cg

annotate grant.html @ 51:3ebb8f4ea921

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author bshanks@bshanks.dyndns.org
date Fri Apr 17 12:47:51 2009 -0700 (16 years ago)
parents a872ffae2d48
children 074e2be60b38

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bshanks@0 1 Specific aims
bshanks@42 2 Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, or in situ trans-
bshanks@42 3 genic reporter allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated
bshanks@42 4 methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical
bshanks@42 5 regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:
bshanks@30 6 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target
bshanks@30 7 anatomical regions
bshanks@42 8 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns
bshanks@42 9 in gene expression
bshanks@33 10 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse
bshanks@35 11 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of
bshanks@35 12 Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).
bshanks@30 13 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce
bshanks@30 14 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project
bshanks@33 15 will support the development of new ways to selectively target cortical areas, and it will support the development of a
bshanks@33 16 method for identifying the cortical areal boundaries present in small tissue samples.
bshanks@33 17 All algorithms that we develop will be implemented in an open-source software toolkit. The toolkit, as well as the
bshanks@30 18 machine-readable datasets developed in aim (3), will be published and freely available for others to use.
bshanks@30 19 Background and significance
bshanks@30 20 Aim 1
bshanks@30 21 Machine learning terminology: supervised learning
bshanks@42 22 The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the
bshanks@42 23 expression level of those genes is known, then the locations of the regions can be inferred.
bshanks@42 24 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we
bshanks@42 25 are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to
bshanks@42 26 which region each voxel within the structure belongs. We call this a classification task, because each voxel is being assigned
bshanks@42 27 to a class (namely, its region).
bshanks@30 28 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of
bshanks@42 29 the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels
bshanks@42 30 within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs.
bshanks@42 31 We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called a label
bshanks@42 32 (or a class label).
bshanks@30 33 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a
bshanks@30 34 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be
bshanks@30 35 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning
bshanks@33 36 procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used
bshanks@33 37 in the construction of the classifier is called training data.
bshanks@30 38 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a
bshanks@30 39 task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances
bshanks@42 40 (voxels) for which the labels (regions) are known.
bshanks@30 41 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection.
bshanks@33 42 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with
bshanks@33 43 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.
bshanks@30 44 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then
bshanks@30 45 chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic
bshanks@30 46 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise
bshanks@30 47 the score. Such procedures are called “stepwise” or “greedy”.
bshanks@30 48 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the
bshanks@30 49 learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature
bshanks@30 50 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to
bshanks@30 51 each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If
bshanks@30 52 only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only
bshanks@30 53 information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.
bshanks@30 54 Key questions when choosing a learning method are: What are the instances? What are the features? How are the
bshanks@30 55 features chosen? Here are four principles that outline our answers to these questions.
bshanks@30 56 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be
bshanks@30 57 identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene
bshanks@30 58 included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at
bshanks@30 59 combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary
bshanks@30 60 Results). Therefore, each instance should contain multiple features (genes).
bshanks@30 61 Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is
bshanks@30 62 only allowed to look at the expression of the genes which have been selected as features. The more data that is available to
bshanks@30 63 a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a
bshanks@30 64 strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations
bshanks@30 65 in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as
bshanks@30 66 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the
bshanks@30 67 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the
bshanks@33 68 level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order
bshanks@30 69 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as
bshanks@30 70 features.
bshanks@30 71 Principle 3: Use geometry in feature selection
bshanks@33 72 _________________________________________
bshanks@33 73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
bshanks@30 74 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of
bshanks@30 75 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information
bshanks@30 76 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See
bshanks@30 77 Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.
bshanks@30 78 Principle 4: Work in 2-D whenever possible
bshanks@30 79 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When
bshanks@30 80 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis
bshanks@33 81 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D
bshanks@33 82 data.
bshanks@30 83 Therefore, when possible, the instances should represent pixels, not voxels.
bshanks@43 84 Related work
bshanks@44 85 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data
bshanks@44 86 which is not fundamentally spatial2.
bshanks@43 87 As noted above, there has been much work on both supervised learning and there are many available algorithms for
bshanks@43 88 each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the
bshanks@43 89 way that this framework is set up has a large impact on performance. Creating a good framework can require creatively
bshanks@43 90 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,
bshanks@43 91 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may
bshanks@43 92 be necessary in order to achieve the best results in this application.
bshanks@51 93 We are aware of five existing efforts to find marker genes using spatial gene expression data using automated methods.
