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| bshanks@0 | 1 Specific aims
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| bshanks@33 | 2 Massive new datasets obtained with techniques such as in situ hybridization (ISH) and BAC-transgenics allow the expres-
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| bshanks@33 | 3 sion levels of many genes at many locations to be compared. Our goal is to develop automated methods to relate spatial
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| bshanks@33 | 4 variation in gene expression to anatomy. We want to find marker genes for specific anatomical regions, and also to draw
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| bshanks@33 | 5 new anatomical maps based on gene expression patterns. We have three specific aims:
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| bshanks@30 | 6 (1) develop an algorithm to screen spatial gene expression data for combinations of marker genes which selectively target
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| bshanks@30 | 7 anatomical regions
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| bshanks@30 | 8 (2) develop an algorithm to suggest new ways of carving up a structure into anatomical subregions, based on spatial
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| bshanks@30 | 9 patterns in gene expression
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| bshanks@33 | 10 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that contains a flattened version of the Allen Mouse
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| bshanks@33 | 11 Brain Atlas ISH data, as well as the boundaries of cortical anatomical areas. Use this dataset to validate the methods
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| bshanks@33 | 12 developed in (1) and (2).
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| bshanks@30 | 13 In addition to validating the usefulness of the algorithms, the application of these methods to cerebral cortex will produce
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| bshanks@30 | 14 immediate benefits, because there are currently no known genetic markers for many cortical areas. The results of the project
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| bshanks@33 | 15 will support the development of new ways to selectively target cortical areas, and it will support the development of a
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| bshanks@33 | 16 method for identifying the cortical areal boundaries present in small tissue samples.
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| bshanks@33 | 17 All algorithms that we develop will be implemented in an open-source software toolkit. The toolkit, as well as the
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| bshanks@30 | 18 machine-readable datasets developed in aim (3), will be published and freely available for others to use.
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| bshanks@30 | 19 Background and significance
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| bshanks@30 | 20 Aim 1
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| bshanks@30 | 21 Machine learning terminology: supervised learning
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| bshanks@30 | 22 The task of looking for marker genes for anatomical subregions means that one is looking for a set of genes such that, if
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| bshanks@30 | 23 the expression level of those genes is known, then the locations of the subregions can be inferred.
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| bshanks@30 | 24 If we define the subregions so that they cover the entire anatomical structure to be divided, then instead of saying that we
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| bshanks@30 | 25 are using gene expression to find the locations of the subregions, we may say that we are using gene expression to determine
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| bshanks@30 | 26 to which subregion each voxel within the structure belongs. We call this a classification task, because each voxel is being
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| bshanks@30 | 27 assigned to a class (namely, its subregion).
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| bshanks@30 | 28 Therefore, an understanding of the relationship between the combination of their expression levels and the locations of
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| bshanks@33 | 29 the subregions may be expressed as a function. The input to this function is a voxel, along with the gene expression levels
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| bshanks@30 | 30 within that voxel; the output is the subregional identity of the target voxel, that is, the subregion to which the target voxel
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| bshanks@30 | 31 belongs. We call this function a classifier. In general, the input to a classifier is called an instance, and the output is called
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| bshanks@30 | 32 a label (or a class label).
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| bshanks@30 | 33 The object of aim 1 is not to produce a single classifier, but rather to develop an automated method for determining a
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| bshanks@30 | 34 classifier for any known anatomical structure. Therefore, we seek a procedure by which a gene expression dataset may be
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| bshanks@30 | 35 analyzed in concert with an anatomical atlas in order to produce a classifier. Such a procedure is a type of a machine learning
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| bshanks@33 | 36 procedure. The construction of the classifier is called training (also learning), and the initial gene expression dataset used
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| bshanks@33 | 37 in the construction of the classifier is called training data.
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| bshanks@30 | 38 In the machine learning literature, this sort of procedure may be thought of as a supervised learning task, defined as a
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| bshanks@30 | 39 task in which the goal is to learn a mapping from instances to labels, and the training data consists of a set of instances
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| bshanks@30 | 40 (voxels) for which the labels (subregions) are known.
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| bshanks@30 | 41 Each gene expression level is called a feature, and the selection of which genes1 to include is called feature selection.
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| bshanks@33 | 42 Feature selection is one component of the task of learning a classifier. Some methods for learning classifiers start out with
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| bshanks@33 | 43 a separate feature selection phase, whereas other methods combine feature selection with other aspects of training.
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| bshanks@30 | 44 One class of feature selection methods assigns some sort of score to each candidate gene. The top-ranked genes are then
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| bshanks@30 | 45 chosen. Some scoring measures can assign a score to a set of selected genes, not just to a single gene; in this case, a dynamic
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| bshanks@30 | 46 procedure may be used in which features are added and subtracted from the selected set depending on how much they raise
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| bshanks@30 | 47 the score. Such procedures are called “stepwise” or “greedy”.
