| rev |
line source |
| bshanks@0 | 1 Specific aims
|
| bshanks@96 | 2 Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in
|
| bshanks@96 | 3 situ transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many
|
| bshanks@96 | 4 locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expres-
|
| bshanks@96 | 5 sion to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical
|
| bshanks@96 | 6 maps based on gene expression patterns. We have three specific aims:
|
| bshanks@96 | 7 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which
|
| bshanks@96 | 8 selectively target anatomical regions
|
| bshanks@96 | 9 (2) develop an algorithm to suggest new ways of carving up a structure into anatomically distinct regions,
|
| bshanks@96 | 10 based on spatial patterns in gene expression
|
| bshanks@96 | 11 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen
|
| bshanks@96 | 12 Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending
|
| bshanks@96 | 13 the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the
|
| bshanks@96 | 14 methods developed in (1) and (2).
|
| bshanks@96 | 15 Although our particular application involves the 3D spatial distribution of gene expression, we anticipate that
|
| bshanks@96 | 16 the methods developed in aims (1) and (2) will generalize to any sort of high-dimensional data over points located
|
| bshanks@96 | 17 in a low-dimensional space. In particular, our method could be applied to genome-wide sequencing data derived
|
| bshanks@96 | 18 from sets of tissues and disease states.
|
| bshanks@96 | 19 In terms of the application of the methods to cerebral cortex, aim (1) is to go from cortical areas to marker
|
| bshanks@96 | 20 genes, and aim (2) is to let the gene profile define the cortical areas. In addition to validating the usefulness
|
| bshanks@96 | 21 of the algorithms, the application of these methods to cortex will produce immediate benefits, because there
|
| bshanks@96 | 22 are currently no known genetic markers for most cortical areas. The results of the project will support the
|
| bshanks@96 | 23 development of new ways to selectively target cortical areas, and it will support the development of a method for
|
| bshanks@96 | 24 identifying the cortical areal boundaries present in small tissue samples.
|
| bshanks@96 | 25 All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well
|
| bshanks@96 | 26 as the machine-readable datasets developed in aim (3), will be published and freely available for others to use.
|
| bshanks@87 | 27 The challenge topic
|
| bshanks@96 | 28 This proposal addresses challenge topic 06-HG-101. Massive new datasets obtained with techniques such as
|
| bshanks@96 | 29 in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others,
|
| bshanks@96 | 30 allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated
|
| bshanks@96 | 31 methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific
|
| bshanks@96 | 32 anatomical regions, and also to draw new anatomical maps based on gene expression patterns.
|
| bshanks@87 | 33 The Challenge and Potential impact
|
| bshanks@96 | 34 Each of our three aims will be discussed in turn. For each aim, we will develop a conceptual framework for
|
| bshanks@96 | 35 thinking about the task, and we will present our strategy for solving it. Next we will discuss related work. At the
|
| bshanks@96 | 36 conclusion of each section, we will summarize why our strategy is different from what has been done before. At
|
| bshanks@96 | 37 the end of this section, we will describe the potential impact.
|
| bshanks@84 | 38 Aim 1: Given a map of regions, find genes that mark the regions
|
| bshanks@96 | 39 Machine learning terminology: classifiers The task of looking for marker genes for known anatomical regions
|
| bshanks@96 | 40 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 | 41 locations of the regions can be inferred.
|
| bshanks@96 | 42 If we define the regions so that they cover the entire anatomical structure to be subdivided, we may say that
|
| bshanks@96 | 43 we are using gene expression in each voxel to assign that voxel to the proper area. We call this a classification
|
| bshanks@96 | 44 task, because each voxel is being assigned to a class (namely, its region). An understanding of the relationship
|
| bshanks@96 | 45 between the combination of their expression levels and the locations of the regions may be expressed as a
|
| bshanks@96 | 46 function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is
|
| bshanks@96 | 47 the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function
|
| bshanks@96 | 48 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 | 49 label).
|
| bshanks@96 | 50 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for
|
| bshanks@96 | 51 determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene
|
| bshanks@96 | 52 expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. The
|
| bshanks@96 | 53 initial gene expression dataset used in the construction of the classifier is called training data. In the machine
|
| bshanks@96 | 54 learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a task in
|
| bshanks@96 | 55 which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances
|
| bshanks@96 | 56 (voxels) for which the labels (regions) are known.
|
| bshanks@96 | 57 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature
|
| bshanks@96 | 58 selection. Feature selection is one component of the task of learning a classifier. Some methods for learning
|
| bshanks@96 | 59 classifiers start out with a separate feature selection phase, whereas other methods combine feature selection
|
| bshanks@96 | 60 with other aspects of training.
|
| bshanks@96 | 61 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked
|
| bshanks@96 | 62 genes are then chosen. Some scoring measures can assign a score to a set of selected genes, not just to a
|
| bshanks@96 | 63 single gene; in this case, a dynamic procedure may be used in which features are added and subtracted from the
|
| bshanks@96 | 64 selected set depending on how much they raise the score. Such procedures are called “stepwise” or “greedy”.
|
| bshanks@96 | 65 Although the classifier itself may only look at the gene expression data within each voxel before classifying
|
| bshanks@96 | 66 that voxel, the algorithm which constructs the classifier may look over the entire dataset. We can categorize
|
| bshanks@96 | 67 score-based feature selection methods depending on how the score of calculated. Often the score calculation
|
| bshanks@96 | 68 consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the
|
| bshanks@96 | 69 aggregation is often a sum or a sum of squares or average). If only information from nearby voxels is used to
|
| bshanks@96 | 70 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 | 71 used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.
|
| bshanks@96 | 72 _________________________________________
|
| bshanks@96 | 73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
|
| bshanks@96 | 74 Both gene expression data and anatomical atlases have errors, due to a variety of factors. Individual subjects
|
| bshanks@96 | 75 have idiosyncratic anatomy. Subjects may be improperly registred to the atlas. The method used to measure
|
| bshanks@96 | 76 gene expression may be noisy. The atlas may have errors. It is even possible that some areas in the anatomical
|
| bshanks@96 | 77 atlas are “wrong” in that they do not have the same shape as the natural domains of gene expression to which
|
| bshanks@96 | 78 they correspond. These sources of error can affect the displacement and the shape of both the gene expression
|
| bshanks@96 | 79 data and the anatomical target areas. Therefore, it is important to use feature selection methods which are
|
| bshanks@96 | 80 robust to these kinds of errors.
|
| bshanks@85 | 81 Our strategy for Aim 1
|
| bshanks@96 | 82 Key questions when choosing a learning method are: What are the instances? What are the features? How are
|
| bshanks@96 | 83 the features chosen? Here are four principles that outline our answers to these questions.
|
| bshanks@84 | 84 Principle 1: Combinatorial gene expression
|
| bshanks@96 | 85 It is too much to hope that every anatomical region of interest will be identified by a single gene. For example,
|
| bshanks@96 | 86 in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas
|
| bshanks@96 | 87 (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes
|
| bshanks@96 | 88 (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Studies,
|
| bshanks@96 | 89 Figure 4). Therefore, each instance should contain multiple features (genes).
|
| bshanks@84 | 90 Principle 2: Only look at combinations of small numbers of genes
|
| bshanks@96 | 91 When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have
|
| bshanks@96 | 92 been selected as features. The more data that are available to a classifier, the better that it can do. For example,
|
| bshanks@96 | 93 perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every
|
| bshanks@96 | 94 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 | 95 gather data about every gene. For example, if we want to use the expression of marker genes as a trigger for
|
| bshanks@96 | 96 some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the
|
| bshanks@96 | 97 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that
|
| bshanks@96 | 98 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 | 99 tissue samples in order to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we
|
| bshanks@96 | 100 must select only a few genes as features.
|
| bshanks@96 | 101 The requirement to find combinations of only a small number of genes limits us from straightforwardly ap-
|
| bshanks@96 | 102 plying many of the most simple techniques from the field of supervised machine learning. In the parlance of
|
| bshanks@96 | 103 machine learning, our task combines feature selection with supervised learning.
|
| bshanks@30 | 104 Principle 3: Use geometry in feature selection
|
| bshanks@96 | 105 When doing feature selection with score-based methods, the simplest thing to do would be to score the per-
|
| bshanks@96 | 106 formance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach
|
| bshanks@96 | 107 is to also use information about the geometric relations between each voxel and its neighbors; this requires non-
|
| bshanks@96 | 108 pointwise, local scoring methods. See Preliminary Studies, figure 3 for evidence of the complementary nature of
|
| bshanks@96 | 109 pointwise and local scoring methods.
|
| bshanks@30 | 110 Principle 4: Work in 2-D whenever possible
|
| bshanks@96 | 111 There are many anatomical structures which are commonly characterized in terms of a two-dimensional
|
| bshanks@96 | 112 manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be
|
| bshanks@96 | 113 improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for
|
| bshanks@96 | 114 humans to visualize and work with 2-D data. Therefore, when possible, the instances should represent pixels,
|
| bshanks@96 | 115 not voxels.
|
| bshanks@43 | 116 Related work
|
| bshanks@96 | 117 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expres-
|
| bshanks@96 | 118 sion data which are not fundamentally spatial2.
|
| bshanks@96 | 119 As noted above, there has been much work on both supervised learning and there are many available
|
| bshanks@96 | 120 algorithms for each. However, the algorithms require the scientist to provide a framework for representing the
|
| bshanks@96 | 121 problem domain, and the way that this framework is set up has a large impact on performance. Creating a
|
| bshanks@96 | 122 good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical
|
| bshanks@96 | 123 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such
|
| bshanks@96 | 124 as gradient similarity, which is discussed in Preliminary Studies) may be necessary in order to achieve the best
|
| bshanks@96 | 125 results in this application.
|
| bshanks@96 | 126 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated
|
| bshanks@96 | 127 methods.
|
| bshanks@96 | 128 [13 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical
|
| bshanks@96 | 129 structure of interest, computing what proportion of this structure is covered by the gene’s spatial region.
|
| bshanks@96 | 130 GeneAtlas[5] and EMAGE [26] allow the user to construct a search query by demarcating regions and then
|
| bshanks@96 | 131 specifing either the strength of expression or the name of another gene or dataset whose expression pattern
|
| bshanks@96 | 132 is to be matched. For the similiarity score (match score) between two images (in this case, the query and the
|
| bshanks@96 | 133 gene expression images), GeneAtlas uses the sum of a weighted L1-norm distance between vectors whose
|
| bshanks@96 | 134 components represent the number of cells within a pixel3 whose expression is within four discretization levels.
|
| bshanks@96 | 135 EMAGE uses Jaccard similarity4. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes
|
| bshanks@96 | 136 that define a region in concert but not separately.
