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| bshanks@0 | 1 Specific aims
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| bshanks@15 | 2 Massive new datasets obtained with techniques such as in situ hybridization
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| bshanks@0 | 3 (ISH) and BAC-transgenics allow the expression levels of many genes at many
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| bshanks@0 | 4 locations to be compared. Our goal is to develop automated methods to relate
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| bshanks@0 | 5 spatial variation in gene expression to anatomy. We want to find marker genes
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| bshanks@0 | 6 for specific anatomical regions, and also to draw new anatomical maps based on
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| bshanks@0 | 7 gene expression patterns. We have three specific aims:
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| bshanks@17 | 8 (1) develop an algorithm to screen spatial gene expression data for combi-
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| bshanks@17 | 9 nations of marker genes which selectively target anatomical regions
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| bshanks@17 | 10 (2) develop an algorithm to suggest new ways of carving up a structure into
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| bshanks@17 | 11 anatomical subregions, based on spatial patterns in gene expression
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| bshanks@17 | 12 (3) create a 2-D “flat map” dataset of the mouse cerebral cortex that con-
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| bshanks@17 | 13 tains a flattened version of the Allen Mouse Brain Atlas ISH data, as well as
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| bshanks@17 | 14 the boundaries of cortical anatomical areas. Use this dataset to validate the
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| bshanks@17 | 15 methods developed in (1) and (2).
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| bshanks@0 | 16 In addition to validating the usefulness of the algorithms, the application of
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| bshanks@0 | 17 these methods to cerebral cortex will produce immediate benefits, because there
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| bshanks@0 | 18 are currently no known genetic markers for many cortical areas. The results
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| bshanks@0 | 19 of the project will support the development of new ways to selectively target
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| bshanks@0 | 20 cortical areas, and it will support the development of a method for identifying
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| bshanks@0 | 21 the cortical areal boundaries present in small tissue samples.
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| bshanks@0 | 22 All algorithms that we develop will be implemented in an open-source soft-
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| bshanks@0 | 23 ware toolkit. The toolkit, as well as the machine-readable datasets developed
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| bshanks@0 | 24 in aim (3), will be published and freely available for others to use.
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| bshanks@0 | 25 Background and significance
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| bshanks@0 | 26 Aim 1
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| bshanks@16 | 27 Machine learning terminology: supervised learning
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| bshanks@16 | 28 The task of looking for marker genes for anatomical subregions means that
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| bshanks@16 | 29 one is looking for a set of genes such that, if the expression level of those genes
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| bshanks@16 | 30 is known, then the locations of the subregions can be inferred.
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| bshanks@0 | 31 If we define the subregions so that they cover the entire anatomical structure
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| bshanks@0 | 32 to be divided, then instead of saying that we are using gene expression to find
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| bshanks@0 | 33 the locations of the subregions, we may say that we are using gene expression to
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| bshanks@0 | 34 determine to which subregion each voxel within the structure belongs. We call
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| bshanks@0 | 35 this a classification task, because each voxel is being assigned to a class (namely,
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| bshanks@0 | 36 its subregion).
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| bshanks@0 | 37 Therefore, an understanding of the relationship between the combination of
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| bshanks@17 | 38 1
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| bshanks@17 | 39
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| bshanks@0 | 40 their expression levels and the locations of the subregions may be expressed as
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| bshanks@16 | 41 a function. The input to this function is a voxel, along with the gene expression
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| bshanks@0 | 42 levels within that voxel; the output is the subregional identity of the target
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| bshanks@0 | 43 voxel, that is, the subregion to which the target voxel belongs. We call this
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| bshanks@0 | 44 function a classifier. In general, the input to a classifier is called an instance,
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| bshanks@15 | 45 and the output is called a label (or a class label).
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| bshanks@0 | 46 The object of aim 1 is not to produce a single classifier, but rather to develop
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| bshanks@0 | 47 an automated method for determining a classifier for any known anatomical
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| bshanks@0 | 48 structure. Therefore, we seek a procedure by which a gene expression dataset
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| bshanks@0 | 49 may be analyzed in concert with an anatomical atlas in order to produce a
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| bshanks@0 | 50 classifier. Such a procedure is a type of a machine learning procedure. The
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| bshanks@0 | 51 construction of the classifier is called training (also learning), and the initial
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| bshanks@0 | 52 gene expression dataset used in the construction of the classifier is called training
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| bshanks@0 | 53 data.
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| bshanks@0 | 54 In the machine learning literature, this sort of procedure may be thought
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| bshanks@0 | 55 of as a supervised learning task, defined as a task in whcih the goal is to learn
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| bshanks@0 | 56 a mapping from instances to labels, and the training data consists of a set of
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| bshanks@0 | 57 instances (voxels) for which the labels (subregions) are known.
