cg

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.
author bshanks@bshanks.dyndns.org
date Mon Apr 20 14:33:20 2009 -0700 (16 years ago)
parents f14c34563ff8
children 60d7c1c1b94f
line source
1 \documentclass{nih-blank}
2 %%\piname{Stevens, Charles F.}
4 == Specific aims ==
6 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:\\
8 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target anatomical regions\\
10 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical regions, based on spatial patterns in gene expression\\
12 (3) create a 2-D "flat map" dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. This will involve extending the functionality of Caret, an existing open-source scientific imaging program. Use this dataset to validate the methods developed in (1) and (2).\\
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.
16 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.
19 \newpage
21 == Background and significance ==
23 === Aim 1 ===
25 \vspace{0.3cm}**Machine learning terminology: supervised learning**
27 The task of looking for marker genes for anatomical regions means that one is looking for a set of genes such that, if the expression level of those genes is known, then the locations of the regions can be inferred.
29 If we define the regions so that they cover the entire anatomical structure to be divided, then instead of saying that we are using gene expression to find the locations of the regions, we may say that we are using gene expression to determine to which region each voxel within the structure belongs. We call this a __classification task__, because each voxel is being assigned to a class (namely, its region).
31 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of the regions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels within that voxel; the output is the regional identity of the target voxel, that is, the region to which the target voxel belongs. We call this function a __classifier__. In general, the input to a classifier is called an __instance__, and the output is called a __label__ (or a __class label__).
33 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning procedure. The construction of the classifier is called __training__ (also __learning__), and the initial gene expression dataset used in the construction of the classifier is called __training data__.
35 In the machine learning literature, this sort of procedure may be thought of as a __supervised learning task__, defined as a task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances (voxels) for which the labels (regions) are known.
37 Each gene expression level is called a __feature__, and the selection of which genes\footnote{Strictly speaking, the features are gene expression levels, but we'll call them genes.} to include is called __feature selection__. Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.
39 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".
41 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__.
43 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.
46 \vspace{0.3cm}**Principle 1: Combinatorial gene expression**
47 It is too much to hope that every anatomical region of interest will be identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary Results). Therefore, each instance should contain multiple features (genes).
50 \vspace{0.3cm}**Principle 2: Only look at combinations of small numbers of genes**
51 When the classifier classifies a voxel, it is only allowed to look at the expression of the genes which have been selected as features. The more data that is available to a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations 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 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the 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 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as features.
53 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task combines feature selection with supervised learning.
56 \vspace{0.3cm}**Principle 3: Use geometry in feature selection**
58 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.
62 \vspace{0.3cm}**Principle 4: Work in 2-D whenever possible**
65 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D data.
67 Therefore, when possible, the instances should represent pixels, not voxels.
70 === Related work ===
71 There is a substantial body of work on the analysis of gene expression data, most of this concerns gene expression data which is not fundamentally spatial\footnote{By "__fundamentally__ spatial" we mean that there is information from a large number of spatial locations indexed by spatial coordinates; not just data which has only a few different locations or which is indexed by anatomical label.}.
73 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.
75 We are aware of six existing efforts to find marker genes using spatial gene expression data using automated methods.
77 %%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.
79 \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.
81 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.
83 \cite{ng_anatomic_2009} describes AGEA, "Anatomic Gene Expression
84 Atlas". AGEA has three
85 components:
87 \begin{itemize}
88 \item Gene Finder: The user selects a seed voxel and the system (1) chooses a
89 cluster which includes the seed voxel, (2) yields a list of genes
90 which are overexpressed in that cluster. (note: the ABA website also contains pre-prepared lists of overexpressed genes for selected structures)
92 \item Correlation: The user selects a seed voxel and
93 the shows the user how much correlation there is between the gene
94 expression profile of the seed voxel and every other voxel.
96 \item Clusters: will be described later
97 \end{itemize}
99 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.
101 \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.
103 \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.
105 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.
110 === Aim 2 ===
112 \vspace{0.3cm}**Machine learning terminology: clustering**
114 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as __unsupervised learning__ in the jargon of machine learning. One thing that you can do with such a dataset is to group instances together. A set of similar instances is called a __cluster__, and the activity of finding grouping the data into clusters is called clustering or cluster analysis.
