1.1 --- a/grant.html Mon Apr 13 03:43:51 2009 -0700 1.2 +++ b/grant.html Mon Apr 13 03:52:58 2009 -0700 1.3 @@ -1,494 +1,359 @@ 1.4 +Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.5 Specific aims 1.6 - Massive new datasets obtained with techniques such as in situ hybridization 1.7 - (ISH) and BAC-transgenics allow the expression levels of many genes at many 1.8 - locations to be compared. Our goal is to develop automated methods to relate 1.9 - spatial variation in gene expression to anatomy. We want to find marker genes 1.10 - for specific anatomical regions, and also to draw new anatomical maps based on 1.11 - gene expression patterns. We have three specific aims: 1.12 - (1) develop an algorithm to screen spatial gene expression data for combi- 1.13 - nations of marker genes which selectively target anatomical regions 1.14 - (2) develop an algorithm to suggest new ways of carving up a structure into 1.15 - anatomical subregions, based on spatial patterns in gene expression 1.16 - (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that con- 1.17 - tains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as 1.18 - the boundaries of cortical anatomical areas. Use this dataset to validate the 1.19 - methods developed in (1) and (2). 1.20 - In addition to validating the usefulness of the algorithms, the application of 1.21 - these methods to cerebral cortex will produce immediate benefits, because there 1.22 - are currently no known genetic markers for many cortical areas. The results 1.23 - of the project will support the development of new ways to selectively target 1.24 - cortical areas, and it will support the development of a method for identifying 1.25 - the cortical areal boundaries present in small tissue samples. 1.26 - All algorithms that we develop will be implemented in an open-source soft- 1.27 - ware toolkit. The toolkit, as well as the machine-readable datasets developed 1.28 - in aim (3), will be published and freely available for others to use. 1.29 - 1 1.30 +Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expression 1.31 +levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation 1.32 +in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical 1.33 +maps based on gene expression patterns. We have three specific aims: 1.34 +(1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target 1.35 +anatomical regions 1.36 +(2) develop an algorithm to suggest new ways of carving up a structure into anatomical subregions, based on spatial 1.37 +patterns in gene expression 1.38 +(3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse Brain 1.39 +Atlas ISH data, as well as the boundaries of cortical anatomical areas. Use this dataset to validate the methods developed 1.40 +in (1) and (2). 1.41 +In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce 1.42 +immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project 1.43 +will support the development of new ways to selectively target cortical areas, and it will support the development of a method 1.44 +for identifying the cortical areal boundaries present in small tissue samples. 1.45 +All algorithms that we develop will be implemented in an open-source software toolkit. The toolkit, as well as the 1.46 +machine-readable datasets developed in aim (3), will be published and freely available for others to use. 1.47 +_______________________________________________________________________________________________________ 1.48 +PHS 398/2590 (Rev. 09/04) Page 1 ___ Continuation Format Page 1.49 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.50 +Background and significance 1.51 +Aim 1 1.52 +Machine learning terminology: supervised learning 1.53 +The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if 1.54 +the expression level of those genes is known, then the locations of the subregions can be inferred. 1.55 +If we define the subregions so that they cover the entire anatomical structure to be divided, then instead of saying that we 1.56 +are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine 1.57 +to which subregion each voxel within the structure belongs. We call this a classification task, because each voxel is being 1.58 +assigned to a class (namely, its subregion). 1.59 +Therefore, an understanding of the relationship between the combination of their expression levels and the locations of 1.60 +the subregions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels 1.61 +within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel 1.62 +belongs. We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called 1.63 +a label (or a class label). 1.64 +The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a 1.65 +classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be 1.66 +analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning 1.67 +procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used in 1.68 +the construction of the classifier is called training data. 1.69 +In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a 1.70 +task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances 1.71 +(voxels) for which the labels (subregions) are known. 1.72 +Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection. 1.73 +Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with a 1.74 +separate feature selection phase, whereas other methods combine feature selection with other aspects of training. 1.75 +One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then 1.76 +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 1.77 +procedure may be used in which features are added and subtracted from the selected set depending on how much they raise 1.78 +the score. Such procedures are called “stepwise” or “greedy”. 1.79 +Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the 1.80 +learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature 1.81 +selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to 1.82 +each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If 1.83 +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 1.84 +information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method. 1.85 +Key questions when choosing a learning method are: What are the instances? What are the features? How are the 1.86 +features chosen? Here are four principles that outline our answers to these questions. 1.87 +Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be 1.88 +identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene 1.89 +included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at 1.90 +combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary 1.91 +Results). Therefore, each instance should contain multiple features (genes). 1.92 +Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is 1.93 +only allowed to look at the expression of the genes which have been selected as features. The more data that is available to 1.94 +a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a 1.95 +strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations 1.96 +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 1.97 +a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the 1.98 +expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the 1.99 +_________________________________________ 1.100 + 1Strictly speaking, the features are gene expression levels, but we’ll call them genes. 