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2.1 --- a/grant.html Tue Apr 14 02:53:00 2009 -0700 2.2 +++ b/grant.html Tue Apr 14 23:33:43 2009 -0700 2.3 @@ -1,12 +1,12 @@ 2.4 Specific aims 2.5 -Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expres- 2.6 -sion levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial 2.7 -variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw 2.8 -new anatomical maps based on gene expression patterns. We have three specific aims: 2.9 +Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, or in situ trans- 2.10 +genic reporter allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated 2.11 +methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical 2.12 +regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims: 2.13 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target 2.14 anatomical regions 2.15 -(2) develop an algorithm to suggest new ways of carving up a structure into anatomical subregions, based on spatial 2.16 -patterns in gene expression 2.17 +(2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns 2.18 +in gene expression 2.19 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse 2.20 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of 2.21 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2). 2.22 @@ -19,17 +19,17 @@ 2.23 Background and significance 2.24 Aim 1 2.25 Machine learning terminology: supervised learning 2.26 -The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if 2.27 -the expression level of those genes is known, then the locations of the subregions can be inferred. 2.28 -If we define the subregions so that they cover the entire anatomical structure to be divided, then instead of saying that we 2.29 -are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine 2.30 -to which subregion each voxel within the structure belongs. We call this a classification task, because each voxel is being 2.31 -assigned to a class (namely, its subregion). 2.32 +The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the 2.33 +expression level of those genes is known, then the locations of the regions can be inferred. 2.34 +If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we 2.35 +are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to 2.36 +which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned 2.37 +to a class (namely, its region). 2.38 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of 2.39 -the subregions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels 2.40 -within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel 2.41 -belongs. We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called 2.42 -a label (or a class label). 2.43 +the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels 2.44 +within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs. 2.45 +We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label 2.46 +(or a class label). 2.47 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a 2.48 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be 2.49 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning 2.50 @@ -37,7 +37,7 @@ 2.51 in the construction of the classifier is called training data. 2.52 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a 2.53 task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances 2.54 -(voxels) for which the labels (subregions) are known. 2.55 +(voxels) for which the labels (regions) are known. 2.56 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection. 2.57 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with 2.58 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training. 2.59 @@ -87,16 +87,16 @@ 2.60 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances 2.61 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called 2.62 clustering or cluster analysis. 2.63 -The task of deciding how to carve up a structure into anatomical subregions can be put into these terms. The instances 2.64 -are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels 2.65 -from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that 2.66 -clustering voxels is the same as finding potential subregions; we seek a partitioning of the voxels into subregions, that is, 2.67 -into clusters of voxels with similar gene expression. 2.68 -It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all; 2.69 -perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial 2.70 -scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion. 2.71 -This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which 2.72 -partition the voxels. This is called hierarchial clustering. 2.73 +The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are 2.74 +once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from 2.75 +the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering 2.76 +voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels 2.77 +with similar gene expression. 2.78 +It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps 2.79 +some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they 2.80 +could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests 2.81 +the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. 2.82 +This is called hierarchial clustering. 2.83 Similarity scores 2.84 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or 2.85 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and 2.86 @@ -124,25 +124,24 @@ 2.87 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced 2.88 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene 2.89 expression levels. 2.90 -Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might 2.91 -want tomake a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions 2.92 -with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points 2.93 -in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of 2.94 -the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find 2.95 -arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction 2.96 -is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction 2.97 -before clustering. 