116 The task of deciding how to carve up a structure into anatomical regions can be put into these terms. The instances are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels from the same region have similar gene expression profiles, at least compared to the other regions. This means that clustering voxels is the same as finding potential regions; we seek a partitioning of the voxels into regions, that is, into clusters of voxels with similar gene expression.
118 It is desirable to determine not just one set of regions, but also how these regions relate to each other, if at all; perhaps some of the regions are more similar to each other than to the rest, suggesting that, although at a fine spatial scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large region. This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which partition the voxels. This is called hierarchial clustering.
121 \vspace{0.3cm}**Similarity scores**
123 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and scoring methods for similarity.
126 \vspace{0.3cm}**Spatially contiguous clusters; image segmentation**
129 We have shown that aim 2 is a type of clustering task. In fact, it is a special type of clustering task because we have an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these results against other methods which guarantee contiguous clusters.
131 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of spatially arranged data, some of these algorithms are specialized for visual images.
134 \vspace{0.3cm}**Dimensionality reduction**
135 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.
137 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.
139 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.
141 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.
144 \vspace{0.3cm}**Clustering genes rather than voxels**
147 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster the features (genes). There are two ways that clusters of genes could be used.
149 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could have one reduced feature for each gene cluster.
151 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.
153 The task of clustering both the instances and the features is called co-clustering, and there are a number of co-clustering algorithms.
155 === Related work ===
156 We are aware of five existing efforts to cluster spatial gene expression data.
158 \cite{thompson_genomic_2008} describes an analysis of the anatomy of
159 the hippocampus using the ABA dataset. In addition to manual analysis,
160 two clustering methods were employed, a modified Non-negative Matrix
161 Factorization (NNMF), and a hierarchial recursive bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the usefulness of computational genomic anatomy. We have run NNMF on the cortical dataset\footnote{We ran "vanilla" NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was needed. The paper under discussion also mentions that they tried a hierarchial variant of NNMF, which we have not yet tried.} and while the results are promising (see Preliminary Data), we think that it will be possible to find an even better method.
163 %% 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.
165 %% \cite{thompson_genomic_2008} reports that both mNNMF and hierarchial mNNMF clustering were useful, and that hierarchial recursive bifurcation gave similar results.
168 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.
170 \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
172 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.
174 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.
178 === Aim 3 ===
180 \vspace{0.3cm}**Background**
182 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can picture an area of the cortex as a slice of many-layered cake.
184 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes, there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas, this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of their approximate location upon the cortical surface.
186 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a single agreed-upon map can be seen by contrasting the recent maps given by Swanson\cite{swanson_brain_2003} on the one hand, and Paxinos and Franklin\cite{paxinos_mouse_2001} on the other. While the maps are certainly very similar in their general arrangement, significant differences remain in the details.
188 \vspace{0.3cm}**The Allen Mouse Brain Atlas dataset**
190 The Allen Mouse Brain Atlas (ABA) data was produced by doing in-situ hybridization on slices of male, 56-day-old C57BL/6J mouse brains. Pictures were taken of the processed slice, and these pictures were semi-automatically analyzed in order to create a digital measurement of gene expression levels at each location in each slice. Per slice, cellular spatial resolution is achieved. Using this method, a single physical slice can only be used to measure one single gene; many different mouse brains were needed in order to measure the expression of many genes.
192 Next, an automated nonlinear alignment procedure located the 2D data from the various slices in a single 3D coordinate system. In the final 3D coordinate system, voxels are cubes with 200 microns on a side. There are 67x41x58 \= 159,326 voxels in the 3D coordinate system, of which 51,533 are in the brain\cite{ng_anatomic_2009}.
194 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}.
196 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.
200 \vspace{0.3cm}**Significance**
202 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively target individual cortical areas.
204 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.
206 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.
209 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.