|
| bshanks@96 | 137 [15 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components. Gene Finder: The
|
| bshanks@96 | 138 user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2) yields a list
|
| bshanks@96 | 139 of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of
|
| bshanks@96 | 140 overexpressed genes for selected structures). Correlation: The user selects a seed voxel and the system then
|
| bshanks@96 | 141 shows the user how much correlation there is between the gene expression profile of the seed voxel and every
|
| bshanks@96 | 142 other voxel. Clusters: will be described later
|
| bshanks@96 | 143 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes,
|
| bshanks@96 | 144 whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a
|
| bshanks@96 | 145 marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score5,
|
| bshanks@96 | 146 whereas we will also use geometric scores such as gradient similarity (described in Preliminary Studies). Figures
|
| bshanks@96 | 147 4, 2, and 3 in the Preliminary Studies section contains evidence that each of our three choices is the right one.
|
| bshanks@96 | 148 [6 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test
|
| bshanks@96 | 149 with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in
|
| bshanks@96 | 150 the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being
|
| bshanks@96 | 151 analyzed), it is not being used to look for underexpression, and does not look for combinations of genes.
|
| bshanks@96 | 152 [10 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use
|
| bshanks@96 | 153 an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to
|
| bshanks@96 | 154 match a target image. Their match score is Jaccard similarity.
|
| bshanks@96 | 155 In summary, there has been fruitful work on finding marker genes, but only one of the previous projects
|
| bshanks@96 | 156 explores combinations of marker genes, and none of these publications compare the results obtained by using
|
| bshanks@96 | 157 different algorithms or scoring methods.
|
| bshanks@84 | 158 Aim 2: From gene expression data, discover a map of regions
|
| bshanks@30 | 159 Machine learning terminology: clustering
|
| bshanks@96 | 160 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates;
|
| bshanks@96 | 161 not just data which have only a few different locations or which is indexed by anatomical label.
|
| bshanks@96 | 162 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.
|
| bshanks@96 | 163 4the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.
|
| bshanks@96 | 164 5“Expression energy ratio”, which captures overexpression.
|
| bshanks@96 | 165 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is
|
| bshanks@96 | 166 referred to as unsupervised learning in the jargon of machine learning. One thing that you can do with such a
|
| bshanks@96 | 167 dataset is to group instances together. A set of similar instances is called a cluster, and the activity of finding
|
| bshanks@96 | 168 grouping the data into clusters is called clustering or cluster analysis.
|
| bshanks@96 | 169 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The
|
| bshanks@96 | 170 instances are once again voxels (or pixels) along with their associated gene expression profiles. We make
|
| bshanks@96 | 171 the assumption that voxels from the same anatomical region have similar gene expression profiles, at least
|
| bshanks@96 | 172 compared to the other regions. This means that clustering voxels is the same as finding potential regions; we
|
| bshanks@96 | 173 seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.
|
| bshanks@96 | 174 It is desirable to determine not just one set of regions, but also how these regions relate to each other. The
|
| bshanks@96 | 175 outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the
|
| bshanks@96 | 176 voxels. This is called hierarchial clustering.
|
| bshanks@96 | 177 Similarity scores A crucial choice when designing a clustering method is how to measure similarity, across
|
| bshanks@96 | 178 either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature
|
| bshanks@96 | 179 selection (discussed above under Aim 1) and scoring methods for similarity.
|
| bshanks@96 | 180 Spatially contiguous clusters; image segmentation We have shown that aim 2 is a type of clustering
|
| bshanks@96 | 181 task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels
|
| bshanks@96 | 182 grouped together into a cluster must be spatially contiguous. In Preliminary Studies, we show that one can get
|
| bshanks@96 | 183 reasonable results without enforcing this constraint; however, we plan to compare these results against other
|
| bshanks@96 | 184 methods which guarantee contiguous clusters.
|
| bshanks@96 | 185 Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous
|
| bshanks@96 | 186 clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are
|
| bshanks@96 | 187 thousands of color channels (one for each gene), rather than just three6. A more crucial difference is that there
|
| bshanks@96 | 188 are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not
|
| bshanks@96 | 189 appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation
|
| bshanks@96 | 190 algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these
|
| bshanks@96 | 191 algorithms are specialized for visual images.
|
| bshanks@96 | 192 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression
|
| bshanks@96 | 193 feature vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying
|
| bshanks@96 | 194 data.
|
| bshanks@96 | 195 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion
|
| bshanks@96 | 196 in the instances. However, some clustering algorithms perform better on small numbers of features7. There are
|
| bshanks@96 | 197 techniques which “summarize” a larger number of features using a smaller number of features; these techniques
|
| bshanks@96 | 198 go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique
|
| bshanks@96 | 199 yields is called the reduced feature set. Note that the features in the reduced feature set do not necessarily
|
| bshanks@96 | 200 correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.
|
| bshanks@96 | 201 Clustering genes rather than voxels Although the ultimate goal is to cluster the instances (voxels or pixels),
|
| bshanks@96 | 202 one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes
|
| bshanks@96 | 203 could be used.
|
| bshanks@96 | 204 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene,
|
| bshanks@96 | 205 we could have one reduced feature for each gene cluster.
|
| bshanks@96 | 206 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes
|
| bshanks@96 | 207 have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems
|
| bshanks@96 | 208 likely that an anatomically interesting region will have multiple genes which each individually pick it out8. This
|
| bshanks@94 | 209 _________________________________________
|
| bshanks@96 | 210 6There are imaging tasks which use more than three colors, for example multispectral imaging and hyperspectral imaging, which are
|
| bshanks@96 | 211 often used to process satellite imagery.
|
| bshanks@96 | 212 7First, because the number of features in the reduced dataset is less than in the original dataset, the running time of clustering
|
| bshanks@96 | 213 algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.
|
| bshanks@96 | 214 8This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However,
|
| bshanks@96 | 215 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 | 216 expression; perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another
|
| bshanks@96 | 217 suggests the following procedure: cluster together genes which pick out similar regions, and then to use the
|
| bshanks@96 | 218 more popular common regions as the final clusters. In Preliminary Studies, Figure 7, we show that a number
|
| bshanks@96 | 219 of anatomically recognized cortical regions, as well as some “superregions” formed by lumping together a few
|
| bshanks@96 | 220 regions, are associated with gene clusters in this fashion.
|
| bshanks@96 | 221 The task of clustering both the instances and the features is called co-clustering, and there are a number of
|
| bshanks@96 | 222 co-clustering algorithms.
|
| bshanks@43 | 223 Related work
|
| bshanks@96 | 224 Some researchers have attempted to parcellate cortex on the basis of non-gene expression data. For example,
|
| bshanks@96 | 225 [18 ], [2 ], [19], and [1] associate spots on the cortex with the radial profile9 of response to some stain ([12] uses
|
| bshanks@96 | 226 MRI), extract features from this profile, and then use similarity between surface pixels to cluster. Features used
|
| bshanks@96 | 227 include statistical moments, wavelets, and the excess mass functional. Some of these features are motivated
|
| bshanks@96 | 228 by the presence of tangential lines of stain intensity which correspond to laminar structure. Some methods use
|
| bshanks@96 | 229 standard clustering procedures, whereas others make use of the spatial nature of the data to look for sudden
|
| bshanks@96 | 230 transitions, which are identified as areal borders.
|
| bshanks@96 | 231 [23 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual
|
| bshanks@96 | 232 analysis, two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and
|
| bshanks@96 | 233 a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper
|
| bshanks@96 | 234 yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on
|
| bshanks@96 | 235 the cortical dataset10 and while the results are promising, they also demonstrate that NNMF is not necessarily
|
| bshanks@96 | 236 the best dimensionality reduction method for this application (see Preliminary Studies, Figure 6).
|
| bshanks@96 | 237 AGEA[15] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with
|
| bshanks@96 | 238 correlation as the similarity metric. EMAGE[26] allows the user to select a dataset from among a large number
|
| bshanks@96 | 239 of alternatives, or by running a search query, and then to cluster the genes within that dataset. EMAGE clusters
|
| bshanks@96 | 240 via hierarchial complete linkage clustering with un-centred correlation as the similarity score.
|
| bshanks@96 | 241 [6 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and
|
| bshanks@96 | 242 which were highly correlated with many other genes. They computed the matrix of (rank) correlations between
|
| bshanks@96 | 243 pairs of these genes, and ordered the rows of this matrix as follows: “the first row of the matrix was chosen to
|
| bshanks@96 | 244 show the strongest contrast between the highest and lowest correlation coefficient for that row. The remaining
|
| bshanks@96 | 245 rows were then arranged in order of decreasing similarity using a least squares metric”. The resulting matrix
|
| bshanks@96 | 246 showed four clusters. For each cluster, prototypical spatial expression patterns were created by averaging the
|
| bshanks@96 | 247 genes in the cluster. The prototypes were analyzed manually, without clustering voxels.
|
| bshanks@96 | 248 [10 ] applies their technique for finding combinations of marker genes for the purpose of clustering genes
|
| bshanks@96 | 249 around a “seed gene”. They do this by using the pattern of expression of the seed gene as the target image, and
|
| bshanks@96 | 250 then searching for other genes which can be combined to reproduce this pattern. Other genes which are found
|
| bshanks@96 | 251 are considered to be related to the seed. The same team also describes a method[25] for finding “association
|
| bshanks@96 | 252 rules” such as, “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the
|
| bshanks@96 | 253 same gene”. This could be useful as part of a procedure for clustering voxels.
|
| bshanks@96 | 254 In summary, although these projects obtained clusterings, there has not been much comparison between
|
| bshanks@96 | 255 different algorithms or scoring methods, so it is likely that the best clustering method for this application has not
|
| bshanks@96 | 256 yet been found. The projects using gene expression on cortex did not attempt to make use of the radial profile
|
| bshanks@96 | 257 of gene expression. Also, none of these projects did a separate dimensionality reduction step before clustering
|
| bshanks@96 | 258 pixels, none tried to cluster genes first in order to guide automated clustering of pixels into spatial regions, and
|
| bshanks@96 | 259 none used co-clustering algorithms.
|
| bshanks@96 | 260 ________
|
| bshanks@96 | 261 possibility is that, although the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the
|
| bshanks@96 | 262 prototype.
|
| bshanks@96 | 263 9A radial profile is a profile along a line perpendicular to the cortical surface.
|
| bshanks@96 | 264 10We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding
|
| bshanks@96 | 265 a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional
|
| bshanks@96 | 266 constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet
|
| bshanks@96 | 267 tried.