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| bshanks@0 | 58 Each gene expression level is called a feature, and the selection of which
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| bshanks@0 | 59 genes to include is called feature selection. Feature selection is one component
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| bshanks@0 | 60 of the task of learning a classifier. Some methods for learning classifiers start
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| bshanks@0 | 61 out with a separate feature selection phase, whereas other methods combine
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| bshanks@0 | 62 feature selection with other aspects of training.
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| bshanks@0 | 63 One class of feature selection methods assigns some sort of score to each
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| bshanks@0 | 64 candidate gene. The top-ranked genes are then chosen. Some scoring measures
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| bshanks@0 | 65 can assign a score to a set of selected genes, not just to a single gene; in this
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| bshanks@0 | 66 case, a dynamic procedure may be used in which features are added and sub-
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| bshanks@0 | 67 tracted from the selected set depending on how much they raise the score. Such
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| bshanks@0 | 68 procedures are called “stepwise” or “greedy”.
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| bshanks@0 | 69 Although the classifier itself may only look at the gene expression data within
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| bshanks@0 | 70 each voxel before classifying that voxel, the learning algorithm which constructs
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| bshanks@0 | 71 the classifier may look over the entire dataset. We can categorize score-based
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| bshanks@0 | 72 feature selection methods depending on how the score of calculated. Often
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| bshanks@0 | 73 the score calculation consists of assigning a sub-score to each voxel, and then
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| bshanks@0 | 74 aggregating these sub-scores into a final score (the aggregation is often a sum or
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| bshanks@0 | 75 a sum of squares). If only information from nearby voxels is used to calculate a
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| bshanks@0 | 76 voxel’s sub-score, then we say it is a local scoring method. If only information
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| bshanks@0 | 77 from the voxel itself is used to calculate a voxel’s sub-score, then we say it is a
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| bshanks@0 | 78 pointwise scoring method.
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| bshanks@0 | 79 Key questions when choosing a learning method are: What are the instances?
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| bshanks@0 | 80 What are the features? How are the features chosen? Here are four principles
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| bshanks@0 | 81 that outline our answers to these questions.
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| bshanks@16 | 82 Principle 1: Combinatorial gene expression
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| bshanks@16 | 83 Above, we defined an “instance” as the combination of a voxel with the
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| bshanks@16 | 84 “associated gene expression data”. In our case this refers to the expression level
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| bshanks@16 | 85 of genes within the voxel, but should we include the expression levels of all
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| bshanks@17 | 86 2
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| bshanks@17 | 87
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| bshanks@16 | 88 genes, or only a few of them?
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| bshanks@16 | 89 It is too much to hope that every anatomical region of interest will be iden-
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| bshanks@0 | 90 tified by a single gene. For example, in the cortex, there are some areas which
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| bshanks@0 | 91 are not clearly delineated by any gene included in the Allen Brain Atlas (ABA)
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| bshanks@0 | 92 dataset. However, at least some of these areas can be delineated by looking
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| bshanks@0 | 93 at combinations of genes (an example of an area for which multiple genes are
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| bshanks@0 | 94 necessary and sufficient is provided in Preliminary Results).
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| bshanks@16 | 95 Principle 2: Only look at combinations of small numbers of genes
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| bshanks@16 | 96 When the classifier classifies a voxel, it is only allowed to look at the expres-
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| bshanks@16 | 97 sion of the genes which have been selected as features. The more data that is
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| bshanks@16 | 98 available to a classifier, the better that it can do. For example, perhaps there
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| bshanks@16 | 99 are weak correlations over many genes that add up to a strong signal. So, why
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| bshanks@16 | 100 not include every gene as a feature? The reason is that we wish to employ
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| bshanks@16 | 101 the classifier in situations in which it is not feasible to gather data about every
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| bshanks@16 | 102 gene. For example, if we want to use the expression of marker genes as a trigger
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| bshanks@16 | 103 for some regionally-targeted intervention, then our intervention must contain a
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| bshanks@16 | 104 molecular mechanism to check the expression level of each marker gene before
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| bshanks@16 | 105 it triggers. It is currently infeasible to design a molecular trigger that checks
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| bshanks@16 | 106 the level of more than a handful of genes. Similarly, if the goal is to develop a
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| bshanks@16 | 107 procedure to do ISH on tissue samples in order to label their anatomy, then it
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| bshanks@16 | 108 is infeasible to label more than a few genes. Therefore, we must select only a
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| bshanks@16 | 109 few genes as features.
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| bshanks@16 | 110 Principle 3: Use geometry in feature selection
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| bshanks@16 | 111 When doing feature selection with score-based methods, the simplest thing
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| bshanks@16 | 112 to do would be to score the performance of each voxel by itself and then com-
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| bshanks@16 | 113 bine these scores (pointwise scoring). A more powerful approach is to also use
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| bshanks@16 | 114 information about the geometric relations between each voxel and its neighbors;
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| bshanks@16 | 115 this requires non-pointwise, local scoring methods. See Preliminary Results for
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| bshanks@16 | 116 evidence of the complementary nature of pointwise and local scoring methods.