212 === Related work ===
214 \cite{ng_anatomic_2009} describes the application of AGEA to the cortex. The paper describes interesting results on the structure of correlations between voxel gene expression profiles within a handful of cortical areas. However, this sort of analysis is not related to either of our aims, as it neither finds marker genes, nor does it suggest a cortical map based on gene expression data. Neither of the other components of AGEA can be applied to cortical areas; AGEA's Gene Finder cannot be used to find marker genes for the cortical areas; and AGEA's hierarchial clustering does not produce clusters corresponding to the cortical areas\footnote{In both cases, the root cause is that pairwise correlations between the gene expression of voxels in different areas but the same layer are often stronger than pairwise correlations between the gene expression of voxels in different layers but the same area. Therefore, a pairwise voxel correlation clustering algorithm will tend to create clusters representing cortical layers, not areas. This is why the hierarchial clustering does not 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 many layer-area intersection clusters, further work is needed to make sense of these). The reason that Gene Finder cannot find marker genes for 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, and it creates that ROI by (pairwise voxel correlation) clustering around the seed.}.
217 %% Most of the projects which have been discussed have been done by the same groups that develop the public datasets. Although these projects make their algorithms available for use on their own website, none of them have released an open-source software toolkit; instead, users are restricted to using the provided algorithms only on their own dataset.
219 In summary, for all three aims, (a) only one of the previous projects explores combinations of marker genes, (b) there has been almost no comparison of different algorithms or scoring methods, and (c) there has been no work on computationally finding marker genes for cortical areas, or on finding a hierarchial clustering that will yield a map of cortical areas de novo from gene expression data.
221 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.
225 \newpage
227 == Preliminary work ==
229 === Format conversion between SEV, MATLAB, NIFTI ===
230 We have created software to (politely) download all of the SEV files from the Allen Institute website. We have also created software to convert between the SEV, MATLAB, and NIFTI file formats, as well as some of Caret's file formats.
233 === Flatmap of cortex ===
234 We downloaded the ABA data and applied a mask to select only those voxels which belong to cerebral cortex. We divided the cortex into hemispheres.
236 Using Caret\cite{van_essen_integrated_2001}, we created a mesh representation of the surface of the selected voxels. For each gene, for each node of the mesh, we calculated an average of the gene expression of the voxels "underneath" that mesh node. We then flattened the cortex, creating a two-dimensional mesh.
238 We sampled the nodes of the irregular, flat mesh in order to create a regular grid of pixel values. We converted this grid into a MATLAB matrix.
240 We manually traced the boundaries of each of 49 cortical areas from the ABA coronal reference atlas slides. We then converted these manual traces into Caret-format regional boundary data on the mesh surface. We projected the regions onto the 2-d mesh, and then onto the grid, and then we converted the region data into MATLAB format.
242 At this point, the data is in the form of a number of 2-D matrices, all in registration, with the matrix entries representing a grid of points (pixels) over the cortical surface:
244 * A 2-D matrix whose entries represent the regional label associated with each surface pixel
245 * For each gene, a 2-D matrix whose entries represent the average expression level underneath each surface pixel
247 We created a normalized version of the gene expression data by subtracting each gene's mean expression level (over all surface pixels) and dividing each gene by its standard deviation.
249 The features and the target area are both functions on the surface pixels. They can be referred to as scalar fields over the space of surface pixels; alternately, they can be thought of as images which can be displayed on the flatmapped surface.
251 To move beyond a single average expression level for each surface pixel, we plan to create a separate matrix for each cortical layer to represent the average expression level within that layer. Cortical layers are found at different depths in different parts of the cortex. In preparation for extracting the layer-specific datasets, we have extended Caret with routines that allow the depth of the ROI for volume-to-surface projection to vary.
253 In the Research Plan, we describe how we will automatically locate the layer depths. For validation, we have manually demarcated the depth of the outer boundary of cortical layer 5 throughout the cortex.
261 === Feature selection and scoring methods ===
263 \vspace{0.3cm}**Underexpression of a gene can serve as a marker**
264 Underexpression of a gene can sometimes serve as a marker. See, for example, Figure \ref{hole}.
267 \begin{figure}\centering
268 \includegraphics[scale=.31]{holeExample_2682_SS_jet.eps}
269 \caption{Gene Pitx2 is selectively underexpressed in area SS (somatosensory).}
270 \label{hole}\end{figure}
273 \vspace{0.3cm}**Correlation**
274 Recall that the instances are surface pixels, and consider the problem of attempting to classify each instance as either a member of a particular anatomical area, or not. The target area can be represented as a boolean mask over the surface pixels.
