bshanks@0: Specific aims bshanks@96: Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in bshanks@96: situ transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many bshanks@96: locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expres- bshanks@96: sion to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical bshanks@96: maps based on gene expression patterns. We have three specific aims: bshanks@96: (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which bshanks@96: selectively target anatomical regions bshanks@96: (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions, bshanks@96: based on spatial patterns in gene expression bshanks@96: (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen bshanks@96: Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending bshanks@96: the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the bshanks@96: methods developed in (1) and (2). bshanks@96: Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that bshanks@96: the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located bshanks@96: in a low-dimensional space. In particular, our method could be applied to genome-wide sequencing data derived bshanks@96: from sets of tissues and disease states. bshanks@96: In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker bshanks@96: genes, and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness bshanks@96: of the algorithms, the application of these methods to cortex will produce immediate benefits, because there bshanks@96: are currently no known genetic markers for most cortical areas. The results of the project will support the bshanks@96: development of new ways to selectively target cortical areas, and it will support the development of a method for bshanks@96: identifying the cortical areal boundaries present in small tissue samples. bshanks@96: All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well bshanks@96: as the machine-readable datasets developed in aim (3), will be published and freely available for others to use. bshanks@87: The challenge topic bshanks@96: This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as bshanks@96: in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others, bshanks@96: allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated bshanks@96: methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific bshanks@96: anatomical regions, and also to draw new anatomical maps based on gene expression patterns. bshanks@87: The Challenge and Potential impact bshanks@96: Each of our three aims will be discussed in turn. For each aim, we will develop a conceptual framework for bshanks@96: thinking about the task, and we will present our strategy for solving it. Next we will discuss related work. At the bshanks@96: conclusion of each section, we will summarize why our strategy is different from what has been done before. At bshanks@96: the end of this section, we will describe the potential impact. bshanks@84: Aim 1: Given a map of regions, find genes that mark the regions bshanks@96: Machine learning terminology: classifiers The task of looking for marker genes for known anatomical regions bshanks@96: means that one is looking for a set of genes such that, if the expression level of those genes is known, then the bshanks@96: locations of the regions can be inferred. bshanks@96: If we define the regions so that they cover the entire anatomical structure to be subdivided, we may say that bshanks@96: we are using gene expression in each voxel to assign that voxel to the proper area. We call this a classification bshanks@96: task, because each voxel is being assigned to a class (namely, its region). An understanding of the relationship bshanks@96: between the combination of their expression levels and the locations of the regions may be expressed as a bshanks@96: function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is bshanks@96: the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function bshanks@96: a classifier. In general, the input to a classifier is called an instance, and the output is called a label (or a class bshanks@96: label). bshanks@96: The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for bshanks@96: determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene bshanks@96: expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. The bshanks@96: initial gene expression dataset used in the construction of the classifier is called training data. In the machine bshanks@96: learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a task in bshanks@96: which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances bshanks@96: (voxels) for which the labels (regions) are known. bshanks@96: Each gene expression level is called a feature, and the selection of which genes1 to include is called feature bshanks@96: selection. Feature selection is one component of the task of learning a classifier. Some methods for learning bshanks@96: classifiers start out with a separate feature selection phase, whereas other methods combine feature selection bshanks@96: with other aspects of training. bshanks@96: One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked bshanks@96: genes are then chosen. Some scoring measures can assign a score to a set of selected genes, not just to a bshanks@96: single gene; in this case, a dynamic procedure may be used in which features are added and subtracted from the bshanks@96: selected set depending on how much they raise the score. Such procedures are called “stepwise” or “greedy”. bshanks@96: Although the classifier itself may only look at the gene expression data within each voxel before classifying bshanks@96: that voxel, the algorithm which constructs the classifier may look over the entire dataset. We can categorize bshanks@96: score-based feature selection methods depending on how the score of calculated. Often the score calculation bshanks@96: consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the bshanks@96: aggregation is often a sum or a sum of squares or average). If only information from nearby voxels is used to bshanks@96: calculate a voxel’s sub-score, then we say it is a local scoring method. If only information from the voxel itself is bshanks@96: used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method. bshanks@96: _________________________________________ bshanks@96: 1Strictly speaking, the features are gene expression levels, but we’ll call them genes. bshanks@96: Both gene expression data and anatomical atlases have errors, due to a variety of factors. Individual subjects bshanks@96: have idiosyncratic anatomy. Subjects may be improperly registred to the atlas. The method used to measure bshanks@96: gene expression may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical bshanks@96: atlas are “wrong” in that they do not have the same shape as the natural domains of gene expression to which bshanks@96: they correspond. These sources of error can affect the displacement and the shape of both the gene expression bshanks@96: data and the anatomical target areas. Therefore, it is important to use feature selection methods which are bshanks@96: robust to these kinds of errors. bshanks@85: Our strategy for Aim 1 bshanks@96: Key questions when choosing a learning method are: What are the instances? What are the features? How are bshanks@96: the features chosen? Here are four principles that outline our answers to these questions. bshanks@84: Principle 1: Combinatorial gene expression bshanks@96: It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, bshanks@96: in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas bshanks@96: (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes bshanks@96: (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies, bshanks@96: Figure 4). Therefore, each instance should contain multiple features (genes). bshanks@84: Principle 2: Only look at combinations of small numbers of genes bshanks@96: When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have bshanks@96: been selected as features. The more data that are available to a classifier, the better that it can do. For example, bshanks@96: perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every bshanks@96: gene as a feature? The reason is that we wish to employ the classifier in situations in which it is not feasible to bshanks@96: gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for bshanks@96: some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the bshanks@96: expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that bshanks@96: checks the level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on bshanks@96: tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we bshanks@96: must select only a few genes as features. bshanks@96: The requirement to find combinations of only a small number of genes limits us from straightforwardly ap- bshanks@96: plying many of the most simple techniques from the field of supervised machine learning. In the parlance of bshanks@96: machine learning, our task combines feature selection with supervised learning. bshanks@30: Principle 3: Use geometry in feature selection bshanks@96: When doing feature selection with score-based methods, the simplest thing to do would be to score the per- bshanks@96: formance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach bshanks@96: is to also use information about the geometric relations between each voxel and its neighbors; this requires non- bshanks@96: pointwise, local scoring methods. See Preliminary Studies, figure 3 for evidence of the complementary nature of bshanks@96: pointwise and local scoring methods. bshanks@30: Principle 4: Work in 2-D whenever possible bshanks@96: There are many anatomical structures which are commonly characterized in terms of a two-dimensional bshanks@96: manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be bshanks@96: improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for bshanks@96: humans to visualize and work with 2-D data. Therefore, when possible, the instances should represent pixels, bshanks@96: not voxels. bshanks@43: Related work bshanks@96: There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expres- bshanks@96: sion data which are not fundamentally spatial2. bshanks@96: As noted above, there has been much work on both supervised learning and there are many available bshanks@96: algorithms for each. However, the algorithms require the scientist to provide a framework for representing the bshanks@96: problem domain, and the way that this framework is set up has a large impact on performance. Creating a bshanks@96: good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical bshanks@96: “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such bshanks@96: as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best bshanks@96: results in this application. bshanks@96: We are aware of six existing efforts to find marker genes using spatial gene expression data using automated bshanks@96: methods. bshanks@96: [13 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical bshanks@96: structure of interest, computing what proportion of this structure is covered by the gene’s spatial region. bshanks@96: GeneAtlas[5] and EMAGE [26] allow the user to construct a search query by demarcating regions and then bshanks@96: specifing either the strength of expression or the name of another gene or dataset whose expression pattern bshanks@96: is to be matched. For the similiarity score (match score) between two images (in this case, the query and the bshanks@96: gene expression images), GeneAtlas uses the sum of a weighted L1-norm distance between vectors whose bshanks@96: components represent the number of cells within a pixel3 whose expression is within four discretization levels. bshanks@96: EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes bshanks@96: that define a region in concert but not separately. bshanks@96: [15 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The bshanks@96: user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list bshanks@96: of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of bshanks@96: overexpressed genes for selected structures). Correlation: The user selects a seed voxel and the system then bshanks@96: shows the user how much correlation there is between the gene expression profile of the seed voxel and every bshanks@96: other voxel. Clusters: will be described later bshanks@96: Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, bshanks@96: whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a bshanks@96: marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score5, bshanks@96: whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies). Figures bshanks@96: 4, 2, and 3 in the Preliminary Studies section contains evidence that each of our three choices is the right one. bshanks@96: [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test bshanks@96: with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in bshanks@96: the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being bshanks@96: analyzed), it is not being used to look for underexpression, and does not look for combinations of genes. bshanks@96: [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use bshanks@96: an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to bshanks@96: match a target image. Their match score is Jaccard similarity. bshanks@96: In summary, there has been fruitful work on finding marker genes, but only one of the previous projects bshanks@96: explores combinations of marker genes, and none of these publications compare the results obtained by using bshanks@96: different algorithms or scoring methods. bshanks@84: Aim 2: From gene expression data, discover a map of regions bshanks@30: Machine learning terminology: clustering bshanks@96: 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; bshanks@96: not just data which have only a few different locations or which is indexed by anatomical label. bshanks@96: 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity. bshanks@96: 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union. bshanks@96: 5“Expression energy ratio”, which captures overexpression. bshanks@96: If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is bshanks@96: referred to as unsupervised learning in the jargon of machine learning. One thing that you can do with such a bshanks@96: dataset is to group instances together. A set of similar instances is called a cluster, and the activity of finding bshanks@96: grouping the data into clusters is called clustering or cluster analysis. bshanks@96: The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The bshanks@96: instances are once again voxels (or pixels) along with their associated gene expression profiles. We make bshanks@96: the assumption that voxels from the same anatomical region have similar gene expression profiles, at least bshanks@96: compared to the other regions. This means that clustering voxels is the same as finding potential regions; we bshanks@96: seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression. bshanks@96: It is desirable to determine not just one set of regions, but also how these regions relate to each other. The bshanks@96: outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the bshanks@96: voxels. This is called hierarchial clustering. bshanks@96: Similarity scores A crucial choice when designing a clustering method is how to measure similarity, across bshanks@96: either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature bshanks@96: selection (discussed above under Aim 1) and scoring methods for similarity. bshanks@96: Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering bshanks@96: task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels bshanks@96: grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get bshanks@96: reasonable results without enforcing this constraint; however, we plan to compare these results against other bshanks@96: methods which guarantee contiguous clusters. bshanks@96: Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous bshanks@96: clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are bshanks@96: thousands of color channels (one for each gene), rather than just three6. A more crucial difference is that there bshanks@96: are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not bshanks@96: appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation bshanks@96: algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these bshanks@96: algorithms are specialized for visual images. bshanks@96: Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression bshanks@96: feature vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying bshanks@96: data. bshanks@96: Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion bshanks@96: in the instances. However, some clustering algorithms perform better on small numbers of features7. There are bshanks@96: techniques which “summarize” a larger number of features using a smaller number of features; these techniques bshanks@96: go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique bshanks@96: yields is called the reduced feature set. Note that the features in the reduced feature set do not necessarily bshanks@96: correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels. bshanks@96: Clustering genes rather than voxels Although the ultimate goal is to cluster the instances (voxels or pixels), bshanks@96: one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes bshanks@96: could be used. bshanks@96: Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, bshanks@96: we could have one reduced feature for each gene cluster. bshanks@96: Gene clusters could also be used to directly yield a clustering on instances. This is because many genes bshanks@96: have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems bshanks@96: likely that an anatomically interesting region will have multiple genes which each individually pick it out8. This bshanks@94: _________________________________________ bshanks@96: 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are bshanks@96: often used to process satellite imagery. bshanks@96: 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering bshanks@96: algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data. bshanks@96: 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, bshanks@96: it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene bshanks@96: expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another bshanks@96: suggests the following procedure: cluster together genes which pick out similar regions, and then to use the bshanks@96: more popular common regions as the final clusters. In Preliminary Studies, Figure 7, we show that a number bshanks@96: of anatomically recognized cortical regions, as well as some “superregions” formed by lumping together a few bshanks@96: regions, are associated with gene clusters in this fashion. bshanks@96: The task of clustering both the instances and the features is called co-clustering, and there are a number of bshanks@96: co-clustering algorithms. bshanks@43: Related work bshanks@96: Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example, bshanks@96: [18 ], [2 ], [19], and [1] associate spots on the cortex with the radial profile9 of response to some stain ([12] uses bshanks@96: MRI), extract features from this profile, and then use similarity between surface pixels to cluster. Features used bshanks@96: include statistical moments, wavelets, and the excess mass functional. Some of these features are motivated bshanks@96: by the presence of tangential lines of stain intensity which correspond to laminar structure. Some methods use bshanks@96: standard clustering procedures, whereas others make use of the spatial nature of the data to look for sudden bshanks@96: transitions, which are identified as areal borders. bshanks@96: [23 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual bshanks@96: analysis, two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and bshanks@96: a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper bshanks@96: yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on bshanks@96: the cortical dataset10 and while the results are promising, they also demonstrate that NNMF is not necessarily bshanks@96: the best dimensionality reduction method for this application (see Preliminary Studies, Figure 6). bshanks@96: AGEA[15] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with bshanks@96: correlation as the similarity metric. EMAGE[26] allows the user to select a dataset from among a large number bshanks@96: of alternatives, or by running a search query, and then to cluster the genes within that dataset. EMAGE clusters bshanks@96: via hierarchial complete linkage clustering with un-centred correlation as the similarity score. bshanks@96: [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and bshanks@96: which were highly correlated with many other genes. They computed the matrix of (rank) correlations between bshanks@96: pairs of these genes, and ordered the rows of this matrix as follows: “the first row of the matrix was chosen to bshanks@96: show the strongest contrast between the highest and lowest correlation coefficient for that row. The remaining bshanks@96: rows were then arranged in order of decreasing similarity using a least squares metric”. The resulting matrix bshanks@96: showed four clusters. For each cluster, prototypical spatial expression patterns were created by averaging the bshanks@96: genes in the cluster. The prototypes were analyzed manually, without clustering voxels. bshanks@96: [10 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes bshanks@96: around a “seed gene”. They do this by using the pattern of expression of the seed gene as the target image, and bshanks@96: then searching for other genes which can be combined to reproduce this pattern. Other genes which are found bshanks@96: are considered to be related to the seed. The same team also describes a method[25] for finding “association bshanks@96: rules” such as, “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the bshanks@96: same gene”. This could be useful as part of a procedure for clustering voxels. bshanks@96: In summary, although these projects obtained clusterings, there has not been much comparison between bshanks@96: different algorithms or scoring methods, so it is likely that the best clustering method for this application has not bshanks@96: yet been found. The projects using gene expression on cortex did not attempt to make use of the radial profile bshanks@96: of gene expression. Also, none of these projects did a separate dimensionality reduction step before clustering bshanks@96: pixels, none tried to cluster genes first in order to guide automated clustering of pixels into spatial regions, and bshanks@96: none used co-clustering algorithms. bshanks@96: ________ bshanks@96: possibility is that, although the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the bshanks@96: prototype. bshanks@96: 9A radial profile is a profile along a line perpendicular to the cortical surface. bshanks@96: 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding bshanks@96: a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional bshanks@96: constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet bshanks@96: tried. bshanks@94: Aim 3: apply the methods developed to the cerebral cortex bshanks@94: Background bshanks@96: The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation bshanks@96: of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the bshanks@96: boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The bshanks@96: layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of a six-layered bshanks@96: cake11 . bshanks@96: It is known that different cortical areas have distinct roles in both normal functioning and in disease processes, bshanks@96: yet there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample bshanks@96: into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and bshanks@96: interpret them in the context of their approximate location upon the cortical surface. bshanks@96: Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are bshanks@96: still not completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, bshanks@96: the lack of a single agreed-upon map can be seen by contrasting the recent maps given by Swanson[22] on the bshanks@96: one hand, and Paxinos and Franklin[17] on the other. While the maps are certainly very similar in their general bshanks@96: arrangement, significant differences remain. bshanks@36: The Allen Mouse Brain Atlas dataset bshanks@96: The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male, bshanks@96: 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi- bshanks@96: automatically analyzed to create a digital measurement of gene expression levels at each location in each slice. bshanks@96: Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used bshanks@96: to measure one single gene; many different mouse brains were needed in order to measure the expression