bshanks@51 94 GeneAtlas[1] and EMAGE [11] allow the user to construct a search query by demarcating regions and then specifing
bshanks@51 95 either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For
bshanks@51 96 the similiarity score (match score), GeneAtlas appears to use strength of expression, and EMAGE uses Jaccard similarity,
bshanks@51 97 which is equal to the number of true pixels in the intersection of the two images, divided by the number of pixels in their
bshanks@51 98 union. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes that together match a region.
bshanks@44 99 [6 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components:
bshanks@43 100 * Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)
bshanks@43 101 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of
bshanks@43 102 overexpressed genes for selected structures)
bshanks@43 103 * Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene
bshanks@43 104 expression profile of the seed voxel and every other voxel.
bshanks@43 105 * Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm
bshanks@43 106 with correlation as the similarity metric.
bshanks@43 107 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we
bshanks@43 108 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also
bshanks@51 109 search for underexpression. Third, Gene Finder uses a simple pointwise score3, whereas we will also use geometric scores
bshanks@43 110 such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.
bshanks@51 111 [? ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni
bshanks@51 112 correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,
bshanks@51 113 this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for
bshanks@51 114 underexpression, and does not look for combinations of genes.
bshanks@46 115 [4 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary
bshanks@46 116 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their
bshanks@51 117 match score is Jaccard similarity.
bshanks@51 118 In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores
bshanks@51 119 combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or
bshanks@51 120 scoring methods.
bshanks@30 121 Aim 2
bshanks@30 122 Machine learning terminology: clustering
bshanks@30 123 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as
bshanks@30 124 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances
bshanks@44 125 _________________________________________
bshanks@48 126 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
bshanks@48 127 just data which has only a few different locations or which is indexed by anatomical label.
bshanks@51 128 3“Expression energy ratio”, which captures overexpression.
bshanks@46 129 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called
bshanks@46 130 clustering or cluster analysis.
bshanks@46 131 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are
bshanks@46 132 once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from
bshanks@42 133 the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering
bshanks@42 134 voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels
bshanks@42 135 with similar gene expression.
bshanks@42 136 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps
bshanks@44 137 some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they
bshanks@42 138 could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests
bshanks@42 139 the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels.
bshanks@42 140 This is called hierarchial clustering.
bshanks@30 141 Similarity scores
bshanks@30 142 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or
bshanks@33 143 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and
bshanks@30 144 scoring methods for similarity.
bshanks@30 145 Spatially contiguous clusters; image segmentation
bshanks@33 146 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have
bshanks@33 147 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary
bshanks@33 148 Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these
bshanks@33 149 results against other methods which guarantee contiguous clusters.
bshanks@30 150 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a
bshanks@33 151 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into
bshanks@30 152 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in
bshanks@30 153 our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which
bshanks@33 154 use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used
bshanks@33 155 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting
bshanks@33 156 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene
bshanks@33 157 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of
bshanks@33 158 spatially arranged data, some of these algorithms are specialized for visual images.
bshanks@51 159 Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature
bshanks@51 160 vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.
bshanks@33 161 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the
bshanks@30 162 instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which
bshanks@30 163 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature
bshanks@30 164 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature
bshanks@30 165 set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features
bshanks@30 166 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced
bshanks@30 167 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene
bshanks@30 168 expression levels.
bshanks@51 169 Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the
bshanks@51 170 reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second,
bshanks@51 171 it is thought that some clustering algorithms may give better results on reduced data.
bshanks@51 172 Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example,
bshanks@51 173 one might want to make a 2-D plot upon which each region is represented by a single point, and with the property that regions
bshanks@51 174 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points
bshanks@51 175 in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of
bshanks@51 176 the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find
bshanks@51 177 arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction
bshanks@51 178 is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction
bshanks@51 179 before clustering.
bshanks@30 180 Clustering genes rather than voxels
bshanks@30 181 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster
bshanks@30 182 the features (genes). There are two ways that clusters of genes could be used.
bshanks@30 183 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could
bshanks@30 184 have one reduced feature for each gene cluster.
bshanks@30 185 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression
bshanks@51 186 patternwhich seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically
bshanks@51 187 interesting region will have multiple genes which each individually pick it out4. This suggests the following procedure:
bshanks@42 188 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.
bshanks@42 189 In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”
bshanks@42 190 formed by lumping together a few regions, are associated with gene clusters in this fashion.
bshanks@51 191 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering
bshanks@51 192 algorithms.
