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changeset 55:51c00dc05ff4
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author | bshanks@bshanks-salk.dyndns.org |
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date | Sat Apr 18 23:33:04 2009 -0700 (16 years ago) |
parents | 45e29b9e000f 304d07e0ac94 |
children | 1a2a8d08b7c3 |
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2.4 Specific aims
2.5 -Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, or in situ trans-
2.6 -genic reporter allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated
2.7 -methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical
2.8 -regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:
2.9 +Massivenew datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic
2.10 +reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared.
2.11 +Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker
2.12 +genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have
2.13 +three specific aims:
2.14 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target
2.15 anatomical regions
2.16 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns
2.17 @@ -14,7 +15,7 @@
2.18 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project
2.19 will support the development of new ways to selectively target cortical areas, and it will support the development of a
2.20 method for identifying the cortical areal boundaries present in small tissue samples.
2.21 -All algorithms that we develop will be implemented in an open-source software toolkit. The toolkit, as well as the
2.22 +All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the
2.23 machine-readable datasets developed in aim (3), will be published and freely available for others to use.
2.24 Background and significance
2.25 Aim 1
2.26 @@ -48,9 +49,10 @@
2.27 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the
2.28 learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature
2.29 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to
2.30 -each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If
2.31 -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
2.32 -information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.
2.33 +each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or
2.34 +average). If only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring
2.35 +method. If only information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring
2.36 +method.
2.37 Key questions when choosing a learning method are: What are the instances? What are the features? How are the
2.38 features chosen? Here are four principles that outline our answers to these questions.
2.39 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be
2.40 @@ -90,42 +92,46 @@
2.41 reconceptualizing the problem domain, and is not merely a mechanical “fine-tuning” of numerical parameters. For example,
2.42 we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may
2.43 be necessary in order to achieve the best results in this application.
2.44 -We are aware of four existing efforts to find marker genes using spatial gene expression data using automated methods.
2.45 -[1 ] describes GeneAtlas. GeneAtlas allows the user to construct a search query by freely demarcating one or two 2-D
2.46 -regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression
2.47 -pattern is to be matched. GeneAtlas differs from our Aim 1 in at least two ways. First, GeneAtlas finds only single genes,
2.48 -whereas we will also look for combinations of genes3. Second, at least for the custom spatial search, Gene Atlas appears to
2.49 -use a simple pointwise scoring method (strength of expression), whereas we will also use geometric metrics such as gradient
2.50 -similarity.
2.51 -[6 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components:
2.52 +We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.
2.53 +[8 ] mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of
2.54 +interest, computing what proportion of this structure is covered by the gene’s spatial region.
2.55 +GeneAtlas[3] and EMAGE [18] allow the user to construct a search query by demarcating regions and then specifing
2.56 +either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the
2.57 +similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses
2.58 +the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel3
2.59 +whose expression is within four discretization levels. EMAGE uses Jaccard similarity, which is equal to the number of true
2.60 +pixels in the intersection of the two images, divided by the number of pixels in their union. Neither GeneAtlas nor EMAGE
2.61 +allow one to search for combinations of genes that define a region in concert but not separately.
2.62 +[10 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA has three components:
2.63 * Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)
2.64 yields a list of genes which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of
2.65 overexpressed genes for selected structures)
2.66 * Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene
2.67 expression profile of the seed voxel and every other voxel.
2.68 -* Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm
2.69 -with correlation as the similarity metric.
2.70 +* Clusters: will be described later
2.71 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we
2.72 will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also
2.73 search for underexpression. Third, Gene Finder uses a simple pointwise score4, whereas we will also use geometric scores
2.74 such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.
2.75 -[11 ] todo
2.76 -[4 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary
2.77 +[4 ] looks at the mean expression level of genes within anatomical regions, and applies a Student’s t-test with Bonferroni
2.78 +correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA,
2.79 +this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for
2.80 +underexpression, and does not look for combinations of genes.
2.81 +[7 ] describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary
2.82 algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their
2.83 -match score is Jaccard similarity, which is equal to the number of true pixels in the intersection of the two images, divided
2.84 -by the number of pixels in their union.
2.85 -In summary, only one of the previous projects explores combinations of marker genes, and none of their publications
2.86 -compare the results obtained by using different algorithms or scoring methods.
2.87 +match score is Jaccard similarity.
2.88 +In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores
2.89 +combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or
2.90 +scoring methods.
2.91 +___________________________
2.92 + 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
2.93 +just data which has only a few different locations or which is indexed by anatomical label.
2.94 + 3Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.
2.95 + 4“Expression energy ratio”, which captures overexpression.
2.96 Aim 2
2.97 Machine learning terminology: clustering
2.98 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as
2.99 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances
2.100 -_________________________________________
2.101 - 2By “fundamentally spatial” we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not
2.102 -just data which has only a few different locations or which is indexed by anatomical label.
2.103 - 3See Preliminary Data for an example of an area which cannot be marked by any single gene in the dataset, but which can be marked by a
2.104 -combination.
2.105 - 4“Expression energy ratio”, which captures overexpression.
2.106 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called
2.107 clustering or cluster analysis.
2.108 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are
2.109 @@ -156,7 +162,8 @@
2.110 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene
2.111 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of
2.112 spatially arranged data, some of these algorithms are specialized for visual images.