|
| bshanks@94 | 268 Aim 3: apply the methods developed to the cerebral cortex
|
| bshanks@94 | 269 Background
|
| bshanks@96 | 270 The cortex is divided into areas and layers. Because of the cortical columnar organization, the parcellation
|
| bshanks@96 | 271 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 | 272 boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The
|
| bshanks@96 | 273 layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of a six-layered
|
| bshanks@96 | 274 cake11 .
|
| bshanks@96 | 275 It is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
|
| bshanks@96 | 276 yet there are no known marker genes for most cortical areas. When it is necessary to divide a tissue sample
|
| bshanks@96 | 277 into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and
|
| bshanks@96 | 278 interpret them in the context of their approximate location upon the cortical surface.
|
| bshanks@96 | 279 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are
|
| bshanks@96 | 280 still not completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent,
|
| bshanks@96 | 281 the lack of a single agreed-upon map can be seen by contrasting the recent maps given by Swanson[22] on the
|
| bshanks@96 | 282 one hand, and Paxinos and Franklin[17] on the other. While the maps are certainly very similar in their general
|
| bshanks@96 | 283 arrangement, significant differences remain.
|
| bshanks@36 | 284 The Allen Mouse Brain Atlas dataset
|
| bshanks@96 | 285 The Allen Mouse Brain Atlas (ABA) data were produced by doing in-situ hybridization on slices of male,
|
| bshanks@96 | 286 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-
|
| bshanks@96 | 287 automatically analyzed to create a digital measurement of gene expression levels at each location in each slice.
|
| bshanks@96 | 288 Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used
|
| bshanks@96 | 289 to measure one single gene; many different mouse brains were needed in order to measure the expression of
|
| bshanks@96 | 290 many genes.
|
| bshanks@96 | 291 An automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D
|
| bshanks@96 | 292 coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are
|
| bshanks@96 | 293 67x41x58 = 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain[15].
|
| bshanks@96 | 294 Mus musculus is thought to contain about 22,000 protein-coding genes[28]. The ABA contains data on about
|
| bshanks@96 | 295 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
|
| bshanks@96 | 296 dataset is derived from only the coronal subset of the ABA12.
|
| bshanks@96 | 297 The ABA is not the only large public spatial gene expression dataset13. With the exception of the ABA,
|
| bshanks@96 | 298 GenePaint, and EMAGE, most of the other resources have not (yet) extracted the expression intensity from the
|
| bshanks@96 | 299 ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE
|
| bshanks@96 | 300 make this form of data available for public download from the website14. Many of these resources focus on
|
| bshanks@96 | 301 developmental gene expression.
|
| bshanks@63 | 302 Related work
|
| bshanks@96 | 303 [15 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure
|
| bshanks@96 | 304 of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort
|
| bshanks@96 | 305 of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical
|
| bshanks@96 | 306 map based on gene expression data. Neither of the other components of AGEA can be applied to cortical
|
| bshanks@96 | 307 _________________________________________
|
| bshanks@96 | 308 11Outside of isocortex, the number of layers varies.
|
| bshanks@96 | 309 12The sagittal data do not cover the entire cortex, and also have greater registration error[15]. Genes were selected by the Allen
|
| bshanks@96 | 310 Institute for coronal sectioning based on, “classes of known neuroscientific interest... or through post hoc identification of a marked
|
| bshanks@96 | 311 non-ubiquitous expression pattern”[15].
|
| bshanks@96 | 312 13Other such resources include GENSAT[8], GenePaint[27], its sister project GeneAtlas[5], BGEM[14], EMAGE[26], EurExpress
|
| bshanks@96 | 313 (http://www.eurexpress.org/ee/; EurExpress data are also entered into EMAGE), EADHB (http://www.ncl.ac.uk/ihg/EADHB/
|
| bshanks@96 | 314 database/EADHB_database.html), MAMEP (http://mamep.molgen.mpg.de/index.php), Xenbase (http://xenbase.org/), ZFIN[21],
|
| bshanks@96 | 315 Aniseed (http://aniseed-ibdm.univ-mrs.fr/), VisiGene (http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some
|
| bshanks@96 | 316 of the other listed data sources), GEISHA[4], Fruitfly.org[24], COMPARE (http://compare.ibdml.univ-mrs.fr/), GXD[20], GEO[3]
|
| bshanks@96 | 317 (GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.)
|
| bshanks@96 | 318 14without prior offline registration
|
| bshanks@96 | 319 areas; AGEA’s Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA’s hierarchial
|
| bshanks@96 | 320 clustering does not produce clusters corresponding to the cortical areas15.
|
| bshanks@96 | 321 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes,
|
| bshanks@96 | 322 (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no
|
| bshanks@96 | 323 work on computationally finding marker genes for cortical areas, or on finding a hierarchial clustering that will
|
| bshanks@96 | 324 yield a map of cortical areas de novo from gene expression data.
|
| bshanks@96 | 325 Our project is guided by a concrete application with a well-specified criterion of success (how well we can
|
| bshanks@96 | 326 find marker genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing
|
| bshanks@96 | 327 different methods.
|
| bshanks@94 | 328 Significance
|
| bshanks@85 | 329
|
| bshanks@85 | 330
|
| bshanks@96 | 331 Figure 1: Top row: Genes Nfic
|
| bshanks@96 | 332 and A930001M12Rik are the most
|
| bshanks@96 | 333 correlated with area SS (somatosen-
|
| bshanks@96 | 334 sory cortex). Bottom row: Genes
|
| bshanks@96 | 335 C130038G02Rik and Cacna1i are
|
| bshanks@96 | 336 those with the best fit using logistic
|
| bshanks@96 | 337 regression. Within each picture, the
|
| bshanks@96 | 338 vertical axis roughly corresponds to
|
| bshanks@96 | 339 anterior at the top and posterior at the
|
| bshanks@96 | 340 bottom, and the horizontal axis roughly
|
| bshanks@96 | 341 corresponds to medial at the left and
|
| bshanks@96 | 342 lateral at the right. The red outline is
|
| bshanks@96 | 343 the boundary of region SS. Pixels are
|
| bshanks@96 | 344 colored according to correlation, with
|
| bshanks@96 | 345 red meaning high correlation and blue
|
| bshanks@96 | 346 meaning low. The method developed in aim (1) will be applied to each cortical area to
|
| bshanks@96 | 347 find a set of marker genes such that the combinatorial expression pat-
|
| bshanks@96 | 348 tern of those genes uniquely picks out the target area. Finding marker
|
| bshanks@96 | 349 genes will be useful for drug discovery as well as for experimentation
|
| bshanks@96 | 350 because marker genes can be used to design interventions which se-
|
| bshanks@96 | 351 lectively target individual cortical areas.
|
| bshanks@96 | 352 The application of the marker gene finding algorithm to the cortex
|
| bshanks@96 | 353 will also support the development of new neuroanatomical methods. In
|
| bshanks@96 | 354 addition to finding markers for each individual cortical areas, we will
|
| bshanks@96 | 355 find a small panel of genes that can find many of the areal boundaries
|
| bshanks@96 | 356 at once. This panel of marker genes will allow the development of an
|
| bshanks@96 | 357 ISH protocol that will allow experimenters to more easily identify which
|
| bshanks@96 | 358 anatomical areas are present in small samples of cortex.
|
| bshanks@96 | 359 The method developed in aim (2) will provide a genoarchitectonic
|
| bshanks@96 | 360 viewpoint that will contribute to the creation of a better map. The de-
|
| bshanks@96 | 361 velopment of present-day cortical maps was driven by the application
|
| bshanks@96 | 362 of histological stains. If a different set of stains had been available
|
| bshanks@96 | 363 which identified a different set of features, then today’s cortical maps
|
| bshanks@96 | 364 may have come out differently. It is likely that there are many repeated,
|
| bshanks@96 | 365 salient spatial patterns in the gene expression which have not yet been
|
| bshanks@96 | 366 captured by any stain. Therefore, cortical anatomy needs to incorpo-
|
| bshanks@96 | 367 rate what we can learn from looking at the patterns of gene expression.
|
| bshanks@96 | 368 While we do not here propose to analyze human gene expression
|
| bshanks@96 | 369 data, it is conceivable that the methods we propose to develop could
|
| bshanks@96 | 370 be used to suggest modifications to the human cortical map as well. In
|
| bshanks@96 | 371 fact, the methods we will develop will be applicable to other datasets
|
| bshanks@96 | 372 beyond the brain. We will provide an open-source toolbox to allow
|
| bshanks@96 | 373 other researchers to easily use our methods. With these methods, re-
|
| bshanks@96 | 374 searchers with gene expression for any area of the body will be able to
|
| bshanks@96 | 375 efficiently find marker genes for anatomical regions, or to use gene expression to discover new anatomical pat-
|
| bshanks@96 | 376 terning. As described above, marker genes have a variety of uses in the development of drugs and experimental
|
| bshanks@96 | 377 manipulations, and in the anatomical characterization of tissue samples. The discovery of new ways to carve up
|
| bshanks@96 | 378 anatomical structures into regions may lead to the discovery of new anatomical subregions in various structures,
|
| bshanks@96 | 379 _________________________________________
|
| bshanks@96 | 380 15In both cases, the cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer
|
| bshanks@96 | 381 are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a
|
| bshanks@96 | 382 pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas (there may be clusters
|
| bshanks@96 | 383 which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area intersection
|
| bshanks@96 | 384 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 | 385 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 | 386 (pairwise voxel correlation) clustering around the seed.
|
| bshanks@96 | 387 which will widely impact all areas of biology.
|
| bshanks@75 | 388
|
| bshanks@96 | 389 Figure 2: Gene Pitx2
|
| bshanks@96 | 390 is selectively underex-
|
| bshanks@96 | 391 pressed in area SS. Although our particular application involves the 3D spatial distribution of gene ex-
|
| bshanks@96 | 392 pression, we anticipate that the methods developed in aims (1) and (2) will not be limited
|
| bshanks@96 | 393 to gene expression data, but rather will generalize to any sort of high-dimensional data
|
| bshanks@96 | 394 over points located in a low-dimensional space.
|
| bshanks@96 | 395 The approach: Preliminary Studies
|
| bshanks@93 | 396 Format conversion between SEV, MATLAB, NIFTI
|
| bshanks@96 | 397 We have created software to (politely) download all of the SEV files16 from the Allen
|
| bshanks@96 | 398 Institute website. We have also created software to convert between the SEV, MATLAB,
|
| bshanks@96 | 399 and NIFTI file formats, as well as some of Caret’s file formats.
|
| bshanks@93 | 400 Flatmap of cortex
|
| bshanks@96 | 401 We downloaded the ABA data and applied a mask to select only those voxels which
|
| bshanks@96 | 402 belong to cerebral cortex. We divided the cortex into hemispheres.