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| bshanks@16 | 117 Principle 4: Work in 2-D whenever possible
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| bshanks@16 | 118 There are many anatomical structures which are commonly characterized in
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| bshanks@0 | 119 terms of a two-dimensional manifold. When it is known that the structure that
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| bshanks@0 | 120 one is looking for is two-dimensional, the results may be improved by allowing
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| bshanks@0 | 121 the analysis algorithm to take advantage of this prior knowledge. In addition,
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| bshanks@0 | 122 it is easier for humans to visualize and work with 2-D data.
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| bshanks@0 | 123 Therefore, when possible, the instances should represent pixels, not voxels.
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| bshanks@1 | 124 Aim 2
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| bshanks@16 | 125 Machine learning terminology: clustering
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| bshanks@16 | 126 If one is given a dataset consisting merely of instances, with no class labels,
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| bshanks@16 | 127 then analysis of the dataset is referred to as unsupervised learning in the jargon
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| bshanks@16 | 128 of machine learning. One thing that you can do with such a dataset is to group
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| bshanks@15 | 129 instances together. A set of similar instances is called a cluster, and the activity
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| bshanks@15 | 130 of finding grouping the data into clusters is called clustering or cluster analysis.
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| bshanks@17 | 131 3
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| bshanks@17 | 132
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| bshanks@15 | 133 The task of deciding how to carve up a structure into anatomical subregions
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| bshanks@15 | 134 can be put into these terms. The instances are once again voxels (or pixels)
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| bshanks@15 | 135 along with their associated gene expression profiles. We make the assumption
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| bshanks@15 | 136 that voxels from the same subregion have similar gene expression profiles, at
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| bshanks@15 | 137 least compared to the other subregions. This means that clustering voxels is
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| bshanks@15 | 138 the same as finding potential subregions; we seek a partitioning of the voxels
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| bshanks@15 | 139 into subregions, that is, into clusters of voxels with similar gene expression.
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| bshanks@15 | 140 It is desirable to determine not just one set of subregions, but also how
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| bshanks@15 | 141 these subregions relate to each other, if at all; perhaps some of the subregions
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| bshanks@15 | 142 are more similar to each other than to the rest, suggesting that, although at a
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| bshanks@15 | 143 fine spatial scale they could be considered separate, on a coarser spatial scale
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| bshanks@15 | 144 they could be grouped together into one large subregion. This suggests the
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| bshanks@15 | 145 outcome of clustering may be a hierarchial tree of clusters, rather than a single
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| bshanks@15 | 146 set of clusters which partition the voxels. This is called hierarchial clustering.
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| bshanks@16 | 147 Similarity scores
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| bshanks@18 | 148 A crucial choice when designing a clustering method is how to measure
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| bshanks@18 | 149 similarity, across either pairs of instances, or clusters, or both. There is much
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| bshanks@18 | 150 overlap between scoring methods for feature selection (discussed above under
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| bshanks@18 | 151 Aim 1) and scoring methods for similarity.
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| bshanks@16 | 152 Spatially contiguous clusters; image segmentation
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| bshanks@16 | 153 We have shown that aim 2 is a type of clustering task. In fact, it is a
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| bshanks@16 | 154 special type of clustering task because we have an additional constraint on
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| bshanks@16 | 155 clusters; voxels grouped together into a cluster must be spatially contiguous.
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| bshanks@16 | 156 In Preliminary Results, we show that one can get reasonable results without
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| bshanks@16 | 157 enforcing this constraint, however, we plan to compare these results against
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| bshanks@16 | 158 other methods which guarantee contiguous clusters.
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| bshanks@15 | 159 Perhaps the biggest source of continguous clustering algorithms is the field
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| bshanks@15 | 160 of computer vision, which has produced a variety of image segmentation algo-
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| bshanks@15 | 161 rithms. Image segmentation is the task of partitioning the pixels in a digital
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| bshanks@15 | 162 image into clusters, usually contiguous clusters. Aim 2 is similar to an image
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| bshanks@15 | 163 segmentation task. There are two main differences; in our task, there are thou-
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| bshanks@15 | 164 sands of color channels (one for each gene), rather than just three. There are
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| bshanks@15 | 165 imaging tasks which use more than three colors, however, for example multispec-
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| bshanks@15 | 166 tral imaging and hyperspectral imaging, which are often used to process satellite
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| bshanks@15 | 167 imagery. A more crucial difference is that there are various cues which are ap-
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| bshanks@15 | 168 propriate for detecting sharp object boundaries in a visual scene but which are
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| bshanks@15 | 169 not appropriate for segmenting abstract spatial data such as gene expression.
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| bshanks@15 | 170 Although many image segmentation algorithms can be expected to work well
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| bshanks@15 | 171 for segmenting other sorts of spatially arranged data, some of these algorithms
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| bshanks@15 | 172 are specialized for visual images.