1.101 +_______________________________________________________________________________________________________ 1.102 +PHS 398/2590 (Rev. 09/04) Page 2 ___ Continuation Format Page 1.103 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.104 +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 1.105 +to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as 1.106 +features. 1.107 +Principle 3: Use geometry in feature selection 1.108 +When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of 1.109 +each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information 1.110 +about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See 1.111 +Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods. 1.112 +Principle 4: Work in 2-D whenever possible 1.113 +There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When 1.114 +it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis 1.115 +algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D data. 1.116 +Therefore, when possible, the instances should represent pixels, not voxels. 1.117 +Aim 2 1.118 +Machine learning terminology: clustering 1.119 +If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as 1.120 +unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances 1.121 +together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called 1.122 +clustering or cluster analysis. 1.123 +The task of deciding how to carve up a structure into anatomical subregions can be put into these terms. The instances 1.124 +are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels 1.125 +from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that 1.126 +clustering voxels is the same as finding potential subregions; we seek a partitioning of the voxels into subregions, that is, into 1.127 +clusters of voxels with similar gene expression. 1.128 +It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all; 1.129 +perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale 1.130 +they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion. This 1.131 +suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition 1.132 +the voxels. This is called hierarchial clustering. 1.133 +Similarity scores 1.134 +A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or 1.135 +clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and 1.136 +scoring methods for similarity. 1.137 +Spatially contiguous clusters; image segmentation 1.138 +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 1.139 +additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Results, 1.140 +we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these results 1.141 +against other methods which guarantee contiguous clusters. 1.142 +Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a 1.143 +variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into 1.144 +clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in 1.145 +our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which 1.146 +use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used to 1.147 +process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting sharp 1.148 +object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression. 1.149 +Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged 1.150 +data, some of these algorithms are specialized for visual images. 1.151 +Dimensionality reduction 1.152 +_______________________________________________________________________________________________________ 1.153 +PHS 398/2590 (Rev. 09/04) Page 3 ___ Continuation Format Page 1.154 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.155 +Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the 1.156 +instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which 1.157 +“summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature 1.158 +extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature 1.159 +set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features 1.160 +the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced 1.161 +feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene 1.162 +expression levels. 1.163 +Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might 1.164 +want to make a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions 1.165 +with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points 1.166 +in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of 1.167 +the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find 1.168 +arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction 1.169 +is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction 1.170 +before clustering. 1.171 +Clustering genes rather than voxels 1.172 +Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster 1.173 +the features (genes). There are two ways that clusters of genes could be used. 1.174 +Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could 1.175 +have one reduced feature for each gene cluster. 1.176 +Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression 1.177 +pattern which seems to pick out a single, spatially continguous subregion. Therefore, it seems likely that an anatomically 1.178 +interesting subregion will have multiple genes which each individually pick it out2. This suggests the following procedure: 1.179 +cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the 1.180 +final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some 1.181 +“superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion. 1.182 +Aim 3 1.183 +Background 1.184 +The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can be drawn 1.185 +as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue downwards 1.186 +into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an 1.187 +area of the cortex as a slice of many-layered cake. 1.188 +Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes, 1.189 +there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas, 1.190 +this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of 1.191 +their approximate location upon the cortical surface. 1.192 +Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not 1.193 +completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a 1.194 +single agreed-upon map can be seen by contrasting the recent maps given by Swanson?? on the one hand, and Paxinos 1.195 +and Franklin?? on the other. While the maps are certainly very similar in their general arrangement, significant differences 1.196 +remain in the details. 1.197 +Significance 1.198 +The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the 1.199 +combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for 1.200 +drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively 1.201 +target individual cortical areas. 1.202 +_______________ 1.203 + 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible 1.204 +that the currently accepted cortical maps divide the cortex into subregions which are unnatural from the point of view of gene expression; perhaps 1.205 +there is some other way to map the cortex for which each subregion can be identified by single genes. 