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| bshanks@30 | 48 Although the classifier itself may only look at the gene expression data within each voxel before classifying that voxel, the
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| bshanks@30 | 49 learning algorithm which constructs the classifier may look over the entire dataset. We can categorize score-based feature
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| bshanks@30 | 50 selection methods depending on how the score of calculated. Often the score calculation consists of assigning a sub-score to
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| bshanks@30 | 51 each voxel, and then aggregating these sub-scores into a final score (the aggregation is often a sum or a sum of squares). If
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| bshanks@30 | 52 only information from nearby voxels is used to calculate a voxel’s sub-score, then we say it is a local scoring method. If only
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| bshanks@30 | 53 information from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a pointwise scoring method.
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| bshanks@30 | 54 Key questions when choosing a learning method are: What are the instances? What are the features? How are the
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| bshanks@30 | 55 features chosen? Here are four principles that outline our answers to these questions.
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| bshanks@30 | 56 Principle 1: Combinatorial gene expression It is too much to hope that every anatomical region of interest will be
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| bshanks@30 | 57 identified by a single gene. For example, in the cortex, there are some areas which are not clearly delineated by any gene
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| bshanks@30 | 58 included in the Allen Brain Atlas (ABA) dataset. However, at least some of these areas can be delineated by looking at
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| bshanks@30 | 59 combinations of genes (an example of an area for which multiple genes are necessary and sufficient is provided in Preliminary
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| bshanks@30 | 60 Results). Therefore, each instance should contain multiple features (genes).
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| bshanks@30 | 61 Principle 2: Only look at combinations of small numbers of genes When the classifier classifies a voxel, it is
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| bshanks@30 | 62 only allowed to look at the expression of the genes which have been selected as features. The more data that is available to
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| bshanks@30 | 63 a classifier, the better that it can do. For example, perhaps there are weak correlations over many genes that add up to a
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| bshanks@30 | 64 strong signal. So, why not include every gene as a feature? The reason is that we wish to employ the classifier in situations
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| bshanks@30 | 65 in which it is not feasible to gather data about every gene. For example, if we want to use the expression of marker genes as
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| bshanks@30 | 66 a trigger for some regionally-targeted intervention, then our intervention must contain a molecular mechanism to check the
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| bshanks@30 | 67 expression level of each marker gene before it triggers. It is currently infeasible to design a molecular trigger that checks the
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| bshanks@33 | 68 level of more than a handful of genes. Similarly, if the goal is to develop a procedure to do ISH on tissue samples in order
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| bshanks@30 | 69 to label their anatomy, then it is infeasible to label more than a few genes. Therefore, we must select only a few genes as
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| bshanks@30 | 70 features.
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| bshanks@30 | 71 Principle 3: Use geometry in feature selection
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| bshanks@33 | 72 _________________________________________
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| bshanks@33 | 73 1Strictly speaking, the features are gene expression levels, but we’ll call them genes.
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| bshanks@30 | 74 When doing feature selection with score-based methods, the simplest thing to do would be to score the performance of
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| bshanks@30 | 75 each voxel by itself and then combine these scores (pointwise scoring). A more powerful approach is to also use information
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| bshanks@30 | 76 about the geometric relations between each voxel and its neighbors; this requires non-pointwise, local scoring methods. See
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| bshanks@30 | 77 Preliminary Results for evidence of the complementary nature of pointwise and local scoring methods.
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| bshanks@30 | 78 Principle 4: Work in 2-D whenever possible
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| bshanks@30 | 79 There are many anatomical structures which are commonly characterized in terms of a two-dimensional manifold. When
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| bshanks@30 | 80 it is known that the structure that one is looking for is two-dimensional, the results may be improved by allowing the analysis
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| bshanks@33 | 81 algorithm to take advantage of this prior knowledge. In addition, it is easier for humans to visualize and work with 2-D
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| bshanks@33 | 82 data.
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| bshanks@30 | 83 Therefore, when possible, the instances should represent pixels, not voxels.
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| bshanks@30 | 84 Aim 2
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| bshanks@30 | 85 Machine learning terminology: clustering
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| bshanks@30 | 86 If one is given a dataset consisting merely of instances, with no class labels, then analysis of the dataset is referred to as
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| bshanks@30 | 87 unsupervised learning in the jargon of machine learning. One thing that you can do with such a dataset is to group instances
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| bshanks@30 | 88 together. A set of similar instances is called a cluster, and the activity of finding grouping the data into clusters is called
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| bshanks@30 | 89 clustering or cluster analysis.