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| bshanks@16 | 173 Dimensionality reduction
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| bshanks@16 | 174 Unlike aim 1, there is no externally-imposed need to select only a handful
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| bshanks@16 | 175 of informative genes for inclusion in the instances. However, some clustering
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| bshanks@16 | 176 algorithms perform better on small numbers of features. There are techniques
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| bshanks@15 | 177 which “summarize” a larger number of features using a smaller number of fea-
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| bshanks@15 | 178 tures; these techniques go by the name of feature extraction or dimensionality
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| bshanks@18 | 179 4
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| bshanks@18 | 180
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| bshanks@15 | 181 reduction. The small set of features that such a technique yields is called the
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| bshanks@15 | 182 reduced feature set. After the reduced feature set is created, the instances may
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| bshanks@15 | 183 be replaced by reduced instances, which have as their features the reduced fea-
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| bshanks@15 | 184 ture set rather than the original feature set of all gene expression levels. Note
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| bshanks@15 | 185 that the features in the reduced feature set do not necessarily correspond to
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| bshanks@15 | 186 genes; each feature in the reduced set may be any function of the set of gene
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| bshanks@15 | 187 expression levels.
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| bshanks@15 | 188 Another use for dimensionality reduction is to visualize the relationships
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| bshanks@15 | 189 between subregions. For example, one might want to make a 2-D plot upon
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| bshanks@15 | 190 which each subregion is represented by a single point, and with the property
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| bshanks@15 | 191 that subregions with similar gene expression profiles should be nearby on the
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| bshanks@15 | 192 plot (that is, the property that distance between pairs of points in the plot
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| bshanks@15 | 193 should be proportional to some measure of dissimilarity in gene expression). It
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| bshanks@15 | 194 is likely that no arrangement of the points on a 2-D plan will exactly satisfy
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| bshanks@15 | 195 this property – however, dimensionality reduction techniques allow one to find
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| bshanks@15 | 196 arrangements of points that approximately satisfy that property. Note that
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| bshanks@15 | 197 in this application, dimensionality reduction is being applied after clustering;
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| bshanks@15 | 198 whereas in the previous paragraph, we were talking about using dimensionality
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| bshanks@15 | 199 reduction before clustering.
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| bshanks@16 | 200 Clustering genes rather than voxels
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| bshanks@16 | 201 Although the ultimate goal is to cluster the instances (voxels or pixels), one
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| bshanks@15 | 202 strategy to achieve this goal is to first cluster the features (genes). There are
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| bshanks@15 | 203 two ways that clusters of genes could be used.
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| bshanks@15 | 204 Gene clusters could be used as part of dimensionality reduction: rather than
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| bshanks@15 | 205 have one feature for each gene, we could have one reduced feature for each gene
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| bshanks@15 | 206 cluster.
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| bshanks@15 | 207 Gene clusters could also be used to directly yield a clustering on instances.
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| bshanks@15 | 208 This is because many genes have an expression pattern which seems to pick
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| bshanks@15 | 209 out a single, spatially continguous subregion. Therefore, it seems likely that an
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| bshanks@15 | 210 anatomically interesting subregion will have multiple genes which each individ-
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| bshanks@15 | 211 ually pick it out1. This suggests the following procedure: cluster together genes
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| bshanks@15 | 212 which pick out similar subregions, and then to use the more popular common
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| bshanks@15 | 213 subregions as the final clusters. In the Preliminary Data we show that a num-
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| bshanks@15 | 214 ber of anatomically recognized cortical regions, as well as some “superregions”
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| bshanks@15 | 215 formed by lumping together a few regions, are associated with gene clusters in
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| bshanks@15 | 216 this fashion.
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| bshanks@0 | 217 Aim 3
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| bshanks@16 | 218 Background
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| bshanks@18 | 219 _______________
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| bshanks@16 | 220 1This would seem to contradict our finding in aim 1 that some cortical areas are combina-
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| bshanks@16 | 221 torially coded by multiple genes. However, it is possible that the currently accepted cortical
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| bshanks@16 | 222 maps divide the cortex into subregions which are unnatural from the point of view of gene
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| bshanks@16 | 223 expression; perhaps there is some other way to map the cortex for which each subregion can
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| bshanks@16 | 224 be identified by single genes.
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| bshanks@16 | 225 5
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| bshanks@16 | 226
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| bshanks@18 | 227 The cortex is divided into areas and layers. To a first approximation, the
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| bshanks@18 | 228 parcellation of the cortex into areas can be drawn as a 2-D map on the surface of
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| bshanks@18 | 229 the cortex. In the third dimension, the boundaries between the areas continue
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| bshanks@18 | 230 downwards into the cortical depth, perpendicular to the surface. The layer
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| bshanks@17 | 231 boundaries run parallel to the surface. One can picture an area of the cortex as
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| bshanks@17 | 232 a slice of many-layered cake.