|
| bshanks@96 | 403 Using Caret[7], we created a mesh representation of the surface of the selected voxels. For each gene, and
|
| bshanks@96 | 404 for each node of the mesh, we calculated an average of the gene expression of the voxels “underneath” that
|
| bshanks@96 | 405 mesh node. We then flattened the cortex, creating a two-dimensional mesh.
|
| bshanks@85 | 406
|
| bshanks@85 | 407
|
| bshanks@96 | 408 Figure 3: The top row shows the two
|
| bshanks@96 | 409 genes which (individually) best predict
|
| bshanks@96 | 410 area AUD, according to logistic regres-
|
| bshanks@96 | 411 sion. The bottom row shows the two
|
| bshanks@96 | 412 genes which (individually) best match
|
| bshanks@96 | 413 area AUD, according to gradient sim-
|
| bshanks@96 | 414 ilarity. From left to right and top to
|
| bshanks@96 | 415 bottom, the genes are Ssr1, Efcbp1,
|
| bshanks@96 | 416 Ptk7, and Aph1a. We sampled the nodes of the irregular, flat mesh in order to create
|
| bshanks@96 | 417 a regular grid of pixel values. We converted this grid into a MATLAB
|
| bshanks@96 | 418 matrix.
|
| bshanks@96 | 419 We manually traced the boundaries of each of 49 cortical areas
|
| bshanks@96 | 420 from the ABA coronal reference atlas slides. We then converted these
|
| bshanks@96 | 421 manual traces into Caret-format regional boundary data on the mesh
|
| bshanks@96 | 422 surface. We projected the regions onto the 2-d mesh, and then onto
|
| bshanks@96 | 423 the grid, and then we converted the region data into MATLAB format.
|
| bshanks@96 | 424 At this point, the data are in the form of a number of 2-D matrices,
|
| bshanks@96 | 425 all in registration, with the matrix entries representing a grid of points
|
| bshanks@96 | 426 (pixels) over the cortical surface:
|
| bshanks@96 | 427 ∙ A 2-D matrix whose entries represent the regional label associ-
|
| bshanks@96 | 428 ated with each surface pixel
|
| bshanks@96 | 429 ∙ For each gene, a 2-D matrix whose entries represent the average
|
| bshanks@96 | 430 expression level underneath each surface pixel
|
| bshanks@96 | 431 We created a normalized version of the gene expression data by
|
| bshanks@96 | 432 subtracting each gene’s mean expression level (over all surface pixels)
|
| bshanks@96 | 433 and dividing the expression level of each gene by its standard deviation.
|
| bshanks@96 | 434 The features and the target area are both functions on the surface
|
| bshanks@96 | 435 pixels. They can be referred to as scalar fields over the space of sur-
|
| bshanks@96 | 436 face pixels; alternately, they can be thought of as images which can be
|
| bshanks@96 | 437 displayed on the flatmapped surface.
|
| bshanks@96 | 438 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix
|
| bshanks@96 | 439 for each cortical layer to represent the average expression level within that layer. Cortical layers are found at
|
| bshanks@96 | 440 different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have
|
| bshanks@96 | 441 extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary.
|
| bshanks@96 | 442 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have
|
| bshanks@96 | 443 manually demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.
|
| bshanks@96 | 444 _________________________________________
|
| bshanks@96 | 445 16SEV is a sparse format for spatial data. It is the format in which the ABA data is made available.
|
| bshanks@94 | 446 Feature selection and scoring methods
|
| bshanks@96 | 447 Underexpression of a gene can serve as a marker Underexpression of a gene can sometimes serve as a
|
| bshanks@96 | 448 marker. See, for example, Figure 2.
|
| bshanks@93 | 449
|
| bshanks@93 | 450
|
| bshanks@96 | 451 Figure 4: Upper left: wwc1. Upper
|
| bshanks@96 | 452 right: mtif2. Lower left: wwc1 + mtif2
|
| bshanks@96 | 453 (each pixel’s value on the lower left is
|
| bshanks@96 | 454 the sum of the corresponding pixels in
|
| bshanks@96 | 455 the upper row). Correlation Recall that the instances are surface pixels, and con-
|
| bshanks@96 | 456 sider the problem of attempting to classify each instance as either a
|
| bshanks@96 | 457 member of a particular anatomical area, or not. The target area can be
|
| bshanks@96 | 458 represented as a boolean mask over the surface pixels.
|
| bshanks@96 | 459 One class of feature selection scoring methods contains methods
|
| bshanks@96 | 460 which calculate some sort of “match” between each gene image and
|
| bshanks@96 | 461 the target image. Those genes which match the best are good candi-
|
| bshanks@96 | 462 dates for features.
|
| bshanks@96 | 463 One of the simplest methods in this class is to use correlation as
|
| bshanks@96 | 464 the match score. We calculated the correlation between each gene
|
| bshanks@96 | 465 and each cortical area. The top row of Figure 1 shows the three genes
|
| bshanks@96 | 466 most correlated with area SS.
|
| bshanks@96 | 467 Conditional entropy An information-theoretic scoring method is
|
| bshanks@96 | 468 to find features such that, if the features (gene expression levels) are
|
| bshanks@96 | 469 known, uncertainty about the target (the regional identity) is reduced.
|
| bshanks@96 | 470 Entropy measures uncertainty, so what we want is to find features such
|
| bshanks@96 | 471 that the conditional distribution of the target has minimal entropy. The
|
| bshanks@96 | 472 distribution to which we are referring is the probability distribution over
|
| bshanks@96 | 473 the population of surface pixels.
|
| bshanks@96 | 474 The simplest way to use information theory is on discrete data, so we discretized our gene expression data
|
| bshanks@96 | 475 by creating, for each gene, five thresholded boolean masks of the gene data. For each gene, we created a
|
| bshanks@96 | 476 boolean mask of its expression levels using each of these thresholds: the mean of that gene, the mean minus
|
| bshanks@96 | 477 one standard deviation, the mean minus two standard deviations, the mean plus one standard deviation, the
|
| bshanks@96 | 478 mean plus two standard deviations.
|
| bshanks@96 | 479 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene
|
| bshanks@96 | 480 expression boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon
|
| bshanks@96 | 481 the pair of gene expression boolean masks, is minimized.
|
| bshanks@96 | 482 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the
|
| bshanks@96 | 483 question, “Is this surface pixel a member of the target area?”. Its advantage over linear methods such as logistic
|
| bshanks@96 | 484 regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables
|
| bshanks@96 | 485 predicts the target, conditional entropy would notice, whereas linear methods would not.
|
| bshanks@96 | 486 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found
|
| bshanks@96 | 487 genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed
|
| bshanks@96 | 488 a non-pointwise local scoring method to detect when a gene had a pattern of expression which looked like it had
|
| bshanks@96 | 489 a boundary whose shape is similar to the shape of the target region. We call this scoring method “gradient
|
| bshanks@96 | 490 similarity”.
|
| bshanks@96 | 491 One might say that gradient similarity attempts to measure how much the border of the area of gene expres-
|
| bshanks@96 | 492 sion and the border of the target region overlap. However, since gene expression falls off continuously rather
|
| bshanks@96 | 493 than jumping from its maximum value to zero, the spatial pattern of a gene’s expression often does not have a
|
| bshanks@96 | 494 discrete border. Therefore, instead of looking for a discrete border, we look for large gradients. Gradient similarity
|
| bshanks@96 | 495 is a symmetric function over two images (i.e. two scalar fields). It is is high to the extent that matching pixels
|
| bshanks@96 | 496 which have large values and large gradients also have gradients which are oriented in a similar direction. The
|
| bshanks@96 | 497 formula is:
|
| bshanks@96 | 498 ∑
|
| bshanks@96 | 499 pixel<img src="cmsy8-32.png" alt="∈" />pixels cos(abs(∠∇1 -∠∇2)) ⋅|∇1| + |∇2|
|
| bshanks@96 | 500 2 ⋅ pixel_value1 + pixel_value2
|
| bshanks@96 | 501 2
|
| bshanks@96 | 502
|
| bshanks@85 | 503
|
| bshanks@85 | 504
|
| bshanks@85 | 505
|
| bshanks@85 | 506
|
| bshanks@96 | 507 Figure 5: From left to right and top
|
| bshanks@96 | 508 to bottom, single genes which roughly
|
| bshanks@96 | 509 identify areas SS (somatosensory pri-
|
| bshanks@96 | 510 mary + supplemental), SSs (supple-
|
| bshanks@96 | 511 mental somatosensory), PIR (piriform),
|
| bshanks@96 | 512 FRP (frontal pole), RSP (retrosple-
|
| bshanks@96 | 513 nial), COApm (Cortical amygdalar, pos-
|
| bshanks@96 | 514 terior part, medial zone). Grouping
|
| bshanks@96 | 515 some areas together, we have also
|
| bshanks@96 | 516 found genes to identify the groups
|
| bshanks@85 | 517 ACA+PL+ILA+DP+ORB+MO (anterior
|
| bshanks@96 | 518 cingulate, prelimbic, infralimbic, dor-
|
| bshanks@96 | 519 sal peduncular, orbital, motor), poste-
|
| bshanks@96 | 520 rior and lateral visual (VISpm, VISpl,
|
| bshanks@96 | 521 VISI, VISp; posteromedial, posterolat-
|
| bshanks@96 | 522 eral, lateral, and primary visual; the
|
| bshanks@96 | 523 posterior and lateral visual area is dis-
|
| bshanks@96 | 524 tinguished from its neighbors, but not
|
| bshanks@96 | 525 from the entire rest of the cortex). The
|
| bshanks@96 | 526 genes are Pitx2, Aldh1a2, Ppfibp1,
|
| bshanks@96 | 527 Slco1a5, Tshz2, Trhr, Col12a1, Ets1. where ∇1 and ∇2 are the gradient vectors of the two images at the
|
| bshanks@96 | 528 current pixel; ∠∇i is the angle of the gradient of image i at the current
|
| bshanks@96 | 529 pixel; |∇i| is the magnitude of the gradient of image i at the current
|
| bshanks@96 | 530 pixel; and pixel_valuei is the value of the current pixel in image i.
|
| bshanks@96 | 531 The intuition is that we want to see if the borders of the pattern in
|
| bshanks@96 | 532 the two images are similar; if the borders are similar, then both images
|
| bshanks@96 | 533 will have corresponding pixels with large gradients (because this is a
|
| bshanks@96 | 534 border) which are oriented in a similar direction (because the borders
|
| bshanks@96 | 535 are similar).
|
| bshanks@93 | 536 Most of the genes in Figure 5 were identified via gradient similarity.