bshanks@43 193 Related work
bshanks@51 194 We are aware of five existing efforts to cluster spatial gene expression data.
bshanks@44 195 [9 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,
bshanks@43 196 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive
bshanks@44 197 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving
bshanks@51 198 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset5 and while the results are
bshanks@44 199 promising (see Preliminary Data), we think that it will be possible to find an even better method.
bshanks@51 200 AGEA’s[6] hierarchial clustering was described above. EMAGE[11] allows the user to select a dataset from among a
bshanks@51 201 large number of alternatives, or by running a search query, and then to cluster the genes within that dataset. Clustering is
bshanks@51 202 hierarchial complete linkage clustering with un-centred correlation as the similarity score.
bshanks@51 203 todo [?]
bshanks@46 204 In an interesting twist, [4] applies their technique for finding combinations of marker genes for the purpose of clustering
bshanks@46 205 genes around a “seed gene”. The way they do this is by using the pattern of expression of the seed gene as the target image,
bshanks@46 206 and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found
bshanks@46 207 are considered to be related to the seed. The same team also describes a method[10] for finding “association rules” such as,
bshanks@46 208 “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene”. This could be
bshanks@46 209 useful as part of a procedure for clustering voxels.
bshanks@46 210 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-
bshanks@51 211 rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. Also,
bshanks@51 212 none of these projects did a separate dimensionality reduction step before clustering pixels, or tried to cluster genes first in
bshanks@51 213 order to guide the clustering of pixels into spatial regions, or used co-clustering algorithms.
bshanks@30 214 Aim 3
bshanks@30 215 Background
bshanks@33 216 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can
bshanks@33 217 be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue
bshanks@33 218 downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can
bshanks@33 219 picture an area of the cortex as a slice of many-layered cake.
bshanks@30 220 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
bshanks@30 221 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,
bshanks@30 222 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of
bshanks@30 223 their approximate location upon the cortical surface.
bshanks@33 224 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not
bshanks@33 225 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a
bshanks@44 226 single agreed-upon map can be seen by contrasting the recent maps given by Swanson[8] on the one hand, and Paxinos
bshanks@44 227 and Franklin[7] on the other. While the maps are certainly very similar in their general arrangement, significant differences
bshanks@30 228 remain in the details.
bshanks@36 229 The Allen Mouse Brain Atlas dataset
bshanks@36 230 The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old
bshanks@36 231 C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed
bshanks@36 232 in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial
bshanks@51 233 _________________________________________
bshanks@51 234 4This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is
bshanks@51 235 possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;
bshanks@51 236 perhaps there is some other way to map the cortex for which each region can be identified by single genes. Another possibility is that, although
bshanks@51 237 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.
bshanks@51 238 5We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft
bshanks@51 239 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was
bshanks@51 240 needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.
bshanks@36 241 resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different
bshanks@36 242 mouse brains were needed in order to measure the expression of many genes.
bshanks@36 243 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate
bshanks@36 244 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326
bshanks@44 245 voxels in the 3D coordinate system, of which 51,533 are in the brain[6].
bshanks@46 246 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[13]. The ABA contains
bshanks@36 247 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
bshanks@46 248 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and
bshanks@46 249 also has greater registration error[6]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes of
bshanks@46 250 known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[6].
bshanks@51 251 The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[3],
bshanks@51 252 GenePaint[12], its sister project GeneAtlas[1], BGEM[5], EMAGE[11], EurExpress6, EADHB7, MAMEP8, Xenbase9, ZFIN[?],
bshanks@51 253 Aniseed10, VisiGene11, GEISHA[?], Fruitfly.org[?], COMPARE[?] todo. With the exception of the ABA, GenePaint, and
bshanks@51 254 EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH images and registered the
bshanks@51 255 results into a single 3-D space, and only ABA and EMAGE make this form of data available for public download from the
bshanks@51 256 website12. Many of these resources focus on developmental gene expression.
bshanks@46 257 Significance
bshanks@43 258 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the
bshanks@42 259 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for
bshanks@30 260 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively
bshanks@30 261 target individual cortical areas.
bshanks@30 262 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom-
bshanks@33 263 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can
bshanks@33 264 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that
bshanks@30 265 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.
bshanks@33 266 The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of
bshanks@33 267 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is
bshanks@33 268 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s
bshanks@33 269 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of
bshanks@33 270 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been
bshanks@33 271 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking
bshanks@33 272 at the patterns of gene expression.
bshanks@30 273 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to
bshanks@30 274 develop could be used to suggest modifications to the human cortical map as well.