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| bshanks@30 | 90 The task of deciding how to carve up a structure into anatomical subregions can be put into these terms. The instances
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| bshanks@33 | 91 are once again voxels (or pixels) along with their associated gene expression profiles. We make the assumption that voxels
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| bshanks@33 | 92 from the same subregion have similar gene expression profiles, at least compared to the other subregions. This means that
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| bshanks@33 | 93 clustering voxels is the same as finding potential subregions; we seek a partitioning of the voxels into subregions, that is,
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| bshanks@33 | 94 into clusters of voxels with similar gene expression.
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| bshanks@30 | 95 It is desirable to determine not just one set of subregions, but also how these subregions relate to each other, if at all;
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| bshanks@33 | 96 perhaps some of the subregions are more similar to each other than to the rest, suggesting that, although at a fine spatial
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| bshanks@33 | 97 scale they could be considered separate, on a coarser spatial scale they could be grouped together into one large subregion.
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| bshanks@33 | 98 This suggests the outcome of clustering may be a hierarchial tree of clusters, rather than a single set of clusters which
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| bshanks@33 | 99 partition the voxels. This is called hierarchial clustering.
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| bshanks@30 | 100 Similarity scores
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| bshanks@30 | 101 A crucial choice when designing a clustering method is how to measure similarity, across either pairs of instances, or
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| bshanks@33 | 102 clusters, or both. There is much overlap between scoring methods for feature selection (discussed above under Aim 1) and
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| bshanks@30 | 103 scoring methods for similarity.
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| bshanks@30 | 104 Spatially contiguous clusters; image segmentation
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| bshanks@33 | 105 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
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| bshanks@33 | 106 an additional constraint on clusters; voxels grouped together into a cluster must be spatially contiguous. In Preliminary
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| bshanks@33 | 107 Results, we show that one can get reasonable results without enforcing this constraint, however, we plan to compare these
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| bshanks@33 | 108 results against other methods which guarantee contiguous clusters.
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| bshanks@30 | 109 Perhaps the biggest source of continguous clustering algorithms is the field of computer vision, which has produced a
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| bshanks@33 | 110 variety of image segmentation algorithms. Image segmentation is the task of partitioning the pixels in a digital image into
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| bshanks@30 | 111 clusters, usually contiguous clusters. Aim 2 is similar to an image segmentation task. There are two main differences; in
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| bshanks@30 | 112 our task, there are thousands of color channels (one for each gene), rather than just three. There are imaging tasks which
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| bshanks@33 | 113 use more than three colors, however, for example multispectral imaging and hyperspectral imaging, which are often used
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| bshanks@33 | 114 to process satellite imagery. A more crucial difference is that there are various cues which are appropriate for detecting
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| bshanks@33 | 115 sharp object boundaries in a visual scene but which are not appropriate for segmenting abstract spatial data such as gene
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| bshanks@33 | 116 expression. Although many image segmentation algorithms can be expected to work well for segmenting other sorts of
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| bshanks@33 | 117 spatially arranged data, some of these algorithms are specialized for visual images.
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| bshanks@30 | 118 Dimensionality reduction
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| bshanks@33 | 119 Unlike aim 1, there is no externally-imposed need to select only a handful of informative genes for inclusion in the
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| bshanks@30 | 120 instances. However, some clustering algorithms perform better on small numbers of features. There are techniques which
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| bshanks@30 | 121 “summarize” a larger number of features using a smaller number of features; these techniques go by the name of feature
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| bshanks@30 | 122 extraction or dimensionality reduction. The small set of features that such a technique yields is called the reduced feature
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| bshanks@30 | 123 set. After the reduced feature set is created, the instances may be replaced by reduced instances, which have as their features
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| bshanks@30 | 124 the reduced feature set rather than the original feature set of all gene expression levels. Note that the features in the reduced
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| bshanks@30 | 125 feature set do not necessarily correspond to genes; each feature in the reduced set may be any function of the set of gene
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| bshanks@30 | 126 expression levels.
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| bshanks@30 | 127 Another use for dimensionality reduction is to visualize the relationships between subregions. For example, one might
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| bshanks@33 | 128 want tomake a 2-D plot upon which each subregion is represented by a single point, and with the property that subregions
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| bshanks@30 | 129 with similar gene expression profiles should be nearby on the plot (that is, the property that distance between pairs of points
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| bshanks@33 | 130 in the plot should be proportional to some measure of dissimilarity in gene expression). It is likely that no arrangement of
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| bshanks@30 | 131 the points on a 2-D plan will exactly satisfy this property – however, dimensionality reduction techniques allow one to find
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| bshanks@30 | 132 arrangements of points that approximately satisfy that property. Note that in this application, dimensionality reduction
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| bshanks@30 | 133 is being applied after clustering; whereas in the previous paragraph, we were talking about using dimensionality reduction
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| bshanks@30 | 134 before clustering.