of bshanks@96: many genes. bshanks@96: An automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D bshanks@96: coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are bshanks@96: 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain[15]. bshanks@96: Mus musculus is thought to contain about 22,000 protein-coding genes[28]. The ABA contains data on about bshanks@96: 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our bshanks@96: dataset is derived from only the coronal subset of the ABA12. bshanks@96: The ABA is not the only large public spatial gene expression dataset13. With the exception of the ABA, bshanks@96: GenePaint, and EMAGE, most of the other resources have not (yet) extracted the expression intensity from the bshanks@96: ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE bshanks@96: make this form of data available for public download from the website14. Many of these resources focus on bshanks@96: developmental gene expression. bshanks@63: Related work bshanks@96: [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure bshanks@96: of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort bshanks@96: of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical bshanks@96: map based on gene expression data. Neither of the other components of AGEA can be applied to cortical bshanks@96: _________________________________________ bshanks@96: 11Outside of isocortex, the number of layers varies. bshanks@96: 12The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen bshanks@96: Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked bshanks@96: non-ubiquitous expression pattern”[15]. bshanks@96: 13Other such resources include GENSAT[8], GenePaint[27], its sister project GeneAtlas[5], BGEM[14], EMAGE[26], EurExpress bshanks@96: (http://www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE), EADHB (http://www.ncl.ac.uk/ihg/EADHB/ bshanks@96: database/EADHB_database.html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[21], bshanks@96: Aniseed (http://aniseed-ibdm.univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some bshanks@96: of the other listed data sources), GEISHA[4], Fruitfly.org[24], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[20], GEO[3] bshanks@96: (GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.) bshanks@96: 14without prior offline registration bshanks@96: areas; AGEA’s Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA’s hierarchial bshanks@96: clustering does not produce clusters corresponding to the cortical areas15. bshanks@96: In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, bshanks@96: (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no bshanks@96: work on computationally finding marker genes for cortical areas, or on finding a hierarchial clustering that will bshanks@96: yield a map of cortical areas de novo from gene expression data. bshanks@96: Our project is guided by a concrete application with a well-specified criterion of success (how well we can bshanks@96: find marker genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing bshanks@96: different methods. bshanks@94: Significance bshanks@85: bshanks@85: bshanks@96: Figure 1: Top row: Genes Nfic bshanks@96: and A930001M12Rik are the most bshanks@96: correlated with area SS (somatosen- bshanks@96: sory cortex). Bottom row: Genes bshanks@96: C130038G02Rik and Cacna1i are bshanks@96: those with the best fit using logistic bshanks@96: regression. Within each picture, the bshanks@96: vertical axis roughly corresponds to bshanks@96: anterior at the top and posterior at the bshanks@96: bottom, and the horizontal axis roughly bshanks@96: corresponds to medial at the left and bshanks@96: lateral at the right. The red outline is bshanks@96: the boundary of region SS. Pixels are bshanks@96: colored according to correlation, with bshanks@96: red meaning high correlation and blue bshanks@96: meaning low. The method developed in aim (1) will be applied to each cortical area to bshanks@96: find a set of marker genes such that the combinatorial expression pat- bshanks@96: tern of those genes uniquely picks out the target area. Finding marker bshanks@96: genes will be useful for drug discovery as well as for experimentation bshanks@96: because marker genes can be used to design interventions which se- bshanks@96: lectively target individual cortical areas. bshanks@96: The application of the marker gene finding algorithm to the cortex bshanks@96: will also support the development of new neuroanatomical methods. In bshanks@96: addition to finding markers for each individual cortical areas, we will bshanks@96: find a small panel of genes that can find many of the areal boundaries bshanks@96: at once. This panel of marker genes will allow the development of an bshanks@96: ISH protocol that will allow experimenters to more easily identify which bshanks@96: anatomical areas are present in small samples of cortex. bshanks@96: The method developed in aim (2) will provide a genoarchitectonic bshanks@96: viewpoint that will contribute to the creation of a better map. The de- bshanks@96: velopment of present-day cortical maps was driven by the application bshanks@96: of histological stains. If a different set of stains had been available bshanks@96: which identified a different set of features, then today’s cortical maps bshanks@96: may have come out differently. It is likely that there are many repeated, bshanks@96: salient spatial patterns in the gene expression which have not yet been bshanks@96: captured by any stain. Therefore, cortical anatomy needs to incorpo- bshanks@96: rate what we can learn from looking at the patterns of gene expression. bshanks@96: While we do not here propose to analyze human gene expression bshanks@96: data, it is conceivable that the methods we propose to develop could bshanks@96: be used to suggest modifications to the human cortical map as well. In bshanks@96: fact, the methods we will develop will be applicable to other datasets bshanks@96: beyond the brain. We will provide an open-source toolbox to allow bshanks@96: other researchers to easily use our methods. With these methods, re- bshanks@96: searchers with gene expression for any area of the body will be able to bshanks@96: efficiently find marker genes for anatomical regions, or to use gene expression to discover new anatomical pat- bshanks@96: terning. As described above, marker genes have a variety of uses in the development of drugs and experimental bshanks@96: manipulations, and in the anatomical characterization of tissue samples. The discovery of new ways to carve up bshanks@96: anatomical structures into regions may lead to the discovery of new anatomical subregions in various structures, bshanks@96: _________________________________________ bshanks@96: 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer bshanks@96: are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a bshanks@96: pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters bshanks@96: which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection bshanks@96: clusters, further work is needed to make sense of these). The reason that Gene Finder cannot the find marker genes for cortical areas bshanks@96: is that, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found, and it creates that ROI by bshanks@96: (pairwise voxel correlation) clustering around the seed. bshanks@96: which will widely impact all areas of biology. bshanks@75: bshanks@96: Figure 2: Gene Pitx2 bshanks@96: is selectively underex- bshanks@96: pressed in area SS. Although our particular application involves the 3D spatial distribution of gene ex- bshanks@96: pression, we anticipate that the methods developed in aims (1) and (2) will not be limited bshanks@96: to gene expression data, but rather will generalize to any sort of high-dimensional data bshanks@96: over points located in a low-dimensional space. bshanks@96: The approach: Preliminary Studies bshanks@93: Format conversion between SEV, MATLAB, NIFTI bshanks@96: We have created software to (politely) download all of the SEV files16 from the Allen bshanks@96: Institute website. We have also created software to convert between the SEV, MATLAB, bshanks@96: and NIFTI file formats, as well as some of Caret’s file formats. bshanks@93: Flatmap of cortex bshanks@96: We downloaded the ABA data and applied a mask to select only those