276 One class of feature selection scoring method are those which calculate some sort of "match" between each gene image and the target image. Those genes which match the best are good candidates for features.
278 One of the simplest methods in this class is to use correlation as the match score. We calculated the correlation between each gene and each cortical area. The top row of Figure \ref{SScorrLr} shows the three genes most correlated with area SS.
280 \begin{figure}\centering
281 \includegraphics[scale=.31]{singlegene_SS_corr_top_1_2365_jet.eps}
282 \includegraphics[scale=.31]{singlegene_SS_corr_top_2_242_jet.eps}
283 \includegraphics[scale=.31]{singlegene_SS_corr_top_3_654_jet.eps}
284 \\
285 \includegraphics[scale=.31]{singlegene_SS_lr_top_1_654_jet.eps}
286 \includegraphics[scale=.31]{singlegene_SS_lr_top_2_685_jet.eps}
287 \includegraphics[scale=.31]{singlegene_SS_lr_top_3_724_jet.eps}
290 \caption{Top row: Genes Nfic, A930001M12Rik, C130038G02Rik are the most correlated with area SS (somatosensory cortex). Bottom row: Genes C130038G02Rik, Cacna1i, Car10 are those with the best fit using logistic regression. Within each picture, the vertical axis roughly corresponds to anterior at the top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right. The red outline is the boundary of region MO. Pixels are colored according to correlation, with red meaning high correlation and blue meaning low.}
291 \label{SScorrLr}\end{figure}
295 \vspace{0.3cm}**Conditional entropy**
296 An information-theoretic scoring method is to find features such that, if the features (gene expression levels) are known, uncertainty about the target (the regional identity) is reduced. Entropy measures uncertainty, so what we want is to find features such that the conditional distribution of the target has minimal entropy. The distribution to which we are referring is the probability distribution over the population of surface pixels.
298 The simplest way to use information theory is on discrete data, so we discretized our gene expression data by creating, for each gene, five thresholded boolean masks of the gene data. For each gene, we created a boolean mask of its expression levels using each of these thresholds: the mean of that gene, the mean minus one standard deviation, the mean minus two standard deviations, the mean plus one standard deviation, the mean plus two standard deviations.
300 Now, for each region, we created and ran a forward stepwise procedure which attempted to find pairs of gene expression boolean masks such that the conditional entropy of the target area's boolean mask, conditioned upon the pair of gene expression boolean masks, is minimized.
302 This finds pairs of genes which are most informative (at least at these discretization thresholds) relative to the question, "Is this surface pixel a member of the target area?". Its advantage over linear methods such as logistic regression is that it takes account of arbitrarily nonlinear relationships; for example, if the XOR of two variables predicts the target, conditional entropy would notice, whereas linear methods would not.
305 \vspace{0.3cm}**Gradient similarity**
306 We noticed that the previous two scoring methods, which are pointwise, often found genes whose pattern of expression did not look similar in shape to the target region. For this reason we designed a non-pointwise local scoring method to detect when a gene had a pattern of expression which looked like it had a boundary whose shape is similar to the shape of the target region. We call this scoring method "gradient similarity".
308 One might say that gradient similarity attempts to measure how much the border of the area of gene expression and the border of the target region overlap. However, since gene expression falls off continuously rather than jumping from its maximum value to zero, the spatial pattern of a gene's expression often does not have a discrete border. Therefore, instead of looking for a discrete border, we look for large gradients. Gradient similarity is a symmetric function over two images (i.e. two scalar fields). It is is high to the extent that matching pixels which have large values and large gradients also have gradients which are oriented in a similar direction. The formula is:
310 \begin{align*}
311 \sum_{pixel \in pixels} cos(abs(\angle \nabla_1 - \angle \nabla_2)) \cdot \frac{\vert \nabla_1 \vert + \vert \nabla_2 \vert}{2} \cdot \frac{pixel\_value_1 + pixel\_value_2}{2}
312 \end{align*}
314 where $\nabla_1$ and $\nabla_2$ are the gradient vectors of the two images at the current pixel; $\angle \nabla_i$ is the angle of the gradient of image $i$ at the current pixel; $\vert \nabla_i \vert$ is the magnitude of the gradient of image $i$ at the current pixel; and $pixel\_value_i$ is the value of the current pixel in image $i$.