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| bshanks@30 | 135 Clustering genes rather than voxels
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| bshanks@30 | 136 Although the ultimate goal is to cluster the instances (voxels or pixels), one strategy to achieve this goal is to first cluster
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| bshanks@30 | 137 the features (genes). There are two ways that clusters of genes could be used.
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| bshanks@30 | 138 Gene clusters could be used as part of dimensionality reduction: rather than have one feature for each gene, we could
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| bshanks@30 | 139 have one reduced feature for each gene cluster.
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| bshanks@30 | 140 Gene clusters could also be used to directly yield a clustering on instances. This is because many genes have an expression
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| bshanks@30 | 141 pattern which seems to pick out a single, spatially continguous subregion. Therefore, it seems likely that an anatomically
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| bshanks@30 | 142 interesting subregion will have multiple genes which each individually pick it out2. This suggests the following procedure:
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| bshanks@33 | 143 cluster together genes which pick out similar subregions, and then to use the more popular common subregions as the
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| bshanks@33 | 144 final clusters. In the Preliminary Data we show that a number of anatomically recognized cortical regions, as well as some
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| bshanks@30 | 145 “superregions” formed by lumping together a few regions, are associated with gene clusters in this fashion.
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| bshanks@30 | 146 Aim 3
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| bshanks@30 | 147 Background
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| bshanks@33 | 148 The cortex is divided into areas and layers. To a first approximation, the parcellation of the cortex into areas can
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| bshanks@33 | 149 be drawn as a 2-D map on the surface of the cortex. In the third dimension, the boundaries between the areas continue
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| bshanks@33 | 150 downwards into the cortical depth, perpendicular to the surface. The layer boundaries run parallel to the surface. One can
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| bshanks@33 | 151 picture an area of the cortex as a slice of many-layered cake.
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| bshanks@30 | 152 Although it is known that different cortical areas have distinct roles in both normal functioning and in disease processes,
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| bshanks@30 | 153 there are no known marker genes for many cortical areas. When it is necessary to divide a tissue sample into cortical areas,
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| bshanks@30 | 154 this is a manual process that requires a skilled human to combine multiple visual cues and interpret them in the context of
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| bshanks@30 | 155 their approximate location upon the cortical surface.
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| bshanks@33 | 156 Even the questions of how many areas should be recognized in cortex, and what their arrangement is, are still not
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| bshanks@33 | 157 completely settled. A proposed division of the cortex into areas is called a cortical map. In the rodent, the lack of a
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| bshanks@33 | 158 single agreed-upon map can be seen by contrasting the recent maps given by Swanson[?] on the one hand, and Paxinos
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| bshanks@33 | 159 and Franklin[?] on the other. While the maps are certainly very similar in their general arrangement, significant differences
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| bshanks@30 | 160 remain in the details.
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| bshanks@30 | 161 Significance
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| bshanks@30 | 162 The method developed in aim (1) will be applied to each cortical area to find a set of marker genes such that the
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| bshanks@33 | 163 combinatorial expression pattern of those genes uniquely picks out the target area. Finding marker genes will be useful for
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| bshanks@30 | 164 drug discovery as well as for experimentation because marker genes can be used to design interventions which selectively
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| bshanks@30 | 165 target individual cortical areas.
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| bshanks@30 | 166 The application of the marker gene finding algorithm to the cortex will also support the development of new neuroanatom-
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| bshanks@33 | 167 ical methods. In addition to finding markers for each individual cortical areas, we will find a small panel of genes that can
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| bshanks@33 | 168 find many of the areal boundaries at once. This panel of marker genes will allow the development of an ISH protocol that
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| bshanks@30 | 169 will allow experimenters to more easily identify which anatomical areas are present in small samples of cortex.
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| bshanks@33 | 170 The method developed in aim (3) will provide a genoarchitectonic viewpoint that will contribute to the creation of
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| bshanks@33 | 171 a better map. The development of present-day cortical maps was driven by the application of histological stains. It is
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| bshanks@33 | 172 conceivable that if a different set of stains had been available which identified a different set of features, then the today’s
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| bshanks@33 | 173 cortical maps would have come out differently. Since the number of classes of stains is small compared to the number of
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| bshanks@33 | 174 genes, it is likely that there are many repeated, salient spatial patterns in the gene expression which have not yet been
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| bshanks@33 | 175 captured by any stain. Therefore, current ideas about cortical anatomy need to incorporate what we can learn from looking
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| bshanks@33 | 176 at the patterns of gene expression.
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| bshanks@30 | 177 While we do not here propose to analyze human gene expression data, it is conceivable that the methods we propose to
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| bshanks@30 | 178 develop could be used to suggest modifications to the human cortical map as well.