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| bshanks@0 | 233 Although it is known that different cortical areas have distinct roles in both
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| bshanks@0 | 234 normal functioning and in disease processes, there are no known marker genes
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| bshanks@0 | 235 for many cortical areas. When it is necessary to divide a tissue sample into
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| bshanks@0 | 236 cortical areas, this is a manual process that requires a skilled human to combine
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| bshanks@0 | 237 multiple visual cues and interpret them in the context of their approximate
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| bshanks@0 | 238 location upon the cortical surface.
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| bshanks@0 | 239 Even the questions of how many areas should be recognized in cortex, and
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| bshanks@0 | 240 what their arrangement is, are still not completely settled. A proposed division
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| bshanks@0 | 241 of the cortex into areas is called a cortical map. In the rodent, the lack of a
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| bshanks@0 | 242 single agreed-upon map can be seen by contrasting the recent maps given by
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| bshanks@0 | 243 Swanson?? on the one hand, and Paxinos and Franklin?? on the other. While
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| bshanks@0 | 244 the maps are certainly very similar in their general arrangement, significant
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| bshanks@0 | 245 differences remain in the details.
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| bshanks@16 | 246 Significance
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| bshanks@16 | 247 The method developed in aim (1) will be applied to each cortical area to find
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| bshanks@0 | 248 a set of marker genes such that the combinatorial expression pattern of those
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| bshanks@0 | 249 genes uniquely picks out the target area. Finding marker genes will be useful
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| bshanks@0 | 250 for drug discovery as well as for experimentation because marker genes can be
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| bshanks@0 | 251 used to design interventions which selectively target individual cortical areas.
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| bshanks@0 | 252 The application of the marker gene finding algorithm to the cortex will
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| bshanks@0 | 253 also support the development of new neuroanatomical methods. In addition to
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| bshanks@0 | 254 finding markers for each individual cortical areas, we will find a small panel
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| bshanks@0 | 255 of genes that can find many of the areal boundaries at once. This panel of
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| bshanks@0 | 256 marker genes will allow the development of an ISH protocol that will allow
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| bshanks@0 | 257 experimenters to more easily identify which anatomical areas are present in
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| bshanks@0 | 258 small samples of cortex.
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| bshanks@0 | 259 The method developed in aim (3) will provide a genoarchitectonic viewpoint
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| bshanks@0 | 260 that will contribute to the creation of a better map. The development of present-
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| bshanks@0 | 261 day cortical maps was driven by the application of histological stains. It is
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| bshanks@0 | 262 conceivable that if a different set of stains had been available which identified
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| bshanks@0 | 263 a different set of features, then the today’s cortical maps would have come out
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| bshanks@0 | 264 differently. Since the number of classes of stains is small compared to the number
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| bshanks@0 | 265 of genes, it is likely that there are many repeated, salient spatial patterns in
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| bshanks@0 | 266 the gene expression which have not yet been captured by any stain. Therefore,
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| bshanks@0 | 267 current ideas about cortical anatomy need to incorporate what we can learn
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| bshanks@0 | 268 from looking at the patterns of gene expression.
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| bshanks@0 | 269 While we do not here propose to analyze human gene expression data, it is
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| bshanks@0 | 270 conceivable that the methods we propose to develop could be used to suggest
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| bshanks@0 | 271 modifications to the human cortical map as well.
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| bshanks@18 | 272 6
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| bshanks@18 | 273
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| bshanks@0 | 274 Related work
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| bshanks@18 | 275 There does not appear to be much work on the automated analysis of spatial
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| bshanks@18 | 276 gene expression data.
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| bshanks@18 | 277 There is a substantial body of work on the analysis of gene expression data,
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| bshanks@18 | 278 however, most of this concerns gene expression data which is not fundamentally
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| bshanks@18 | 279 spatial, for example, microarray datasets. In some cases, a few locations have
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| bshanks@18 | 280 been sampled, but such a dataset is still of a fundamentally different character
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| bshanks@18 | 281 than a dataset containing a large grid of sampling points distributed over space.
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| bshanks@18 | 282 In relating gene expression to anatomy, it is the spatial aspects of the problem
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| bshanks@18 | 283 which are the most important.
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| bshanks@18 | 284 As noted above, there has been much work on both supervised learning and
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| bshanks@18 | 285 clustering, and there are many available algorithms for each. Many of these
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| bshanks@18 | 286 algorithms are flexible enough to accomodate new scoring measures; and the
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| bshanks@18 | 287 performance of most of the algorithms is greatly affected by preprocessing and
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| bshanks@18 | 288 by the choice of which representation to use for feature values. We think it likely
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| bshanks@18 | 289 that for this application, the development of domain-specific scoring measures
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| bshanks@18 | 290 (such as gradient similarity, which is discussed in Preliminary Work) will be
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| bshanks@18 | 291 necessary in order to achieve the best results. In essence, the machine learning
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| bshanks@18 | 292 community has provided algorithms, but the scientist must provide a framework
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| bshanks@18 | 293 for representing the problem domain, and the way that this framework is set
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| bshanks@18 | 294 up has a large impact on performance. Creating a good framework can require
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| bshanks@18 | 295 creatively reconceptualizing the problem domain, and is not merely a mechanical
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| bshanks@18 | 296 “fine-tuning” of numerical parameters. Therefore, the completion of Aims 1
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| bshanks@18 | 297 and 2 involves more than just reimplementing an existing algorithm, and more
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| bshanks@18 | 298 than just choosing between a set of existing algorithms, and will constitute a
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| bshanks@18 | 299 substantial contribution to biology.