bshanks@30 275 Related work
bshanks@44 276 [6 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations
bshanks@46 277 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either
bshanks@46 278 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of
bshanks@46 279 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes
bshanks@48 280 for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas13.
bshanks@46 281 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has
bshanks@43 282 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally
bshanks@43 283 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo
bshanks@43 284 from gene expression data.
bshanks@51 285 ___________________
bshanks@51 286 6http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE
bshanks@51 287 7http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
bshanks@51 288 8http://mamep.molgen.mpg.de/index.php
bshanks@51 289 9http://xenbase.org/
bshanks@51 290 10http://aniseed-ibdm.univ-mrs.fr/
bshanks@51 291 11http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
bshanks@51 292 12without prior offline registration
bshanks@48 293 13In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
bshanks@44 294 often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel
bshanks@46 295 correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not
bshanks@44 296 find most cortical areas (there are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have
bshanks@44 297 many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for
bshanks@44 298 most cortical areas is that in Gene Finder, although the user chooses a seed voxel, Gene Finder chooses the ROI for which genes will be found,
bshanks@44 299 and it creates that ROI by (pairwise voxel correlation) clustering around the seed.
bshanks@51 300 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker
bshanks@51 301 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.
bshanks@30 302 Preliminary work
bshanks@30 303 Format conversion between SEV, MATLAB, NIFTI
bshanks@35 304 We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created
bshanks@38 305 software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret’s file formats.
bshanks@30 306 Flatmap of cortex
bshanks@36 307 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided
bshanks@36 308 the cortex into hemispheres.
bshanks@44 309 Using Caret[2], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of
bshanks@42 310 the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened
bshanks@42 311 the cortex, creating a two-dimensional mesh.
bshanks@36 312 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid
bshanks@36 313 into a MATLAB matrix.
bshanks@36 314 We manually traced the boundaries of each cortical area from the ABA coronal reference atlas slides. We then converted
bshanks@42 315 these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d
bshanks@42 316 mesh, and then onto the grid, and then we converted the region data into MATLAB format.
bshanks@37 317 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing
bshanks@37 318 a grid of points (pixels) over the cortical surface:
bshanks@36 319 ∙A 2-D matrix whose entries represent the regional label associated with each surface pixel
bshanks@36 320 ∙For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel
bshanks@38 321 We created a normalized version of the gene expression data by subtracting each gene’s mean expression level (over all
bshanks@38 322 surface pixels) and dividing each gene by its standard deviation.
bshanks@40 323 The features and the target area are both functions on the surface pixels. They can be referred to as scalar fields over
bshanks@40 324 the space of surface pixels; alternately, they can be thought of as images which can be displayed on the flatmapped surface.
bshanks@37 325 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix for each
bshanks@37 326 cortical layer to represent the average expression level within that layer. Cortical layers are found at different depths in
bshanks@37 327 different parts of the cortex. In preparation for extracting the layer-specific datasets, we have extended Caret with routines
bshanks@37 328 that allow the depth of the ROI for volume-to-surface projection to vary.
bshanks@36 329 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually
bshanks@36 330 demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.
bshanks@38 331 Feature selection and scoring methods
bshanks@38 332 Correlation Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance
bshanks@46 333 as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the
bshanks@38 334 surface pixels.
bshanks@40 335 One class of feature selection scoring method are those which calculate some sort of “match” between each gene image
bshanks@40 336 and the target image. Those genes which match the best are good candidates for features.
bshanks@38 337 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between
bshanks@38 338 each gene and each cortical area.
bshanks@39 339 todo: fig
bshanks@38 340 Conditional entropy An information-theoretic scoring method is to find features such that, if the features (gene
bshanks@38 341 expression levels) are known, uncertainty about the target (the regional identity) is reduced. Entropy measures uncertainty,
bshanks@38 342 so what we want is to find features such that the conditional distribution of the target has minimal entropy. The distribution
bshanks@38 343 to which we are referring is the probability distribution over the population of surface pixels.
bshanks@38 344 The simplest way to use information theory is on discrete data, so we discretized our gene expression data by creating,
bshanks@46 345 for each gene, five thresholded boolean masks of the gene data. For each gene, we created a boolean mask of its expression
bshanks@40 346 levels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the mean minus two
bshanks@40 347 standard deviations, the mean plus one standard deviation, the mean plus two standard deviations.
bshanks@39 348 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene expression
bshanks@46 349 boolean masks such that the conditional entropy of the target area’s boolean mask, conditioned upon the pair of gene
bshanks@46 350 expression boolean masks, is minimized.