316 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, then both images will have corresponding pixels with large gradients (because this is a border) which are oriented in a similar direction (because the borders are similar).
318 Most of the genes in Figure \ref{singleSoFar} were identified via gradient similarity.
320 \vspace{0.3cm}**Gradient similarity provides information complementary to correlation**
322 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.
325 \begin{figure}\centering
326 \includegraphics[scale=.31]{singlegene_AUD_lr_top_1_3386_jet.eps}
327 \includegraphics[scale=.31]{singlegene_AUD_lr_top_2_1258_jet.eps}
328 \includegraphics[scale=.31]{singlegene_AUD_lr_top_3_420_jet.eps}
330 \includegraphics[scale=.31]{singlegene_AUD_gr_top_1_2856_jet.eps}
331 \includegraphics[scale=.31]{singlegene_AUD_gr_top_2_420_jet.eps}
332 \includegraphics[scale=.31]{singlegene_AUD_gr_top_3_2072_jet.eps}
333 \caption{The top row shows the three genes which (individually) best predict area AUD, according to logistic regression. The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From left to right and top to bottom, the genes are $Ssr1$, $Efcbp1$, $Aph1a$, $Ptk7$, $Aph1a$ again, and $Lepr$}
334 \label{AUDgeometry}\end{figure}
337 \vspace{0.3cm}**Areas which can be identified by single genes**
338 Using gradient similarity, we have already found single genes which roughly identify some areas and groupings of areas. For each of these areas, an example of a gene which roughly identifies it is shown in Figure \ref{singleSoFar}. We have not yet cross-verified these genes in other atlases.
340 In addition, there are a number of areas which are almost identified by single genes: COAa+NLOT (anterior part of cortical amygdalar area, nucleus of the lateral olfactory tract), ENT (entorhinal), ACAv (ventral anterior cingulate), VIS (visual), AUD (auditory).
343 \begin{figure}\centering
344 \includegraphics[scale=.31]{singlegene_example_2682_Pitx2_SS_jet.eps}
345 \includegraphics[scale=.31]{singlegene_example_371_Aldh1a2_SSs_jet.eps}
346 \includegraphics[scale=.31]{singlegene_example_2759_Ppfibp1_PIR_jet.eps}
347 \includegraphics[scale=.31]{singlegene_example_3310_Slco1a5_FRP_jet.eps}
348 \includegraphics[scale=.31]{singlegene_example_3709_Tshz2_RSP_jet.eps}
349 \includegraphics[scale=.31]{singlegene_example_3674_Trhr_COApm_jet.eps}
350 \includegraphics[scale=.31]{singlegene_example_925_Col12a1_ACA+PL+ILA+DP+ORB+MO_jet.eps}
351 \includegraphics[scale=.31]{singlegene_example_1334_Ets1_post_lat_vis_jet.eps}
353 \caption{From left to right and top to bottom, single genes which roughly identify areas SS (somatosensory primary + supplemental), SSs (supplemental somatosensory), PIR (piriform), FRP (frontal pole), RSP (retrosplenial), COApm (Cortical amygdalar, posterior part, medial zone). Grouping some areas together, we have also found genes to identify the groups ACA+PL+ILA+DP+ORB+MO (anterior cingulate, prelimbic, infralimbic, dorsal peduncular, orbital, motor), posterior and lateral visual (VISpm, VISpl, VISI, VISp; posteromedial, posterolateral, lateral, and primary visual; the posterior and lateral visual area is distinguished from its neighbors, but not from the entire rest of the cortex). The genes are $Pitx2$, $Aldh1a2$, $Ppfibp1$, $Slco1a5$, $Tshz2$, $Trhr$, $Col12a1$, $Ets1$.}
354 \label{singleSoFar}\end{figure}
358 \vspace{0.3cm}**Combinations of multiple genes are useful and necessary for some areas**
360 In Figure \ref{MOcombo}, we give an example of a cortical area which is not marked by any single gene, but which can be identified combinatorially.
362 %% wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652}
363 %% mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784}
365 %%Acccording to logistic regression, gene wwc1\footnote{"WW, C2 and coiled-coil domain containing 1"; EntrezGene ID 211652} is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface.