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| bshanks@33 | 179 _________________________________________
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| bshanks@33 | 180 2This would seem to contradict our finding in aim 1 that some cortical areas are combinatorially coded by multiple genes. However, it is
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| bshanks@33 | 181 possible that the currently accepted cortical maps divide the cortex into subregions which are unnatural from the point of view of gene expression;
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| bshanks@33 | 182 perhaps there is some other way to map the cortex for which each subregion can be identified by single genes.
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| bshanks@30 | 183 Related work
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| bshanks@30 | 184 There does not appear to be much work on the automated analysis of spatial gene expression data.
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| bshanks@30 | 185 There is a substantial body of work on the analysis of gene expression data, however, most of this concerns gene expression
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| bshanks@30 | 186 data which is not fundamentally spatial.
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| bshanks@30 | 187 As noted above, there has been much work on both supervised learning and clustering, and there are many available
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| bshanks@30 | 188 algorithms for each. However, the completion of Aims 1 and 2 involves more than just choosing between a set of existing
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| bshanks@33 | 189 algorithms, and will constitute a substantial contribution to biology. The algorithms require the scientist to provide a
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| bshanks@30 | 190 framework for representing the problem domain, and the way that this framework is set up has a large impact on performance.
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| bshanks@30 | 191 Creating a good framework can require creatively reconceptualizing the problem domain, and is not merely a mechanical
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| bshanks@30 | 192 “fine-tuning” of numerical parameters. For example, we believe that domain-specific scoring measures (such as gradient
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| bshanks@30 | 193 similarity, which is discussed in Preliminary Work) may be necessary in order to achieve the best results in this application.
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| bshanks@30 | 194 We are aware of two existing efforts to relate spatial gene expression data to anatomy through computational methods.
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| bshanks@33 | 195 [3 ] describes an analysis of the anatomy of the hippocampus using the ABA dataset. In addition to manual analysis,
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| bshanks@32 | 196 two clustering methods were employed, a modified Non-negative Matrix Factorization (NNMF), and a hierarchial recursive
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| bshanks@32 | 197 bifurcation clustering scheme based on correlation as the similarity score. The paper yielded impressive results, proving the
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| bshanks@34 | 198 usefulness of such research. We have run NNMF on the cortical dataset3 and while the results are promising (see Preliminary
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| bshanks@34 | 199 Data), we think that it will be possible to find a better method (we also think that more automation of the parts that this
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| bshanks@32 | 200 paper’s authors did manually will be possible).
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| bshanks@33 | 201 [2 ] describes AGEA, ”Anatomic Gene Expression Atlas”. AGEA is an analysis tool for the ABA dataset. AGEA has
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| bshanks@32 | 202 three components:
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| bshanks@33 | 203 * Gene Finder: The user selects a seed voxel and the system (1) chooses a cluster which includes the seed voxel, (2)
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| bshanks@33 | 204 yields a list of genes which are overexpressed in that cluster.
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| bshanks@32 | 205 * Correlation: The user selects a seed voxel and the shows the user how much correlation there is between the gene
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| bshanks@32 | 206 expression profile of the seed voxel and every other voxel.
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| bshanks@33 | 207 * Clusters: AGEA includes a precomputed hierarchial clustering of voxels based on a recursive bifurcation algorithm
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| bshanks@33 | 208 with correlation as the similarity metric.
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| bshanks@34 | 209 Gene Finder is different from our Aim 1 in at least four ways. First, although the user chooses a seed voxel, Gene
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| bshanks@34 | 210 Finder, not the user, chooses the cluster for which genes will be found, and in our experience it never chooses cortical areas,
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| bshanks@34 | 211 instead preferring cortical layers4. Therefore, Gene Finder cannot be used to find marker genes for cortical areas. Second,
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| bshanks@34 | 212 Gene Finder finds only single genes, whereas we will also look for combinations of genes5. Third, gene finder can only use
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| bshanks@34 | 213 overexpression as a marker, whereas in the Preliminary Data we show that underexpression can also be used. Fourth, Gene
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| bshanks@34 | 214 Finder uses a simple pointwise score6, whereas we will also use geometric metrics such as gradient similarity.
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| bshanks@34 | 215 The hierarchial clustering is different from our Aim 2 in at least three ways. First, the clustering finds clusters cor-
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| bshanks@34 | 216 responding to layers, but no clusters corresponding to areas7 8 Our Aim 2 will not be accomplished until a clustering is
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| bshanks@34 | 217 produced which yields areas. Second, AGEA uses perhaps the simplest possible similarity score (correlation), and does no
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| bshanks@34 | 218 dimensionality reduction before calculating similarity. While it is possible that a more complex system will not do any better
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| bshanks@34 | 219 than this, we believe further exploration of alternative methods of scoring and dimensionality reduction is warranted. Third,
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| bshanks@34 | 220 AGEA did not look at clusters of genes; in Preliminary Data we have shown that clusters of genes may identify intersting
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| bshanks@34 | 221 spatial subregions such as cortical areas.