1.206 +_______________________________________________________________________________________________________ 1.207 +PHS 398/2590 (Rev. 09/04) Page 4 ___ Continuation Format Page 1.208 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.209 +The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom- 1.210 +ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can 1.211 +find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that 1.212 +will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex. 1.213 +The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of a better 1.214 +map. The development of present-day cortical maps was driven by the application of histological stains. It is conceivable 1.215 +that if a different set of stains had been available which identified a different set of features, then the today’s cortical maps 1.216 +would have come out differently. Since the number of classes of stains is small compared to the number of genes, it is likely 1.217 +that there are many repeated, salient spatial patterns in the gene expression which have not yet been captured by any stain. 1.218 +Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking at the patterns of gene 1.219 +expression. 1.220 +While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to 1.221 +develop could be used to suggest modifications to the human cortical map as well. 1.222 +Related work 1.223 +There does not appear to be much work on the automated analysis of spatial gene expression data. 1.224 +There is a substantial body of work on the analysis of gene expression data, however, most of this concerns gene expression 1.225 +data which is not fundamentally spatial. 1.226 +As noted above, there has been much work on both supervised learning and clustering, and there are many available 1.227 +algorithms for each. However, the completion of Aims 1 and 2 involves more than just choosing between a set of existing 1.228 +algorithms, and will constitute a substantial contribution to biology. The algorithms require the scientist to provide a 1.229 +framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. 1.230 +Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical 1.231 +“fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient 1.232 +similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application. 1.233 +We are aware of two existing efforts to relate spatial gene expression data to anatomy through computational methods. 1.234 +[? ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis, 1.235 +two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial bifurcation 1.236 +clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness 1.237 +of such research. We have run NNMF on the cortical dataset and while the results are promising (see Preliminary Data), we 1.238 +think that it will be possible to find a better method3 (we also think that more automation of the parts that this paper’s 1.239 +authors did manually will be possible). 1.240 +and [?] describes AGEA. todo 1.241 +_____________ 1.242 + 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft 1.243 +spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was 1.244 +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 1.245 +that those result were not any more impressive than the results of the non-hierarchial variant. 1.246 +_______________________________________________________________________________________________________ 1.247 +PHS 398/2590 (Rev. 09/04) Page 5 ___ Continuation Format Page 1.248 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.249 + 1.250 1.251 - Background and significance 1.252 - Aim 1 1.253 - Machine learning terminology: supervised learning 1.254 - The task of looking for marker genes for anatomical subregions means that 1.255 - one is looking for a set of genes such that, if the expression level of those genes 1.256 - is known, then the locations of the subregions can be inferred. 1.257 - If we define the subregions so that they cover the entire anatomical structure 1.258 - to be divided, then instead of saying that we are using gene expression to find 1.259 - the locations of the subregions, we may say that we are using gene expression to 1.260 - determine to which subregion each voxel within the structure belongs. We call 1.261 - this a classification task, because each voxel is being assigned to a class (namely, 1.262 - its subregion). 1.263 - Therefore, an understanding of the relationship between the combination of 1.264 - their expression levels and the locations of the subregions may be expressed as 1.265 - a function. The input to this function is a voxel, along with the gene expression 1.266 - levels within that voxel; the output is the subregional identity of the target 1.267 - voxel, that is, the subregion to which the target voxel belongs. We call this 1.268 - function a classifier. In general, the input to a classifier is called an instance, 1.269 - and the output is called a label (or a class label). 1.270 - The object of aim 1 is not to produce a single classifier, but rather to develop 1.271 - an automated method for determining a classifier for any known anatomical 1.272 - structure. Therefore, we seek a procedure by which a gene expression dataset 1.273 - may be analyzed in concert with an anatomical atlas in order to produce a 1.274 - classifier. Such a procedure is a type of a machine learning procedure. The 1.275 - construction of the classifier is called training (also learning), and the initial 1.276 - gene expression dataset used in the construction of the classifier is called training 1.277 - data. 1.278 - In the machine learning literature, this sort of procedure may be thought 1.279 - of as a supervised learning task, defined as a task in which the goal is to learn 1.280 - a mapping from instances to labels, and the training data consists of a set of 1.281 - instances (voxels) for which the labels (subregions) are known. 1.282 - Each gene expression level is called a feature, and the selection of which 1.283 - genes1 to include is called feature selection. Feature selection is one component 1.284 - of the task of learning a classifier. Some methods for learning classifiers start 1.285 - out with a separate feature selection phase, whereas other methods combine 1.286 - feature selection with other aspects of training. 1.287 - One class of feature selection methods assigns some sort of score to each 1.288 - candidate gene. The top-ranked genes are then chosen. Some scoring measures 1.289 - can assign a score to a set of selected genes, not just to a single gene; in this 1.290 - case, a dynamic procedure may be used in which features are added and sub- 1.291 - tracted from the selected set depending on how much they raise the score. Such 1.292 - procedures are called “stepwise” or “greedy”. 1.293 -__________________________ 1.294 - 1Strictly speaking, the features are gene expression levels, but we’ll call them genes. 1.295 - 2 1.296 - 1.297 - Although the classifier itself may only look at the gene expression data within 1.298 - each voxel before classifying that voxel, the learning algorithm which constructs 1.299 - the classifier may look over the entire dataset. We can categorize score-based 1.300 - feature selection methods depending on how the score of calculated. Often 1.301 - the score calculation consists of assigning a sub-score to each voxel, and then 1.302 - aggregating these sub-scores into a final score (the aggregation is often a sum or 1.303 - a sum of squares). If only information from nearby voxels is used to calculate a 1.304 - voxel’s sub-score, then we say it is a local scoring method. If only information 1.305 - from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a 1.306 - pointwise scoring method. 