367 %%Gene mtif2\footnote{"mitochondrial translational initiation factor 2"; EntrezGene ID 76784} is shown in figure the upper-right of Fig. \ref{MOcombo}. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left of Figure \ref{MOcombo}. This combination captures area MO much better than any single gene.
369 \begin{figure}\centering
370 \includegraphics[scale=.36]{MO_vs_Wwc1_jet.eps}
371 \includegraphics[scale=.36]{MO_vs_Mtif2_jet.eps}
373 \includegraphics[scale=.36]{MO_vs_Wwc1_plus_Mtif2_jet.eps}
374 \caption{Upper left: $wwc1$. Upper right: $mtif2$. Lower left: wwc1 + mtif2 (each pixel's value on the lower left is the sum of the corresponding pixels in the upper row). Acccording to logistic regression, gene wwc1 is the best fit single gene for predicting whether or not a pixel on the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure \ref{MOcombo} shows wwc1's spatial expression pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the overshoot is the medial surface of the cortex. MO is only found on the lateral surface. Gene mtif2 is shown in the upper-right. Mtif2 captures MO's upper-left boundary, but not its lower-right boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these two figures, we get the lower-left image. This combination captures area MO much better than any single gene. }
375 \label{MOcombo}\end{figure}
384 \vspace{0.3cm}**Feature selection integrated with prediction**
385 As noted earlier, in general, any predictive method can be used for feature selection by running it inside a stepwise wrapper. Also, some predictive methods integrate soft constraints on number of features used. Examples of both of these will be seen in the section "Multivariate Predictive methods".
388 === Multivariate Predictive methods ===
389 \vspace{0.3cm}**Forward stepwise logistic regression**
390 As a pilot run, for five cortical areas (SS, AUD, RSP, VIS, and MO), we performed forward stepwise logistic regression to find single genes, pairs of genes, and triplets of genes which predict areal identify. This is an example of feature selection integrated with prediction using a stepwise wrapper. Some of the single genes found were shown in various figures throughout this document, and Figure \ref{MOcombo} shows a combination of genes which was found.
392 We felt that, for single genes, gradient similarity did a better job than logistic regression at capturing our subjective impression of a "good gene".
395 \vspace{0.3cm}**SVM on all genes at once**
397 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 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%\footnote{5-fold cross-validation.}. As noted above, however, a classifier that looks at all the genes at once isn't as practically useful as a classifier that uses only a few genes.
403 === Data-driven redrawing of the cortical map ===
405 We have applied the following dimensionality reduction algorithms to reduce the dimensionality of the gene expression profile associated with each voxel: Principal Components Analysis (PCA), Simple PCA (SPCA), Multi-Dimensional Scaling (MDS), Isomap, Landmark Isomap, Laplacian eigenmaps, Local Tangent Space Alignment (LTSA), Hessian locally linear embedding, Diffusion maps, Stochastic Neighbor Embedding (SNE), Stochastic Proximity Embedding (SPE), Fast Maximum Variance Unfolding (FastMVU), Non-negative Matrix Factorization (NNMF). Space constraints prevent us from showing many of the results, but as a sample, PCA, NNMF, and landmark Isomap are shown in the second, third, and fourth rows of Figure \ref{dimReduc}.
407 After applying the dimensionality reduction, we ran clustering algorithms on the reduced data. To date we have tried k-means and spectral clustering. The results of k-means after PCA, NNMF, and landmark Isomap are shown in the last row of Figure \ref{dimReduc}. To compare, the first row of Figure \ref{dimReduc} shows some of the major subdivisions of cortex.