|
| bshanks@96 | 537 Gradient similarity provides information complementary to
|
| bshanks@96 | 538 correlation
|
| bshanks@96 | 539 To show that gradient similarity can provide useful information that
|
| bshanks@96 | 540 cannot be detected via pointwise analyses, consider Fig. 3. The top
|
| bshanks@96 | 541 row of Fig. 3 displays the 3 genes which most match area AUD, ac-
|
| bshanks@96 | 542 cording to a pointwise method17. The bottom row displays the 3 genes
|
| bshanks@96 | 543 which most match AUD according to a method which considers local
|
| bshanks@96 | 544 geometry18 The pointwise method in the top row identifies genes which
|
| bshanks@96 | 545 express more strongly in AUD than outside of it; its weakness is that
|
| bshanks@96 | 546 this includes many areas which don’t have a salient border matching
|
| bshanks@96 | 547 the areal border. The geometric method identifies genes whose salient
|
| bshanks@96 | 548 expression border seems to partially line up with the border of AUD;
|
| bshanks@96 | 549 its weakness is that this includes genes which don’t express over the
|
| bshanks@96 | 550 entire area. Genes which have high rankings using both pointwise and
|
| bshanks@96 | 551 border criteria, such as Aph1a in the example, may be particularly good
|
| bshanks@96 | 552 markers. None of these genes are, individually, a perfect marker for
|
| bshanks@96 | 553 AUD; we deliberately chose a “difficult” area in order to better contrast
|
| bshanks@96 | 554 pointwise with geometric methods.
|
| bshanks@96 | 555 Areas which can be identified by single genes Using gradient
|
| bshanks@96 | 556 similarity, we have already found single genes which roughly identify
|
| bshanks@96 | 557 some areas and groupings of areas. For each of these areas, an ex-
|
| bshanks@96 | 558 ample of a gene which roughly identifies it is shown in Figure 5. We
|
| bshanks@96 | 559 have not yet cross-verified these genes in other atlases.
|
| bshanks@96 | 560 In addition, there are a number of areas which are almost identified
|
| bshanks@96 | 561 by single genes: COAa+NLOT (anterior part of cortical amygdalar area,
|
| bshanks@96 | 562 nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral
|
| bshanks@96 | 563 anterior cingulate), VIS (visual), AUD (auditory).
|
| bshanks@96 | 564 These results validate our expectation that the ABA dataset can
|
| bshanks@96 | 565 be exploited to find marker genes for many cortical areas, while also
|
| bshanks@96 | 566 validating the relevancy of our new scoring method, gradient similarity.
|
| bshanks@96 | 567 Combinations of multiple genes are useful and necessary for
|
| bshanks@96 | 568 some areas
|
| bshanks@96 | 569 In Figure 4, we give an example of a cortical area which is not
|
| bshanks@96 | 570 marked by any single gene, but which can be identified combinatorially.
|
| bshanks@96 | 571 Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on
|
| bshanks@96 | 572 the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure 4 shows wwc1’s spatial
|
| bshanks@92 | 573 _________________________________________
|
| bshanks@96 | 574 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 | 575 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 | 576 in terms of how well they predict area AUD.
|
| bshanks@96 | 577 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 | 578 area AUD, was calculated, and this was used to rank the genes.
|
| bshanks@96 | 579 expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene,
|
| bshanks@96 | 580 but the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the
|
| bshanks@96 | 581 area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the dorsal surface.
|
| bshanks@96 | 582 Gene mtif2 is shown in the upper-right. Mtif2 captures MO’s upper-left boundary, but not its lower-right boundary.
|
| bshanks@96 | 583 Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these
|
| bshanks@96 | 584 two figures, we get the lower-left image. This combination captures area MO much better than any single gene.
|
| bshanks@96 | 585 This shows that our proposal to develop a method to find combinations of marker genes is both possible and
|
| bshanks@96 | 586 necessary.
|
| bshanks@96 | 587 Feature selection integrated with prediction As noted earlier, in general, any classifier can be used for fea-
|
| bshanks@96 | 588 ture selection by running it inside a stepwise wrapper. Also, some learning algorithms integrate soft constraints
|
| bshanks@96 | 589 on number of features used. Examples of both of these will be seen in the section “Multivariate supervised
|
| bshanks@96 | 590 learning”.
|
| bshanks@94 | 591 Multivariate supervised learning
|
| bshanks@60 | 592
|
| bshanks@69 | 593
|
| bshanks@69 | 594
|
| bshanks@69 | 595
|
| bshanks@96 | 596 Figure 6: First row: the first 6 reduced dimensions, using PCA. Sec-
|
| bshanks@96 | 597 ond row: the first 6 reduced dimensions, using NNMF. Third row:
|
| bshanks@96 | 598 the first six reduced dimensions, using landmark Isomap. Bottom
|
| bshanks@96 | 599 row: examples of kmeans clustering applied to reduced datasets
|
| bshanks@96 | 600 to find 7 clusters. Left: 19 of the major subdivisions of the cortex.
|
| bshanks@96 | 601 Second from left: PCA. Third from left: NNMF. Right: Landmark
|
| bshanks@96 | 602 Isomap. Additional details: In the third and fourth rows, 7 dimen-
|
| bshanks@96 | 603 sions were found, but only 6 displayed. In the last row: for PCA,
|
| bshanks@96 | 604 50 dimensions were used; for NNMF, 6 dimensions were used; for
|
| bshanks@96 | 605 landmark Isomap, 7 dimensions were used. Forward stepwise logistic regression
|
| bshanks@96 | 606 Logistic regression is a popular method
|
| bshanks@96 | 607 for predictive modeling of categorial data.
|
| bshanks@96 | 608 As a pilot run, for five cortical areas (SS,
|
| bshanks@96 | 609 AUD, RSP, VIS, and MO), we performed
|
| bshanks@96 | 610 forward stepwise logistic regression to find
|
| bshanks@96 | 611 single genes, pairs of genes, and triplets
|
| bshanks@96 | 612 of genes which predict areal identify. This
|
| bshanks@96 | 613 is an example of feature selection inte-
|
| bshanks@96 | 614 grated with prediction using a stepwise
|
| bshanks@96 | 615 wrapper. Some of the single genes found
|
| bshanks@96 | 616 were shown in various figures throughout
|
| bshanks@96 | 617 this document, and Figure 4 shows a com-
|
| bshanks@96 | 618 bination of genes which was found.
|
| bshanks@96 | 619 We felt that, for single genes, gradi-
|
| bshanks@96 | 620 ent similarity did a better job than logistic
|
| bshanks@96 | 621 regression at capturing our subjective im-
|
| bshanks@96 | 622 pression of a “good gene”.
|
| bshanks@96 | 623 SVM on all genes at once
|
| bshanks@96 | 624 In order to see how well one can do
|
| bshanks@96 | 625 when looking at all genes at once, we ran
|
| bshanks@96 | 626 a support vector machine to classify corti-
|
| bshanks@96 | 627 cal surface pixels based on their gene ex-
|
| bshanks@96 | 628 pression profiles. We achieved classifica-
|
| bshanks@96 | 629 tion accuracy of about 81%19. This shows
|
| bshanks@96 | 630 that the genes included in the ABA dataset
|
| bshanks@96 | 631 are sufficient to define much of cortical
|
| bshanks@96 | 632 anatomy. However, as noted above, a clas-
|
| bshanks@96 | 633 sifier that looks at all the genes at once isn’t
|
| bshanks@96 | 634 as practically useful as a classifier that uses only a few genes.
|
| bshanks@94 | 635 _________________________________________
|
| bshanks@96 | 636 195-fold cross-validation.
|
| bshanks@96 | 637 Data-driven redrawing of the cortical map
|
| bshanks@96 | 638 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene
|
| bshanks@96 | 639 expression profile associated with each pixel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-
|
| bshanks@96 | 640 Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment
|
| bshanks@96 | 641 (LTSA), Stochastic Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative
|
| bshanks@96 | 642 Matrix Factorization (NNMF). Space constraints prevent us from showing many of the results, but as a sample,
|
| bshanks@96 | 643 PCA, NNMF, and landmark Isomap are shown in the first, second, and third rows of Figure 6.
|
| bshanks@96 | 644 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we
|
| bshanks@96 | 645 have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are
|
| bshanks@96 | 646 shown in the last row of Figure 6. To compare, the leftmost picture on the bottom row of Figure 6 shows some
|
| bshanks@96 | 647 of the major subdivisions of cortex. These results clearly show that different dimensionality reduction techniques
|
| bshanks@96 | 648 capture different aspects of the data and lead to different clusterings, indicating the utility of our proposal to
|
| bshanks@96 | 649 produce a detailed comparion of these techniques as applied to the domain of genomic anatomy.
|
| bshanks@71 | 650
|
| bshanks@96 | 651 Figure 7: Prototypes corresponding to sample gene
|
| bshanks@96 | 652 clusters, clustered by gradient similarity. Region bound-
|
| bshanks@96 | 653 aries for the region that most matches each prototype
|
| bshanks@96 | 654 are overlayed. Many areas are captured by clusters of genes
|
| bshanks@96 | 655 We also clustered the genes using gradient similarity
|
| bshanks@96 | 656 to see if the spatial regions defined by any clusters
|
| bshanks@96 | 657 matched known anatomical regions. Figure 7 shows,
|
| bshanks@96 | 658 for ten sample gene clusters, each cluster’s average
|
| bshanks@96 | 659 expression pattern, compared to a known anatomical
|
| bshanks@96 | 660 boundary. This suggests that it is worth attempting to
|
| bshanks@96 | 661 cluster genes, and then to use the results to cluster
|
| bshanks@96 | 662 pixels.
|
| bshanks@92 | 663 The approach: what we plan to do
|
| bshanks@92 | 664 Flatmap cortex and segment cortical layers
|
| bshanks@96 | 665 There are multiple ways to flatten 3-D data into 2-D.
|
| bshanks@96 | 666 We will compare mappings from manifolds to planes
|
| bshanks@96 | 667 which attempt to preserve size (such as the one used
|
| bshanks@96 | 668 by Caret[7]) with mappings which preserve angle (conformal maps). Our method will include a statistical test
|
| bshanks@96 | 669 that warns the user if the assumption of 2-D structure seems to be wrong.
|
| bshanks@96 | 670 We have not yet made use of radial profiles. While the radial profiles may be used “raw”, for laminar structures
|
| bshanks@96 | 671 like the cortex another strategy is to group together voxels in the same cortical layer; each surface pixel would
|
| bshanks@96 | 672 then be associated with one expression level per gene per layer. We will develop a segmentation algorithm to
|
| bshanks@96 | 673 automatically identify the layer boundaries.