voxels which bshanks@96: belong to cerebral cortex. We divided the cortex into hemispheres. bshanks@96: Using Caret[7], we created a mesh representation of the surface of the selected voxels. For each gene, and bshanks@96: for each node of the mesh, we calculated an average of the gene expression of the voxels “underneath” that bshanks@96: mesh node. We then flattened the cortex, creating a two-dimensional mesh. bshanks@85: bshanks@85: bshanks@96: Figure 3: The top row shows the two bshanks@96: genes which (individually) best predict bshanks@96: area AUD, according to logistic regres- bshanks@96: sion. The bottom row shows the two bshanks@96: genes which (individually) best match bshanks@96: area AUD, according to gradient sim- bshanks@96: ilarity. From left to right and top to bshanks@96: bottom, the genes are Ssr1, Efcbp1, bshanks@96: Ptk7, and Aph1a. We sampled the nodes of the irregular, flat mesh in order to create bshanks@96: a regular grid of pixel values. We converted this grid into a MATLAB bshanks@96: matrix. bshanks@96: We manually traced the boundaries of each of 49 cortical areas bshanks@96: from the ABA coronal reference atlas slides. We then converted these bshanks@96: manual traces into Caret-format regional boundary data on the mesh bshanks@96: surface. We projected the regions onto the 2-d mesh, and then onto bshanks@96: the grid, and then we converted the region data into MATLAB format. bshanks@96: At this point, the data are in the form of a number of 2-D matrices, bshanks@96: all in registration, with the matrix entries representing a grid of points bshanks@96: (pixels) over the cortical surface: bshanks@96: ∙ A 2-D matrix whose entries represent the regional label associ- bshanks@96: ated with each surface pixel bshanks@96: ∙ For each gene, a 2-D matrix whose entries represent the average bshanks@96: expression level underneath each surface pixel bshanks@96: We created a normalized version of the gene expression data by bshanks@96: subtracting each gene’s mean expression level (over all surface pixels) bshanks@96: and dividing the expression level of each gene by its standard deviation. bshanks@96: The features and the target area are both functions on the surface bshanks@96: pixels. They can be referred to as scalar fields over the space of sur- bshanks@96: face pixels; alternately, they can be thought of as images which can be bshanks@96: displayed on the flatmapped surface. bshanks@96: To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix bshanks@96: for each cortical layer to represent the average expression level within that layer. Cortical layers are found at bshanks@96: different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have bshanks@96: extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary. bshanks@96: In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have bshanks@96: manually demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex. bshanks@96: _________________________________________ bshanks@96: 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available. bshanks@94: Feature selection and scoring methods bshanks@96: Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a bshanks@96: marker. See, for example, Figure 2. bshanks@93: bshanks@93: bshanks@96: Figure 4: Upper left: wwc1. Upper bshanks@96: right: mtif2. Lower left: wwc1 + mtif2 bshanks@96: (each pixel’s value on the lower left is bshanks@96: the sum of the corresponding pixels in bshanks@96: the upper row). Correlation Recall that the instances are surface pixels, and con- bshanks@96: sider the problem of attempting to classify each instance as either a bshanks@96: member of a particular anatomical area, or not. The target area can be bshanks@96: represented as a boolean mask over the surface pixels. bshanks@96: One class of feature selection scoring methods contains methods bshanks@96: which calculate some sort of “match” between each gene image and bshanks@96: the target image. Those genes which match the best are good candi- bshanks@96: dates for features. bshanks@96: One of the simplest methods in this class is to use correlation as bshanks@96: the match score. We calculated the correlation between each gene bshanks@96: and each cortical area. The top row of Figure 1 shows the three genes bshanks@96: most correlated with area SS. bshanks@96: Conditional entropy An information-theoretic scoring method is bshanks@96: to find features such that, if the features (gene expression levels) are bshanks@96: known, uncertainty about the target (the regional identity) is reduced. bshanks@96: Entropy measures uncertainty, so what we want is to find features such bshanks@96: that the conditional distribution of the target has minimal entropy. The bshanks@96: distribution to which we are referring is the probability distribution over bshanks@96: the population of surface pixels. bshanks@96: The simplest way to use information theory is on discrete data, so we discretized our gene expression data bshanks@96: by creating, for each gene, five thresholded boolean masks of the gene data. For each gene, we created a bshanks@96: boolean mask of its expression levels using each of these thresholds: the mean of that gene, the mean minus bshanks@96: one standard deviation, the mean minus two standard deviations, the mean plus one standard deviation, the bshanks@96: mean plus two standard deviations. bshanks@96: Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene bshanks@96: expression boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon bshanks@96: the pair of gene expression boolean masks, is minimized. bshanks@96: This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the bshanks@96: question, “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic bshanks@96: regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables bshanks@96: predicts the target, conditional entropy would notice, whereas linear methods would not. bshanks@96: Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found bshanks@96: genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed bshanks@96: a non-pointwise local scoring method to detect when a gene had a pattern of expression which looked like it had bshanks@96: a boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient bshanks@96: similarity”. bshanks@96: One might say that gradient similarity attempts to measure how much the border of the area of gene expres- bshanks@96: sion and the border of the target region overlap. However, since gene expression falls off continuously rather bshanks@96: than jumping from its maximum value to zero, the spatial pattern of a gene’s expression often does not have a bshanks@96: discrete border. Therefore, instead of looking for a discrete border, we look for large gradients. Gradient similarity bshanks@96: is a symmetric function over two images (i.e. two scalar fields). It is is high to the extent that matching pixels bshanks@96: which have large values and large gradients also have gradients which are oriented in a similar direction. The bshanks@96: formula is: bshanks@96: ∑ bshanks@96: pixel∈pixels cos(abs(∠∇1 -∠∇2)) ⋅|∇1| + |∇2| bshanks@96: 2 ⋅ pixel_value1 + pixel_value2 bshanks@96: 2 bshanks@96: bshanks@85: bshanks@85: bshanks@85: bshanks@85: bshanks@96: Figure 5: From left to right and top bshanks@96: to bottom, single genes which roughly bshanks@96: identify areas SS (somatosensory pri- bshanks@96: mary + supplemental), SSs (supple- bshanks@96: mental somatosensory), PIR (piriform), bshanks@96: FRP (frontal pole), RSP (retrosple- bshanks@96: nial), COApm (Cortical amygdalar, pos- bshanks@96: terior part, medial zone). Grouping bshanks@96: some areas together, we have also bshanks@96: found genes to identify the groups bshanks@85: ACA+PL+ILA+DP+ORB+MO (anterior bshanks@96: cingulate, prelimbic, infralimbic, dor- bshanks@96: sal peduncular, orbital, motor), poste- bshanks@96: rior and lateral visual (VISpm, VISpl, bshanks@96: VISI, VISp; posteromedial, posterolat- bshanks@96: eral, lateral, and primary visual; the bshanks@96: posterior and lateral visual area is dis- bshanks@96: tinguished from its neighbors, but not bshanks@96: from the entire rest of the cortex). The bshanks@96: genes are Pitx2, Aldh1a2, Ppfibp1, bshanks@96: Slco1a5, Tshz2, Trhr, Col12a1, Ets1. where ∇1 and ∇2 are the gradient vectors of the two images at the bshanks@96: current pixel; ∠∇i