2.98 +Another use for dimensionality reduction is to visualize the relationships between regions. For example, one might want 2.99 +to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar 2.100 +gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot 2.101 +should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on 2.102 +a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find arrangements 2.103 +of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied 2.104 +after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering. 2.105 Clustering genes rather than voxels 2.106 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster 2.107 the features (genes). There are two ways that clusters of genes could be used. 2.108 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could 2.109 have one reduced feature for each gene cluster. 2.110 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression 2.111 -pattern which seems to pick out a single, spatially continguous subregion. Therefore, it seems likely that an anatomically 2.112 -interesting subregion will have multiple genes which each individually pick it out2. This suggests the following procedure: 2.113 -cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the 2.114 -final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some 2.115 -“superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion. 2.116 +pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically 2.117 +interesting region will have multiple genes which each individually pick it out2. This suggests the following procedure: 2.118 +cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. 2.119 +In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions” 2.120 +formed by lumping together a few regions, are associated with gene clusters in this fashion. 2.121 Aim 3 2.122 Background 2.123 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can 2.124 @@ -172,13 +171,19 @@ 2.125 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, 2.126 and has greater registration error[2]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes of 2.127 known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[2]. 2.128 -Significance 2.129 -The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the 2.130 -combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for 2.131 +The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[?], 2.132 +GenePaint[?], its sister project GeneAtlas[?], BGEM[?], EMAGE[?], EurExpress (http://www.eurexpress.org/ee/; Eur- 2.133 +Express data is also entered into EMAGE), todo. With the exception of the ABA, GenePaint, and EMAGE, most of these 2.134 +resources, have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D 2.135 +space, and only ABA and EMAGE make this form of data available for public download from the website. Many of these 2.136 +resources focus on developmental gene expression. 2.137 _________________________________________ 2.138 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is 2.139 -possible that the currently accepted cortical maps divide the cortex into subregions which are unnatural from the point of view of gene expression; 2.140 -perhaps there is some other way to map the cortex for which each subregion can be identified by single genes. 2.141 +possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; 2.142 +perhaps there is some other way to map the cortex for which each region can be identified by single genes. 2.143 +Significance 2.144 +Themethod developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the 2.145 +combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for 2.146 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively 2.147 target individual cortical areas. 2.148 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom- 2.149 @@ -195,7 +200,6 @@ 2.150 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to 2.151 develop could be used to suggest modifications to the human cortical map as well. 2.152 Related work 2.153 -There does not appear to be much work on the automated analysis of spatial gene expression data. 2.154 There is a substantial body of work on the analysis of gene expression data, however, most of this concerns gene expression 2.155 data which is not fundamentally spatial. 2.156 As noted above, there has been much work on both supervised learning and clustering, and there are many available 2.157 @@ -205,48 +209,63 @@ 2.158 Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical 2.159 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient 2.160 similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application. 2.161 -We are aware of two existing efforts to relate spatial gene expression data to anatomy through computational methods. 2.162 +We are aware of four existing efforts to relate spatial gene expression data to anatomy through computational methods. 2.163 +[? ] refers to GeneAtlas. GeneAtlas allows the user to construct a search query by freely demarcating one or two 2-D 2.164 +regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression 2.165 +pattern is to be matched. GeneAtlas differs from our Aim 1 in at least two ways. First, GeneAtlas finds only single genes, 2.166 +whereas we will also look for combinations of genes3. Second, at least for the custom spatial search, Gene Atlas appears to 2.167 +use a simple pointwise scoring method (strength of expression), whereas we will also use geometric metrics such as gradient 2.168 +similarity. 2.169 +[? ] todo 2.170 [5 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis, 2.171 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive 2.172 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the 2.173 -usefulness of such research. We have run NNMF on the cortical dataset3 and while the results are promising (see Preliminary 2.174 +usefulness of such research. We have run NNMF on the cortical dataset4 and while the results are promising (see Preliminary 2.175 Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this 2.176 paper’s authors did manually will be possible). 