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

2.1 Binary file grant.odt has changed

3.1 Binary file grant.pdf has changed

4.1 --- a/grant.txt Mon Apr 13 03:43:51 2009 -0700 4.2 +++ b/grant.txt Mon Apr 13 03:52:58 2009 -0700 4.3 @@ -1,3 +1,6 @@ 4.4 +\documentclass{nih} 4.5 +\piname{Stevens, Charles F.} 4.6 + 4.7 == Specific aims == 4.8 4.9 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:\\ 4.10 @@ -167,10 +170,10 @@ 4.11 Gnee mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784} is shown in figure the upper-right of Fig. \ref{MOcombo}. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left of Figure \ref{MOcombo}. This combination captures area MO much better than any single gene. 4.12 4.13 \begin{figure}\label{MOcombo} 4.14 -\includegraphics[scale=.4]{MO_vs_Wwc1_jet.eps} 4.15 -\includegraphics[scale=.4]{MO_vs_Mtif2_jet.eps} 4.16 - 4.17 -\includegraphics[scale=.4]{MO_vs_Wwc1_plus_Mtif2_jet.eps} 4.18 +\includegraphics[scale=.36]{MO_vs_Wwc1_jet.eps} 4.19 +\includegraphics[scale=.36]{MO_vs_Mtif2_jet.eps} 4.20 + 4.21 +\includegraphics[scale=.36]{MO_vs_Wwc1_plus_Mtif2_jet.eps} 4.22 \caption{Upper left: $wwc1$. Upper right: $mtif2$. Lower left: wwc1 + mtif2 (each pixel's value on the lower left is the sum of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right. The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells underneath each pixel, with red meaning a lot of expression and blue meaning little.} 4.23 \end{figure} 4.24