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| bshanks@34 | 222 _______
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| bshanks@30 | 223 3We ran “vanilla” NNMF, whereas the paper under discussion used a modified method. Their main modification consisted of adding a soft
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| bshanks@30 | 224 spatial contiguity constraint. However, on our dataset, NNMF naturally produced spatially contiguous clusters, so no additional constraint was
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| bshanks@33 | 225 needed. The paper under discussion mentions that they also tried a hierarchial variant of NNMF, but since they didn’t report its results, we
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| bshanks@33 | 226 assume that those result were not any more impressive than the results of the non-hierarchial variant.
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| bshanks@34 | 227 4Because of the way in which Gene Finder chooses a cluster, layers will always be preferred to areas if pairwise correlations between the gene
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| bshanks@34 | 228 expression of voxels in different areas but the same layer are stronger than pairwise correlatios between the gene expression of voxels in different
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| bshanks@34 | 229 layers but the same area. This appears to be the case.
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| bshanks@34 | 230 5See 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
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| bshanks@34 | 231 combination.
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| bshanks@34 | 232 6“Expression energy ratio”, which captures overexpression.
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| bshanks@34 | 233 7This is for the same reason as in footnote 4.
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| bshanks@34 | 234 8There are clusters which presumably correspond to the intersection of a layer and an area, but since one area will have many layer-area
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| bshanks@34 | 235 intersection clusters, further work is needed to make sense of these.
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| bshanks@33 | 236
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| bshanks@30 | 237
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| bshanks@26 | 238
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| bshanks@30 | 239 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2 (each pixel’s value on the lower left is the sum
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| bshanks@30 | 240 of the corresponding pixels in the upper row). Within each picture, the vertical axis roughly corresponds to anterior at the
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| bshanks@30 | 241 top and posterior at the bottom, and the horizontal axis roughly corresponds to medial at the left and lateral at the right.
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| bshanks@30 | 242 The red outline is the boundary of region MO. Pixels are colored approximately according to the density of expressing cells
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| bshanks@30 | 243 underneath each pixel, with red meaning a lot of expression and blue meaning little.
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| bshanks@30 | 244 Preliminary work
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| bshanks@30 | 245 Format conversion between SEV, MATLAB, NIFTI
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| bshanks@30 | 246 todo
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| bshanks@30 | 247 Flatmap of cortex
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| bshanks@30 | 248 todo
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| bshanks@30 | 249 Using combinations of multiple genes is necessary and sufficient to delineate some cortical areas
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| bshanks@30 | 250 Here we give an example of a cortical area which is not marked by any single gene, but which can be identified combi-
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| bshanks@34 | 251 natorially. according to logistic regression, gene wwc19 is the best fit single gene for predicting whether or not a pixel on
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| bshanks@30 | 252 the cortical surface belongs to the motor area (area MO). The upper-left picture in Figure shows wwc1’s spatial expression
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| bshanks@30 | 253 pattern over the cortex. The lower-right boundary of MO is represented reasonably well by this gene, however the gene
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| bshanks@33 | 254 overshoots the upper-left boundary. This flattened 2-D representation does not show it, but the area corresponding to the
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| bshanks@30 | 255 overshoot is the medial surface of the cortex. MO is only found on the lateral surface (todo).
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| bshanks@34 | 256 Gnee mtif210 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s upper-left boundary, but not its lower-right
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| bshanks@33 | 257 boundary. Mtif2 does not express very much on the medial surface. By adding together the values at each pixel in these
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| bshanks@33 | 258 two figures, we get the lower-left of Figure . This combination captures area MO much better than any single gene.
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| bshanks@30 | 259 Correlation todo
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| bshanks@30 | 260 Conditional entropy todo
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| bshanks@30 | 261 Gradient similarity todo
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| bshanks@30 | 262 Geometric and pointwise scoring methods provide complementary information
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| bshanks@30 | 263 To show that local geometry can provide useful information that cannot be detected via pointwise analyses, consider Fig.
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| bshanks@34 | 264 . The top row of Fig. displays the 3 genes which most match area AUD, according to a pointwise method11. The bottom
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| bshanks@34 | 265 row displays the 3 genes which most match AUD according to a method which considers local geometry12 The pointwise
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| bshanks@33 | 266 method in the top row identifies genes which express more strongly in AUD than outside of it; its weakness is that this
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| bshanks@30 | 267 _________________________________________
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| bshanks@34 | 268 9“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
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| bshanks@34 | 269 10“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
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| bshanks@34 | 270 11For each gene, a logistic regression in which the response variable was whether or not a surface pixel was within area AUD, and the predictor
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| bshanks@30 | 271 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
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| bshanks@33 | 272 they predict area AUD.