1.307 - Key questions when choosing a learning method are: What are the instances? 1.308 - What are the features? How are the features chosen? Here are four principles 1.309 - that outline our answers to these questions. 1.310 - Principle 1: Combinatorial gene expression It is too much to hope 1.311 - that every anatomical region of interest will be identified by a single gene. For 1.312 - example, in the cortex, there are some areas which are not clearly delineated 1.313 - by any gene included in the Allen Brain Atlas (ABA) dataset. However, at 1.314 - least some of these areas can be delineated by looking at combinations of genes 1.315 - (an example of an area for which multiple genes are necessary and sufficient 1.316 - is provided in Preliminary Results). Therefore, each instance should contain 1.317 - multiple features (genes). 1.318 - Principle 2: Only look at combinations of small numbers of genes 1.319 - When the classifier classifies a voxel, it is only allowed to look at the expression of 1.320 - the genes which have been selected as features. The more data that is available 1.321 - to a classifier, the better that it can do. For example, perhaps there are weak 1.322 - correlations over many genes that add up to a strong signal. So, why not include 1.323 - every gene as a feature? The reason is that we wish to employ the classifier in 1.324 - situations in which it is not feasible to gather data about every gene. For 1.325 - example, if we want to use the expression of marker genes as a trigger for some 1.326 - regionally-targeted intervention, then our intervention must contain a molecular 1.327 - mechanism to check the expression level of each marker gene before it triggers. 1.328 - It is currently infeasible to design a molecular trigger that checks the level of 1.329 - more than a handful of genes. Similarly, if the goal is to develop a procedure to 1.330 - do ISH on tissue samples in order to label their anatomy, then it is infeasible 1.331 - to label more than a few genes. Therefore, we must select only a few genes as 1.332 - features. 1.333 - Principle 3: Use geometry in feature selection 1.334 - When doing feature selection with score-based methods, the simplest thing 1.335 - to do would be to score the performance of each voxel by itself and then com- 1.336 - bine these scores (pointwise scoring). A more powerful approach is to also use 1.337 - information about the geometric relations between each voxel and its neighbors; 1.338 - this requires non-pointwise, local scoring methods. See Preliminary Results for 1.339 - evidence of the complementary nature of pointwise and local scoring methods. 1.340 - 3 1.341 - 1.342 - Principle 4: Work in 2-D whenever possible 1.343 - There are many anatomical structures which are commonly characterized in 1.344 - terms of a two-dimensional manifold. When it is known that the structure that 1.345 - one is looking for is two-dimensional, the results may be improved by allowing 1.346 - the analysis algorithm to take advantage of this prior knowledge. In addition, 1.347 - it is easier for humans to visualize and work with 2-D data. 1.348 - Therefore, when possible, the instances should represent pixels, not voxels. 1.349 - Aim 2 1.350 - Machine learning terminology: clustering 1.351 - If one is given a dataset consisting merely of instances, with no class labels, 1.352 - then analysis of the dataset is referred to as unsupervised learning in the jargon 1.353 - of machine learning. One thing that you can do with such a dataset is to group 1.354 - instances together. A set of similar instances is called a cluster, and the activity 1.355 - of finding grouping the data into clusters is called clustering or cluster analysis. 1.356 - The task of deciding how to carve up a structure into anatomical subregions 1.357 - can be put into these terms. The instances are once again voxels (or pixels) 1.358 - along with their associated gene expression profiles. We make the assumption 1.359 - that voxels from the same subregion have similar gene expression profiles, at 1.360 - least compared to the other subregions. This means that clustering voxels is 1.361 - the same as finding potential subregions; we seek a partitioning of the voxels 1.362 - into subregions, that is, into clusters of voxels with similar gene expression. 1.363 - It is desirable to determine not just one set of subregions, but also how 1.364 - these subregions relate to each other, if at all; perhaps some of the subregions 1.365 - are more similar to each other than to the rest, suggesting that, although at a 1.366 - fine spatial scale they could be considered separate, on a coarser spatial scale 1.367 - they could be grouped together into one large subregion. This suggests the 1.368 - outcome of clustering may be a hierarchial tree of clusters, rather than a single 1.369 - set of clusters which partition the voxels. This is called hierarchial clustering. 1.370 - Similarity scores 1.371 - A crucial choice when designing a clustering method is how to measure 1.372 - similarity, across either pairs of instances, or clusters, or both. There is much 1.373 - overlap between scoring methods for feature selection (discussed above under 1.374 - Aim 1) and scoring methods for similarity. 1.375 - Spatially contiguous clusters; image segmentation 1.376 - We have shown that aim 2 is a type of clustering task. In fact, it is a 1.377 - special type of clustering task because we have an additional constraint on 1.378 - clusters; voxels grouped together into a cluster must be spatially contiguous. 1.379 - In Preliminary Results, we show that one can get reasonable results without 1.380 - enforcing this constraint, however, we plan to compare these results against 1.381 - other methods which guarantee contiguous clusters. 1.382 - Perhaps the biggest source of continguous clustering algorithms is the field 1.383 - of computer vision, which has produced a variety of image segmentation algo- 1.384 - 4 1.385 - 1.386 - rithms. Image segmentation is the task of partitioning the pixels in a digital 1.387 - image into clusters, usually contiguous clusters. Aim 2 is similar to an image 1.388 - segmentation task. There are two main differences; in our task, there are thou- 1.389 - sands of color channels (one for each gene), rather than just three. There are 1.390 - imaging tasks which use more than three colors, however, for example multispec- 1.391 - tral imaging and hyperspectral imaging, which are often used to process satellite 1.392 - imagery. A more crucial difference is that there are various cues which are ap- 1.393 - propriate for detecting sharp object boundaries in a visual scene but which are 1.394 - not appropriate for segmenting abstract spatial data such as gene expression. 1.395 - Although many image segmentation algorithms can be expected to work well 1.396 - for segmenting other sorts of spatially arranged data, some of these algorithms 1.397 - are specialized for visual images. 