bshanks@39 351 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the question,
bshanks@39 352 “Is this surface pixel a member of the target area?”.
bshanks@38 353
bshanks@41 354
bshanks@41 355
bshanks@41 356 Figure 1: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.
bshanks@41 357 The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From
bshanks@41 358 left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr
bshanks@39 359 todo: fig
bshanks@39 360 Gradient similarity We noticed that the previous two scoring methods, which are pointwise, often found genes whose
bshanks@39 361 pattern of expression did not look similar in shape to the target region. Fort his reason we designed a non-pointwise local
bshanks@39 362 scoring method to detect when a gene had a pattern of expression which looked like it had a boundary whose shape is similar
bshanks@40 363 to the shape of the target region. We call this scoring method “gradient similarity”.
bshanks@40 364 One might say that gradient similarity attempts to measure how much the border of the area of gene expression and
bshanks@40 365 the border of the target region overlap. However, since gene expression falls off continuously rather than jumping from its
bshanks@40 366 maximum value to zero, the spatial pattern of a gene’s expression often does not have a discrete border. Therefore, instead
bshanks@40 367 of looking for a discrete border, we look for large gradients. Gradient similarity is a symmetric function over two images
bshanks@40 368 (i.e. two scalar fields). It is is high to the extent that matching pixels which have large values and large gradients also have
bshanks@40 369 gradients which are oriented in a similar direction. The formula is:
bshanks@41 370 ∑
bshanks@41 371 pixel<img src="cmsy7-32.png" alt="&#x2208;" />pixels cos(abs(&#x2220;&#x2207;1 -&#x2220;&#x2207;2)) &#x22C5;|&#x2207;1| + |&#x2207;2|
bshanks@41 372 2 &#x22C5; pixel_value1 + pixel_value2
bshanks@41 373 2
bshanks@40 374 where &#x2207;1 and &#x2207;2 are the gradient vectors of the two images at the current pixel; &#x2220;&#x2207;i is the angle of the gradient of
bshanks@41 375 image i at the current pixel; |&#x2207;i| is the magnitude of the gradient of image i at the current pixel; and pixel_valuei is the
bshanks@40 376 value of the current pixel in image i.
bshanks@40 377 The intuition is that we want to see if the borders of the pattern in the two images are similar; if the borders are similar,
bshanks@40 378 then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a
bshanks@40 379 similar direction (because the borders are similar).
bshanks@43 380 Gradient similarity provides information complementary to correlation
bshanks@41 381 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider
bshanks@48 382 Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method14. The
bshanks@48 383 bottom row displays the 3 genes which most match AUD according to a method which considers local geometry15 The
bshanks@46 384 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is
bshanks@46 385 that this includes many areas which don&#8217;t have a salient border matching the areal border. The geometric method identifies
bshanks@46 386 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes
bshanks@46 387 genes which don&#8217;t express over the entire area. Genes which have high rankings using both pointwise and border criteria,
bshanks@46 388 such as Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker
bshanks@46 389 for AUD; we deliberately chose a &#8220;difficult&#8221; area in order to better contrast pointwise with geometric methods.
bshanks@43 390 Combinations of multiple genes are useful
bshanks@30 391 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi-
bshanks@48 392 natorially. according to logistic regression, gene wwc116 is the best fit single gene for predicting whether or not a pixel on
bshanks@48 393 _________________________________________
bshanks@48 394 14For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
bshanks@41 395 variable was the value of the expression of the gene underneath that pixel. The resulting scores were used to rank the genes in terms of how well
bshanks@41 396 they predict area AUD.
bshanks@48 397 15For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the
bshanks@41 398 shape of area AUD, was calculated, and this was used to rank the genes.
bshanks@48 399 16&#8220;WW, C2 and coiled-coil domain containing 1&#8221;; EntrezGene ID 211652
bshanks@41 400
bshanks@41 401
bshanks@41 402
bshanks@41 403 Figure 2: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel&#8217;s value on the lower left is the sum
bshanks@41 404 of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the
bshanks@41 405 top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right.
bshanks@41 406 The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells
bshanks@41 407 underneath each pixel, with red meaning a lot of expression and blue meaning little.
bshanks@30 408 the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure shows wwc1&#8217;s spatial expression
bshanks@30 409 pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene
bshanks@33 410 overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the
bshanks@30 411 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo).