|
| bshanks@30 | 674 Develop algorithms that find genetic markers for anatomical regions
|
| bshanks@96 | 675 Scoring measures and feature selection We will develop scoring methods for evaluating how good individual
|
| bshanks@96 | 676 genes are at marking areas. We will compare pointwise, geometric, and information-theoretic measures. We
|
| bshanks@96 | 677 already developed one entirely new scoring method (gradient similarity), but we may develop more. Scoring
|
| bshanks@96 | 678 measures that we will explore will include the L1 norm, correlation, expression energy ratio, conditional entropy,
|
| bshanks@96 | 679 gradient similarity, Jaccard similarity, Dice similarity, Hough transform, and statistical tests such as Student’s t-
|
| bshanks@96 | 680 test, and the Mann-Whitney U test (a non-parametric test). In addition, any classifier induces a scoring measure
|
| bshanks@96 | 681 on genes by taking the prediction error when using that gene to predict the target.
|
| bshanks@96 | 682 Using some combination of these measures, we will develop a procedure to find single marker genes for
|
| bshanks@96 | 683 anatomical regions: for each cortical area, we will rank the genes by their ability to delineate each area. We
|
| bshanks@96 | 684 will quantitatively compare the list of single genes generated by our method to the lists generated by previous
|
| bshanks@96 | 685 methods which are mentioned in Aim 1 Related Work.
|
| bshanks@96 | 686 Some cortical areas have no single marker genes but can be identified by combinatorial coding. This requires
|
| bshanks@96 | 687 multivariate scoring measures and feature selection procedures. Many of the measures, such as expression
|
| bshanks@96 | 688 energy, gradient similarity, Jaccard, Dice, Hough, Student’s t, and Mann-Whitney U are univariate. We will extend
|
| bshanks@96 | 689 these scoring measures for use in multivariate feature selection, that is, for scoring how well combinations of
|
| bshanks@96 | 690 genes, rather than individual genes, can distinguish a target area. There are existing multivariate forms of some
|
| bshanks@96 | 691 of the univariate scoring measures, for example, Hotelling’s T-square is a multivariate analog of Student’s t.
|
| bshanks@96 | 692 We will develop a feature selection procedure for choosing the best small set of marker genes for a given
|
| bshanks@96 | 693 anatomical area. In addition to using the scoring measures that we develop, we will also explore (a) feature
|
| bshanks@96 | 694 selection using a stepwise wrapper over “vanilla” classifiers such as logistic regression, (b) supervised learning
|
| bshanks@96 | 695 methods such as decision trees which incrementally/greedily combine single gene markers into sets, and (c)
|
| bshanks@96 | 696 supervised learning methods which use soft constraints to minimize number of features used, such as sparse
|
| bshanks@96 | 697 support vector machines.
|
| bshanks@96 | 698 Since errors of displacement and of shape may cause genes and target areas to match less than they should,
|
| bshanks@96 | 699 we will consider the robustness of feature selection methods in the presence of error. Some of these methods,
|
| bshanks@96 | 700 such as the Hough transform, are designed to be resistant in the presence of error, but many are not. We will
|
| bshanks@96 | 701 consider extensions to scoring measures that may improve their robustness; for example, a wrapper that runs a
|
| bshanks@96 | 702 scoring method on small displacements and distortions of the data adds robustness to registration error at the
|
| bshanks@96 | 703 expense of computation time.
|
| bshanks@96 | 704 An area may be difficult to identify because the boundaries are misdrawn in the atlas, or because the shape
|
| bshanks@96 | 705 of the natural domain of gene expression corresponding to the area is different from the shape of the area as
|
| bshanks@96 | 706 recognized by anatomists. We will extend our procedure to handle difficult areas by combining areas or redrawing
|
| bshanks@96 | 707 their boundaries. We will develop extensions to our procedure which (a) detect when a difficult area could be
|
| bshanks@96 | 708 fit if its boundary were redrawn slightly20, and (b) detect when a difficult area could be combined with adjacent
|
| bshanks@96 | 709 areas to create a larger area which can be fit.
|
| bshanks@96 | 710 A future publication on the method that we develop in Aim 1 will review the scoring measures and quantita-
|
| bshanks@96 | 711 tively compare their performance in order to provide a foundation for future research of methods of marker gene
|
| bshanks@96 | 712 finding. We will measure the robustness of the scoring measures as well as their absolute performance on our
|
| bshanks@96 | 713 dataset.
|
| bshanks@96 | 714 Classifiers We will explore and compare different classifiers. As noted above, this activity is not separate
|
| bshanks@96 | 715 from the previous one, because some supervised learning algorithms include feature selection, and any clas-
|
| bshanks@96 | 716 sifier can be combined with a stepwise wrapper for use as a feature selection method. We will explore logistic
|
| bshanks@96 | 717 regression (including spatial models[16]), decision trees21, sparse SVMs, generative mixture models (including
|
| bshanks@96 | 718 naive bayes), kernel density estimation, instance-based learning methods (such as k-nearest neighbor), genetic
|
| bshanks@96 | 719 algorithms, and artificial neural networks.
|
| bshanks@30 | 720 Develop algorithms to suggest a division of a structure into anatomical parts
|
| bshanks@96 | 721 Explore dimensionality reduction on gene expression profiles We have already described the application
|
| bshanks@96 | 722 of ten dimensionality reduction algorithms for the purpose of replacing the gene expression profiles, which are
|
| bshanks@96 | 723 vectors of about 4000 gene expression levels, with a smaller number of features. We plan to further explore
|
| bshanks@96 | 724 and interpret these results, as well as to apply other unsupervised learning algorithms, including independent
|
| bshanks@96 | 725 components analysis, self-organizing maps, and generative models such as deep Boltzmann machines. We
|
| bshanks@96 | 726 will explore ways to quantitatively compare the relevance of the different dimensionality reduction methods for
|
| bshanks@96 | 727 identifying cortical areal boundaries.
|
| bshanks@96 | 728 Explore dimensionality reduction on pixels Instead of applying dimensionality reduction to the gene ex-
|
| bshanks@94 | 729 _________________________________________
|
| bshanks@96 | 730 20Not just any redrawing is acceptable, only those which appear to be justified as a natural spatial domain of gene expression by
|
| bshanks@96 | 731 multiple sources of evidence. Interestingly, the need to detect “natural spatial domains of gene expression” in a data-driven fashion
|
| bshanks@96 | 732 means that the methods of Aim 2 might be useful in achieving Aim 1, as well – particularly discriminative dimensionality reduction.
|
| bshanks@96 | 733 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 | 734 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 | 735 too large. We plan to implement a pruning procedure to generate trees that use fewer genes.
|
| bshanks@96 | 736 pression profiles, the same techniques can be applied instead to the pixels22. It is possible that the features
|
| bshanks@96 | 737 generated in this way by some dimensionality reduction techniques will directly correspond to interesting spatial
|
| bshanks@96 | 738 regions.
|
| bshanks@96 | 739 Explore clustering and segmentation algorithms on pixels We will explore clustering and segmenta-
|
| bshanks@96 | 740 tion algorithms in order to segment the pixels into regions. We will explore k-means, spectral clustering, gene
|
| bshanks@96 | 741 shaving[9], recursive division clustering, multivariate generalizations of edge detectors, multivariate generaliza-
|
| bshanks@96 | 742 tions of watershed transformations, region growing, active contours, graph partitioning methods, and recursive
|
| bshanks@96 | 743 agglomerative clustering with various linkage functions. These methods can be combined with dimensionality
|
| bshanks@96 | 744 reduction.
|
| bshanks@96 | 745 Explore clustering on genes We have already shown that the procedure of clustering genes according to
|
| bshanks@96 | 746 gradient similarity, and then creating an averaged prototype of each cluster’s expression pattern, yields some
|
| bshanks@96 | 747 spatial patterns which match cortical areas. We will further explore the clustering of genes.
|
| bshanks@96 | 748 In addition to using the cluster expression prototypes directly to identify spatial regions, this might be useful
|
| bshanks@96 | 749 as a component of dimensionality reduction. For example, one could imagine clustering similar genes and then
|
| bshanks@96 | 750 replacing their expression levels with a single average expression level, thereby removing some redundancy from
|
| bshanks@96 | 751 the gene expression profiles. One could then perform clustering on pixels (possibly after a second dimensionality
|
| bshanks@96 | 752 reduction step) in order to identify spatial regions. It remains to be seen whether removal of redundancy would
|
| bshanks@96 | 753 help or hurt the ultimate goal of identifying interesting spatial regions.
|
| bshanks@96 | 754 Explore co-clustering There are some algorithms which simultaineously incorporate clustering on instances
|
| bshanks@96 | 755 and on features (in our case, genes and pixels), for example, IRM[11]. These are called co-clustering or biclus-
|
| bshanks@96 | 756 tering algorithms.
|
| bshanks@96 | 757 Quantitatively compare different methods In order to tell which method is best for genomic anatomy, for
|
| bshanks@96 | 758 each experimental method we will compare the cortical map found by unsupervised learning to a cortical map
|
| bshanks@96 | 759 derived from the Allen Reference Atlas. In order to compare the experimental clustering with the reference
|
| bshanks@96 | 760 clustering, we will explore various quantitative metrics that purport to measure how similar two clusterings are,
|
| bshanks@96 | 761 such as Jaccard, Rand index, Fowlkes-Mallows, variation of information, Larsen, Van Dongen, and others.
|
| bshanks@96 | 762 Discriminative dimensionality reduction In addition to using a purely data-driven approach to identify
|
| bshanks@96 | 763 spatial regions, it might be useful to see how well the known regions can be reconstructed from a small number
|
| bshanks@96 | 764 of features, even if those features are chosen by using knowledge of the regions. For example, linear discriminant
|
| bshanks@96 | 765 analysis could be used as a dimensionality reduction technique in order to identify a few features which are the
|
| bshanks@96 | 766 best linear summary of gene expression profiles for the purpose of discriminating between regions. This reduced
|
| bshanks@96 | 767 feature set could then be used to cluster pixels into regions. Perhaps the resulting clusters will be similar to the
|
| bshanks@96 | 768 reference atlas, yet more faithful to natural spatial domains of gene expression than the reference atlas is.
|
| bshanks@96 | 769 Apply the new methods to the cortex
|
| bshanks@96 | 770 Using the methods developed in Aim 1, we will present, for each cortical area, a short list of markers to identify
|
| bshanks@96 | 771 that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once.
|
| bshanks@96 | 772 Because in most cases the ABA coronal dataset only contains one ISH per gene, it is possible for an unrelated
|
| bshanks@96 | 773 combination of genes to seem to identify an area when in fact it is only coincidence. There are two ways we will
|
| bshanks@96 | 774 validate our marker genes to guard against this. First, we will confirm that putative combinations of marker genes
|
| bshanks@96 | 775 express the same pattern in both hemispheres. Second, we will manually validate our final results on other gene
|
| bshanks@96 | 776 expression datasets such as EMAGE, GeneAtlas, and GENSAT.