1.398 - Dimensionality reduction 1.399 - Unlike aim 1, there is no externally-imposed need to select only a handful 1.400 - of informative genes for inclusion in the instances. However, some clustering 1.401 - algorithms perform better on small numbers of features. There are techniques 1.402 - which “summarize” a larger number of features using a smaller number of fea- 1.403 - tures; these techniques go by the name of feature extraction or dimensionality 1.404 - reduction. The small set of features that such a technique yields is called the 1.405 - reduced feature set. After the reduced feature set is created, the instances may 1.406 - be replaced by reduced instances, which have as their features the reduced fea- 1.407 - ture set rather than the original feature set of all gene expression levels. Note 1.408 - that the features in the reduced feature set do not necessarily correspond to 1.409 - genes; each feature in the reduced set may be any function of the set of gene 1.410 - expression levels. 1.411 - Another use for dimensionality reduction is to visualize the relationships 1.412 - between subregions. For example, one might want to make a 2-D plot upon 1.413 - which each subregion is represented by a single point, and with the property 1.414 - that subregions with similar gene expression profiles should be nearby on the 1.415 - plot (that is, the property that distance between pairs of points in the plot 1.416 - should be proportional to some measure of dissimilarity in gene expression). It 1.417 - is likely that no arrangement of the points on a 2-D plan will exactly satisfy 1.418 - this property – however, dimensionality reduction techniques allow one to find 1.419 - arrangements of points that approximately satisfy that property. Note that 1.420 - in this application, dimensionality reduction is being applied after clustering; 1.421 - whereas in the previous paragraph, we were talking about using dimensionality 1.422 - reduction before clustering. 1.423 - Clustering genes rather than voxels 1.424 - Although the ultimate goal is to cluster the instances (voxels or pixels), one 1.425 - strategy to achieve this goal is to first cluster the features (genes). There are 1.426 - two ways that clusters of genes could be used. 1.427 - Gene clusters could be used as part of dimensionality reduction: rather than 1.428 - have one feature for each gene, we could have one reduced feature for each gene 1.429 - cluster. 1.430 - 5 1.431 - 1.432 - Gene clusters could also be used to directly yield a clustering on instances. 1.433 - This is because many genes have an expression pattern which seems to pick 1.434 - out a single, spatially continguous subregion. Therefore, it seems likely that an 1.435 - anatomically interesting subregion will have multiple genes which each individ- 1.436 - ually pick it out2. This suggests the following procedure: cluster together genes 1.437 - which pick out similar subregions, and then to use the more popular common 1.438 - subregions as the final clusters. In the Preliminary Data we show that a num- 1.439 - ber of anatomically recognized cortical regions, as well as some “superregions” 1.440 - formed by lumping together a few regions, are associated with gene clusters in 1.441 - this fashion. 1.442 - Aim 3 1.443 - Background 1.444 - The cortex is divided into areas and layers. To a first approximation, the 1.445 - parcellation of the cortex into areas can be drawn as a 2-D map on the surface of 1.446 - the cortex. In the third dimension, the boundaries between the areas continue 1.447 - downwards into the cortical depth, perpendicular to the surface. The layer 1.448 - boundaries run parallel to the surface. One can picture an area of the cortex as 1.449 - a slice of many-layered cake. 1.450 - Although it is known that different cortical areas have distinct roles in both 1.451 - normal functioning and in disease processes, there are no known marker genes 1.452 - for many cortical areas. When it is necessary to divide a tissue sample into 1.453 - cortical areas, this is a manual process that requires a skilled human to combine 1.454 - multiple visual cues and interpret them in the context of their approximate 1.455 - location upon the cortical surface. 1.456 - Even the questions of how many areas should be recognized in cortex, and 1.457 - what their arrangement is, are still not completely settled. A proposed division 1.458 - of the cortex into areas is called a cortical map. In the rodent, the lack of a 1.459 - single agreed-upon map can be seen by contrasting the recent maps given by 1.460 - Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While 1.461 - the maps are certainly very similar in their general arrangement, significant 1.462 - differences remain in the details. 1.463 - Significance 1.464 - The method developed in aim (1) will be applied to each cortical area to find 1.465 - a set of marker genes such that the combinatorial expression pattern of those 1.466 - genes uniquely picks out the target area. Finding marker genes will be useful 1.467 - for drug discovery as well as for experimentation because marker genes can be 1.468 - used to design interventions which selectively target individual cortical areas. 1.469 -__________________________ 1.470 - 2This would seem to contradict our finding in aim 1 that some cortical areas are combina- 1.471 -torially coded by multiple genes. However, it is possible that the currently accepted cortical 1.472 -maps divide the cortex into subregions which are unnatural from the point of view of gene 1.473 -expression; perhaps there is some other way to map the cortex for which each subregion can 1.474 -be identified by single genes. 1.475 - 6 1.476 - 1.477 - The application of the marker gene finding algorithm to the cortex will 1.478 - also support the development of new neuroanatomical methods. In addition to 1.479 - finding markers for each individual cortical areas, we will find a small panel 1.480 - of genes that can find many of the areal boundaries at once. This panel of 1.481 - marker genes will allow the development of an ISH protocol that will allow 1.482 - experimenters to more easily identify which anatomical areas are present in 1.483 - small samples of cortex. 1.484 - The method developed in aim (3) will provide a genoarchitectonic viewpoint 1.485 - that will contribute to the creation of a better map. The development of present- 1.486 - day cortical maps was driven by the application of histological stains. It is 1.487 - conceivable that if a different set of stains had been available which identified 1.488 - a different set of features, then the today’s cortical maps would have come out 1.489 - differently. Since the number of classes of stains is small compared to the number 1.490 - of genes, it is likely that there are many repeated, salient spatial patterns in 1.491 - the gene expression which have not yet been captured by any stain. Therefore, 1.492 - current ideas about cortical anatomy need to incorporate what we can learn 1.493 - from looking at the patterns of gene expression. 1.494 - While we do not here propose to analyze human gene expression data, it is 1.495 - conceivable that the methods we propose to develop could be used to suggest 1.496 - modifications to the human cortical map as well. 1.497 - Related work 1.498 - There does not appear to be much work on the automated analysis of spatial 1.499 - gene expression data. 1.500 - There is a substantial body of work on the analysis of gene expression data, 1.501 - however, most of this concerns gene expression data which is not fundamentally 1.502 - spatial. 