2.113 -Dimensionality reduction
2.114 +Dimensionality reduction In this section, we discuss reducing the length of the per-pixel gene expression feature
2.115 +vector. By “dimension”, we mean the dimension of this vector, not the spatial dimension of the underlying data.
2.116 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the
2.117 instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which
2.118 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature
2.119 @@ -165,13 +172,17 @@
2.120 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced
2.121 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene
2.122 expression levels.
2.123 -Another use for dimensionality reduction is to visualize the relationships between regions. For example, one might want
2.124 -to make a 2-D plot upon which each region is represented by a single point, and with the property that regions with similar
2.125 -gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot
2.126 -should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on
2.127 -a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find arrangements
2.128 -of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied
2.129 -after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.
2.130 +Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the
2.131 +reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second,
2.132 +it is thought that some clustering algorithms may give better results on reduced data.
2.133 +Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example,
2.134 +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
2.135 +with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points
2.136 +in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of
2.137 +the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find
2.138 +arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction
2.139 +is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction
2.140 +before clustering.
2.141 Clustering genes rather than voxels
2.142 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster
2.143 the features (genes). There are two ways that clusters of genes could be used.
2.144 @@ -180,34 +191,39 @@
2.145 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression
2.146 pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically
2.147 interesting region will have multiple genes which each individually pick it out5. This suggests the following procedure:
2.148 -_________________________________________
2.149 - 5This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is
2.150 -possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;
2.151 -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
2.152 cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters.
2.153 In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some “superregions”
2.154 formed by lumping together a few regions, are associated with gene clusters in this fashion.
2.155 +The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering
2.156 +algorithms.
2.157 Related work
2.158 -We are aware of four existing efforts to cluster spatial gene expression data.
2.159 -[9 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,
2.160 +We are aware of five existing efforts to cluster spatial gene expression data.
2.161 +[15 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,
2.162 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive
2.163 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving
2.164 the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset6 and while the results are
2.165 promising (see Preliminary Data), we think that it will be possible to find an even better method.
2.166 -In an interesting twist, [4] applies their technique for finding combinations of marker genes for the purpose of clustering
2.167 +AGEA[10] includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation
2.168 +as the similarity metric. EMAGE[18] allows the user to select a dataset from among a large number of alternatives, or by
2.169 +running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage
2.170 +clustering with un-centred correlation as the similarity score.
2.171 +[4 ] clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were
2.172 +highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and
2.173 +ordered the rows of this matrix as follows: “the first row of the matrix was chosen to show the strongest contrast between
2.174 +the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing
2.175 +similarity using a least squares metric”. The resulting matrix showed four clusters. For each cluster, prototypical spatial
2.176 +expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without
2.177 +clustering voxels
2.178 +In an interesting twist, [7] applies their technique for finding combinations of marker genes for the purpose of clustering
2.179 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,
2.180 and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found
2.181 -are considered to be related to the seed. The same team also describes a method[10] for finding “association rules” such as,
2.182 +are considered to be related to the seed. The same team also describes a method[17] for finding “association rules” such as,
2.183 “if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene”. This could be
2.184 useful as part of a procedure for clustering voxels.
2.185 -AGEA’s[6] hierarchial clustering differs from our Aim 2 in at least two ways. First, AGEA uses perhaps the simplest
2.186 -possible similarity score (correlation), and does no dimensionality reduction before calculating similarity. While it is possible
2.187 -that a more complex system will not do any better than this, we believe further exploration of alternative methods of scoring
2.188 -and dimensionality reduction is warranted. Second, AGEA did not look at clusters of genes; in Preliminary Data we have
2.189 -shown that clusters of genes may identify interesting spatial regions such as cortical areas.
2.190 -[11 ] todo
2.191 In summary, although these projects obtained clusterings, there has not been much comparison between different algo-
2.192 -rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found.
2.193 +rithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. Also,
2.194 +none of these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first
2.195 +in order to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.
2.196 Aim 3
2.197 Background
2.198 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can
2.199 @@ -216,12 +232,20 @@
2.200 picture an area of the cortex as a slice of many-layered cake.
2.201 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
2.202 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,
2.203 +_________________________________________
2.204 + 5This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is
2.205 +possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression;
2.206 +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
2.207 +the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.
2.208 + 6We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft
2.209 +spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was
2.210 +needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.
2.211 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of
2.212 their approximate location upon the cortical surface.
2.213 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not
2.214 -completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a
2.215 -single agreed-upon map can be seen by contrasting the recent maps given by Swanson[8] on the one hand, and Paxinos
2.216 -and Franklin[7] on the other. While the maps are certainly very similar in their general arrangement, significant differences
2.217 +completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single
2.218 +agreed-upon map can be seen by contrasting the recent maps given by Swanson[14] on the one hand, and Paxinos and
2.219 +Franklin[11] on the other. While the maps are certainly very similar in their general arrangement, significant differences
2.220 remain in the details.
2.221 The Allen Mouse Brain Atlas dataset
2.222 The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old
2.223 @@ -231,23 +255,18 @@
2.224 mouse brains were needed in order to measure the expression of many genes.
2.225 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate
2.226 system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 = 159,326
2.227 -voxels in the 3D coordinate system, of which 51,533 are in the brain[6].