409 \begin{figure}\centering
410 \includegraphics[scale=.31]{paint_merge3_major.eps}
411 \\
412 \includegraphics[scale=1]{merge3_norm_hv_PCA_ndims50_prototypes_collage_sm_border.eps}
413 \includegraphics[scale=1]{nnmf_ndims7_collage_border.eps}
414 \includegraphics[scale=1]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_prototypes_collage_sm_border.eps}
415 \\
416 \includegraphics[scale=.31]{merge3_norm_hv_PCA_ndims50_kmeans_7clust.eps}
417 \includegraphics[scale=.31]{norm_hv_NNMF_3_norm_kmeans_4clust.eps}
418 \includegraphics[scale=.31]{merge3_norm_hv_k150_LandmarkIsomap_ndims7_kmeans_7clust.eps}
419 \caption{Top row: 19 of the major subdivisions of the cortex. Second row: the first 6 reduced dimensions, using PCA. Third row: the first 6 reduced dimensions, using NNMF. Fourth row: the first six reduced dimensions, using landmark Isomap. Bottom row: examples of kmeans clustering applied to reduced datasets to find 7 clusters. Left: PCA. Middle: NNMF. Right: Landmark Isomap. Additional details: In the third and fourth rows, 7 dimensions were found, but only 6 displayed. In the last row: for PCA, 50 dimensions were used; for NNMF, 6 dimensions were used; for landmark Isomap, 7 dimensions were used.}
420 \label{dimReduc}\end{figure}
422 todo: nnmf 7
424 \vspace{0.3cm}**Many areas are captured by clusters of genes**
426 todo
438 todo
442 \newpage
443 == Research plan ==
446 \vspace{0.3cm}**Further work on flatmapping**
449 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo), 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 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.
451 In the case of the cerebral cortex, it remains to be seen which method of mapping the manifold into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used by Caret\cite{van_essen_integrated_2001}) with mappings which preserve angle (conformal maps).
453 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional. If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D structure seems to be wrong.
456 todo amongst other things:
459 layerfinding
464 \vspace{0.3cm}**Develop algorithms that find genetic markers for anatomical regions**
466 # Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise, geometric, and information-theoretic measures.
467 # Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining the scoring measures developed, we will rank the genes by their ability to delineate each area.
468 # 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.
469 # 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.
471 # Linear discriminant analysis
474 \vspace{0.3cm}**Decision trees**
475 todo
477 For each cortical area, we used the C4.5 algorithm to find a pruned decision tree and ruleset for that area. We achieved estimated classification accuracy of more than 99.6% on each cortical area (as evaluated on the __training data__ without cross-validation; so actual accuracy is expected to be lower). However, the resulting decision trees each made use of many genes.
480 \vspace{0.3cm}**Apply these algorithms to the cortex**
482 # Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert between SEV, NIFTI and MATLAB formats.
483 # Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.
484 # Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.
485 # 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.
489 \vspace{0.3cm}**Develop algorithms to suggest a division of a structure into anatomical parts**
491 # mixture models, etc
493 # Explore dimensionality reduction algorithms applied to pixels: including TODO
494 # Explore dimensionality reduction algorithms applied to genes: including TODO
495 # Explore clustering algorithms applied to pixels: including TODO
496 # Explore clustering algorithms applied to genes: including gene shaving, TODO
497 # Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
498 # Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
500 # Linear discriminant analysis
502 # jbt, coclustering
504 # self-organizing map
506 # confirm with EMAGE, GeneAtlas, GENSAT, etc, to fight overfitting
508 # compare using clustering scores
510 # multivariate gradient similarity
512 # deep belief nets
514 # note: slice artifact
516 \newpage
518 \bibliographystyle{plain}
519 \bibliography{grant}
521 \newpage
523 ----
525 stuff i dunno where to put yet (there is more scattered through grant-oldtext):
528 \vspace{0.3cm}**Principle 4: Work in 2-D whenever possible**
533 %%if we need citations for aim 3 significance, http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WSS-4V70FHY-9&_user=4429&_coverDate=12%2F26%2F2008&_rdoc=1&_fmt=full&_orig=na&_cdi=7054&_docanchor=&_acct=C000059602&_version=1&_urlVersion=0&_userid=4429&md5=551eccc743a2bfe6e992eee0c3194203#app2 has examples of genetic targeting to specific anatomical regions
535 ---
537 note:
542 two hemis
545 %%"genomic anatomy" is a name found in the titles of one of the cited papers which seems good; maybe "computational genomic anatomy"
547 %% todo: actually i'm pretty sure AGEA doesn't find ANY areas, but i said "most" and "often" to be cautious.
549 %% todo: MO is only found on the lateral surface (todo).
550 %% todo: predicted genes like Riken
552 %% todo: should we disclose genes?