cusick, Zackery L. Riley, Susan M. Sunkin, Amy Bernard, Ralph B. Puchalski, Fred H. Gage, Allan R. Jones,

463 Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the hippocampus. Neuron, 60(6):1010&#8211;

464 1021, December 2008.

465 [6]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agarwala,

466 Rachel Ainscough, Marina Alexandersson, Peter An, Stylianos E Antonarakis, John Attwood, Robert Baertsch, Jonathon

467 Bailey, Karen Barlow, Stephan Beck, Eric Berry, Bruce Birren, Toby Bloom, Peer Bork, Marc Botcherby, Nicolas Bray,

468 Michael R Brent, Daniel G Brown, Stephen D Brown, Carol Bult, John Burton, Jonathan Butler, Robert D Campbell,

469 Piero Carninci, Simon Cawley, Francesca Chiaromonte, Asif T Chinwalla, Deanna M Church, Michele Clamp, Christopher

470 Clee, Francis S Collins, Lisa L Cook, Richard R Copley, Alan Coulson, Olivier Couronne, James Cuff, Val Curwen, Tim

471 Cutts, Mark Daly, Robert David, Joy Davies, Kimberly D Delehaunty, Justin Deri, Emmanouil T Dermitzakis, Colin

472 Dewey, Nicholas J Dickens, Mark Diekhans, Sheila Dodge, Inna Dubchak, Diane M Dunn, Sean R Eddy, Laura Elnitski,

473 Richard D Emes, Pallavi Eswara, Eduardo Eyras, Adam Felsenfeld, Ginger A Fewell, Paul Flicek, Karen Foley, Wayne N

474 Frankel, Lucinda A Fulton, Robert S Fulton, Terrence S Furey, Diane Gage, Richard A Gibbs, Gustavo Glusman, Sante

475 Gnerre, Nick Goldman, Leo Goodstadt, Darren Grafham, Tina A Graves, Eric D Green, Simon Gregory, Roderic Guig,

476 Mark Guyer, Ross C Hardison, David Haussler, Yoshihide Hayashizaki, LaDeana W Hillier, Angela Hinrichs, Wratko

477 Hlavina, Timothy Holzer, Fan Hsu, Axin Hua, Tim Hubbard, Adrienne Hunt, Ian Jackson, David B Jaffe, L Steven

478 Johnson, Matthew Jones, Thomas A Jones, Ann Joy, Michael Kamal, Elinor K Karlsson, Donna Karolchik, Arkadiusz

479 Kasprzyk, Jun Kawai, Evan Keibler, Cristyn Kells, W James Kent, Andrew Kirby, Diana L Kolbe, Ian Korf, Raju S

480 Kucherlapati, Edward J Kulbokas, David Kulp, Tom Landers, J P Leger, Steven Leonard, Ivica Letunic, Rosie Levine, Jia

481 Li, Ming Li, Christine Lloyd, Susan Lucas, Bin Ma, Donna R Maglott, Elaine R Mardis, Lucy Matthews, Evan Mauceli,

482 John H Mayer, Megan McCarthy, W Richard McCombie, Stuart McLaren, Kirsten McLay, John D McPherson, Jim

483 Meldrim, Beverley Meredith, Jill P Mesirov, Webb Miller, Tracie L Miner, Emmanuel Mongin, Kate T Montgomery,

484 Michael Morgan, Richard Mott, James C Mullikin, Donna M Muzny, William E Nash, Joanne O Nelson, Michael N

485 Nhan, Robert Nicol, Zemin Ning, Chad Nusbaum, Michael J O&#8217;Connor, Yasushi Okazaki, Karen Oliver, Emma Overton-

486 Larty, Lior Pachter, Gens Parra, Kymberlie H Pepin, Jane Peterson, Pavel Pevzner, Robert Plumb, Craig S Pohl, Alex

487 Poliakov, Tracy C Ponce, Chris P Ponting, Simon Potter, Michael Quail, Alexandre Reymond, Bruce A Roe, Krishna M

488 Roskin, Edward M Rubin, Alistair G Rust, Ralph Santos, Victor Sapojnikov, Brian Schultz, Jrg Schultz, Matthias S

489 Schwartz, Scott Schwartz, Carol Scott, Steven Seaman, Steve Searle, Ted Sharpe, Andrew Sheridan, Ratna Shownkeen,

490 Sarah Sims, Jonathan B Singer, Guy Slater, Arian Smit, Douglas R Smith, Brian Spencer, Arne Stabenau, Nicole Stange-

491 Thomann, Charles Sugnet, Mikita Suyama, Glenn Tesler, Johanna Thompson, David Torrents, Evanne Trevaskis, John

492 Tromp, Catherine Ucla, Abel Ureta-Vidal, Jade P Vinson, Andrew C Von Niederhausern, Claire M Wade, Melanie Wall,

493 Ryan J Weber, Robert B Weiss, Michael C Wendl, Anthony P West, Kris Wetterstrand, Raymond Wheeler, Simon

494 Whelan, Jamey Wierzbowski, David Willey, Sophie Williams, Richard K Wilson, Eitan Winter, Kim C Worley, Dudley

495 Wyman, Shan Yang, Shiaw-Pyng Yang, Evgeny M Zdobnov, Michael C Zody, and Eric S Lander. Initial sequencing and

496 comparative analysis of the mouse genome. Nature, 420(6915):520&#8211;62, December 2002. PMID: 12466850.

497

498 _______________________________________________________________________________________________________

499 stuff i dunno where to put yet (there is more scattered through grant-oldtext):

500 Principle 4: Work in 2-D whenever possible

501 &#8212;

502 note:

503 do we need to cite: no known markers, impressive results?

504 two hemis

505 &#8220;genomic anatomy&#8221; is a name found in the titles of one of the cited papers which seems good

506

507