2.177 [2 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA is an analysis tool for the ABA dataset. AGEA has 2.178 three components: 2.179 * Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) 2.180 -yields a list of genes which are overexpressed in that cluster. 2.181 +yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of 2.182 +overexpressed genes for selected structures) 2.183 * Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene 2.184 expression profile of the seed voxel and every other voxel. 2.185 * Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm 2.186 with correlation as the similarity metric. 2.187 Gene Finder is different from our Aim 1 in at least four ways. First, although the user chooses a seed voxel, Gene 2.188 Finder, not the user, chooses the cluster for which genes will be found, and in our experience it never chooses cortical areas, 2.189 -instead preferring cortical layers4. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second, 2.190 -Gene Finder finds only single genes, whereas we will also look for combinations of genes5. Third, gene finder can only use 2.191 +_________________________________________ 2.192 + 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 2.193 +combination. 2.194 + 4We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft 2.195 +spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was 2.196 +needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried. 2.197 +instead preferring cortical layers5. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second, 2.198 +Gene Finder finds only single genes, whereas we will also look for combinations of genes6. Third, gene finder can only use 2.199 overexpression as a marker, whereas in the Preliminary Data we show that underexpression can also be used. Fourth, Gene 2.200 -Finder uses a simple pointwise score6, whereas we will also use geometric metrics such as gradient similarity. 2.201 +Finder uses a simple pointwise score7, whereas we will also use geometric metrics such as gradient similarity. 2.202 +The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters corre- 2.203 +sponding to layers, but no clusters corresponding to cortical areas8 9 Our Aim 2 will not be accomplished until a clustering 2.204 +is produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does 2.205 +no dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any 2.206 +better than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. 2.207 +Third, AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify 2.208 +intersting spatial regions such as cortical areas. 2.209 +Finally, with the except of [5], none of the publications discussed above compare the results obtained by using different 2.210 +algorithms or scoring methods. [5] reports that both mNNMF and hierarchial mNNMF clustering were useful, and that 2.211 +hierarchial recursive bifurcation gave similar results. 2.212 +To summarize, in comparison to our Aim 1, none of the previous projects explores combinations of marker genes, and 2.213 +w/r/t both aims, there has been almost no experimentation with or comparison of different algorithms or scoring methods. 2.214 +todo 2.215 _________________________________________ 2.216 - 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft 2.217 -spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was 2.218 -needed. The paper under discussion mentions that they also tried a hierarchial variant of NNMF, but since they didn’t report its results, we 2.219 -assume that those result were not any more impressive than the results of the non-hierarchial variant. 2.220 - 4Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene 2.221 + 5Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene 2.222 expression of voxels in different areas but the same layer are stronger than pairwise correlatios between the gene expression of voxels in different 2.223 layers but the same area. This appears to be the case. 2.224 - 5See 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 2.225 + 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 2.226 combination. 2.227 - 6“Expression energy ratio”, which captures overexpression. 2.228 -The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters cor- 2.229 -responding to layers, but no clusters corresponding to areas7 8 Our Aim 2 will not be accomplished until a clustering is 2.230 -produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does no 2.231 -dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better 2.232 -than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Third, 2.233 -AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify intersting 2.234 -spatial subregions such as cortical areas. 2.235 -_______ 2.236 - 7This is for the same reason as in footnote 4. 2.237 - 8There are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area 2.238 + 7“Expression energy ratio”, which captures overexpression. 2.239 + 8This is for the same reason as in footnote 5. 2.240 + 9There are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area 2.241 intersection clusters, further work is needed to make sense of these. 2.242 Preliminary work 2.243 Format conversion between SEV, MATLAB, NIFTI 2.244 @@ -255,14 +274,14 @@ 2.245 Flatmap of cortex 2.246 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided 2.247 the cortex into hemispheres. 2.248 -Using Caret[1], we created a mesh representation of the surface of the selected region. For each gene, for each node of 2.249 -the mesh, we used Caret to calculate an average of the gene expression of the voxels “underneath” that mesh node. We 2.250 -then used Caret to flatten the cortex, creating a two-dimensional mesh. 2.251 +Using Caret[1], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of 2.252 +the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened 2.253 +the cortex, creating a two-dimensional mesh. 2.254 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid 2.255 into a MATLAB matrix. 