1.503 - As noted above, there has been much work on both supervised learning and 1.504 - clustering, and there are many available algorithms for each. However, the 1.505 - completion of Aims 1 and 2 involves more than just choosing between a set of 1.506 - existing algorithms, and will constitute a substantial contribution to biology. 1.507 - The algorithms require the scientist to provide a framework for representing the 1.508 - problem domain, and the way that this framework is set up has a large impact 1.509 - on performance. Creating a good framework can require creatively reconcep- 1.510 - tualizing the problem domain, and is not merely a mechanical “fine-tuning” 1.511 - of numerical parameters. For example, we believe that domain-specific scoring 1.512 - measures (such as gradient similarity, which is discussed in Preliminary Work) 1.513 - may be necessary in order to achieve the best results in this application. 1.514 - We are aware of two existing efforts to relate spatial gene expression data to 1.515 - anatomy through computational methods. 1.516 - [?] describes an analysis of the anatomy of the hippocampus using the ABA 1.517 - dataset. In addition to manual analysis, two clustering methods were employed, 1.518 - a modified Non-negative Matrix Factorization (NNMF), and a hierarchial bifur- 1.519 - cation clustering scheme based on correlation as the similarity score. The paper 1.520 - yielded impressive results, proving the usefulness of such research. We have run 1.521 - 7 1.522 - 1.523 - NNMF on the cortical dataset and while the results are promising (see Prelim- 1.524 - inary Data), we think that it will be possible to find a better method3 (we also 1.525 - think that more automation of the parts that this paper’s authors did manually 1.526 - will be possible). 1.527 - and [?] describes AGEA. todo 1.528 -__________________________ 1.529 - 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. 1.530 -Their main modification consisted of adding a soft spatial contiguity constraint. However, 1.531 -on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional 1.532 -constraint was needed. The paper under discussion mentions that they also tried a hierarchial 1.533 -variant of NNMF, but since they didn’t report its results, we assume that those result were 1.534 -not any more impressive than the results of the non-hierarchial variant. 1.535 - 8 1.536 - 1.537 - Preliminary work 1.538 - Format conversion between SEV, MATLAB, NIFTI 1.539 - todo 1.540 - Flatmap of cortex 1.541 - todo 1.542 - Using combinations of multiple genes is necessary and sufficient to 1.543 - delineate some cortical areas 1.544 - Here we give an example of a cortical area which is not marked by any 1.545 - single gene, but which can be identified combinatorially. according to logistic 1.546 - regression, gene wwc14 is the best fit single gene for predicting whether or not a 1.547 - pixel on the cortical surface belongs to the motor area (area MO). The upper-left 1.548 - picture in Figure shows wwc1’s spatial expression pattern over the cortex. The 1.549 - lower-right boundary of MO is represented reasonably well by this gene, however 1.550 - the gene overshoots the upper-left boundary. This flattened 2-D representation 1.551 - does not show it, but the area corresponding to the overshoot is the medial 1.552 - surface of the cortex. MO is only found on the lateral surface (todo). 1.553 - Gnee mtif25 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s 1.554 - upper-left boundary, but not its lower-right boundary. Mtif2 does not express 1.555 - very much on the medial surface. By adding together the values at each pixel 1.556 - in these two figures, we get the lower-left of Figure . This combination captures 1.557 - area MO much better than any single gene. 1.558 - Correlation todo 1.559 - Conditional entropy todo 1.560 - Gradient similarity todo 1.561 - Geometric and pointwise scoring methods provide complementary 1.562 - information 1.563 - To show that local geometry can provide useful information that cannot be 1.564 - detected via pointwise analyses, consider Fig. . The top row of Fig. displays the 1.565 - 3 genes which most match area AUD, according to a pointwise method6. The 1.566 - bottom row displays the 3 genes which most match AUD according to a method 1.567 - which considers local geometry7 The pointwise method in the top row identifies 1.568 -__________________________ 1.569 +Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel’s value on the lower left is the sum 1.570 +of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the 1.571 +top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right. 1.572 +The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells 1.573 +underneath each pixel, with red meaning a lot of expression and blue meaning little. 1.574 +Preliminary work 1.575 +Format conversion between SEV, MATLAB, NIFTI 1.576 +todo 1.577 +Flatmap of cortex 1.578 +todo 1.579 +Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas 1.580 +Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi- 1.581 +natorially. according to logistic regression, gene wwc14 is the best fit single gene for predicting whether or not a pixel on 1.582 +the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure shows wwc1’s spatial expression 1.583 +pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene 1.584 +overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the 1.585 +overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo). 1.586 +Gnee mtif25 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right 1.587 +boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two 1.588 +figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene. 1.589 +Correlation todo 1.590 +Conditional entropy todo 1.591 +Gradient similarity todo 1.592 +Geometric and pointwise scoring methods provide complementary information 1.593 +To show that local geometry can provide useful information that cannot be detected via pointwise analyses, consider Fig. 1.594 +. The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method6. The bottom row 1.595 +_________________________________________ 1.596 4“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652 1.597 5“mitochondrial translational initiation factor 2”; EntrezGene ID 76784 1.598 - 6For each gene, a logistic regression in which the response variable was whether or not a 1.599 -surface pixel was within area AUD, and the predictor variable was the value of the expression 1.600 -of the gene underneath that pixel. The resulting scores were used to rank the genes in terms 1.601 -of how well they predict area AUD. 1.602 - 7For each gene the gradient similarity (see section ??) between (a) a map of the expression 1.603 -of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this 1.604 -was used to rank the genes. 