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| bshanks@18 | 300 We are aware of one other effort to computationally analyze spatial gene
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| bshanks@18 | 301 expression data.
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| bshanks@18 | 302 In the Preliminary Work, we show that
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| bshanks@18 | 303 The creation of a domain-specific scoring measure may be required in order
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| bshanks@18 | 304 to achieve good performance, and it is not impossible that the algorithms them-
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| bshanks@18 | 305 selves will have to be extended. We plan to test out existing algorithms and
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| bshanks@18 | 306 scoring measures,
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| bshanks@18 | 307 Therefore, we anticipate
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| bshanks@18 | 308 Therefore, it is unclear which of the
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| bshanks@18 | 309 todo
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| bshanks@15 | 310 vs. AGEA – i wrote something on this but i’m going to rewrite it
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| bshanks@0 | 311 Preliminary work
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| bshanks@15 | 312 Format conversion between SEV, MATLAB, NIFTI
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| bshanks@15 | 313 todo
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| bshanks@18 | 314 7
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| bshanks@18 | 315
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| bshanks@15 | 316 Flatmap of cortex
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| bshanks@15 | 317 todo
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| bshanks@16 | 318 Using combinations of multiple genes is necessary and sufficient to
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| bshanks@15 | 319 delineate some cortical areas
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| bshanks@16 | 320 Here we give an example of a cortical area which is not marked by any
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| bshanks@16 | 321 single gene, but which can be identified combinatorially. according to logistic
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| bshanks@16 | 322 regression, gene wwc12 is the best fit single gene for predicting whether or not a
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| bshanks@16 | 323 pixel on the cortical surface belongs to the motor area (area MO). The upper-left
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| bshanks@0 | 324 picture in Figure shows wwc1’s spatial expression pattern over the cortex. The
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| bshanks@0 | 325 lower-right boundary of MO is represented reasonably well by this gene, however
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| bshanks@0 | 326 the gene overshoots the upper-left boundary. This flattened 2-D representation
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| bshanks@0 | 327 does not show it, but the area corresponding to the overshoot is the medial
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| bshanks@0 | 328 surface of the cortex. MO is only found on the lateral surface (todo).
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| bshanks@15 | 329 Gnee mtif23 is shown in figure the upper-right of Fig. . Mtif2 captures MO’s
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| bshanks@0 | 330 upper-left boundary, but not its lower-right boundary. Mtif2 does not express
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| bshanks@0 | 331 very much on the medial surface. By adding together the values at each pixel
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| bshanks@16 | 332 in these two figures, we get the lower-left of Figure . This combination captures
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| bshanks@16 | 333 area MO much better than any single gene.
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| bshanks@17 | 334 Correlation todo
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| bshanks@17 | 335 Conditional entropy todo
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| bshanks@17 | 336 Gradient similarity todo
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| bshanks@16 | 337 Geometric and pointwise scoring methods provide complementary
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| bshanks@16 | 338 information
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| bshanks@16 | 339 To show that local geometry can provide useful information that cannot be
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| bshanks@16 | 340 detected via pointwise analyses, consider Fig. . The top row of Fig. displays the
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| bshanks@16 | 341 3 genes which most match area AUD, according to a pointwise method4. The
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| bshanks@16 | 342 bottom row displays the 3 genes which most match AUD according to a method
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| bshanks@16 | 343 which considers local geometry5 The pointwise method in the top row identifies
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| bshanks@16 | 344 genes which express more strongly in AUD than outside of it; its weakness is that
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| bshanks@16 | 345 this includes many areas which don’t have a salient border matching the areal
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| bshanks@16 | 346 border. The geometric method identifies genes whose salient expression border
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| bshanks@18 | 347 seems to partially line up with the border of AUD; its weakness is that this
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| bshanks@18 | 348 includes genes which don’t express over the entire area. Genes which have high
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| bshanks@18 | 349 rankings using both pointwise and border criteria, such as Aph1a in the example,
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| bshanks@18 | 350 may be particularly good markers. None of these genes are, individually, a
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| bshanks@18 | 351 perfect marker for AUD; we deliberately chose a “difficult” area in order to
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| bshanks@18 | 352 better contrast pointwise with geometric methods.