is the angle of the gradient of image i at the current bshanks@96: pixel; |∇i| is the magnitude of the gradient of image i at the current bshanks@96: pixel; and pixel_valuei is the value of the current pixel in image i. bshanks@96: The intuition is that we want to see if the borders of the pattern in bshanks@96: the two images are similar; if the borders are similar, then both images bshanks@96: will have corresponding pixels with large gradients (because this is a bshanks@96: border) which are oriented in a similar direction (because the borders bshanks@96: are similar). bshanks@93: Most of the genes in Figure 5 were identified via gradient similarity. bshanks@96: Gradient similarity provides information complementary to bshanks@96: correlation bshanks@96: To show that gradient similarity can provide useful information that bshanks@96: cannot be detected via pointwise analyses, consider Fig. 3. The top bshanks@96: row of Fig. 3 displays the 3 genes which most match area AUD, ac- bshanks@96: cording to a pointwise method17. The bottom row displays the 3 genes bshanks@96: which most match AUD according to a method which considers local bshanks@96: geometry18 The pointwise method in the top row identifies genes which bshanks@96: express more strongly in AUD than outside of it; its weakness is that bshanks@96: this includes many areas which don’t have a salient border matching bshanks@96: the areal border. The geometric method identifies genes whose salient bshanks@96: expression border seems to partially line up with the border of AUD; bshanks@96: its weakness is that this includes genes which don’t express over the bshanks@96: entire area. Genes which have high rankings using both pointwise and bshanks@96: border criteria, such as Aph1a in the example, may be particularly good bshanks@96: markers. None of these genes are, individually, a perfect marker for bshanks@96: AUD; we deliberately chose a “difficult” area in order to better contrast bshanks@96: pointwise with geometric methods. bshanks@96: Areas which can be identified by single genes Using gradient bshanks@96: similarity, we have already found single genes which roughly identify bshanks@96: some areas and groupings of areas. For each of these areas, an ex- bshanks@96: ample of a gene which roughly identifies it is shown in Figure 5. We bshanks@96: have not yet cross-verified these genes in other atlases. bshanks@96: In addition, there are a number of areas which are almost identified bshanks@96: by single genes: COAa+NLOT (anterior part of cortical amygdalar area, bshanks@96: nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral bshanks@96: anterior cingulate), VIS (visual), AUD (auditory). bshanks@96: These results validate our expectation that the ABA dataset can bshanks@96: be exploited to find marker genes for many cortical areas, while also bshanks@96: validating the relevancy of our new scoring method, gradient similarity. bshanks@96: Combinations of multiple genes are useful and necessary for bshanks@96: some areas bshanks@96: In Figure 4, we give an example of a cortical area which is not bshanks@96: marked by any single gene, but which can be identified combinatorially. bshanks@96: Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on bshanks@96: the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1’s spatial bshanks@92: _________________________________________ bshanks@96: 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the bshanks@96: predictor variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes bshanks@96: in terms of how well they predict area AUD. bshanks@96: 18For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of bshanks@96: area AUD, was calculated, and this was used to rank the genes. bshanks@96: expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, bshanks@96: but the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the bshanks@96: area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface. bshanks@96: Gene mtif2 is shown in the upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary. bshanks@96: Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these bshanks@96: two figures, we get the lower-left image. This combination captures area MO much better than any single gene. bshanks@96: This shows that our proposal to develop a method to find combinations of marker genes is both possible and bshanks@96: necessary. bshanks@96: Feature selection integrated with prediction As noted earlier, in general, any classifier can be used for fea- bshanks@96: ture selection by running it inside a stepwise wrapper. Also, some learning algorithms integrate soft constraints bshanks@96: on number of features used. Examples of both of these will be seen in the section “Multivariate supervised bshanks@96: learning”. bshanks@94: Multivariate supervised learning bshanks@60: bshanks@69: bshanks@69: bshanks@69: bshanks@96: Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec- bshanks@96: ond row: the first 6 reduced dimensions, using NNMF. Third row: bshanks@96: the first six reduced dimensions, using landmark Isomap. Bottom bshanks@96: row: examples of kmeans clustering applied to reduced datasets bshanks@96: to find 7 clusters. Left: 19 of the major subdivisions of the cortex. bshanks@96: Second from left: PCA. Third from left: NNMF. Right: Landmark bshanks@96: Isomap. Additional details: In the third and fourth rows, 7 dimen- bshanks@96: sions were found, but only 6 displayed. In the last row: for PCA, bshanks@96: 50 dimensions were used; for NNMF, 6 dimensions were used; for bshanks@96: landmark Isomap, 7 dimensions were used. Forward stepwise logistic regression bshanks@96: Logistic regression is a popular method bshanks@96: for predictive modeling of categorial data. bshanks@96: As a pilot run, for five cortical areas (SS, bshanks@96: AUD, RSP, VIS, and MO), we performed bshanks@96: forward stepwise logistic regression to find bshanks@96: single genes, pairs of genes, and triplets bshanks@96: of genes which predict areal identify. This bshanks@96: is an example of feature selection inte- bshanks@96: grated with prediction using a stepwise bshanks@96: wrapper. Some of the single genes found bshanks@96: were shown in various figures throughout bshanks@96: this document, and Figure 4 shows a com- bshanks@96: bination of genes which was found. bshanks@96: We felt that, for single genes, gradi- bshanks@96: ent similarity did a better job than logistic bshanks@96: regression at capturing our subjective im- bshanks@96: pression of a “good gene”. bshanks@96: SVM on all genes at once bshanks@96: In order to see how well one can do bshanks@96: when looking at all genes at once, we ran bshanks@96: a support vector machine to classify corti- bshanks@96: cal surface pixels based on their gene ex- bshanks@96: pression profiles. We achieved classifica- bshanks@96: tion accuracy of about 81%19. This shows bshanks@96: that the genes included in the ABA dataset bshanks@96: are sufficient to define much of cortical bshanks@96: anatomy. However, as noted above, a clas- bshanks@96: sifier that looks at all the genes at once isn’t bshanks@96: as practically useful as a classifier that uses only a few genes. bshanks@94: _________________________________________ bshanks@96: 195-fold cross-validation. bshanks@96: Data-driven redrawing of the cortical map bshanks@96: We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene bshanks@96: expression profile associated with each pixel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi- bshanks@96: Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment bshanks@96: (LTSA), Stochastic Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative bshanks@96: Matrix Factorization (NNMF). Space constraints prevent us from showing many of the results, but as a sample, bshanks@96: PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of Figure 6. bshanks@96: After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we bshanks@96: have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are bshanks@96: shown in the last row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some bshanks@96: of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques bshanks@96: capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to bshanks@96: produce a detailed comparion of these techniques as applied to the domain of genomic anatomy. bshanks@71: bshanks@96: Figure 7: Prototypes corresponding to sample gene bshanks@96: clusters, clustered by gradient similarity. Region bound- bshanks@96: aries for the region that most matches each prototype bshanks@96: are overlayed. Many areas are captured by clusters of genes bshanks@96: We also clustered the genes using gradient similarity bshanks@96: to see if the spatial regions defined by any clusters bshanks@96: matched known anatomical regions. Figure 7 shows, bshanks@96: for ten sample gene clusters, each cluster’s average bshanks@96: expression pattern, compared to a known anatomical bshanks@96: boundary. This suggests that it is worth attempting to bshanks@96: cluster genes, and then to use the results to cluster bshanks@96: pixels. bshanks@92: The approach: what we plan to do bshanks@92: Flatmap cortex and segment cortical layers bshanks@96: There are multiple ways to flatten 3-D data into 2-D. bshanks@96: We will compare mappings from manifolds to planes bshanks@96: which attempt to preserve size (such as the one used bshanks@96: by Caret[7]) with mappings which preserve angle (conformal maps). Our method will include a statistical test bshanks@96: that warns the user if the assumption of 2-D structure seems to be wrong. bshanks@96: We have not yet made use of radial profiles. While the radial profiles may be used “raw”, for laminar structures bshanks@96: like the cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would bshanks@96: then be associated with one expression level per gene per layer. We will develop a segmentation algorithm to bshanks@96: automatically identify the layer boundaries. bshanks@30: Develop algorithms that find genetic markers for anatomical regions bshanks@96: Scoring measures and feature selection We will develop scoring methods for evaluating how good individual bshanks@96: genes are at marking areas. We will compare pointwise, geometric, and information-theoretic measures. We bshanks@96: already developed one entirely new scoring method (gradient similarity), but we may develop more. Scoring bshanks@96: measures that we will explore will include the L1 norm, correlation, expression energy ratio, conditional entropy, bshanks@96: gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such as Student’s t- bshanks@96: test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring measure bshanks@96: on genes by taking the prediction error when using that gene to predict the target. bshanks@96: Using some combination of these measures, we will develop a procedure to find single marker genes for bshanks@96: anatomical regions: for each cortical area, we will rank the genes by their ability to delineate each area. We bshanks@96: will quantitatively compare the list of single genes generated by our method to the lists generated by previous bshanks@96: methods which are mentioned in Aim 1 Related Work. bshanks@96: Some cortical areas have no single marker genes but can be identified by combinatorial coding. This requires bshanks@96: multivariate scoring measures and feature selection procedures. Many of the measures, such as expression bshanks@96: energy, gradient similarity, Jaccard, Dice, Hough, Student’s t, and Mann-Whitney U are univariate. We will extend bshanks@96: these scoring measures for use in multivariate feature selection, that is, for scoring how well combinations of bshanks@96: genes, rather than individual genes, can distinguish a target area. There are existing multivariate forms of some bshanks@96: of the univariate scoring measures, for example, Hotelling’s T-square is a multivariate analog of Student’s t. bshanks@96: We will develop a feature selection procedure for choosing the best small set of marker genes for a given bshanks@96: anatomical area. In addition to using the scoring measures that we develop, we will also explore (a) feature bshanks@96: selection using a stepwise wrapper over “vanilla” classifiers such as logistic regression, (b) supervised learning bshanks@96: methods such as decision trees which incrementally/greedily combine single gene markers into sets, and (c) bshanks@96: supervised learning methods which use soft constraints to minimize number of features used, such as sparse bshanks@96: support vector machines. bshanks@96: Since errors of displacement and of shape may cause genes and target areas to match less than they should, bshanks@96: we will consider the robustness of feature selection methods in the presence of error. Some of these methods, bshanks@96: such as the Hough transform, are designed to be resistant in the presence of error, but many are not. We will bshanks@96: consider extensions to scoring measures that may improve their robustness; for example, a wrapper that runs a bshanks@96: scoring method on small displacements and distortions of the data adds robustness to registration error at the bshanks@96: expense of computation time. bshanks@96: An area may be difficult to identify because the boundaries are misdrawn in the atlas, or because the shape bshanks@96: of the natural domain of gene expression corresponding to the area is different from the shape of the area as bshanks@96: recognized by anatomists. We will extend our procedure to handle difficult areas by combining areas or redrawing bshanks@96: their boundaries. We will develop extensions to our procedure which (a) detect when a difficult area could be bshanks@96: fit if its boundary were redrawn slightly20, and (b) detect when a difficult area could be combined with adjacent bshanks@96: areas to create a larger area which can be fit. bshanks@96: A future publication on the method that we develop in Aim 1 will review the scoring measures and quantita- bshanks@96: tively compare their performance in order to provide a foundation for future research of methods of marker gene bshanks@96: finding. We will measure the robustness of the scoring measures as well as their absolute performance on our bshanks@96: dataset. bshanks@96: Classifiers We will explore and compare different classifiers. As noted above, this activity is not separate bshanks@96: from the previous one, because some supervised learning algorithms include feature selection, and any clas- bshanks@96: sifier can be combined with a stepwise wrapper for use as a feature selection method. We will explore logistic bshanks@96: regression (including spatial models[16]), decision trees21, sparse SVMs, generative mixture models (including bshanks@96: naive bayes), kernel density estimation, instance-based learning methods (such as k-nearest neighbor), genetic bshanks@96: algorithms, and artificial neural networks. bshanks@30: Develop algorithms to suggest a division of a structure into anatomical parts bshanks@96: Explore dimensionality reduction on gene expression profiles We have already described the application bshanks@96: of ten dimensionality reduction algorithms for the purpose of replacing the gene expression profiles, which are bshanks@96: vectors of about 4000 gene expression levels, with a smaller number of features. We plan to further explore bshanks@96: and interpret these results, as well as to apply other unsupervised learning algorithms, including independent bshanks@96: components analysis, self-organizing maps, and generative models such as deep Boltzmann machines. We bshanks@96: will explore ways to quantitatively compare the relevance of the different dimensionality reduction methods for bshanks@96: identifying cortical areal boundaries. bshanks@96: Explore dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene ex- bshanks@94: _________________________________________ bshanks@96: 20Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by bshanks@96: multiple sources of evidence. Interestingly, the need to detect “natural spatial domains of gene expression” in a data-driven fashion bshanks@96: means that the methods of Aim 2 might be useful in achieving Aim 1, as well – particularly discriminative dimensionality reduction. bshanks@96: 21Actually, we have already begun to explore decision trees. For each cortical area, we have used the C4.5 algorithm to find a decision bshanks@96: tree for that area. We achieved good classification accuracy on our training set, but the number of genes that appeared in each tree was bshanks@96: too large. We plan to implement a pruning procedure to generate trees that use fewer genes. bshanks@96: pression profiles, the same techniques can be applied instead to the pixels22. It is possible that the features bshanks@96: generated in this way by some dimensionality reduction techniques will directly correspond to interesting spatial bshanks@96: regions. bshanks@96: Explore clustering and segmentation algorithms on pixels We will explore clustering and segmenta- bshanks@96: tion algorithms in order to segment the pixels into regions. We will explore k-means, spectral clustering, gene bshanks@96: shaving[9], recursive division clustering, multivariate generalizations of edge detectors, multivariate generaliza- bshanks@96: tions of watershed transformations, region growing, active contours, graph partitioning methods, and recursive bshanks@96: agglomerative clustering with various linkage functions. These methods can be combined with dimensionality bshanks@96: reduction. bshanks@96: Explore clustering on genes We have already shown that the procedure of clustering genes according to bshanks@96: gradient similarity, and then creating an averaged prototype of each cluster’s expression pattern, yields some bshanks@96: spatial patterns which match cortical areas. We will further explore the clustering of genes. bshanks@96: In addition to using the cluster expression prototypes directly to identify spatial regions, this might be useful bshanks@96: as a component of dimensionality reduction. For example, one could imagine clustering similar genes and then bshanks@96: replacing their expression levels with a single average expression level, thereby removing some redundancy from bshanks@96: the gene expression profiles. One could then perform clustering on pixels (possibly after a second dimensionality bshanks@96: reduction step) in order to identify spatial regions. It remains to be seen whether removal of redundancy would bshanks@96: help or hurt the ultimate goal of identifying interesting spatial regions. bshanks@96: Explore co-clustering There are some algorithms which simultaineously incorporate clustering on instances bshanks@96: and on features (in our case, genes and pixels), for example, IRM[11]. These are called co-clustering or biclus- bshanks@96: tering algorithms. bshanks@96: Quantitatively compare different methods In order to tell which method is best for genomic anatomy, for bshanks@96: each experimental method we will compare the cortical map found by unsupervised learning to a cortical map bshanks@96: derived from the Allen Reference Atlas. In order to compare the experimental clustering with the reference bshanks@96: clustering, we will explore various quantitative metrics that purport to measure how similar two clusterings are, bshanks@96: such as Jaccard, Rand index, Fowlkes-Mallows, variation of information, Larsen, Van Dongen, and others. bshanks@96: Discriminative dimensionality reduction In addition to using a purely data-driven approach to identify bshanks@96: spatial regions, it might be useful to see how well the known regions can be reconstructed from a small number bshanks@96: of features, even if those features are chosen by using knowledge of the regions. For example, linear discriminant bshanks@96: analysis could be used as a dimensionality reduction technique in order to identify a few features which are the bshanks@96: best linear summary of gene expression profiles for the purpose of discriminating between regions. This reduced bshanks@96: feature set could then be used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the bshanks@96: reference atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is. bshanks@96: Apply the new methods to the cortex bshanks@96: Using the methods developed in Aim 1, we will present, for each cortical area, a short list of markers to identify bshanks@96: that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once. bshanks@96: Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible for an unrelated bshanks@96: combination of genes to seem to identify an area when in fact it is only coincidence. There are two ways we will bshanks@96: validate our marker genes to guard against this. First, we will confirm that putative combinations of marker genes bshanks@96: express the same pattern in both hemispheres. Second, we will manually validate our final results on other gene bshanks@96: expression datasets such as EMAGE, GeneAtlas, and GENSAT. bshanks@96: Using the methods developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify bshanks@96: and explain how the statistical structure in the gene expression data led to any unexpected or interesting features bshanks@96: _________________________________________ bshanks@96: 22Consider a matrix whose rows represent pixel locations, and whose columns represent genes. An entry in this matrix represents the bshanks@96: gene expression level at a given pixel. One can look at this matrix as a collection of pixels, each corresponding to a vector of many gene bshanks@96: expression levels; or one can look at it as a collection of genes, each corresponding to a vector giving that gene’s expression at each bshanks@96: pixel. Similarly, dimensionality reduction can be used to replace a large number of genes with a small number of features, or it can be bshanks@96: used to replace a large number of pixels with a small number of features. bshanks@96: of these maps, and we will provide biological hypotheses to interpret any new cortical areas, or groupings of bshanks@96: areas, which are discovered. bshanks@87: Timeline and milestones bshanks@90: Finding marker genes bshanks@96: September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers bshanks@96: November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information bshanks@96: for each layer bshanks@96: October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks. bshanks@96: Also test out various dimensionality reduction schemes in combination with supervised learning. create or extend bshanks@96: supervised learning frameworks which use multivariate versions of the best scoring methods. bshanks@96: January 2010 (milestone): Submit a publication on single marker genes for cortical areas bshanks@96: February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the bshanks@96: best way to integrate radial profiles with supervised learning. Explore the best way to make supervised learning bshanks@96: techniques robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly bshanks@96: off). Quantitatively compare the performance of different supervised learning techniques. Validate marker genes bshanks@96: found in the ABA dataset by checking against other gene expression datasets. Create documentation and unit bshanks@96: tests for software toolbox for Aim 1. Respond to user bug reports for Aim 1 software toolbox. bshanks@96: June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox. bshanks@96: July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a bshanks@96: small number of marker genes that can, in combination, define most of the areas at once bshanks@90: Revealing new ways to parcellate a structure into regions bshanks@96: June 2010-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial bshanks@96: clustering algorithms, used in combination with dimensionality reduction, for Aim 2. Explore co-clustering algo- bshanks@96: rithms. Think about how radial profile information can be used for Aim 2. Adapt clustering algorithms to use radial bshanks@96: profile information. Quantitatively compare the performance of different dimensionality reduction and clustering bshanks@96: techniques. Quantitatively compare the value of different flatmapping methods and ways of representing radial bshanks@96: profiles. bshanks@96: March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox. bshanks@96: February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If bshanks@96: new ways of organizing the cortex into areas are discovered, read the literature and talk to people to learn about bshanks@96: research related to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2. bshanks@96: Respond to user bug reports for Aim 2 software toolbox. bshanks@96: May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in bshanks@96: Aim 2 bshanks@96: May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1. bshanks@96: Follow up on responses to our papers. 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