2.256 We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted 2.257 -these manual traces into Caret-format regional boundary data on the mesh surface. Using Caret, we projected the regions 2.258 -onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 2.259 +these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d 2.260 +mesh, and then onto the grid, and then we converted the region data into MATLAB format. 2.261 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing 2.262 a grid of points (pixels) over the cortical surface: 2.263 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel 2.264 @@ -328,8 +347,8 @@ 2.265 similar direction (because the borders are similar). 2.266 Geometric and pointwise scoring methods provide complementary information 2.267 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider 2.268 -Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method9. The 2.269 -bottom row displays the 3 genes which most match AUD according to a method which considers local geometry10 The 2.270 +Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method10. The 2.271 +bottom row displays the 3 genes which most match AUD according to a method which considers local geometry11 The 2.272 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is 2.273 that this includes many areas which don’t have a salient border matching the areal border. The geometric method identifies 2.274 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes 2.275 @@ -338,14 +357,14 @@ 2.276 for AUD; we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods. 2.277 Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas 2.278 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi- 2.279 -natorially. according to logistic regression, gene wwc111 is the best fit single gene for predicting whether or not a pixel on 2.280 +natorially. according to logistic regression, gene wwc112 is the best fit single gene for predicting whether or not a pixel on 2.281 _________________________________________ 2.282 - 9For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor 2.283 + 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 2.284 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 2.285 they predict area AUD. 2.286 - 10For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the 2.287 + 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 2.288 shape of area AUD, was calculated, and this was used to rank the genes. 2.289 - 11“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652 2.290 + 12“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652 2.291 2.292 2.293 2.294 @@ -358,7 +377,7 @@ 2.295 pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene 2.296 overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the 2.297 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo). 2.298 -Gene mtif212 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right 2.299 +Gene mtif213 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right 2.300 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these 2.301 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene. 2.302 Areas which can be identified by single genes 2.303 @@ -369,7 +388,7 @@ 2.304 Forward stepwise logistic regression todo 2.305 SVM on all genes at once 2.306 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 2.307 -surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%13. As noted above, 2.308 +surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%14. As noted above, 2.309 however, a classifier that looks at all the genes at once isn’t practically useful. 2.310 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many 2.311 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task 2.312 @@ -381,13 +400,23 @@ 2.313 todo 2.314 (might want to incld nnMF since mentioned above) 2.315 _________________________________________ 2.316 - 12“mitochondrial translational initiation factor 2”; EntrezGene ID 76784 2.317 - 135-fold cross-validation. 2.318 + 13“mitochondrial translational initiation factor 2”; EntrezGene ID 76784 2.319 + 145-fold cross-validation. 2.320 Dimensionality reduction plus K-means or spectral clustering 2.321 Many areas are captured by clusters of genes 2.322 todo 2.323 todo 2.324 Research plan 2.325 +Further work on flatmapping 2.326 +In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 2.327 +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 2.328 +in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 2.329 +In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal 2.330 +for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[1]) with 2.331 +mappings which preserve angle (conformal maps). 2.332 +Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. 2.333 +If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D 2.334 +structure seems to be wrong. 2.335 todo amongst other things: 2.336 Develop algorithms that find genetic markers for anatomical regions 2.337 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, 2.338 @@ -469,19 +498,10 @@ 2.339 _______________________________________________________________________________________________________ 2.340 stuff i dunno where to put yet (there is more scattered through grant-oldtext): 2.341 Principle 4: Work in 2-D whenever possible 2.342 - In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 2.343 -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 2.344 -in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 2.345 - The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that 2.346 -characterized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold 2.347 -into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used 2.348 -by Caret[1]) with mappings which preserve angle (conformal maps). 2.349 - Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. 2.350 -If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D 2.351 -structure seems to be wrong. 2.352 — 2.353 note: 2.354 do we need to cite: no known markers, impressive results? 2.355 two hemis 2.356 + “genomic anatomy” is a name found in the titles of one of the cited papers which seems good 2.357 2.358