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| bshanks@15 | 353 __________________________
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| bshanks@15 | 354 2“WW, C2 and coiled-coil domain containing 1”; EntrezGene ID 211652
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| bshanks@15 | 355 3“mitochondrial translational initiation factor 2”; EntrezGene ID 76784
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| bshanks@16 | 356 4For each gene, a logistic regression in which the response variable was whether or not a
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| bshanks@16 | 357 surface pixel was within area AUD, and the predictor variable was the value of the expression
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| bshanks@16 | 358 of the gene underneath that pixel. The resulting scores were used to rank the genes in terms
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| bshanks@16 | 359 of how well they predict area AUD.
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| bshanks@16 | 360 5For each gene the gradient similarity (see section ??) between (a) a map of the expression
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| bshanks@16 | 361 of each gene on the cortical surface and (b) the shape of area AUD, was calculated, and this
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| bshanks@16 | 362 was used to rank the genes.
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| bshanks@18 | 363 8
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| bshanks@0 | 364
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| bshanks@0 | 365
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| bshanks@0 | 366
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| bshanks@0 | 367 Figure 1: Upper left: wwc1. Upper right: mtif2. Lower left: wwc1 + mtif2
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| bshanks@0 | 368 (each pixel’s value on the lower left is the sum of the corresponding pixels in
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| bshanks@0 | 369 the upper row). Within each picture, the vertical axis roughly corresponds to
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| bshanks@0 | 370 anterior at the top and posterior at the bottom, and the horizontal axis roughly
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| bshanks@0 | 371 corresponds to medial at the left and lateral at the right. The red outline is
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| bshanks@0 | 372 the boundary of region MO. Pixels are colored approximately according to the
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| bshanks@0 | 373 density of expressing cells underneath each pixel, with red meaning a lot of
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| bshanks@0 | 374 expression and blue meaning little.
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| bshanks@15 | 375
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| bshanks@15 | 376
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| bshanks@15 | 377 Figure 2: The top row shows the three genes which (individually) best predict
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| bshanks@15 | 378 area AUD, according to logistic regression. The bottom row shows the three
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| bshanks@15 | 379 genes which (individually) best match area AUD, according to gradient similar-
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| bshanks@15 | 380 ity. From left to right and top to bottom, the genes are Ssr1, Efcbp1, Aph1a,
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| bshanks@15 | 381 Ptk7, Aph1a again, and Lepr
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| bshanks@18 | 382 9
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| bshanks@18 | 383
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| bshanks@16 | 384 Areas which can be identified by single genes
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| bshanks@16 | 385 todo
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| bshanks@18 | 386 Specific to Aim 1 (and Aim 3)
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| bshanks@17 | 387 Forward stepwise logistic regression todo
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| bshanks@17 | 388 SVM on all genes at once
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| bshanks@16 | 389 In order to see how well one can do when looking at all genes at once, we
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| bshanks@16 | 390 ran a support vector machine to classify cortical surface pixels based on their
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| bshanks@16 | 391 gene expression profiles. We achieved classification accuracy of about 81%6.
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| bshanks@16 | 392 As noted above, however, a classifier that looks at all the genes at once isn’t
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| bshanks@16 | 393 practically useful.
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| bshanks@16 | 394 The requirement to find combinations of only a small number of genes limits
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| bshanks@16 | 395 us from straightforwardly applying many of the most simple techniques from
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| bshanks@17 | 396 the field of supervised machine learning. In the parlance of machine learning,
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| bshanks@17 | 397 our task combines feature selection with supervised learning.
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| bshanks@17 | 398 Decision trees
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| bshanks@17 | 399 todo
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| bshanks@18 | 400 Specific to Aim 2 (and Aim 3)
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| bshanks@18 | 401 Raw dimensionality reduction results
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| bshanks@18 | 402 Dimensionality reduction plus K-means or spectral clustering
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| bshanks@18 | 403 Many areas are captured by clusters of genes
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| bshanks@16 | 404 todo
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| bshanks@15 | 405 todo
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| bshanks@15 | 406 Research plan
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| bshanks@18 | 407 todo amongst other things:
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| bshanks@16 | 408 Develop algorithms that find genetic markers for anatomical re-
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| bshanks@16 | 409 gions
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| bshanks@0 | 410 1. Develop scoring measures for evaluating how good individual genes are at
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| bshanks@0 | 411 marking areas: we will compare pointwise, geometric, and information-
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| bshanks@0 | 412 theoretic measures.
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| bshanks@0 | 413 2. Develop a procedure to find single marker genes for anatomical regions: for
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| bshanks@0 | 414 each cortical area, by using or combining the scoring measures developed,
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| bshanks@0 | 415 we will rank the genes by their ability to delineate each area.
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| bshanks@0 | 416 3. Extend the procedure to handle difficult areas by using combinatorial cod-
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| bshanks@0 | 417 ing: for areas that cannot be identified by any single gene, identify them
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| bshanks@0 | 418 with a handful of genes. We will consider both (a) algorithms that incre-
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| bshanks@0 | 419 mentally/greedily combine single gene markers into sets, such as forward
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| bshanks@18 | 420 __________________________
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| bshanks@18 | 421 65-fold cross-validation.