2.228 -Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[13]. The ABA contains
2.229 +voxels in the 3D coordinate system, of which 51,533 are in the brain[10].
2.230 +Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes[20]. The ABA contains
2.231 data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our
2.232 dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and
2.233 -_________________________________________
2.234 -the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.
2.235 - 6We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft
2.236 -spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was
2.237 -needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.
2.238 -also has greater registration error[6]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes of
2.239 -known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[6].
2.240 -TheABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[3],
2.241 -GenePaint[12], its sister project GeneAtlas[1], BGEM[5], EMAGE[11], EurExpress7, EADHB8, MAMEP9, Xenbase10,
2.242 -ZFIN[? ], Aniseed11, VisiGene12, GEISHA[?], Fruitfly.org[?], COMPARE[?] todo. With the exception of the ABA, Gene-
2.243 -Paint, and EMAGE, most of these resources, have not (yet) extracted the expression intensity from the ISH images and
2.244 -registered the results into a single 3-D space, and only ABA and EMAGE make this form of data available for public
2.245 -download from the website. Many of these resources focus on developmental gene expression.
2.246 +also has greater registration error[10]. Genes were selected by the Allen Institute for coronal sectioning based on, “classes
2.247 +of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern”[10].
2.248 +The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT[6],
2.249 +GenePaint[19], its sister project GeneAtlas[3], BGEM[9], EMAGE[18], EurExpress7, EADHB8, MAMEP9, Xenbase10,
2.250 +ZFIN[13], Aniseed11, VisiGene12, GEISHA[2], Fruitfly.org[16], COMPARE13 GXD[12], GEO[1]14. With the exception of
2.251 +the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH
2.252 +images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of
2.253 +data available for public download from the website15. Many of these resources focus on developmental gene expression.
2.254 Significance
2.255 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the
2.256 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for
2.257 @@ -257,7 +276,7 @@
2.258 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can
2.259 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that
2.260 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.
2.261 -The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of
2.262 +The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation of
2.263 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is
2.264 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s
2.265 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of
2.266 @@ -267,11 +286,21 @@
2.267 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to
2.268 develop could be used to suggest modifications to the human cortical map as well.
2.269 Related work
2.270 -[6 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations
2.271 +[10 ] describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations
2.272 between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either
2.273 +_________________________________________
2.274 + 7http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE
2.275 + 8http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
2.276 + 9http://mamep.molgen.mpg.de/index.php
2.277 + 10http://xenbase.org/
2.278 + 11http://aniseed-ibdm.univ-mrs.fr/
2.279 + 12http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
2.280 + 13http://compare.ibdml.univ-mrs.fr/
2.281 + 14GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.
2.282 + 15without prior offline registration
2.283 of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of
2.284 the other components of AGEA can be applied to cortical areas; AGEA’s Gene Finder cannot be used to find marker genes
2.285 -for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas13.
2.286 +for the cortical areas; and AGEA’s hierarchial clustering does not produce clusters corresponding to the cortical areas16.
2.287 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has
2.288 been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally
2.289 finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo
2.290 @@ -279,13 +308,7 @@
2.291 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker
2.292 genes for / reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.
2.293 _________________________________________
2.294 - 7http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE
2.295 - 8http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html
2.296 - 9http://mamep.molgen.mpg.de/index.php
2.297 - 10http://xenbase.org/
2.298 - 11http://aniseed-ibdm.univ-mrs.fr/
2.299 - 12http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources
2.300 - 13In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
2.301 + 16In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are
2.302 often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel
2.303 correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not
2.304 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
2.305 @@ -299,7 +322,7 @@
2.306 Flatmap of cortex
2.307 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided
2.308 the cortex into hemispheres.
2.309 -Using Caret[2], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of
2.310 +Using Caret[5], we created a mesh representation of the surface of the selected voxels. For each gene, for each node of
2.311 the mesh, we calculated an average of the gene expression of the voxels “underneath” that mesh node. We then flattened
2.312 the cortex, creating a two-dimensional mesh.
2.313 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid
2.314 @@ -372,8 +395,8 @@
2.315 similar direction (because the borders are similar).
2.316 Gradient similarity provides information complementary to correlation
2.317 To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider
2.318 -Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method14. The
2.319 -bottom row displays the 3 genes which most match AUD according to a method which considers local geometry15 The
2.320 +Fig. . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method17. The
2.321 +bottom row displays the 3 genes which most match AUD according to a method which considers local geometry18 The
2.322 pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is
2.323 that this includes many areas which don’t have a salient border matching the areal border. The geometric method identifies
2.324 genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes
2.325 @@ -382,14 +405,14 @@
2.326 for AUD; we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods.
2.327 Combinations of multiple genes are useful
2.328 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi-
2.329 -natorially. according to logistic regression, gene wwc116 is the best fit single gene for predicting whether or not a pixel on
2.330 +natorially. according to logistic regression, gene wwc119 is the best fit single gene for predicting whether or not a pixel on
2.331 _________________________________________
2.332 - 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
2.333 + 17For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
2.334 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
2.335 they predict area AUD.
2.336 - 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
2.337 -shape of area AUD, was calculated, and this was used to rank the genes.
2.338 - 16“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
2.339 + 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 area AUD,
2.340 +was calculated, and this was used to rank the genes.