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| bshanks@34 | 273 12For each gene the gradient similarity (see section ??) between (a) a map of the expression of each gene on the cortical surface and (b) the
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| bshanks@33 | 274 shape of area AUD, was calculated, and this was used to rank the genes.
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| bshanks@33 | 275
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| bshanks@30 | 276
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| bshanks@30 | 277
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| bshanks@33 | 278 Figure 2: The top row shows the three genes which (individually) best predict area AUD, according to logistic regression.
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| bshanks@30 | 279 The bottom row shows the three genes which (individually) best match area AUD, according to gradient similarity. From
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| bshanks@30 | 280 left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a, Ptk7, Aph1a again, and Lepr
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| bshanks@33 | 281 includes many areas which don’t have a salient border matching the areal border. The geometric method identifies genes
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| bshanks@33 | 282 whose salient expression border seems to partially line up with the border of AUD; its weakness is that this includes genes
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| bshanks@33 | 283 which don’t express over the entire area. Genes which have high rankings using both pointwise and border criteria, such as
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| bshanks@33 | 284 Aph1a in the example, may be particularly good markers. None of these genes are, individually, a perfect marker for AUD;
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| bshanks@33 | 285 we deliberately chose a “difficult” area in order to better contrast pointwise with geometric methods.
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| bshanks@30 | 286 Areas which can be identified by single genes
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| bshanks@30 | 287 todo
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| bshanks@30 | 288 Specific to Aim 1 (and Aim 3)
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| bshanks@30 | 289 Forward stepwise logistic regression todo
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| bshanks@30 | 290 SVM on all genes at once
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| bshanks@30 | 291 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
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| bshanks@34 | 292 surface pixels based on their gene expression profiles. We achieved classification accuracy of about 81%13. As noted above,
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| bshanks@30 | 293 however, a classifier that looks at all the genes at once isn’t practically useful.
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| bshanks@30 | 294 The requirement to find combinations of only a small number of genes limits us from straightforwardly applying many
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| bshanks@33 | 295 of the most simple techniques from the field of supervised machine learning. In the parlance of machine learning, our task
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| bshanks@30 | 296 combines feature selection with supervised learning.
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| bshanks@30 | 297 Decision trees
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| bshanks@30 | 298 todo
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| bshanks@30 | 299 Specific to Aim 2 (and Aim 3)
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| bshanks@30 | 300 Raw dimensionality reduction results
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| bshanks@30 | 301 todo
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| bshanks@30 | 302 (might want to incld nnMF since mentioned above)
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| bshanks@30 | 303 Dimensionality reduction plus K-means or spectral clustering
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| bshanks@30 | 304 Many areas are captured by clusters of genes
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| bshanks@30 | 305 todo
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| bshanks@30 | 306 todo
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| bshanks@33 | 307 _________________________________________
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| bshanks@34 | 308 135-fold cross-validation.
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| bshanks@30 | 309 Research plan
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| bshanks@30 | 310 todo amongst other things:
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| bshanks@30 | 311 Develop algorithms that find genetic markers for anatomical regions
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| bshanks@30 | 312 1.Develop scoring measures for evaluating how good individual genes are at marking areas: we will compare pointwise,
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| bshanks@30 | 313 geometric, and information-theoretic measures.
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| bshanks@30 | 314 2.Develop a procedure to find single marker genes for anatomical regions: for each cortical area, by using or combining
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| bshanks@30 | 315 the scoring measures developed, we will rank the genes by their ability to delineate each area.
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| bshanks@30 | 316 3.Extend the procedure to handle difficult areas by using combinatorial coding: for areas that cannot be identified by any
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| bshanks@30 | 317 single gene, identify them with a handful of genes. We will consider both (a) algorithms that incrementally/greedily
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| bshanks@30 | 318 combine single gene markers into sets, such as forward stepwise regression and decision trees, and also (b) supervised
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| bshanks@33 | 319 learning techniques which use soft constraints to minimize the number of features, such as sparse support vector
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| bshanks@30 | 320 machines.
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| bshanks@33 | 321 4.Extend the procedure to handle difficult areas by combining or redrawing the boundaries: An area may be difficult
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| bshanks@33 | 322 to identify because the boundaries are misdrawn, or because it does not “really” exist as a single area, at least on the
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| bshanks@30 | 323 genetic level. We will develop extensions to our procedure which (a) detect when a difficult area could be fit if its
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| bshanks@30 | 324 boundary were redrawn slightly, and (b) detect when a difficult area could be combined with adjacent areas to create
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| bshanks@30 | 325 a larger area which can be fit.