1.605 - 9 1.606 - 1.607 - 1.608 - 1.609 - Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 1.610 - (each pixel’s value on the lower left is the sum of the corresponding pixels in 1.611 - the upper row). Within each picture, the vertical axis roughly corresponds to 1.612 - anterior at the top and posterior at the bottom, and the horizontal axis roughly 1.613 - corresponds to medial at the left and lateral at the right. The red outline is 1.614 - the boundary of region MO. Pixels are colored approximately according to the 1.615 - density of expressing cells underneath each pixel, with red meaning a lot of 1.616 - expression and blue meaning little. 1.617 - 10 1.618 - 1.619 - 1.620 - 1.621 - Figure 2: The top row shows the three genes which (individually) best predict 1.622 - area AUD, according to logistic regression. The bottom row shows the three 1.623 - genes which (individually) best match area AUD, according to gradient similar- 1.624 - ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, 1.625 - Ptk7, Aph1a again, and Lepr 1.626 - genes which express more strongly in AUD than outside of it; its weakness is that 1.627 - this includes many areas which don’t have a salient border matching the areal 1.628 - border. The geometric method identifies genes whose salient expression border 1.629 - seems to partially line up with the border of AUD; its weakness is that this 1.630 - includes genes which don’t express over the entire area. Genes which have high 1.631 - rankings using both pointwise and border criteria, such as Aph1a in the example, 1.632 - may be particularly good markers. None of these genes are, individually, a 1.633 - perfect marker for AUD; we deliberately chose a “difficult” area in order to 1.634 - better contrast pointwise with geometric methods. 1.635 - Areas which can be identified by single genes 1.636 - todo 1.637 - Specific to Aim 1 (and Aim 3) 1.638 - Forward stepwise logistic regression todo 1.639 - SVM on all genes at once 1.640 - In order to see how well one can do when looking at all genes at once, we 1.641 - ran a support vector machine to classify cortical surface pixels based on their 1.642 - gene expression profiles. We achieved classification accuracy of about 81%8. 1.643 - As noted above, however, a classifier that looks at all the genes at once isn’t 1.644 - practically useful. 1.645 -____________ 1.646 - 85-fold cross-validation. 1.647 - 11 1.648 - 1.649 - The requirement to find combinations of only a small number of genes limits 1.650 - us from straightforwardly applying many of the most simple techniques from 1.651 - the field of supervised machine learning. In the parlance of machine learning, 1.652 - our task combines feature selection with supervised learning. 1.653 - Decision trees 1.654 - todo 1.655 - Specific to Aim 2 (and Aim 3) 1.656 - Raw dimensionality reduction results 1.657 - todo 1.658 - (might want to incld nnMF since mentioned above) 1.659 - Dimensionality reduction plus K-means or spectral clustering 1.660 - Many areas are captured by clusters of genes 1.661 - todo 1.662 - todo 1.663 - 12 1.664 - 1.665 - Research plan 1.666 - todo amongst other things: 1.667 - Develop algorithms that find genetic markers for anatomical re- 1.668 - gions 1.669 - 1. Develop scoring measures for evaluating how good individual genes are at 1.670 - marking areas: we will compare pointwise, geometric, and information- 1.671 - theoretic measures. 1.672 - 2. Develop a procedure to find single marker genes for anatomical regions: for 1.673 - each cortical area, by using or combining the scoring measures developed, 1.674 - we will rank the genes by their ability to delineate each area. 1.675 - 3. Extend the procedure to handle difficult areas by using combinatorial cod- 1.676 - ing: for areas that cannot be identified by any single gene, identify them 1.677 - with a handful of genes. We will consider both (a) algorithms that incre- 1.678 - mentally/greedily combine single gene markers into sets, such as forward 1.679 - stepwise regression and decision trees, and also (b) supervised learning 1.680 - techniques which use soft constraints to minimize the number of features, 1.681 - such as sparse support vector machines. 1.682 - 4. Extend the procedure to handle difficult areas by combining or redrawing 1.683 - the boundaries: An area may be difficult to identify because the bound- 1.684 - aries are misdrawn, or because it does not “really” exist as a single area, 1.685 - at least on the genetic level. We will develop extensions to our procedure 1.686 - which (a) detect when a difficult area could be fit if its boundary were 1.687 - redrawn slightly, and (b) detect when a difficult area could be combined 1.688 - with adjacent areas to create a larger area which can be fit. 1.689 - Apply these algorithms to the cortex 1.690 - 1. Create open source format conversion tools: we will create tools to bulk 1.691 - download the ABA dataset and to convert between SEV, NIFTI and MAT- 1.692 - LAB formats. 1.693 - 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw 1.694 - the cortical area boundaries onto it. 1.695 - 3. Find layer boundaries: cluster similar voxels together in order to auto- 1.696 - matically find the cortical layer boundaries. 1.697 - 4. Run the procedures that we developed on the cortex: we will present, for 1.698 - each area, a short list of markers to identify that area; and we will also 1.699 - present lists of “panels” of genes that can be used to delineate many areas 1.700 - at once. 1.701 - 13 1.702 - 1.703 - Develop algorithms to suggest a division of a structure into anatom- 1.704 - ical parts 1.705 - 1. Explore dimensionality reduction algorithms applied to pixels: including 1.706 - TODO 1.707 - 2. Explore dimensionality reduction algorithms applied to genes: including 1.708 - TODO 1.709 - 3. Explore clustering algorithms applied to pixels: including TODO 1.710 - 4. Explore clustering algorithms applied to genes: including gene shaving, 1.711 - TODO 1.712 - 5. Develop an algorithm to use dimensionality reduction and/or hierarchial 1.713 - clustering to create anatomical maps 1.714 - 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic 1.715 - map of the cortex 1.716 -______________________________________________ 1.717 - stuff i dunno where to put yet (there is more scattered through grant- 1.718 -oldtext): 1.719 + 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 1.720 +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 1.721 +_______________________________________________________________________________________________________ 1.722 +PHS 398/2590 (Rev. 09/04) Page 6 ___ Continuation Format Page 1.723 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.724 + 1.725 + 1.726 +Figure 2: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression. 1.727 +The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From 1.728 +left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr 1.729 +displays the 3 genes which most match AUD according to a method which considers local geometry7 The pointwise method 1.730 +in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this includes many 1.731 +areas which don’t have a salient border matching the areal border. The geometric method identifies genes whose salient 1.732 +expression border seems to partially line up with the border of AUD; its weakness is that this includes genes which don’t 1.733 +express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as Aph1a in the 1.734 +example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD; we deliberately 1.735 +chose a “difficult” area in order to better contrast pointwise with geometric methods. 