2.341 + 19“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
2.342
2.343
2.344
2.345 @@ -402,7 +425,7 @@
2.346 pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene
2.347 overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the
2.348 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo).
2.349 -Gene mtif217 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right
2.350 +Gene mtif220 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right
2.351 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these
2.352 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene.
2.353 Areas which can be identified by single genes
2.354 @@ -413,7 +436,7 @@
2.355 Forward stepwise logistic regression todo
2.356 SVM on all genes at once
2.357 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
2.358 -surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%18. As noted above,
2.359 +surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%21. As noted above,
2.360 however, a classifier that looks at all the genes at once isn’t practically useful.
2.361 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many
2.362 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task
2.363 @@ -425,8 +448,8 @@
2.364 todo
2.365 (might want to incld nnMF since mentioned above)
2.366 _________________________________________
2.367 - 17“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
2.368 - 185-fold cross-validation.
2.369 + 20“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
2.370 + 215-fold cross-validation.
2.371 Dimensionality reduction plus K-means or spectral clustering
2.372 Many areas are captured by clusters of genes
2.373 todo
2.374 @@ -437,7 +460,7 @@
2.375 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
2.376 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.
2.377 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal
2.378 -for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[2]) with
2.379 +for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret[5]) with
2.380 mappings which preserve angle (conformal maps).
2.381 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.
2.382 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D
2.383 @@ -458,6 +481,7 @@
2.384 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its
2.385 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create
2.386 a larger area which can be fit.
2.387 +# Linear discriminant analysis
2.388 Apply these algorithms to the cortex
2.389 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert
2.390 between SEV, NIFTI and MATLAB formats.
2.391 @@ -472,41 +496,68 @@
2.392 4.Explore clustering algorithms applied to genes: including gene shaving, TODO
2.393 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
2.394 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
2.395 +# Linear discriminant analysis
2.396 +# jbt, coclustering
2.397 +# self-organizing map
2.398 +# confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting
2.399 +# compare using clustering scores
2.400 Bibliography & References Cited
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2.413 +[4]Mark H. Chin, Alex B. Geng, Arshad H. Khan, Wei-Jun Qian, Vladislav A. Petyuk, Jyl Boline, Shawn Levy, Arthur W.
2.414 +Toga, Richard D. Smith, Richard M. Leahy, and Desmond J. Smith. A genome-scale map of expression for a mouse
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2.422 central nervous system based on bacterial artificial chromosomes. Nature, 425(6961):917–925, October 2003.
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2.425 terns, volume 13 of Communications in Computer and Information Science, pages 347–361. Springer Berlin Heidelberg,
2.426 2008.
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2.428 +[8]Erh-Fang Lee, Jyl Boline, and Arthur W. Toga. A High-Resolution anatomical framework of the neonatal mouse brain
2.429 +for managing gene expression data. Frontiers in Neuroinformatics, 1:6, 2007. PMC2525996.
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2.432 Shakya, Perdeep Mehta, and Tom Curran. BGEM: an in situ hybridization database of gene expression in the embryonic
2.433 and adult mouse nervous system. PLoS Biology, 4(4):e86 EP –, April 2006.
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2.435 +[10]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M
2.436 Sunkin, Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann, David J Anderson,
2.437 Ed S Lein, Allan R Jones, and Michael Hawrylycz. An anatomic gene expression atlas of the adult mouse brain. Nat
2.438 Neurosci, 12(3):356–362, March 2009.
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2.441 2001.
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2.444 +[12]Constance M. Smith, Jacqueline H. Finger, Terry F. Hayamizu, Ingeborg J. McCright, Janan T. Eppig, James A.
2.445 +Kadin, Joel E. Richardson, and Martin Ringwald. The mouse gene expression database (GXD): 2007 update. Nucl.
2.446 +Acids Res., 35(suppl_1):D618–623, 2007.
2.447 +[13]Judy Sprague, Leyla Bayraktaroglu, Dave Clements, Tom Conlin, David Fashena, Ken Frazer, Melissa Haendel, Dou-
2.448 +glas G Howe, Prita Mani, Sridhar Ramachandran, Kevin Schaper, Erik Segerdell, Peiran Song, Brock Sprunger, Sierra
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2.451 +[14]Larry Swanson. Brain Maps: Structure of the Rat Brain. Academic Press, 3 edition, November 2003.
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2.453 Allison Cusick, Zackery L. Riley, Susan M. Sunkin, Amy Bernard, Ralph B. Puchalski, Fred H. Gage, Allan R. Jones,
2.454 Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the hippocampus. Neuron, 60(6):1010–
2.455 1021, December 2008.
2.456 -[10]Jano van Hemert and Richard Baldock. Mining Spatial Gene Expression Data for Association Rules, pages 66–76. 2007.
2.457 -[11]Shanmugasundaram Venkataraman, Peter Stevenson, Yiya Yang, Lorna Richardson, Nicholas Burton, Thomas P. Perry,
2.458 +[16]Pavel Tomancak, Amy Beaton, Richard Weiszmann, Elaine Kwan, ShengQiang Shu, Suzanna E Lewis, Stephen
2.459 +Richards, Michael Ashburner, Volker Hartenstein, Susan E Celniker, and Gerald M Rubin. Systematic determina-
2.460 +tion of patterns of gene expression during drosophila embryogenesis. Genome Biology, 3(12):research008818814, 2002.
2.461 +PMC151190.