|
| bshanks@96 | 777 Using the methods developed in Aim 2, we will present one or more hierarchial cortical maps. We will identify
|
| bshanks@96 | 778 and explain how the statistical structure in the gene expression data led to any unexpected or interesting features
|
| bshanks@96 | 779 _________________________________________
|
| bshanks@96 | 780 22Consider a matrix whose rows represent pixel locations, and whose columns represent genes. An entry in this matrix represents the
|
| bshanks@96 | 781 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 | 782 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 | 783 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 | 784 used to replace a large number of pixels with a small number of features.
|
| bshanks@96 | 785 of these maps, and we will provide biological hypotheses to interpret any new cortical areas, or groupings of
|
| bshanks@96 | 786 areas, which are discovered.
|
| bshanks@87 | 787 Timeline and milestones
|
| bshanks@90 | 788 Finding marker genes
|
| bshanks@96 | 789 September-November 2009: Develop an automated mechanism for segmenting the cortical voxels into layers
|
| bshanks@96 | 790 November 2009 (milestone): Have completed construction of a flatmapped, cortical dataset with information
|
| bshanks@96 | 791 for each layer
|
| bshanks@96 | 792 October 2009-April 2010: Develop scoring methods and to test them in various supervised learning frameworks.
|
| bshanks@96 | 793 Also test out various dimensionality reduction schemes in combination with supervised learning. create or extend
|
| bshanks@96 | 794 supervised learning frameworks which use multivariate versions of the best scoring methods.
|
| bshanks@96 | 795 January 2010 (milestone): Submit a publication on single marker genes for cortical areas
|
| bshanks@96 | 796 February-July 2010: Continue to develop scoring methods and supervised learning frameworks. Explore the
|
| bshanks@96 | 797 best way to integrate radial profiles with supervised learning. Explore the best way to make supervised learning
|
| bshanks@96 | 798 techniques robust against incorrect labels (i.e. when the areas drawn on the input cortical map are slightly
|
| bshanks@96 | 799 off). Quantitatively compare the performance of different supervised learning techniques. Validate marker genes
|
| bshanks@96 | 800 found in the ABA dataset by checking against other gene expression datasets. Create documentation and unit
|
| bshanks@96 | 801 tests for software toolbox for Aim 1. Respond to user bug reports for Aim 1 software toolbox.
|
| bshanks@96 | 802 June 2010 (milestone): Submit a paper describing a method fulfilling Aim 1. Release toolbox.
|
| bshanks@96 | 803 July 2010 (milestone): Submit a paper describing combinations of marker genes for each cortical area, and a
|
| bshanks@96 | 804 small number of marker genes that can, in combination, define most of the areas at once
|
| bshanks@90 | 805 Revealing new ways to parcellate a structure into regions
|
| bshanks@96 | 806 June 2010-March 2011: Explore dimensionality reduction algorithms for Aim 2. Explore standard hierarchial
|
| bshanks@96 | 807 clustering algorithms, used in combination with dimensionality reduction, for Aim 2. Explore co-clustering algo-
|
| bshanks@96 | 808 rithms. Think about how radial profile information can be used for Aim 2. Adapt clustering algorithms to use radial
|
| bshanks@96 | 809 profile information. Quantitatively compare the performance of different dimensionality reduction and clustering
|
| bshanks@96 | 810 techniques. Quantitatively compare the value of different flatmapping methods and ways of representing radial
|
| bshanks@96 | 811 profiles.
|
| bshanks@96 | 812 March 2011 (milestone): Submit a paper describing a method fulfilling Aim 2. Release toolbox.
|
| bshanks@96 | 813 February-May 2011: Using the methods developed for Aim 2, explore the genomic anatomy of the cortex. If
|
| bshanks@96 | 814 new ways of organizing the cortex into areas are discovered, read the literature and talk to people to learn about
|
| bshanks@96 | 815 research related to interpreting our results. Create documentation and unit tests for software toolbox for Aim 2.
|
| bshanks@96 | 816 Respond to user bug reports for Aim 2 software toolbox.
|
| bshanks@96 | 817 May 2011 (milestone): Submit a paper on the genomic anatomy of the cortex, using the methods developed in
|
| bshanks@96 | 818 Aim 2
|
| bshanks@96 | 819 May-August 2011: Revisit Aim 1 to see if what was learned during Aim 2 can improve the methods for Aim 1.
|
| bshanks@96 | 820 Follow up on responses to our papers. Possibly submit another paper.
|
| bshanks@33 | 821 Bibliography & References Cited
|
| bshanks@96 | 822 [1]Chris Adamson, Leigh Johnston, Terrie Inder, Sandra Rees, Iven Mareels, and Gary Egan. A Tracking
|
| bshanks@96 | 823 Approach to Parcellation of the Cerebral Cortex, volume Volume 3749/2005 of Lecture Notes in Computer
|
| bshanks@96 | 824 Science, pages 294–301. Springer Berlin / Heidelberg, 2005.
|
| bshanks@96 | 825 [2]J. Annese, A. Pitiot, I. D. Dinov, and A. W. Toga. A myelo-architectonic method for the structural classification
|
| bshanks@96 | 826 of cortical areas. NeuroImage, 21(1):15–26, 2004.
|
| bshanks@96 | 827 [3]Tanya Barrett, Dennis B. Troup, Stephen E. Wilhite, Pierre Ledoux, Dmitry Rudnev, Carlos Evangelista,
|
| bshanks@96 | 828 Irene F. Kim, Alexandra Soboleva, Maxim Tomashevsky, and Ron Edgar. NCBI GEO: mining tens of millions
|
| bshanks@96 | 829 of expression profiles–database and tools update. Nucl. Acids Res., 35(suppl_1):D760–765, 2007.
|
| bshanks@96 | 830 [4]George W. Bell, Tatiana A. Yatskievych, and Parker B. Antin. GEISHA, a whole-mount in situ hybridization
|
| bshanks@96 | 831 gene expression screen in chicken embryos. Developmental Dynamics, 229(3):677–687, 2004.
|
| bshanks@96 | 832 [5]James P Carson, Tao Ju, Hui-Chen Lu, Christina Thaller, Mei Xu, Sarah L Pallas, Michael C Crair, Joe
|
| bshanks@96 | 833 Warren, Wah Chiu, and Gregor Eichele. A digital atlas to characterize the mouse brain transcriptome.
|
| bshanks@96 | 834 PLoS Comput Biol, 1(4):e41, 2005.
|
| bshanks@96 | 835 [6]Mark H. Chin, Alex B. Geng, Arshad H. Khan, Wei-Jun Qian, Vladislav A. Petyuk, Jyl Boline, Shawn Levy,
|
| bshanks@96 | 836 Arthur W. Toga, Richard D. Smith, Richard M. Leahy, and Desmond J. Smith. A genome-scale map of
|
| bshanks@96 | 837 expression for a mouse brain section obtained using voxelation. Physiol. Genomics, 30(3):313–321, August
|
| bshanks@96 | 838 2007.
|
| bshanks@96 | 839 [7]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite
|
| bshanks@96 | 840 for surface-based analyses of cerebral cortex. Journal of the American Medical Informatics Association:
|
| bshanks@96 | 841 JAMIA, 8(5):443–59, 2001. PMID: 11522765.
|
| bshanks@96 | 842 [8]Shiaoching Gong, Chen Zheng, Martin L. Doughty, Kasia Losos, Nicholas Didkovsky, Uta B. Scham-
|
| bshanks@96 | 843 bra, Norma J. Nowak, Alexandra Joyner, Gabrielle Leblanc, Mary E. Hatten, and Nathaniel Heintz. A
|
| bshanks@96 | 844 gene expression atlas of the central nervous system based on bacterial artificial chromosomes. Nature,
|
| bshanks@96 | 845 425(6961):917–925, October 2003.
|
| bshanks@96 | 846 [9]Trevor Hastie, Robert Tibshirani, Michael Eisen, Ash Alizadeh, Ronald Levy, Louis Staudt, Wing Chan,
|
| bshanks@96 | 847 David Botstein, and Patrick Brown. ’Gene shaving’ as a method for identifying distinct sets of genes with
|
| bshanks@96 | 848 similar expression patterns. Genome Biology, 1(2):research0003.1–research0003.21, 2000.
|
| bshanks@96 | 849 [10]Jano Hemert and Richard Baldock. Matching Spatial Regions with Combinations of Interacting Gene Ex-
|
| bshanks@96 | 850 pression Patterns, volume 13 of Communications in Computer and Information Science, pages 347–361.
|
| bshanks@96 | 851 Springer Berlin Heidelberg, 2008.
|
| bshanks@96 | 852 [11]C Kemp, JB Tenenbaum, TL Griffiths, T Yamada, and N Ueda. Learning systems of concepts with an infinite
|
| bshanks@96 | 853 relational model. In AAAI, 2006.
|
| bshanks@96 | 854 [12]F. Kruggel, M. K. Brckner, Th. Arendt, C. J. Wiggins, and D. Y. von Cramon. Analyzing the neocortical
|
| bshanks@96 | 855 fine-structure. Medical Image Analysis, 7(3):251–264, September 2003.
|
| bshanks@96 | 856 [13]Erh-Fang Lee, Jyl Boline, and Arthur W. Toga. A High-Resolution anatomical framework of the neonatal
|
| bshanks@96 | 857 mouse brain for managing gene expression data. Frontiers in Neuroinformatics, 1:6, 2007. PMC2525996.
|
| bshanks@96 | 858 [14]Susan Magdaleno, Patricia Jensen, Craig L. Brumwell, Anna Seal, Karen Lehman, Andrew Asbury, Tony
|
| bshanks@96 | 859 Cheung, Tommie Cornelius, Diana M. Batten, Christopher Eden, Shannon M. Norland, Dennis S. Rice,
|
| bshanks@96 | 860 Nilesh Dosooye, Sundeep Shakya, Perdeep Mehta, and Tom Curran. BGEM: an in situ hybridization
|
| bshanks@96 | 861 database of gene expression in the embryonic and adult mouse nervous system. PLoS Biology, 4(4):e86
|
| bshanks@96 | 862 EP –, April 2006.
|
| bshanks@96 | 863 [15]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Su-
|
| bshanks@96 | 864 san M Sunkin, Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann,
|
| bshanks@96 | 865 David J Anderson, Ed S Lein, Allan R Jones, and Michael Hawrylycz. An anatomic gene expression atlas
|
| bshanks@96 | 866 of the adult mouse brain. Nat Neurosci, 12(3):356–362, March 2009.