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| bshanks@18 | 422 10
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| bshanks@18 | 423
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| bshanks@0 | 424 stepwise regression and decision trees, and also (b) supervised learning
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| bshanks@0 | 425 techniques which use soft constraints to minimize the number of features,
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| bshanks@0 | 426 such as sparse support vector machines.
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| bshanks@0 | 427 4. Extend the procedure to handle difficult areas by combining or redrawing
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| bshanks@0 | 428 the boundaries: An area may be difficult to identify because the bound-
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| bshanks@0 | 429 aries are misdrawn, or because it does not “really” exist as a single area,
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| bshanks@0 | 430 at least on the genetic level. We will develop extensions to our procedure
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| bshanks@0 | 431 which (a) detect when a difficult area could be fit if its boundary were
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| bshanks@0 | 432 redrawn slightly, and (b) detect when a difficult area could be combined
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| bshanks@0 | 433 with adjacent areas to create a larger area which can be fit.
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| bshanks@16 | 434 Apply these algorithms to the cortex
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| bshanks@0 | 435 1. Create open source format conversion tools: we will create tools to bulk
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| bshanks@0 | 436 download the ABA dataset and to convert between SEV, NIFTI and MAT-
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| bshanks@0 | 437 LAB formats.
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| bshanks@0 | 438 2. Flatmap the ABA cortex data: map the ABA data onto a plane and draw
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| bshanks@0 | 439 the cortical area boundaries onto it.
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| bshanks@0 | 440 3. Find layer boundaries: cluster similar voxels together in order to auto-
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| bshanks@0 | 441 matically find the cortical layer boundaries.
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| bshanks@0 | 442 4. Run the procedures that we developed on the cortex: we will present, for
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| bshanks@0 | 443 each area, a short list of markers to identify that area; and we will also
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| bshanks@0 | 444 present lists of “panels” of genes that can be used to delineate many areas
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| bshanks@0 | 445 at once.
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| bshanks@16 | 446 Develop algorithms to suggest a division of a structure into anatom-
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| bshanks@0 | 447 ical parts
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| bshanks@0 | 448 1. Explore dimensionality reduction algorithms applied to pixels: including
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| bshanks@0 | 449 TODO
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| bshanks@0 | 450 2. Explore dimensionality reduction algorithms applied to genes: including
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| bshanks@0 | 451 TODO
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| bshanks@0 | 452 3. Explore clustering algorithms applied to pixels: including TODO
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| bshanks@0 | 453 4. Explore clustering algorithms applied to genes: including gene shaving,
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| bshanks@0 | 454 TODO
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| bshanks@0 | 455 5. Develop an algorithm to use dimensionality reduction and/or hierarchial
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| bshanks@0 | 456 clustering to create anatomical maps
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| bshanks@0 | 457 6. Run this algorithm on the cortex: present a hierarchial, genoarchitectonic
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| bshanks@0 | 458 map of the cortex
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| bshanks@18 | 459 11
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| bshanks@18 | 460
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| bshanks@18 | 461 _______________________________________________________________________________________________________ stuff i dunno where to put yet (there is more scattered through grant-
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| bshanks@15 | 462 oldtext):
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| bshanks@16 | 463 Principle 4: Work in 2-D whenever possible
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| bshanks@16 | 464 In anatomy, the manifold of interest is usually either defined by a combina-
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| bshanks@16 | 465 tion of two relevant anatomical axes (todo), or by the surface of the structure
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| bshanks@16 | 466 (as is the case with the cortex). In the former case, the manifold of interest is
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| bshanks@16 | 467 a plane, but in the latter case it is curved. If the manifold is curved, there are
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| bshanks@16 | 468 various methods for mapping the manifold into a plane.
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| bshanks@16 | 469 The method that we will develop will begin by mapping the data into a
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| bshanks@16 | 470 2-D plane. Although the manifold that characterized cortical areas is known
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| bshanks@16 | 471 to be the cortical surface, it remains to be seen which method of mapping the
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| bshanks@18 | 472 manifold into a plane is optimal for this application. We will compare mappings
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| bshanks@18 | 473 which attempt to preserve size (such as the one used by Caret??) with mappings
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| bshanks@18 | 474 which preserve angle (conformal maps).
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| bshanks@18 | 475 Although there is much 2-D organization in anatomy, there are also struc-
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| bshanks@18 | 476 tures whose shape is fundamentally 3-dimensional. If possible, we would like
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| bshanks@18 | 477 the method we develop to include a statistical test that warns the user if the
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| bshanks@18 | 478 assumption of 2-D structure seems to be wrong.
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| bshanks@18 | 479 todo: replace aim # bullet pts with #s
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| bshanks@17 | 480 12
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| bshanks@17 | 481
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| bshanks@17 | 482
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