2.462 +[17]Jano van Hemert and Richard Baldock. Mining Spatial Gene Expression Data for Association Rules, volume 4414/2007
2.463 +of Lecture Notes in Computer Science, pages 66–76. Springer Berlin / Heidelberg, 2007.
2.464 +[18]Shanmugasundaram Venkataraman, Peter Stevenson, Yiya Yang, Lorna Richardson, Nicholas Burton, Thomas P. Perry,
2.465 Paul Smith, Richard A. Baldock, Duncan R. Davidson, and Jeffrey H. Christiansen. EMAGE edinburgh mouse atlas
2.466 of gene expression: 2008 update. Nucl. Acids Res., 36(suppl_1):D860–865, 2008.
2.467 -[12]Axel Visel, Christina Thaller, and Gregor Eichele. GenePaint.org: an atlas of gene expression patterns in the mouse
2.468 +[19]Axel Visel, Christina Thaller, and Gregor Eichele. GenePaint.org: an atlas of gene expression patterns in the mouse
2.469 embryo. Nucl. Acids Res., 32(suppl_1):D552–556, 2004.
2.470 -[13]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agar-
2.471 +[20]Robert H Waterston, Kerstin Lindblad-Toh, Ewan Birney, Jane Rogers, Josep F Abril, Pankaj Agarwal, Richa Agar-
2.472 wala, Rachel Ainscough, Marina Alexandersson, Peter An, Stylianos E Antonarakis, John Attwood, Robert Baertsch,
2.473 Jonathon Bailey, Karen Barlow, Stephan Beck, Eric Berry, Bruce Birren, Toby Bloom, Peer Bork, Marc Botcherby,
2.474 Nicolas Bray, Michael R Brent, Daniel G Brown, Stephen D Brown, Carol Bult, John Burton, Jonathan Butler,
3.1 Binary file grant.odt has changed
4.1 Binary file grant.pdf has changed
5.1 --- a/grant.txt Sat Apr 18 23:32:01 2009 -0700
5.2 +++ b/grant.txt Sat Apr 18 23:33:04 2009 -0700
5.3 @@ -3,7 +3,7 @@
5.4
5.5 == Specific aims ==
5.6
5.7 -Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, or in situ transgenic reporter allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:\\
5.8 +Massive new datasets obtained with techniques such as in situ hybridization (ISH), immunohistochemistry, in situ transgenic reporter, microarray voxelation, and others, allow the expression levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw new anatomical maps based on gene expression patterns. We have three specific aims:\\
5.9
5.10 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target anatomical regions\\
5.11
5.12 @@ -13,7 +13,7 @@
5.13
5.14 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project will support the development of new ways to selectively target cortical areas, and it will support the development of a method for identifying the cortical areal boundaries present in small tissue samples.
5.15
5.16 -All algorithms that we develop will be implemented in an open-source software toolkit. The toolkit, as well as the machine-readable datasets developed in aim (3), will be published and freely available for others to use.
5.17 +All algorithms that we develop will be implemented in a GPL open-source software toolkit. The toolkit, as well as the machine-readable datasets developed in aim (3), will be published and freely available for others to use.
5.18
5.19
5.20 \newpage
5.21 @@ -38,7 +38,7 @@
5.22
5.23 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then 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 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise the score. Such procedures are called "stepwise" or "greedy".
5.24
5.25 -Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If 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 information from the voxel itself is used to calculate a voxel's sub-score, then we say it is a __pointwise scoring method__.
5.26 +Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares or average). If 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 information from the voxel itself is used to calculate a voxel's sub-score, then we say it is a __pointwise scoring method__.
5.27
5.28 Key questions when choosing a learning method are: What are the instances? What are the features? How are the features chosen? Here are four principles that outline our answers to these questions.
5.29
5.30 @@ -71,9 +71,13 @@
5.31
5.32 As noted above, there has been much work on both supervised learning and there are many available algorithms for each. However, the algorithms require the scientist to provide a framework for representing the problem domain, and the way that this framework is set up has a large impact on performance. Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical "fine-tuning" of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application.
5.33
5.34 -We are aware of four existing efforts to find marker genes using spatial gene expression data using automated methods.
5.35 -
5.36 -\cite{carson_data_2005} describes GeneAtlas. GeneAtlas allows the user to construct a search query by freely demarcating one or two 2-D regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression pattern is to be matched. GeneAtlas differs from our Aim 1 in at least two ways. First, GeneAtlas finds only single genes, whereas we will also look for combinations of genes\footnote{See Preliminary Data for an example of an area which cannot be marked by any single gene in the dataset, but which can be marked by a combination.}. Second, at least for the custom spatial search, Gene Atlas appears to use a simple pointwise scoring method (strength of expression), whereas we will also use geometric metrics such as gradient similarity.
5.37 +We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.
5.38 +
5.39 +%%GeneAtlas\cite{carson_digital_2005} allows the user to construct a search query by freely demarcating one or two 2-D regions on sagittal slices, and then to specify either the strength of expression or the name of another gene whose expression pattern is to be matched.
5.40 +
5.41 +\cite{lee_high-resolution_2007} mentions the possibility of constructing a spatial region for each gene, and then, for each anatomical structure of interest, computing what proportion of this structure is covered by the gene's spatial region.