|
| bshanks@96 | 867 [16]Christopher J. Paciorek. Computational techniques for spatial logistic regression with large data sets. Com-
|
| bshanks@96 | 868 putational Statistics & Data Analysis, 51(8):3631–3653, May 2007.
|
| bshanks@96 | 869 [17]George Paxinos and Keith B.J. Franklin. The Mouse Brain in Stereotaxic Coordinates. Academic Press, 2
|
| bshanks@96 | 870 edition, July 2001.
|
| bshanks@96 | 871 [18]A. Schleicher, N. Palomero-Gallagher, P. Morosan, S. Eickhoff, T. Kowalski, K. Vos, K. Amunts, and
|
| bshanks@96 | 872 K. Zilles. Quantitative architectural analysis: a new approach to cortical mapping. Anatomy and Em-
|
| bshanks@96 | 873 bryology, 210(5):373–386, December 2005.
|
| bshanks@96 | 874 [19]Oliver Schmitt, Lars Hmke, and Lutz Dmbgen. Detection of cortical transition regions utilizing statistical
|
| bshanks@96 | 875 analyses of excess masses. NeuroImage, 19(1):42–63, May 2003.
|
| bshanks@96 | 876 [20]Constance M. Smith, Jacqueline H. Finger, Terry F. Hayamizu, Ingeborg J. McCright, Janan T. Eppig,
|
| bshanks@96 | 877 James A. Kadin, Joel E. Richardson, and Martin Ringwald. The mouse gene expression database (GXD):
|
| bshanks@96 | 878 2007 update. Nucl. Acids Res., 35(suppl_1):D618–623, 2007.
|
| bshanks@96 | 879 [21]Judy Sprague, Leyla Bayraktaroglu, Dave Clements, Tom Conlin, David Fashena, Ken Frazer, Melissa
|
| bshanks@96 | 880 Haendel, Douglas G Howe, Prita Mani, Sridhar Ramachandran, Kevin Schaper, Erik Segerdell, Peiran
|
| bshanks@96 | 881 Song, Brock Sprunger, Sierra Taylor, Ceri E Van Slyke, and Monte Westerfield. The zebrafish information
|
| bshanks@96 | 882 network: the zebrafish model organism database. Nucleic Acids Research, 34(Database issue):D581–5,
|
| bshanks@96 | 883 2006. PMID: 16381936.
|
| bshanks@96 | 884 [22]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.
|
| bshanks@96 | 885 [23]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T.
|
| bshanks@96 | 886 Mortrud, Allison Cusick, Zackery L. Riley, Susan M. Sunkin, Amy Bernard, Ralph B. Puchalski, Fred H.
|
| bshanks@96 | 887 Gage, Allan R. Jones, Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the
|
| bshanks@96 | 888 hippocampus. Neuron, 60(6):1010–1021, December 2008.
|
| bshanks@96 | 889 [24]Pavel Tomancak, Amy Beaton, Richard Weiszmann, Elaine Kwan, ShengQiang Shu, Suzanna E Lewis,
|
| bshanks@96 | 890 Stephen Richards, Michael Ashburner, Volker Hartenstein, Susan E Celniker, and Gerald M Rubin. Sys-
|
| bshanks@96 | 891 tematic determination of patterns of gene expression during drosophila embryogenesis. Genome Biology,
|
| bshanks@96 | 892 3(12):research008818814, 2002. PMC151190.
|
| bshanks@96 | 893 [25]Jano van Hemert and Richard Baldock. Mining Spatial Gene Expression Data for Association Rules, volume
|
| bshanks@96 | 894 4414/2007 of Lecture Notes in Computer Science, pages 66–76. Springer Berlin / Heidelberg, 2007.
|
| bshanks@96 | 895 [26]Shanmugasundaram Venkataraman, Peter Stevenson, Yiya Yang, Lorna Richardson, Nicholas Burton,
|
| bshanks@96 | 896 Thomas P. Perry, Paul Smith, Richard A. Baldock, Duncan R. Davidson, and Jeffrey H. Christiansen.
|
| bshanks@96 | 897 EMAGE edinburgh mouse atlas of gene expression: 2008 update. Nucl. Acids Res., 36(suppl_1):D860–
|
| bshanks@96 | 898 865, 2008.
|
| bshanks@96 | 899 [27]Axel Visel, Christina Thaller, and Gregor Eichele. GenePaint.org: an atlas of gene expression patterns in
|
| bshanks@96 | 900 the mouse embryo. Nucl. Acids Res., 32(suppl_1):D552–556, 2004.
|
| bshanks@96 | 901 [28]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa
|
| bshanks@96 | 902 Agarwala, Rachel Ainscough, Marina Alexandersson, Peter An, Stylianos E Antonarakis, John Attwood,
|
| bshanks@96 | 903 Robert Baertsch, Jonathon Bailey, Karen Barlow, Stephan Beck, Eric Berry, Bruce Birren, Toby Bloom, Peer
|
| bshanks@96 | 904 Bork, Marc Botcherby, Nicolas Bray, Michael R Brent, Daniel G Brown, Stephen D Brown, Carol Bult, John
|
| bshanks@96 | 905 Burton, Jonathan Butler, Robert D Campbell, Piero Carninci, Simon Cawley, Francesca Chiaromonte, Asif T
|
| bshanks@96 | 906 Chinwalla, Deanna M Church, Michele Clamp, Christopher Clee, Francis S Collins, Lisa L Cook, Richard R
|
| bshanks@96 | 907 Copley, Alan Coulson, Olivier Couronne, James Cuff, Val Curwen, Tim Cutts, Mark Daly, Robert David, Joy
|
| bshanks@96 | 908 Davies, Kimberly D Delehaunty, Justin Deri, Emmanouil T Dermitzakis, Colin Dewey, Nicholas J Dickens,
|
| bshanks@96 | 909 Mark Diekhans, Sheila Dodge, Inna Dubchak, Diane M Dunn, Sean R Eddy, Laura Elnitski, Richard D Emes,
|
| bshanks@96 | 910 Pallavi Eswara, Eduardo Eyras, Adam Felsenfeld, Ginger A Fewell, Paul Flicek, Karen Foley, Wayne N
|
| bshanks@96 | 911 Frankel, Lucinda A Fulton, Robert S Fulton, Terrence S Furey, Diane Gage, Richard A Gibbs, Gustavo
|
| bshanks@96 | 912 Glusman, Sante Gnerre, Nick Goldman, Leo Goodstadt, Darren Grafham, Tina A Graves, Eric D Green,
|
| bshanks@96 | 913 Simon Gregory, Roderic Guig, Mark Guyer, Ross C Hardison, David Haussler, Yoshihide Hayashizaki,
|
| bshanks@96 | 914 LaDeana W Hillier, Angela Hinrichs, Wratko Hlavina, Timothy Holzer, Fan Hsu, Axin Hua, Tim Hubbard,
|
| bshanks@96 | 915 Adrienne Hunt, Ian Jackson, David B Jaffe, L Steven Johnson, Matthew Jones, Thomas A Jones, Ann Joy,
|
| bshanks@96 | 916 Michael Kamal, Elinor K Karlsson, Donna Karolchik, Arkadiusz Kasprzyk, Jun Kawai, Evan Keibler, Cristyn
|
| bshanks@96 | 917 Kells, W James Kent, Andrew Kirby, Diana L Kolbe, Ian Korf, Raju S Kucherlapati, Edward J Kulbokas, David
|
| bshanks@96 | 918 Kulp, Tom Landers, J P Leger, Steven Leonard, Ivica Letunic, Rosie Levine, Jia Li, Ming Li, Christine Lloyd,
|
| bshanks@96 | 919 Susan Lucas, Bin Ma, Donna R Maglott, Elaine R Mardis, Lucy Matthews, Evan Mauceli, John H Mayer,
|
| bshanks@96 | 920 Megan McCarthy, W Richard McCombie, Stuart McLaren, Kirsten McLay, John D McPherson, Jim Meldrim,
|
| bshanks@96 | 921 Beverley Meredith, Jill P Mesirov, Webb Miller, Tracie L Miner, Emmanuel Mongin, Kate T Montgomery,
|
| bshanks@96 | 922 Michael Morgan, Richard Mott, James C Mullikin, Donna M Muzny, William E Nash, Joanne O Nelson,
|
| bshanks@96 | 923 Michael N Nhan, Robert Nicol, Zemin Ning, Chad Nusbaum, Michael J O’Connor, Yasushi Okazaki, Karen
|
| bshanks@96 | 924 Oliver, Emma Overton-Larty, Lior Pachter, Gens Parra, Kymberlie H Pepin, Jane Peterson, Pavel Pevzner,
|
| bshanks@96 | 925 Robert Plumb, Craig S Pohl, Alex Poliakov, Tracy C Ponce, Chris P Ponting, Simon Potter, Michael Quail,
|
| bshanks@96 | 926 Alexandre Reymond, Bruce A Roe, Krishna M Roskin, Edward M Rubin, Alistair G Rust, Ralph Santos,
|
| bshanks@96 | 927 Victor Sapojnikov, Brian Schultz, Jrg Schultz, Matthias S Schwartz, Scott Schwartz, Carol Scott, Steven
|
| bshanks@96 | 928 Seaman, Steve Searle, Ted Sharpe, Andrew Sheridan, Ratna Shownkeen, Sarah Sims, Jonathan B Singer,
|
| bshanks@96 | 929 Guy Slater, Arian Smit, Douglas R Smith, Brian Spencer, Arne Stabenau, Nicole Stange-Thomann, Charles
|
| bshanks@96 | 930 Sugnet, Mikita Suyama, Glenn Tesler, Johanna Thompson, David Torrents, Evanne Trevaskis, John Tromp,
|
| bshanks@96 | 931 Catherine Ucla, Abel Ureta-Vidal, Jade P Vinson, Andrew C Von Niederhausern, Claire M Wade, Melanie
|
| bshanks@96 | 932 Wall, Ryan J Weber, Robert B Weiss, Michael C Wendl, Anthony P West, Kris Wetterstrand, Raymond
|
| bshanks@96 | 933 Wheeler, Simon Whelan, Jamey Wierzbowski, David Willey, Sophie Williams, Richard K Wilson, Eitan Win-
|
| bshanks@96 | 934 ter, Kim C Worley, Dudley Wyman, Shan Yang, Shiaw-Pyng Yang, Evgeny M Zdobnov, Michael C Zody, and
|
| bshanks@96 | 935 Eric S Lander. Initial sequencing and comparative analysis of the mouse genome. Nature, 420(6915):520–
|
| bshanks@96 | 936 62, December 2002. PMID: 12466850.
|
| bshanks@33 | 937
|
| bshanks@33 | 938
|