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5.1 --- a/grant.txt Tue Apr 14 02:53:00 2009 -0700 5.2 +++ b/grant.txt Tue Apr 14 23:33:43 2009 -0700 5.3 @@ -3,11 +3,11 @@ 5.4 5.5 == Specific aims == 5.6 5.7 -Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:\\ 5.8 +Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, or in situ transgenic reporter allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:\\ 5.9 5.10 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target anatomical regions\\ 5.11 5.12 -(2) develop an algorithm to suggest new ways of carving up a structure into anatomical subregions, based on spatial patterns in gene expression\\ 5.13 +(2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns in gene expression\\ 5.14 5.15 (3) create a 2-D "flat map" dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).\\ 5.16 5.17 @@ -24,15 +24,15 @@ 5.18 5.19 \vspace{0.3cm}**Machine learning terminology: supervised learning** 5.20 5.21 -The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the locations of the subregions can be inferred. 5.22 - 5.23 -If we define the subregions so that they cover the entire anatomical structure to be divided, then instead of saying that we are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine to which subregion each voxel within the structure belongs. We call this a __classification task__, because each voxel is being assigned to a class (namely, its subregion). 5.24 - 5.25 -Therefore, an understanding of the relationship between the combination of their expression levels and the locations of the subregions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel belongs. We call this function a __classifier__. In general, the input to a classifier is called an __instance__, and the output is called a __label__ (or a __class label__). 5.26 +The task of looking for marker genes for anatomical regions means that one is 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 inferred. 5.27 + 5.28 +If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to which region each voxel within the structure belongs. We call this a __classification task__, because each voxel is being assigned to a class (namely, its region). 5.29 + 5.30 +Therefore, an understanding of the relationship between the combination of their expression levels and the locations of the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function a __classifier__. In general, the input to a classifier is called an __instance__, and the output is called a __label__ (or a __class label__). 5.31 5.32 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning procedure. The construction of the classifier is called __training__ (also __learning__), and the initial gene expression dataset used in the construction of the classifier is called __training data__. 5.33 5.34 -In the machine learning literature, this sort of procedure may be thought of as a __supervised learning task__, defined as a task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances (voxels) for which the labels (subregions) are known. 5.35 +In the machine learning literature, this sort of procedure may be thought of as a __supervised learning task__, defined as a task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances (voxels) for which the labels (regions) are known. 5.36 5.37 Each gene expression level is called a __feature__, and the selection of which genes\footnote{Strictly speaking, the features are gene expression levels, but we'll call them genes.} to include is called __feature selection__. Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with a separate feature selection phase, whereas other methods combine feature selection with other aspects of training. 5.38 5.39 @@ -72,9 +72,9 @@ 5.40 5.41 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as __unsupervised learning__ in the jargon of machine learning. One thing that you can do with such a dataset is to group instances together. A set of similar instances is called a __cluster__, and the activity of finding grouping the data into clusters is called clustering or cluster analysis. 5.42 5.43 -The task of deciding how to carve up a structure into anatomical subregions can be put into these terms. The instances are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that clustering voxels is the same as finding potential subregions; we seek a partitioning of the voxels into subregions, that is, into clusters of voxels with similar gene expression. 5.44 - 5.45 -It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all; perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion. This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called hierarchial clustering. 5.46 +The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression. 5.47 + 5.48 +It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called hierarchial clustering. 5.49 5.50 5.51 \vspace{0.3cm}**Similarity scores** 5.52 @@ -95,7 +95,7 @@ 5.53 5.54 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which "summarize" a larger number of features using a smaller number of features; these techniques go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique yields is called the __reduced feature set__. After the reduced feature set is created, the instances may be replaced by __reduced instances__, which have as their features the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels. 5.55 5.56 -Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might want to make a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property -- however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering. 5.57 +Another use for dimensionality reduction is to visualize the relationships between regions. For example, one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property -- however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering. 5.58 5.59 5.60 \vspace{0.3cm}**Clustering genes rather than voxels** 5.61 @@ -105,7 +105,7 @@ 5.62 5.63 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could have one reduced feature for each gene cluster. 