5.42 +
5.43 +GeneAtlas\cite{carson_digital_2005} and EMAGE \cite{venkataraman_emage_2008} allow the user to construct a search query by demarcating regions and then specifing either the strength of expression or the name of another gene or dataset whose expression pattern is to be matched. For the similiarity score (match score) between two images (in this case, the query and the gene expression images), GeneAtlas uses the sum of a weighted L1-norm distance between vectors whose components represent the number of cells within a pixel\footnote{Actually, many of these projects use quadrilaterals instead of square pixels; but we will refer to them as pixels for simplicity.} whose expression is within four discretization levels. EMAGE uses Jaccard similarity, which is equal to the number of true pixels in the intersection of the two images, divided by the number of pixels in their union. Neither GeneAtlas nor EMAGE allow one to search for combinations of genes that define a region in concert but not separately.
5.44
5.45 \cite{ng_anatomic_2009} describes AGEA, "Anatomic Gene Expression
5.46 Atlas". AGEA has three
5.47 @@ -87,18 +91,15 @@
5.48 the shows the user how much correlation there is between the gene
5.49 expression profile of the seed voxel and every other voxel.
5.50
5.51 -* Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation as the similarity metric.
5.52 +* Clusters: will be described later
5.53
5.54 Gene Finder is different from our Aim 1 in at least three ways. First, Gene Finder finds only single genes, whereas we will also look for combinations of genes. Second, gene finder can only use overexpression as a marker, whereas we will also search for underexpression. Third, Gene Finder uses a simple pointwise score\footnote{"Expression energy ratio", which captures overexpression.}, whereas we will also use geometric scores such as gradient similarity. The Preliminary Data section contains evidence that each of our three choices is the right one.
5.55
5.56 -\cite{venkataraman_emage_2008} todo
5.57 -
5.58 -
5.59 -\cite{chin_genome-scale_2007} uses a Student's t-test with Bonferroni correction to determine whether a gene is overexpressed in a specific anatomical region.
5.60 -
5.61 -\cite{hemert_matching_2008} describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their match score is Jaccard similarity, which is equal to the number of true pixels in the intersection of the two images, divided by the number of pixels in their union.
5.62 -
5.63 -In summary, only one of the previous projects explores combinations of marker genes, and none of their publications compare the results obtained by using different algorithms or scoring methods.
5.64 +\cite{chin_genome-scale_2007} looks at the mean expression level of genes within anatomical regions, and applies a Student's t-test with Bonferroni correction to determine whether the mean expression level of a gene is significantly higher in the target region. Like AGEA, this is a pointwise measure (only the mean expression level per pixel is being analyzed), it is not being used to look for underexpression, and does not look for combinations of genes.
5.65 +
5.66 +\cite{hemert_matching_2008} describes a technique to find combinations of marker genes to pick out an anatomical region. They use an evolutionary algorithm to evolve logical operators which combine boolean (thresholded) images in order to match a target image. Their match score is Jaccard similarity.
5.67 +
5.68 +In summary, there has been fruitful work on finding marker genes, however, only one of the previous projects explores combinations of marker genes, and none of these publications compare the results obtained by using different algorithms or scoring methods.
5.69
5.70
5.71
5.72 @@ -128,11 +129,13 @@
5.73
5.74
5.75 \vspace{0.3cm}**Dimensionality reduction**
5.76 -
5.77 +In this section, we discuss reducing the length of the per-pixel gene expression feature vector. By "dimension", we mean the dimension of this vector, not the spatial dimension of the underlying data.
5.78
5.79 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which "summarize" a larger number of features using a smaller number of features; these techniques go by the name of feature extraction or dimensionality reduction. The small set of features that such a technique yields is called the __reduced feature set__. After the reduced feature set is created, the instances may be replaced by __reduced instances__, which have as their features the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene expression levels.
5.80
5.81 -Another use for dimensionality reduction is to visualize the relationships between regions. For example, 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 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property -- however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.
5.82 +Dimensionality reduction before clustering is useful on large datasets. First, because the number of features in the reduced data set is less than in the original data set, the running time of clustering algorithms may be much less. Second, it is thought that some clustering algorithms may give better results on reduced data.
5.83 +
5.84 +Another use for dimensionality reduction is to visualize the relationships between regions after clustering. For example, 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 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of the points on a 2-D plan will exactly satisfy this property -- however, dimensionality reduction techniques allow one to find arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction before clustering.
5.85
5.86
5.87 \vspace{0.3cm}**Clustering genes rather than voxels**
5.88 @@ -144,10 +147,10 @@
5.89
5.90 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression pattern which seems to pick out a single, spatially continguous region. Therefore, it seems likely that an anatomically interesting region will have multiple genes which each individually pick it out\footnote{This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is possible that the currently accepted cortical maps divide the cortex into regions which are unnatural from the point of view of gene expression; 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 the cluster prototype fits an anatomical region, the individual genes are each somewhat different from the prototype.}. This suggests the following procedure: cluster together genes which pick out similar regions, and then to use the more popular common regions as the final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some "superregions" formed by lumping together a few regions, are associated with gene clusters in this fashion.
5.91
5.92 +The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering algorithms.
5.93
5.94 === Related work ===
5.95 -We are aware of four existing efforts to cluster spatial gene expression data.
5.96 -
5.97 +We are aware of five existing efforts to cluster spatial gene expression data.