bshanks@48 412 Gene mtif217 is shown in figure the upper-right of Fig. . Mtif2 captures MO&#8217;s upper-left boundary, but not its lower-right
bshanks@33 413 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these
bshanks@33 414 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene.
bshanks@38 415 Areas which can be identified by single genes
bshanks@39 416 todo
bshanks@43 417 Underexpression of a gene can serve as a marker
bshanks@39 418 todo
bshanks@39 419 Specific to Aim 1 (and Aim 3)
bshanks@39 420 Forward stepwise logistic regression todo
bshanks@30 421 SVM on all genes at once
bshanks@30 422 In order to see how well one can do when looking at all genes at once, we ran a support vector machine to classify cortical
bshanks@48 423 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%18. As noted above,
bshanks@30 424 however, a classifier that looks at all the genes at once isn&#8217;t practically useful.
bshanks@30 425 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many
bshanks@33 426 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task
bshanks@30 427 combines feature selection with supervised learning.
bshanks@30 428 Decision trees
bshanks@30 429 todo
bshanks@30 430 Specific to Aim 2 (and Aim 3)
bshanks@30 431 Raw dimensionality reduction results
bshanks@30 432 todo
bshanks@30 433 (might want to incld nnMF since mentioned above)
bshanks@41 434 _________________________________________
bshanks@48 435 17&#8220;mitochondrial translational initiation factor 2&#8221;; EntrezGene ID 76784
bshanks@48 436 185-fold cross-validation.
bshanks@30 437 Dimensionality reduction plus K-means or spectral clustering
bshanks@30 438 Many areas are captured by clusters of genes
bshanks@40 439 todo
bshanks@40 440 todo
bshanks@30 441 Research plan
bshanks@42 442 Further work on flatmapping
bshanks@42 443 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),
bshanks@42 444 or by the surface of the structure (as is the case with the cortex). In the former case, the manifold of interest is a plane, but
bshanks@42 445 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.
bshanks@42 446 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal
bshanks@44 447 for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[2]) with
bshanks@42 448 mappings which preserve angle (conformal maps).
bshanks@42 449 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.
bshanks@42 450 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D
bshanks@42 451 structure seems to be wrong.
bshanks@30 452 todo amongst other things:
bshanks@30 453 Develop algorithms that find genetic markers for anatomical regions
bshanks@30 454 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise,
bshanks@30 455 geometric, and information-theoretic measures.
bshanks@30 456 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining
bshanks@30 457 the scoring measures developed, we will rank the genes by their ability to delineate each area.
bshanks@30 458 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any
bshanks@30 459 single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily
bshanks@30 460 combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised
bshanks@33 461 learning techniques which use soft constraints to minimize the number of features, such as sparse support vector
bshanks@30 462 machines.
bshanks@33 463 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult
bshanks@33 464 to identify because the boundaries are misdrawn, or because it does not &#8220;really&#8221; exist as a single area, at least on the
bshanks@30 465 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its
bshanks@30 466 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create
bshanks@30 467 a larger area which can be fit.
bshanks@51 468 # Linear discriminant analysis
bshanks@30 469 Apply these algorithms to the cortex
bshanks@30 470 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert
bshanks@30 471 between SEV, NIFTI and MATLAB formats.
bshanks@30 472 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.
bshanks@30 473 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.
bshanks@30 474 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify
bshanks@30 475 that area; and we will also present lists of &#8220;panels&#8221; of genes that can be used to delineate many areas at once.
bshanks@30 476 Develop algorithms to suggest a division of a structure into anatomical parts
bshanks@30 477 1.Explore dimensionality reduction algorithms applied to pixels: including TODO
bshanks@30 478 2.Explore dimensionality reduction algorithms applied to genes: including TODO
bshanks@30 479 3.Explore clustering algorithms applied to pixels: including TODO
bshanks@30 480 4.Explore clustering algorithms applied to genes: including gene shaving, TODO
bshanks@30 481 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
bshanks@30 482 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
bshanks@51 483 # Linear discriminant analysis
bshanks@51 484 # jbt, coclustering
bshanks@51 485 # self-organizing map
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bshanks@33 553
bshanks@33 554 _______________________________________________________________________________________________________
bshanks@30 555 stuff i dunno where to put yet (there is more scattered through grant-oldtext):
bshanks@16 556 Principle 4: Work in 2-D whenever possible
bshanks@33 557 &#8212;
bshanks@33 558 note:
bshanks@33 559 do we need to cite: no known markers, impressive results?
bshanks@36 560 two hemis
bshanks@33 561
bshanks@33 562