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| bshanks@30 | 326 Apply these algorithms to the cortex
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| bshanks@30 | 327 1.Create open source format conversion tools: we will create tools to bulk download the ABA dataset and to convert
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| bshanks@30 | 328 between SEV, NIFTI and MATLAB formats.
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| bshanks@30 | 329 2.Flatmap the ABA cortex data: map the ABA data onto a plane and draw the cortical area boundaries onto it.
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| bshanks@30 | 330 3.Find layer boundaries: cluster similar voxels together in order to automatically find the cortical layer boundaries.
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| bshanks@30 | 331 4.Run the procedures that we developed on the cortex: we will present, for each area, a short list of markers to identify
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| bshanks@30 | 332 that area; and we will also present lists of “panels” of genes that can be used to delineate many areas at once.
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| bshanks@30 | 333 Develop algorithms to suggest a division of a structure into anatomical parts
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| bshanks@30 | 334 1.Explore dimensionality reduction algorithms applied to pixels: including TODO
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| bshanks@30 | 335 2.Explore dimensionality reduction algorithms applied to genes: including TODO
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| bshanks@30 | 336 3.Explore clustering algorithms applied to pixels: including TODO
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| bshanks@30 | 337 4.Explore clustering algorithms applied to genes: including gene shaving, TODO
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| bshanks@30 | 338 5.Develop an algorithm to use dimensionality reduction and/or hierarchial clustering to create anatomical maps
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| bshanks@30 | 339 6.Run this algorithm on the cortex: present a hierarchial, genoarchitectonic map of the cortex
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| bshanks@33 | 340 Bibliography & References Cited
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| bshanks@33 | 341 [1]D C Van Essen, H A Drury, J Dickson, J Harwell, D Hanlon, and C H Anderson. An integrated software suite for surface-
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| bshanks@33 | 342 based analyses of cerebral cortex. Journal of the American Medical Informatics Association: JAMIA, 8(5):443–59, 2001.
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| bshanks@33 | 343 PMID: 11522765.
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| bshanks@33 | 344 [2]Lydia Ng, Amy Bernard, Chris Lau, Caroline C Overly, Hong-Wei Dong, Chihchau Kuan, Sayan Pathak, Susan M Sunkin,
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| bshanks@33 | 345 Chinh Dang, Jason W Bohland, Hemant Bokil, Partha P Mitra, Luis Puelles, John Hohmann, David J Anderson, Ed S
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| bshanks@33 | 346 Lein, Allan R Jones, and Michael Hawrylycz. An anatomic gene expression atlas of the adult mouse brain. Nat Neurosci,
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| bshanks@33 | 347 12(3):356–362, March 2009.
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| bshanks@33 | 348 [3]Carol L. Thompson, Sayan D. Pathak, Andreas Jeromin, Lydia L. Ng, Cameron R. MacPherson, Marty T. Mortrud,
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| bshanks@33 | 349 Allison Cusick, Zackery L. Riley, Susan M. Sunkin, Amy Bernard, Ralph B. Puchalski, Fred H. Gage, Allan R. Jones,
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| bshanks@33 | 350 Vladimir B. Bajic, Michael J. Hawrylycz, and Ed S. Lein. Genomic anatomy of the hippocampus. Neuron, 60(6):1010–
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| bshanks@33 | 351 1021, December 2008.
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| bshanks@33 | 352
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| bshanks@33 | 353 _______________________________________________________________________________________________________
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| bshanks@30 | 354 stuff i dunno where to put yet (there is more scattered through grant-oldtext):
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| bshanks@16 | 355 Principle 4: Work in 2-D whenever possible
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| bshanks@33 | 356 In anatomy, the manifold of interest is usually either defined by a combination of two relevant anatomical axes (todo),
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| bshanks@33 | 357 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
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| bshanks@33 | 358 in the latter case it is curved. If the manifold is curved, there are various methods for mapping the manifold into a plane.
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| bshanks@33 | 359 The method that we will develop will begin by mapping the data into a 2-D plane. Although the manifold that
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| bshanks@33 | 360 characterized cortical areas is known to be the cortical surface, it remains to be seen which method of mapping the manifold
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| bshanks@33 | 361 into a plane is optimal for this application. We will compare mappings which attempt to preserve size (such as the one used
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| bshanks@33 | 362 by Caret[1]) with mappings which preserve angle (conformal maps).
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| bshanks@33 | 363 Although there is much 2-D organization in anatomy, there are also structures whose shape is fundamentally 3-dimensional.
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| bshanks@30 | 364 If possible, we would like the method we develop to include a statistical test that warns the user if the assumption of 2-D
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| bshanks@30 | 365 structure seems to be wrong.
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| bshanks@33 | 366 —
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| bshanks@33 | 367 note:
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| bshanks@33 | 368 do we need to cite: no known markers, impressive results?
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| bshanks@33 | 369
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| bshanks@33 | 370
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