5.98
5.99 \cite{thompson_genomic_2008} describes an analysis of the anatomy of
5.100 the hippocampus using the ABA dataset. In addition to manual analysis,
5.101 @@ -156,20 +159,16 @@
5.102
5.103 %% In addition, this paper described a visual screening of the data, specifically, a visual analysis of 6000 genes with the primary purpose of observing how the spatial pattern of their expression coincided with the regions that had been identified by NNMF. We propose to do this sort of screening automatically, which would yield an objective, quantifiable result, rather than qualitative observations.
5.104
5.105 -
5.106 -
5.107 -
5.108 -%% todo \cite{thompson_genomic_2008} reports that both mNNMF and hierarchial mNNMF clustering were useful, and that hierarchial recursive bifurcation gave similar results.
5.109 +%% \cite{thompson_genomic_2008} reports that both mNNMF and hierarchial mNNMF clustering were useful, and that hierarchial recursive bifurcation gave similar results.
5.110 +
5.111 +
5.112 +AGEA\cite{ng_anatomic_2009} includes a preset hierarchial clustering of voxels based on a recursive bifurcation algorithm with correlation as the similarity metric. EMAGE\cite{venkataraman_emage_2008} allows the user to select a dataset from among a large number of alternatives, or by running a search query, and then to cluster the genes within that dataset. EMAGE clusters via hierarchial complete linkage clustering with un-centred correlation as the similarity score.
5.113 +
5.114 +\cite{chin_genome-scale_2007} clustered genes, starting out by selecting 135 genes out of 20,000 which had high variance over voxels and which were highly correlated with many other genes. They computed the matrix of (rank) correlations between pairs of these genes, and ordered the rows of this matrix as follows: "the first row of the matrix was chosen to show the strongest contrast between the highest and lowest correlation coefficient for that row. The remaining rows were then arranged in order of decreasing similarity using a least squares metric". The resulting matrix showed four clusters. For each cluster, prototypical spatial expression patterns were created by averaging the genes in the cluster. The prototypes were analyzed manually, without clustering voxels
5.115
5.116 In an interesting twist, \cite{hemert_matching_2008} applies their technique for finding combinations of marker genes for the purpose of clustering 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, and then searching for other genes which can be combined to reproduce this pattern. Those other genes which are found are considered to be related to the seed. The same team also describes a method\cite{van_hemert_mining_2007} for finding "association rules" such as, "if this voxel is expressed in by any gene, then that voxel is probably also expressed in by the same gene". This could be useful as part of a procedure for clustering voxels.
5.117
5.118 -
5.119 -AGEA's\cite{ng_anatomic_2009} hierarchial clustering differs from our Aim 2 in at least two ways. First, AGEA uses perhaps the simplest possible similarity score (correlation), and does no dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Second, AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify interesting spatial regions such as cortical areas.
5.120 -
5.121 -\cite{venkataraman_emage_2008} todo
5.122 -
5.123 -
5.124 -In summary, although these projects obtained clusterings, there has not been much comparison between different algorithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found.
5.125 +In summary, although these projects obtained clusterings, there has not been much comparison between different algorithms or scoring methods, so it is likely that the best clustering method for this application has not yet been found. Also, none of these projects did a separate dimensionality reduction step before clustering pixels, none tried to cluster genes first in order to guide automated clustering of pixels into spatial regions, and none used co-clustering algorithms.
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5.127
5.128
5.129 @@ -191,7 +190,7 @@
5.130
5.131 Mus musculus, the common house mouse, is thought to contain about 22,000 protein-coding genes\cite{waterston_initial_2002}. The ABA contains data on about 20,000 genes in sagittal sections, out of which over 4,000 genes are also measured in coronal sections. Our dataset is derived from only the coronal subset of the ABA, because the sagittal data does not cover the entire cortex, and also has greater registration error\cite{ng_anatomic_2009}. Genes were selected by the Allen Institute for coronal sectioning based on, "classes of known neuroscientific interest... or through post hoc identification of a marked non-ubiquitous expression pattern"\cite{ng_anatomic_2009}.
5.132
5.133 -The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT\cite{gong_gene_2003}, GenePaint\cite{visel_genepaint.org:atlas_2004}, its sister project GeneAtlas\cite{carson_data_2005}, BGEM\cite{magdaleno_bgem:in_2006}, EMAGE\cite{venkataraman_emage_2008}, EurExpress\footnote{http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE}, EADHB\footnote{http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html}, MAMEP\footnote{http://mamep.molgen.mpg.de/index.php}, Xenbase\footnote{http://xenbase.org/}, ZFIN\cite{sprague_zebrafish_2006}, Aniseed\footnote{http://aniseed-ibdm.univ-mrs.fr/}, VisiGene\footnote{http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources}, GEISHA\cite{bell_geisha_2004}, Fruitfly.org\cite{tomancak_systematic_2002}, COMPARE\cite{http://compare.ibdml.univ-mrs.fr/} todo. With the exception of the ABA, GenePaint, and EMAGE, most of these resources, have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D space, and only ABA and EMAGE make this form of data available for public download from the website. Many of these resources focus on developmental gene expression.