1.736 +Areas which can be identified by single genes 1.737 +todo 1.738 +Specific to Aim 1 (and Aim 3) 1.739 +Forward stepwise logistic regression todo 1.740 +SVM on all genes at once 1.741 +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 1.742 +surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%8. As noted above, 1.743 +however, a classifier that looks at all the genes at once isn’t practically useful. 1.744 +The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many 1.745 +of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task 1.746 +combines feature selection with supervised learning. 1.747 +Decision trees 1.748 +todo 1.749 +Specific to Aim 2 (and Aim 3) 1.750 +Raw dimensionality reduction results 1.751 +todo 1.752 +(might want to incld nnMF since mentioned above) 1.753 +_________________________________________ 1.754 +they predict area AUD. 1.755 + 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 1.756 +shape of area AUD, was calculated, and this was used to rank the genes. 1.757 + 85-fold cross-validation. 1.758 +_______________________________________________________________________________________________________ 1.759 +PHS 398/2590 (Rev. 09/04) Page 7 ___ Continuation Format Page 1.760 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.761 +Dimensionality reduction plus K-means or spectral clustering 1.762 +Many areas are captured by clusters of genes 1.763 +todo 1.764 +todo 1.765 +_______________________________________________________________________________________________________ 1.766 +PHS 398/2590 (Rev. 09/04) Page 8 ___ Continuation Format Page 1.767 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.768 +Research plan 1.769 +todo amongst other things: 1.770 +Develop algorithms that find genetic markers for anatomical regions 1.771 +1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, 1.772 +geometric, and information-theoretic measures. 1.773 +2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining 1.774 +the scoring measures developed, we will rank the genes by their ability to delineate each area. 1.775 +3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any 1.776 +single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily 1.777 +combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised 1.778 +learning techniques which use soft constraints to minimize the number of features, such as sparse support vector 1.779 +machines. 1.780 +4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult to 1.781 +identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the 1.782 +genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its 1.783 +boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create 1.784 +a larger area which can be fit. 1.785 +Apply these algorithms to the cortex 1.786 +1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert 1.787 +between SEV, NIFTI and MATLAB formats. 1.788 +2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it. 1.789 +3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries. 1.790 +4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify 1.791 +that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once. 1.792 +Develop algorithms to suggest a division of a structure into anatomical parts 1.793 +1.Explore dimensionality reduction algorithms applied to pixels: including TODO 1.794 +2.Explore dimensionality reduction algorithms applied to genes: including TODO 1.795 +3.Explore clustering algorithms applied to pixels: including TODO 1.796 +4.Explore clustering algorithms applied to genes: including gene shaving, TODO 1.797 +5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps 1.798 +6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex 1.799 +_____________________ 1.800 + stuff i dunno where to put yet (there is more scattered through grant-oldtext): 1.801 Principle 4: Work in 2-D whenever possible 1.802 - In anatomy, the manifold of interest is usually either defined by a combina- 1.803 -tion of two relevant anatomical axes (todo), or by the surface of the structure 1.804 -(as is the case with the cortex). In the former case, the manifold of interest is 1.805 -a plane, but in the latter case it is curved. If the manifold is curved, there are 1.806 -various methods for mapping the manifold into a plane. 1.807 - The method that we will develop will begin by mapping the data into a 1.808 -2-D plane. Although the manifold that characterized cortical areas is known 1.809 -to be the cortical surface, it remains to be seen which method of mapping the 1.810 -manifold into a plane is optimal for this application. We will compare mappings 1.811 -which attempt to preserve size (such as the one used by Caret??) with mappings 1.812 -which preserve angle (conformal maps). 1.813 - Although there is much 2-D organization in anatomy, there are also struc- 1.814 -tures whose shape is fundamentally 3-dimensional. If possible, we would like 1.815 -the method we develop to include a statistical test that warns the user if the 1.816 -assumption of 2-D structure seems to be wrong. 1.817 - if we need citations for aim 3 significance, http://www.sciencedirect. 1.818 -com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_user=4429&_coverDate= 1.819 -12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct= 1.820 -C000059602&_version=1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203# 1.821 -app2 has examples of genetic targeting to specific anatomical regions 1.822 - — 1.823 - note: 1.824 - do we need to cite: no known markers, impressive results? 1.825 - 14 1.826 + In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), or 1.827 +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 1.828 +the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane. 1.829 + The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that charac- 1.830 +terized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold into 1.831 +_______________________________________________________________________________________________________ 1.832 +PHS 398/2590 (Rev. 09/04) Page 9 ___ Continuation Format Page 1.833 + Principal Investigator/Program Director(Last, First, Middle): Stevens, Charles F.___ 1.834 +a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used by 1.835 +Caret?? ) with mappings which preserve angle (conformal maps). 1.836 +Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. 1.837 +If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D 1.838 +structure seems to be wrong. 1.839 +if we need citations for aim 3 significance, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_ 1.840 +user=4429&_coverDate=12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct=C000059602&_version= 1.841 +1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203#app2 has examples of genetic targeting to spe- 1.842 +cific anatomical regions 1.843 +— 1.844 +note: 1.845 +do we need to cite: no known markers, impressive results? 1.846 +_______________________________________________________________________________________________________ 1.847 +PHS 398/2590 (Rev. 09/04) Page 10 ___ Continuation Format Page 1.848 1.849