5.64 5.65 -Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression pattern which seems to pick out a single, spatially continguous subregion. Therefore, it seems likely that an anatomically interesting subregion will have multiple genes which each individually pick it out\footnote{This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible that the currently accepted cortical maps divide the cortex into subregions which are unnatural from the point of view of gene expression; perhaps there is some other way to map the cortex for which each subregion can be identified by single genes.}. This suggests the following procedure: cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some "superregions" formed by lumping together a few regions, are associated with gene clusters in this fashion. 5.66 +Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically interesting region will have multiple genes which each individually pick it out\footnote{This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes.}. This suggests the following procedure: cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some "superregions" formed by lumping together a few regions, are associated with gene clusters in this fashion. 5.67 5.68 5.69 5.70 @@ -129,6 +129,7 @@ 5.71 5.72 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes\cite{waterston_initial_2002}. The ABA contains data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and has greater registration error\cite{ng_anatomic_2009}. Genes were selected by the Allen Institute for coronal sectioning based on, "classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern"\cite{ng_anatomic_2009}. 5.73 5.74 +The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT\cite{gong_gene_2003}, GenePaint\cite{visel_genepaint_2004}, its sister project GeneAtlas\cite{carson_data_2005}, BGEM\cite{magdaleno_bgem_2006}, EMAGE\cite{?}, EurExpress (http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE), todo. With the exception of the ABA, GenePaint, and EMAGE, most of these resources, have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D space, and only ABA and EMAGE make this form of data available for public download from the website. Many of these resources focus on developmental gene expression. 5.75 5.76 5.77 5.78 @@ -144,18 +145,20 @@ 5.79 5.80 5.81 === Related work === 5.82 -There does not appear to be much work on the automated analysis of spatial gene expression data. 5.83 - 5.84 There is a substantial body of work on the analysis of gene expression data, however, most of this concerns gene expression data which is not fundamentally spatial. 5.85 5.86 As noted above, there has been much work on both supervised learning and clustering, and there are many available algorithms for each. However, the completion of Aims 1 and 2 involves more than just choosing between a set of existing algorithms, and will constitute a substantial contribution to biology. The algorithms require the scientist to provide a framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical "fine-tuning" of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application. 5.87 5.88 -We are aware of two existing efforts to relate spatial gene expression data to anatomy through computational methods. 5.89 +We are aware of four existing efforts to relate spatial gene expression data to anatomy through computational methods. 5.90 + 5.91 +\cite{carson_data_2005} refers to GeneAtlas. GeneAtlas allows the user to construct a search query by freely demarcating one or two 2-D regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression pattern is to be matched. GeneAtlas differs from our Aim 1 in at least two ways. First, GeneAtlas finds only single genes, whereas we will also look for combinations of genes\footnote{See 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 combination.}. Second, at least for the custom spatial search, Gene Atlas appears to use a simple pointwise scoring method (strength of expression), whereas we will also use geometric metrics such as gradient similarity. 5.92 + 5.93 +\cite{venkataraman_emage_2008} todo 5.94 5.95 \cite{thompson_genomic_2008} describes an analysis of the anatomy of 5.96 the hippocampus using the ABA dataset. In addition to manual analysis, 5.97 two clustering methods were employed, a modified Non-negative Matrix 5.98 -Factorization (NNMF), and a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness of such research. We have run NNMF on the cortical dataset\footnote{We ran "vanilla" NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was 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 that those result were not any more impressive than the results of the non-hierarchial variant.} and while the results are promising (see Preliminary Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this paper's authors did manually will be possible). 5.99 +Factorization (NNMF), and a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness of such research. We have run NNMF on the cortical dataset\footnote{We ran "vanilla" NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.} and while the results are promising (see Preliminary Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this paper's authors did manually will be possible). 5.100 5.101 5.102 \cite{ng_anatomic_2009} describes AGEA, "Anatomic Gene Expression 5.103 @@ -164,7 +167,7 @@ 5.104 5.105 * Gene Finder: The user selects a seed voxel and the system (1) chooses a 5.106 cluster which includes the seed voxel, (2) yields a list of genes 5.107 -which are overexpressed in that cluster. 5.108 +which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected structures) 5.109 5.110 * Correlation: The user selects a seed voxel and 5.111 the shows the user how much correlation there is between the gene 5.112 @@ -174,9 +177,11 @@ 5.113 5.114 Gene Finder is different from our Aim 1 in at least four ways. First, although the user chooses a seed voxel, Gene Finder, not the user, chooses the cluster for which genes will be found, and in our experience it never chooses cortical areas, instead preferring cortical layers\footnote{\label{layersNotAreas}Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene expression of voxels in different areas but the same layer are stronger than pairwise correlatios between the gene expression of voxels in different layers but the same area. This appears to be the case.}. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second, Gene Finder finds only single genes, whereas we will also look for combinations of genes\footnote{See 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 combination.}. Third, gene finder can only use overexpression as a marker, whereas in the Preliminary Data we show that underexpression can also be used. Fourth, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric metrics such as gradient similarity. 5.115 5.116 -The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters corresponding to layers, but no clusters corresponding to areas\footnote{This is for the same reason as in footnote \ref{layersNotAreas}.} \footnote{There are clusters which presumably correspond to the 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 these.} Our Aim 2 will not be accomplished until a clustering is produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does no dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Third, AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify intersting spatial subregions such as cortical areas. 5.117 - 5.118 - 5.119 +The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters corresponding to layers, but no clusters corresponding to cortical areas\footnote{This is for the same reason as in footnote \ref{layersNotAreas}.} \footnote{There are clusters which presumably correspond to the 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 these.} Our Aim 2 will not be accomplished until a clustering is produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does no dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Third, AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify intersting spatial regions such as cortical areas. 5.120 + 5.121 +Finally, with the except of \cite{thompson_genomic_2008}, none of the publications discussed above compare the results obtained by using different algorithms or scoring methods. \cite{thompson_genomic_2008} reports that both mNNMF and hierarchial mNNMF clustering were useful, and that hierarchial recursive bifurcation gave similar results. 5.122 + 5.123 +To summarize, in comparison to our Aim 1, none of the previous projects explores combinations of marker genes, and w/r/t both aims, there has been almost no experimentation with or comparison of different algorithms or scoring methods. todo 5.124 5.125 \newpage 5.126 5.127 @@ -189,11 +194,11 @@ 5.128 === Flatmap of cortex === 5.129 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided the cortex into hemispheres. 5.130 5.131 -Using Caret\cite{van_essen_integrated_2001}, we created a mesh representation of the surface of the selected region. For each gene, for each node of the mesh, we used Caret to calculate an average of the gene expression of the voxels "underneath" that mesh node. We then used Caret to flatten the cortex, creating a two-dimensional mesh. 5.132 +Using Caret\cite{van_essen_integrated_2001}, we created a mesh representation of the surface of the selected voxels. For each gene, for each node of the mesh, we calculated an average of the gene expression of the voxels "underneath" that mesh node. We then flattened the cortex, creating a two-dimensional mesh. 5.133 5.134 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid into a MATLAB matrix. 5.135 5.136 -We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. Using Caret, we projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 5.137 +We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format. 5.138 5.139 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing a grid of points (pixels) over the cortical surface: 5.140 5.141 @@ -344,9 +349,21 @@ 5.142 \newpage 5.143 == Research plan == 5.144 5.145 + 5.146 +\vspace{0.3cm}**Further work on flatmapping** 5.147 + 5.148 + 5.149 +In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 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 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 5.150 + 5.151 +In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret\cite{van_essen_integrated_2001}) with mappings which preserve angle (conformal maps). 5.152 + 5.153 +Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D structure seems to be wrong. 5.154 + 5.155 + 5.156 todo amongst other things: 5.157 5.158 5.159 + 5.160 \vspace{0.3cm}**Develop algorithms that find genetic markers for anatomical regions** 5.161 5.162 # Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, geometric, and information-theoretic measures. 5.163 @@ -390,12 +407,6 @@ 5.164 \vspace{0.3cm}**Principle 4: Work in 2-D whenever possible** 5.165 5.166 5.167 -In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 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 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 5.168 - 5.169 -The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that characterized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret\cite{van_essen_integrated_2001}) with mappings which preserve angle (conformal maps). 5.170 - 5.171 -Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D structure seems to be wrong. 5.172 - 5.173 5.174 5.175 %%if we need citations for aim 3 significance, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_user=4429&_coverDate=12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct=C000059602&_version=1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203#app2 has examples of genetic targeting to specific anatomical regions 5.176 @@ -409,3 +420,7 @@ 5.177 5.178 5.179 two hemis 5.180 + 5.181 + 5.182 +"genomic anatomy" is a name found in the titles of one of the cited papers which seems good 5.183 +