5.134 +The ABA is not the only large public spatial gene expression dataset. Other such resources include GENSAT\cite{gong_gene_2003}, GenePaint\cite{visel_genepaint.org:atlas_2004}, its sister project GeneAtlas\cite{carson_digital_2005}, BGEM\cite{magdaleno_bgem:in_2006}, EMAGE\cite{venkataraman_emage_2008}, EurExpress\footnote{http://www.eurexpress.org/ee/; EurExpress data is also entered into EMAGE}, EADHB\footnote{http://www.ncl.ac.uk/ihg/EADHB/database/EADHB_database.html}, MAMEP\footnote{http://mamep.molgen.mpg.de/index.php}, Xenbase\footnote{http://xenbase.org/}, ZFIN\cite{sprague_zebrafish_2006}, Aniseed\footnote{http://aniseed-ibdm.univ-mrs.fr/}, VisiGene\footnote{http://genome.ucsc.edu/cgi-bin/hgVisiGene ; includes data from some the other listed data sources}, GEISHA\cite{bell_geishawhole-mount_2004}, Fruitfly.org\cite{tomancak_systematic_2002}, COMPARE\footnote{http://compare.ibdml.univ-mrs.fr/} GXD\cite{smith_mouse_2007}, GEO\cite{barrett_ncbi_2007}\footnote{GXD and GEO contain spatial data but also non-spatial data. All GXD spatial data are also in EMAGE.}. With the exception of the ABA, GenePaint, and EMAGE, most of these resources have not (yet) extracted the expression intensity from the ISH images and registered the results into a single 3-D space, and to our knowledge only ABA and EMAGE make this form of data available for public download from the website\footnote{without prior offline registration}. Many of these resources focus on developmental gene expression.
5.135
5.136
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5.138 @@ -201,7 +200,8 @@
5.139
5.140 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatomical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.
5.141
5.142 -The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of a better map. The development of present-day cortical maps was driven by the application of histological stains. It is conceivable that if a different set of stains had been available which identified a different set of features, then the today's cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking at the patterns of gene expression.
5.143 +The method developed in aim (2) will provide a genoarchitectonic viewpoint that will contribute to the creation of a better map. The development of present-day cortical maps was driven by the application of histological stains. It is conceivable that if a different set of stains had been available which identified a different set of features, then the today's cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking at the patterns of gene expression.
5.144 +
5.145
5.146 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to develop could be used to suggest modifications to the human cortical map as well.
5.147
5.148 @@ -218,7 +218,6 @@
5.149 Our project is guided by a concrete application with a well-specified criterion of success (how well we can find marker genes for \begin{latex}/\end{latex} reproduce the layout of cortical areas), which will provide a solid basis for comparing different methods.
5.150
5.151
5.152 -%% todo: poster; check AGEA cortical data
5.153
5.154 \newpage
5.155
5.156 @@ -294,7 +293,7 @@
5.157
5.158 \vspace{0.3cm}**Gradient similarity provides information complementary to correlation**
5.159
5.160 -To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider Fig. \ref{AUDgeometry}. The top row of Fig. \ref{AUDgeometry} displays the 3 genes which most match area AUD, according to a pointwise method\footnote{For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor 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 they predict area AUD.}. The bottom row displays the 3 genes which most match AUD according to a method which considers local geometry\footnote{For each gene the gradient similarity (see section \ref{gradientSim}) between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this was used to rank the genes.} The pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this includes many areas which don't have a salient border matching the areal border. The geometric method identifies genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes genes which don't express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as $Aph1a$ in the example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD; we deliberately chose a "difficult" area in order to better contrast pointwise with geometric methods.
5.161 +To show that gradient similarity can provide useful information that cannot be detected via pointwise analyses, consider Fig. \ref{AUDgeometry}. The top row of Fig. \ref{AUDgeometry} displays the 3 genes which most match area AUD, according to a pointwise method\footnote{For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor 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 they predict area AUD.}. The bottom row displays the 3 genes which most match AUD according to a method which considers local geometry\footnote{For each gene the gradient similarity between (a) a map of the expression of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this was used to rank the genes.} The pointwise method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this includes many areas which don't have a salient border matching the areal border. The geometric method identifies genes whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes genes which don't express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as $Aph1a$ in the example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD; we deliberately chose a "difficult" area in order to better contrast pointwise with geometric methods.
5.162
5.163
5.164 \begin{figure}\label{AUDgeometry}
5.165 @@ -408,6 +407,7 @@
5.166 # Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised learning techniques which use soft constraints to minimize the number of features, such as sparse support vector machines.
5.167 # Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult to identify because the boundaries are misdrawn, or because it does not "really" exist as a single area, at least on the genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create a larger area which can be fit.
5.168
5.169 +# Linear discriminant analysis
5.170
5.171
5.172 \vspace{0.3cm}**Apply these algorithms to the cortex**
5.173 @@ -418,6 +418,7 @@
5.174 # Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify that area; and we will also present lists of "panels" of genes that can be used to delineate many areas at once.
5.175
5.176
5.177 +
5.178 \vspace{0.3cm}**Develop algorithms to suggest a division of a structure into anatomical parts**
5.179
5.180 # Explore dimensionality reduction algorithms applied to pixels: including TODO
5.181 @@ -427,6 +428,15 @@
5.182 # Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
5.183 # Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
5.184
5.185 +# Linear discriminant analysis
5.186 +
5.187 +# jbt, coclustering
5.188 +
5.189 +# self-organizing map
5.190 +
5.191 +# confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting
5.192 +
5.193 +# compare using clustering scores
5.194
5.195
5.196 \newpage