1 Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___

2 Specific aims

3 Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expression

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

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

6 maps based on gene expression patterns. We have three specific aims:

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

8 anatomical regions

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

10 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 Brain

12 Atlas ISH data, as well as the boundaries of cortical anatomical areas. Use this dataset to validate the methods developed

13 in (1) and (2).

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

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

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

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

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

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

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23 Background and significance

24 Aim 1

25 Machine learning terminology: supervised learning

26 The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if

27 the expression level of those genes is known, then the locations of the subregions can be inferred.

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

29 are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine

30 to which subregion each voxel within the structure belongs. We call this a classification task, because each voxel is being

31 assigned to a class (namely, its subregion).

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

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

34 within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel

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

36 a label (or a class label).

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

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

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

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

41 the construction of the classifier is called training data.

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

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

44 (voxels) for which the labels (subregions) are known.

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

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

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

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

49 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

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

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

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

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

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

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

56 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

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

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

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

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

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

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

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

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

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

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

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

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

69 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

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

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

72 _________________________________________

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

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76 Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___

77 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

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

79 features.

80 Principle 3: Use geometry in feature selection

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

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

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

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

85 Principle 4: Work in 2-D whenever possible

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

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

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

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

90 Aim 2

91 Machine learning terminology: clustering

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

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

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

95 clustering or cluster analysis.

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

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

98 from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that

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

100 clusters of voxels with similar gene expression.

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

102 perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale

103 they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion. This

104 suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition

105 the voxels. This is called hierarchial clustering.

106 Similarity scores

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

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

109 scoring methods for similarity.

110 Spatially contiguous clusters; image segmentation

111 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 an

112 additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Results,

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

114 against other methods which guarantee contiguous clusters.

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

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

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

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

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

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

121 object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression.

122 Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged

123 data, some of these algorithms are specialized for visual images.

124 Dimensionality reduction

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

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

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

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

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

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

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

135 expression levels.

136 Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might

137 want to make a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions

138 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points

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

140 the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find

141 arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction

142 is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction

143 before clustering.

144 Clustering genes rather than voxels

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

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

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

148 have one reduced feature for each gene cluster.

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

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

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

152 cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the

153 final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some

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

155 Aim 3

156 Background

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

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

159 into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an

160 area of the cortex as a slice of many-layered cake.

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

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

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

164 their approximate location upon the cortical surface.

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

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

167 single agreed-upon map can be seen by contrasting the recent maps given by Swanson?? on the one hand, and Paxinos

168 and Franklin?? on the other. While the maps are certainly very similar in their general arrangement, significant differences

169 remain in the details.

170 Significance

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

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

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

174 target individual cortical areas.

175 _______________

176 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible

177 that the currently accepted cortical maps divide the cortex into subregions which are unnatural from the point of view of gene expression; perhaps

178 there is some other way to map the cortex for which each subregion can be identified by single genes.

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

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

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

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

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

187 map. The development of present-day cortical maps was driven by the application of histological stains. It is conceivable

188 that if a different set of stains had been available which identified a different set of features, then the today’s cortical maps

189 would have come out differently. Since the number of classes of stains is small compared to the number of genes, it is likely

190 that there are many repeated, salient spatial patterns in the gene expression which have not yet been captured by any stain.

191 Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking at the patterns of gene

192 expression.

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

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

195 Related work

196 There does not appear to be much work on the automated analysis of spatial gene expression data.

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

198 data which is not fundamentally spatial.

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

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

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

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

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

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

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

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

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

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

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

210 of such research. We have run NNMF on the cortical dataset and while the results are promising (see Preliminary Data), we

211 think that it will be possible to find a better method3 (we also think that more automation of the parts that this paper’s

212 authors did manually will be possible).

213 and [?] describes AGEA. todo

214 _____________

215 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft

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

217 needed. The paper under discussion mentions that they also tried a hierarchial variant of NNMF, but since they didn’t report its results, we assume

218 that those result were not any more impressive than the results of the non-hierarchial variant.

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222

223

224 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel’s value on the lower left is the sum

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

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

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

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

229 Preliminary work

230 Format conversion between SEV, MATLAB, NIFTI

231 todo

232 Flatmap of cortex

233 todo

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

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

236 natorially. according to logistic regression, gene wwc14 is the best fit single gene for predicting whether or not a pixel on

237 the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure shows wwc1’s spatial expression

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

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

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

241 Gnee mtif25 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right

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

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

244 Correlation todo

245 Conditional entropy todo

246 Gradient similarity todo

247 Geometric and pointwise scoring methods provide complementary information

248 To show that local geometry can provide useful information that cannot be detected via pointwise analyses, consider Fig.

249 . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method6. The bottom row

250 _________________________________________

251 4“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652

252 5“mitochondrial translational initiation factor 2”; EntrezGene ID 76784

253 6For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor

254 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

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258

259

260 Figure 2: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.

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

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

263 displays the 3 genes which most match AUD according to a method which considers local geometry7 The pointwise method

264 in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this includes many

265 areas which don’t have a salient border matching the areal border. The geometric method identifies genes whose salient

266 expression border seems to partially line up with the border of AUD; its weakness is that this includes genes which don’t

267 express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as Aph1a in the

268 example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD; we deliberately

269 chose a “difficult” area in order to better contrast pointwise with geometric methods.

270 Areas which can be identified by single genes

271 todo

272 Specific to Aim 1 (and Aim 3)

273 Forward stepwise logistic regression todo

274 SVM on all genes at once

275 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

276 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%8. As noted above,

277 however, a classifier that looks at all the genes at once isn’t practically useful.

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

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

280 combines feature selection with supervised learning.

281 Decision trees

282 todo

283 Specific to Aim 2 (and Aim 3)

284 Raw dimensionality reduction results

285 todo

286 (might want to incld nnMF since mentioned above)

287 _________________________________________

288 they predict area AUD.

289 7For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the

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

291 85-fold cross-validation.

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295 Dimensionality reduction plus K-means or spectral clustering

296 Many areas are captured by clusters of genes

297 todo

298 todo

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302 Research plan

303 todo amongst other things:

304 Develop algorithms that find genetic markers for anatomical regions

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

306 geometric, and information-theoretic measures.

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

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

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

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

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

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

313 machines.

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

315 identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the

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

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

318 a larger area which can be fit.

319 Apply these algorithms to the cortex

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

321 between SEV, NIFTI and MATLAB formats.

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

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

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

325 that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once.

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

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

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

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

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

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

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

333 _____________________

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

335 Principle 4: Work in 2-D whenever possible

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

337 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 in

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

339 The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that charac-

340 terized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold into

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344 a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used by

345 Caret?? ) with mappings which preserve angle (conformal maps).

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

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

348 structure seems to be wrong.

349 if we need citations for aim 3 significance, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_

350 user=4429&_coverDate=12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct=C000059602&_version=

351 1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203#app2 has examples of genetic targeting to spe-

352 cific anatomical regions

353 —

354 note:

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

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358

359